Design of a concept Planar Array for the Biomass Space Mission

Contents

1 Biomass Mission
1.1 Background and justifications
1.2 Space and Ground segment
1.2.1 Observational Requirements
1.2.2 Selection of frequency
1.2.2.1 Polarisation
1.3 Instrument characterization and calibration
1.3.1 Polarimetrie calibration
1.3.2 Transponder requirements

2 Preliminary study
2.1 Initial performance assessment
2.1.1 Aperture sizing
2.1.2 Array sizing
2.1.3 Preliminary design
2.2 Tukey Window Illumination Law

3 ADF-EMS 3D Antenna Modelling
3.1 Introduction
3.2 Antenna CAD
3.2.1 Modelling approach
3.2.2 3D Antenna Modelling
3.3 Array CAD
3.4 Method of Moments
3.4.1 Poeklington’s Integral Equation
3.4.2 Moment Method Solution

4 Preliminary design of the array
4.1 Introduction
4.2 Planar Inverted-F Antenna
4.2.1 PIFA Design
4.2.2 Design of array based on PIFAs

5 Advanced array design
5.1 Folded Planar Inverted-F Antenna
5.1.1 Design of a Folded PIFA
5.1.1.1 Parameter study
5.1.2 Design of an array concept based on folded PIFA , , ,

6 Potential optimisations
6.1 Array of 91 elements
6.2 Optimum array element spacing
6.3 Bandwidth enhancement

7 Antenna prototyping and testing
7.1 Prototyping of the radiating element
7.2 Antenna test
7.2.1 Antenna ranges
7.3 Impedance measurements
7.3.1 Return loss measurements
7.4 Radiation patterns measurements
7.4.1 Xear-field to far-held methods
7.4.2 Directivity and Gain measurements
7.4.2.1 Directivity Gain of the prototype
7.4.2.2 Assessment of the Gain
7.5 Sensitivity analysis

8 Conclusions

A Fundamental parameters and definitions for antennas
A.l Radiation pattern
A.2 Directivity
A.3 Antenna Gain
A.4 Bandwidth
A.5 Polarisation
A.6 Cross Polarisation Discrimination
A.7 Input impedance

В Array

C Meta-surface antenna

Acknowledgements

I would like to express my deepest gratitude to Eng, Mareo Sabbadini who gave me the great opportunity to do an internship, that has been the basis of this thesis, in the culturally stimulating environment which is the European Space Research and Technology Centre at the European Space Agency, in Noordwijk (Netherlands), He has always been kind and helpful to me and has provided precious tips and solutions for my work. Without his guidance and persistent support this thesis and my professional growth would not have been possible.

I would like to express my heartfelt thanks to Professor Gaetano Mar- roeeo, who instilled in me a keen interest in the field of antennas and elec­tromagnetic technologies and gave me the chance to complete my internship abroad by introducing me to Mr, Sabbadini, Together with the members of the Antenna Lab of the University of Roma Tor Vergata, he has always been willing to help me whenever I needed it.

In addition, I would like to thank Eng, Luca Salghetti Drioli and Eng, Gabriele Minatti of ESA/ESTEC who helped me to perform the relevant measurements and to get a better understanding of the meta-surfaee anten­nas, respectively, I would like to thank also Eng, Giancarlo Guida, Eng, Gabriele Scozza and Eng, Valerio Martorelli of IDS Ingegneria dei Sistemi s,p,a, who always shown great kindness and availability by providing me with technical support for the use of the software ADF/EMS throughout the duration of my work. Finally I would like to thank Eng, Andrea Giaeomini and Eng, Luca Taneioni of Microwave Vision Group (Italy) who helped me with the antenna measurements by providing me access to their company facilities.

A special thanks goes to my parents who supported me over the years I spent as an University student and also provided me with everything I need to get going.

Abstract

The Biomass Calibration Radar Transponder Antenna is devoted to receiv­ing and transmitting back the radar pulses generated by the Biomass radar, operating in a B = 10 MHz band centred at f0 = 435 MHz (P-band), to allow its calibration during operations in orbit. The antenna must provide a directive pattern in double linear polarisation with low cross-polar lev­els (XPD > 40dB) and low radiation in the backward hemisphere. Low side-lobe levels close to the horizon are very desirable also in the forward hemisphere (SL < — 45dB), The aim of my work consisted in designing a planar array which meets the requirements, leading to a good solution for the Biomass Transponder Antenna, The present report summarises the results obtained in the preliminary and advanced design of the radiating element and of the whole array, based on available data and on the preliminary per­formance assessment.

Chapter 1 Biomass Mission

1.1 Background and justifications

ESA’s Living Planet Programme consists of seven Earth Explorer missions aimed at understanding deeper the main functional aspects of the Earth system and the impact of human activities on natural processes. After the Feasibility Study (Phase-А) Biomass has been selected as seventh Earth Ex­plorer mission. It will aim to produce the first accurate maps of tropical, temperate and boreal forest biomass, including height and disturbance pat­terns, The main target is the improvement of the understanding of the global carbon cycle and of the global change. Carbon cycle is meant as the storage of carbon in the biosphere and fluxes among different pools, which are sub­divided into sources (emissions) and sinks (uptakes). Emissions are mainly due to fossil fuels, land use change and yearly atmospheric carbon accumu­lation, on the other hand uptakes are dominated by residual terrestrial sink and ocean uptakes.

Forest biomass, which is the amount of living organic matter in a given space (usually mass per unit area), is a crucial parameter that influences the distribution of carbon dioxide all along the biosphere. The 50% of the biomass is carbon and forest comprise about the 80% of terrestrial above ground biomass. As long as the dynamics of forests in terms of biomass distribution and evolution are not completely clear, the scientific community is looking for accurate and frequent information on forest properties in order to observe the changes better.

As we know the terrestrial biosphere absorbs almost the 30% of the car­bon emissions from the atmosphere. However terrestrial ecosystems are also the largest source of uncertainty in the global carbon budget, especially re­garding the key role of forest biomass in fixing the carbon and of tropical deforestation rate in increasing the emissions. As regards the terrestrial car­bon fluxes the main uncertainties concern the estimated emissions, due to the Land Use Change, and uptakes, bound to the Residual Terrestrial Sink, a fundamental parameter in controlling climate warming, that consequently is inaccurate. The land emissions are thought to be mainly due to defor­estation in the Tropics, but there is an uncertainty of around 20% on the total annual net flux. Moreover carbon fluxes are characterised by a great variability from year to year, with the 80% of biomass changes that occurs within the Tropics, Hence the emphasis of Biomass is on boreal and tropical forests, which comprise the 75% of world’s forest cover.

Stated that estimating accurately the biomass means improving the esti­mation of land emissions and uptakes and consequently understanding better the dynamics of terrestrial carbon dioxide, the programs against the increase of carbon emissions can be lead more efficiently. For these reasons Biomass mission will also support global treaties such as the United Nations Frame­work Convention on Climate Change (UXFCCC), which identified biomass as an Essential Climate Variable (ECV)

As mentioned above, despite its importance in the global carbon cycle we have a poor mapping of forest biomass, as at the moment there are not remote-sensing instruments capable of measuring accurately forest biomass. Until now data on forest biomass have been extracted from different spatial mission acquisitions on inappropriate frequencies and explicit biomass maps only exist in some parts of the world, covering small areas, often at low resolution, containing biases due to poor estimations.

Enhanced observations of forest biomass, spatial distribution and change with time will thus contribute to:

- improved knowledge of terrestrial carbon pools by direct inference of carbon stocks from forest biomass and through improved vegetation modelling,
- improved estimation of land absorbtion from forest growth,
- improved estimation of carbon emissions from land-use change and for­est degradation.

With regard to the emissions, the United Nations initiative for Reducing Emission through Deforestation and Forest Degradation (REDD^) aims to mitigate the effects of forest loss by monitoring and maintaining the carbon stores. According to the carbon cycle process REDD^ involves mapping the magnitude of biomass stocks and estimating the changes in carbon fluxes due to disturbance and forest growth, therefore maps consistent with changes are needed. For this aim Biomass mission will last five years and it will provide:

- maps of forest biomass stocks at a spacial resolution of about 100 m, twice a year
- maps of biomass change (due to disturbances, degradation, land-use change and forest growth)
- detection of deforestation through 0,25 ha full resolution instrument.

Below-ground biomass could be also mapped through inference from above­ground biomass using conversion factors.

Maps are the basis for assessing the size of land carbon pool and for modelling carbon emissions due to changes of the land-use. The most of estimations of carbon emissions, Cem from human disturbances are based on the following expression:

illustration not visible in this excerpt

where ΔΑi represents the change in area of the г-type forest, which has mean biomass Bi (in carbon units) and a removal efficiency Ei, that quantifies the fraction of biomass emitted to the atmosphere. Such estimates are used by Dynamic Vegetation Models and Earth System Models,

Finally Biomass data should also be useful for monitoring glaeier and ice sheet velocities, mapping subsurface geology in deserts and mapping the topography of forest floors.

1.2 Space and Ground segment

Biomass space segment consist of a single satellite in a dawn-to-dusk and near-polar orbit at a mean altitude of 662 km. The orbit is optimised to enable repeated interferometric acquisitions and to minimize ionospheric dis­turbances, Multiple acquisitions will be realized by taking advantage of as­cending and descending measurements, with controlled inter-orbit distances between successive revisits. Moreover dawn-dusk orbit will imply negligible effect of scintillations on biomass retrieval perfomanee,

The satellite will be supplied with a P-band Synthetic Aperture Radar operating at 435 MHz (around 69 cm wavelength). The SAR will operate in quad-polarisation in which V-Polarisation and H-Polarisation pulses are transmitted alternatively and both V-POL and H-POL baekseattered signals are received simultaneously. Through Biomass mission Earth’s surface will be explored for the first time using P-band wavelength.

The strongest constraint in the satellite configuration is the very large reflector antenna (about 12m diameter) that will be accommodated in the launcher, A concept of this antenna is based on a Large Deployable Reflector Antenna consisting of a deployable arm and unfurlable reflector (Fig, 1,2,1), The LDR will be illuminated by an array of patch radiators mounted on the satellite. The SAR data will be transmitted to Kiruna ground station via an X-band downlink while auxiliary data, required to study the eharaeteries of the propagation path, will be used in the end-to-end system calibration and processing of the SAR data.

The performance of the SAR instrument is clearly a critical issue that is gorverned both by the design of the spacecraft and the effectiveness of the calibration instrument.

The Ground Segment will take advantage of the generic Earth Explorer ground segment infrastructure.

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Figure 1.2.1: View of a concept Large Deployable Reflector Antenna

1.2.1 Observational Requirements

Through airborne campaings it has been demonstrated that P-band is suit­able for remote sensing, especially for measuring forest biomass, consequently ITU allocate a 6 MHz bandwidth at this band for remote sensing (ITU, 2004), fixing the frequency range 432-438 MHz centred at 435 MHz. To further jus­tify the importance of Biomass mission, it is worth to mention that boreal and tropical forest are poorly documented in terms of P-band SAR data.

Considering the strong attention on forest change, repeated measure­ments of biomass at spadai and temporal scales are required. As the most of Earth Observation missions, Biomass will involve two kind of measurements:

- Remote-sensing of biomass, to estimate the forest features
- In situ measurements of biomass, for calibration and validation

Campaign data displayed that the P-band SAR, in comparison with any other existing satellite mission combined with all the exploited frequencies, offers better performanee in remote sensing of forest properties, as it provides for:

- high sensitivity to biomass
- long coherence time (several weeks), even in dense forest, that will allow retrieval of forest height during tomographic phase
- high sensitivity to disturbances and temporal changes of biomass

For these reasons, the conceived remote sensing component of Biomass is a P-band SAR with full polarimetrie (PolSAR) and multipass interferometric (PolInSAR) capabilities.

Complementary PolInSAR coherence and PolSAR baekseatter observa­tions allow an accurate and consistent retrieval of above-ground biomass, while below-ground biomass can be inferred using conversion factors. Thus, throughout this Chapter, “biomass" denotes “above-ground biomass".

At each acquisition the radar will measure the scattering matrix, from which the baekseattering coefficients will be derived in each of the different linear polarisation combinations (HH, VV, VH & HV), During campaigns on temperate forests it has been found that, among all the possible polarisations combinations, HV and HH are more strongly correlated to biomass, while correlation between VV and biomass shown to be weak. At P-band the main scattering mechanism are double-bounce and volume scattering and studies shown that dominant seatterers are big branches and trunks. The most of forest systems shown to be simple enough to allow accurate biomass inversion methods through mere inversion of P-band HV baekseatter, that offers the largest dynamic range between low and high biomass forest. In contrast, tropical sites displayed high correlation among measured HH, VV and HV polarisations and therefore very similar relationships between baekseattered signals in all three polarisations and biomass.

To detect deforestation a resolution around 0,25 ha (50 m in linear di­mensions) is required, while for areas with potential degradation or biomass accumulation a resolution of around 5 ha (200 m in linear) is sufficient. Given that as biomass growth is not very rapid and the fastest regrowth occurs in tropical forests, two observations over a five-years period is the minimum required to observe changes. However mapping disturbances on a two-years basis is necessary to study the role of changes due to disturbances in relation to the increase of atmosferie carbon dioxide,

Polarimetrie SAR observations will be also used to correct Faraday rota­tion (FR), while ionospheric effects are likely to cause significant disturbance under all conditions. Scintillation effects will be negligible by taking advan­tage of the dawn-to-dusk orbit,

1.2.2 Selection of frequency

Many publications pointed out that SAR baekseatter is more sensitive to forest biomass when frequency is low, P-band also allows to keep a high temporal coherence, which means a finer forest height retrieval. Resistance to temporal decorrelation is mainly due to:

- Deep penetration into the vegetation layer which ensures interaction with the ground,
- High interaction with large tree structures that carry the most of the biomass,
- Ground and large tree structures are more stable scatterers in time than small elements, such as branches,
- Longer wavelengths lead to lower decorrelation caused by motion of scatterers.

Therefore P-band frequencies scatter from larger and more stable elements and at the same time are less sensitive to their motion. In order to map forest biomass across the whole range of forest types, choosing P-band frequency has been clearly fundamental,

1.2.2.1 Polarisation

As mentioned before, different polarisation combinations respond to different properties of the biomass and thus they prove for different information. The terms of the polarimetrie covariance matrix are necessary both for biomass retrieval and forest height retrieval. At the same time full polarimetrie data are useful to map the terrain elevation under dense vegetation and ice prop­erties over land. Finally the algorithm to compensate for Faraday Rotation is based on polarimetrie data. These reasons lead to the requirement of a full polarimetrie mode for the Biomass system.

1.3 Instrument characterization and calibration

As we know, transmitted an received V-POL and H-POL signals are altered in polarisation by ionospheric effects, i.e, propagation and phase delays and Faraday Rotation, which is the rotation of the radar signal polarisation as it propagates through the atmosphere. Therefore calibration techniques are necessary to take account of ionospheric errors, that are also increased by the very long wavelength. Calibration is also necessary to characterise: the beam pointing of the satellite, channel imbalance, cross-polar radiation levels and the antenna gain pattern.

Usually calibration includes the use of both external and internal mea­surement techniques to compute respectively absolute and relative correction factors that will be applied to the measured data. External calibration is based on the use of a target placed on the ground that has a well-known radar cross section (RCS), in this way during the processing of the measure­ment output, data are compared and then calibration is obtained.

Since active transponders can easily achieve a large radar cross-section, they will be the basis for external calibration which will be performed on the ground. In this way they will enable the characterisation of Biomass antenna and of the ionospheric effects. On the other hand, passive point targets, i.e, corner reflectors, would require a very large dimension to achieve a sufficient RCS at the centre frequency of the radar antenna.

The three-swaths observation principle of the Biomass SAR will require a minimum of three transponders to calibrate the Biomass instrument in its three different beam pointing attitudes. This would translate in placing, as a minimum, three transponders for absolute calibration on the magnetic equator, where both scintillation and Faraday Rotation are negligible and thus the calibration can be more accurate, and one at higher latitudes to validate the correction techniques for ionospheric effects, A possible design of the Transponder is illustrated in Fig, 1,3,1, The corrections of ionospheric effects, performed by the receiver function in the transponder and simplified by the location of the transponders in the equatorial region, will be the reference measurements for a most accurate external calibration.

illustration not visible in this excerpt

Figure 1,3,1: Sketch of Biomass transponder.

The positioner, on which the Transponder will be mounted, should enable azimuth and elevation tracking of the spacecraft throughout the over-pass, in order to point the radar antenna of Biomass satellite and therefore to keep a good directivity gain and high polarisation isolation. The structure will be required to operate in extreme enviromental conditions, i.e. with high wind loading and extreme temperatures. It will also need to tolerate possible precipitation and snow cover,

1.3.1 Polarimetrie calibration

The aim of the external calibration is essentially to verify and characterise the channel imbalance and the two-way system gains for each polarisation combinations (HH, VV, HV & VH).

A fully polarimetrie calibration can be expressed in terms of scattering matrix S defined as:

illustration not visible in this excerpt

where the elements are complex numbers representing the reflected signal polarised according to the first subscript when the incident radiation has unitary amplitude and is polarised according to the second subscript. Such matrix is corrupted by the gain imbalance (ƒ) between H and V channels, the cross-talk (5) between H and V channels and the Faraday Rotation, represented by an angle rotation (Ω) of the plane of polarisation. The factors ƒ and δ are complex numbers and may be different for HV and VH.

The Biomass SAR performs multi-polarisation measurements that can be represented in terms of a matrix defined as below:

illustration not visible in this excerpt

where M represents measured radar amplitude values, R describes receiv­ing properties of SAR, F describes the effects of Faraday Rotation (FR), S represents the scattering properties of the Transponder, T describes the transmitting properties of the SAR and X are the unwanted noise terms.

The scattering matrices of the transponders are required to be:

illustration not visible in this excerpt

as the cross-talk can be assumed negligible and thus a good cross-polar per­formance of the Transponder Antenna is feasible.

The proposed external calibration technique is based on a pair of transpon­ders close enough so that the ionospheric effects and the radar slant ranges are the same for each. External ionospheric information is clearly needed to remove ambiguities, due to the large variations of TEC, in the corrections for the FR. However it has been demonstrated that TEC maps are sufficiently accurate for this aim. It is also assumed that the FR angle θ and the matrix F defined as:

illustration not visible in this excerpt

are constant over the SAR integration time. Therefore it is possible to solve the equations 1,3,2, as the correction of Faraday Rotation is given by the redundancy in all the polarimetrie measurements at each pixel. It can be noticed that fully polarimetrie data are essential to separate the baekseatter information.

1.3.2 Transponder requirements

As mentioned above, the requirements of the Transponder Antenna derive from those on the SAR performance and on the allocated contribution to the external calibration error budget.

The Transponder is also required to measure the SAR azimuth pattern, observable during the overpass, therefore it is necessary an accuracy below 1 dB together with a dynamic range sufficient to reconstruct the azimuth pattern down to a side-lobe level of -40 dB.

The conceived solutions for the antenna architecture were: a potter horn, an offset parabola and a planar array. The planar array was selected as it can provide the most practical implementation for the aim of the Trasponder, The advantages of this antenna are: a good overall performance, light weight, low volume, good side-lobe suppression and good cross polar-isolation. More­over a planar array is also practical to fabricate and to transport, and its surface can be easily protected against contamination, i.e, by hermetically sealing each radiating element and equipping the antenna with a weather­proof membrane. On the other hand this solution implies an increased com­plexity of the beam-former design for dual polarisation, the losses of which lead to a larger diameter of the antenna in order to compensate.

As explained above the performance of the Transponder are critically dependent upon the ability of the antenna to reject multipath scattering and to receive separetely V-POL and H-POL signals with negligible cross-talk. Therefore a mechanically scanned pencil-beam planar array is believed to be the best solution to satisfy the requirements. The assumptions about the ealibration technique together with the directivity and the side-lobe levels requirements define directly the requirements on the antenna pattern. Since a cross-talk level of about -30 dB is believed to have a negligible effect on the ealibration, the cross-polar requirement (XPD, Appendix A,6) should be higher than 40 dB in relation to the boresight, over a radial angle of 5°, Side-lobe levels (SL) are required to be less than -45dB below the peak of the main lobe, in order to minimize the antenna gain in the direction from which multipath signals come. At the same time the beam-width of the main lobe must be choose so that the ground is not illuminated during the acquisition. Figure 1,3,2 displays the requirements upon the radiation pattern of the antenna.

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Figure 1,3,2: Radiation pattern requirement

The Biomass Calibration Transponder will thus consist of a single planar antenna subsystem mounted on a positioner capable of azimuth and elevation pointing. The antenna will need an aperture of at least 4m x 4m in order to guarantee the required ealibration accuracy, which is mainly bound by the avoidance of multipath effects through the antenna side lobes and not by the required transponder RCS, The pulses transmitted by the SAR are

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Table 1,1: Transponder perfomanee assessment

separately received in V-POL and H-POL channels and then stored within the digital electronic subsystem. After a simultaneous external calibration of HH and VV responses, a sequence of pulses for each polarisation signals is retransmitted in a repetition interval to coincide with the SAR receive interval.

Having taken into account as explained above, the resulting performance of the Transponder are shown in Table 1,1,

Chapter 2 Preliminary study

Given the transponder requirements, the main factors that influence the pla­nar array design are the following:

- Spatial distribution of the side-lobes and back-lobe levels, that must guarantee the rejection of the multipath scattering
- Cross-polar, that must guarantee the separation between vertical and horizontal polarisation signals with low cross-talk levels
- The array factor determined by the array spacing, that influences the choice and the sizing of the aperture shape
- Number of sub-arrays in which the aperture is divided and modularity
- EM modelling considerations
- Complexity of manufacture, assembly and transport
- Methods of testing
- Costs

The main features of a square array antenna are:

- Peak side-lobe levels are confined to the principal axes for separable aperture distributions

illustration not visible in this excerpt

Figure 2.1.1: Annular slot geometry

- The possibility of exciting the sub-arrays at different amplitudes to have a specific illumination tapering of the aperture distribution and therefore to meet the requirement on the radiation pattern,
- The possibility of derive the main cuts of the radiation pattern from a simple linear array model.

Therefore, the square aperture has been adopted as it provide for a total flexibility which allows to refine the radiation pattern as desired.

As discussed in |3|, a square aperture, consisting of an planar array of 8 x 8 square slot radiators, offers a relatively compact and robust solution and constitutes the reference to which all solutions discussed below are compared,

2.1 Initial performance assessment

The initial assessment, described in |6|, of a possible solution for antenna design based on available data, is the basis of my thesis work.

The assessment has been based on an existing preliminary design consti­tuted by an array of square annular slots fed by a double balanced trans­mission line (one input for each linear polarisation). As depicted in figure 2,1,1, each element is surrounded by 12 pins to form a cavity in order to avoid inter-element coupling with parallel-plate waveguide modes. The feed­ing lines are placed in a separate parallel-plate structure to avoid radiation.

Given the very narrow band, the element is expected to provide performances compatible with the antenna requirements without need of special arrange­ments besides the balanced feeding, A full wave simulation of the complete radiating element shown that the desired cross-polar level is feasible with a proper balanced feeding,

2.1.1 Aperture sizing

Proved the good performance of the radiating element, the aperture sizing has started.

At the array level the major constraints are given by the requirement of a very low radiation in backward hemisphere, which implies low fields at the edge of the array itself, A first assessment of the criticality of this requirement has been made by synthetising an aperture distribution that comes as close as possible to the stated needs. To have a -45dB level back radiation from a square aperture it is necessary to have no more than the same level at the horizon, so that diffraction from the aperture edge cannot contribute a higher field level. An additional margin is required for a circular aperture, because contributions from the whole rim sum in phase in the opposite direction with respect to the beam peak. At the same time it is important to avoid an uneven distribution of the side-lobe levels in azimuth, i.e, moving around the antenna main beam. Therefore, a circularly symmetric radiation pattern offers the best way to achieve the desired low level all around the horizon.

The aperture obtained by synthesis and corresponding to a 7 x 7 element array with the edge elements weakly illuminated and an almost uniformly illuminated area in its centre, shows a satisfactorily low radiated fields toward the horizon in the principal cuts, with side lobes not higher than 50 dB below the peak of the main lobe.

The results were encouraging and the very low radiation levels at the horizon suggested three alternative solutions, illustrated in Figure (2.1.2):

1. A thinned and sparse array to minimize mass and complexity (“array solution")
2. An uniformly-illuminated small array placed at the centre of a meta-

illustration not visible in this excerpt

Figure 2.1.2: Three examples of the possible solutions for the CRTA design, from left to right: planar array, array eombined with a meta-surface and a meta-surface antenna (the one depicted is in circular polarisation).

surface that, when excited by the surface wave launched by the array itself, provides for the tapered illumination of the remaining portion of the radiating aperture (“hybrid solution")

3. A stand-alone meta-surface antenna fed from its centre, that in prin­ciple should be possible to design to provide for the desired pattern (“meta-surface solution")

2.1.2 Array sizing

Given the good results obtained on a continuos aperture, discretising the aperture distribution was considered an acceptable solution and the follow­ing step consisted in sizing two arrays (a square one and a circular one) to assess the feasible field levels. The pattern of the radiating element has been referred to the pattern of the annular slot introduced in Section 2,1, Initial simulations in absence of ground-plane finiteness and inter-element coupling were encouraging and proved that a gain of about 20 dBi would be easily achievable for the antenna, while if a higher gain was needed it would be sufficient to enlarge the array.

The square array is composed by 8 x 8 elements with half wavelength spacing (overall size 4 x 4 m) and excited through an axially symmetric law (Fig, 2,1,3), Achieving a good side-lobe level seemed to require about 15 dB dynamic range for the illumination law, as a consequence the feeding

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Figure 2.1.3: 64 elements square array with related radiation pattern map,

network is dearly eomplex, as it is required to recursively split the signal to obtain lower and lower levels on an increasing large number of elements. Furthermore the square grid, combined with the circular symmetry of the illumination law, results in at least 8 different excitation levels, each used on a limited number of elements, typically 4 or 8, Since corner elements are fed at very low level, they could be removed without affecting significantly the performance or as an alternative they could be substitute with passive elements. The radiation pattern of such square array has an almost circular symmetry thanks to the symmetry of the illumination law, moreover upon a correct sizing it provides a null in correspondence of the horizon. As expected from a square array, since the equivalent aperture is wider along 45° planes and illumination goes down to lower levels than on the principal planes, side-lobes are further lower in such cuts.

To check the effects of mutual coupling and ground-plane finiteness, a mathematical model of the array, which elements are fed with quadratic law excitations, has been produced and simulated with a full wave tool (ADF- EMS/3DAMxLAD), The low impact of mutual coupling on the array perfor­mances has been verified, as it can be observed in Figure 2,1,4 by comparing the radiation pattern of the synthetisch array and of the simulated one. The cross-polar performance of the element is considered to be good as well. Should, upon an accurate modelling of the elements, the asymmetries cause marginal cross-polar levels, it is possible to apply a sort of sequential-rotation

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Figure 2.1.4: Radiation pattem of the square array synthetized (a) and sim­ulated (b)

to average their effects, finding then the layout which provide for a symmet­ric pattern. Finally, low mutual coupling together with the low cross-polar of the element are good indicators that the cross-polar performance of the array is good as well.

Since an array excitation with a quasi-circular symmetry provided a good starting point and the corner elements seemed to be almost irrelevant, a circular array has been also assessed. It is slightly larger than the previous one (4.5 m against 4 m) while it is composed by 61 elements arranged in 4 rings (Fig. 2.1.5a). Edge elements are excited at very low level (-26 dB), so they could be turned into passive elements (reducing the complexity of the feeding network), while removing them would have a negative effect instead (due to the truncation of equivalent aperture field at higher levels). Therefore the advantages compared with the square array are the lower number of elements (3 less) and the lower complexity of the feeding network, which would need only 3 different excitation levels, against 6 values as minimum for the square array without corner elements. The radiation pattern, displayed in Figure 2.1.5b, shows a lower first side-lobe (as expected), however the imperfect symmetry of the aperture layout produces a residual side-lobe level which is not everywhere satisfactory. Since in such lattice the central region of the aperture is poorly sampled, the first few side-lobes rise despite the attempts to improve the performance by make the array sparser. If the

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Figure 2,1,5: 61 elements circular array with related excitations (a) and related radiation pattern map (b)

radiating element could be reduced to 0.36m x 0.36m, an array of 3,6m diameter would have a sidelobe level better than -40dB at the horizon, at the cost of a gain reduction of about 2dB, A hexagonal array of 4,5m diameter could also have a better side-lobe performance, at the cost of a gain loss of about ldB, due to the reduction of the aperture area.

2.1.3 Preliminary design

Having achieved a satisfactory array sizing, the next step consisted in further refining the array layout by removing the constraints on the element shape and size, concentrating on a hexagonal array with 61 elements arranged on a triangular lattice. This configuration is believed to offer the best compromise between regularity and uniform side-lobe distribution in azimuth

An apparent optimum was identified by means of a manual refinement of the array size together with the element spacing and the illumination law. The solution obtained by repeatedly applying basic array design formulas and antenna design expertise, guarantees a very low back radiation (side-lobe level about 60 dB below peak at the horizon). This solution requires a spacing s = 0.48 m (0.7 λ at 435 MHz). The overall diameter is therefore about 4,3 m. The illumination law is based on a Tukey window with a 5% edge taper, the 7 central elements excited with uniform amplitude and an

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Figure 2.1.6: Layout with related excitations and radiation pattern of a hexagonal array made of 61 radiating elements spaced by 0.48 m

overall 26 dB dynamic range. The layout and excitation levels are shown in Figure 2.1.6a. The advantage of such configuration combined with the Tukey window illumination can be noticed by observing the simulated radiation pattern (Fig 2.1.6b) that shows a more regular behaviour of the side-lobes on the principal cuts, in comparison with the previous assessed layouts. Finally an estimation of the radiation pattern over the full sphere has been carried out and, as predicted, the level of back radiation resulted comparable with the side lobes around the horizon.

During the final test of the preliminary design has been observed that the array configurations with higher illumination taper not always show better side-lobes.

A hybrid solution obtained by combining a 7 elements hexagonal array with a meta-surface has been assessed as well. The illumination tapering up to the antenna rim has been designed by combining the effect of the meta-surface outer area with the uniformly illuminated central array, in order to obtain the desired low back radiation radiation. The illumination law is thus derived from the Tukey law used for the array, which can not be easily achieved using the meta-surface alone. The estimated performance of the hybrid solution show the same features of the 61 elements hexagonal array, while having a much simpler structure in the external region and a much simpler implementation of the feeding network, which only has to provide equal power to 7 array elements in total. The presenee of the central array is also useful to respond to the requirement of a double linear polarisation capability.

Finally, the stand-alone meta-surfaee antenna solution is discussed in Ap­pendix C, which also contains a brief description of the concept of meta- surfaee.

In conclusion, the main idea would be to design the hexagonal 61 elements array solution in full detail and compare its performance with that of the hybrid solution, to verify if it can truly offer the same performance with a much simpler structure,

2.2 Tukey Window Illumination Law

As mentioned in Section 2,1 the illumination law conceived for the array feeding is based on a Tukey window, also known as the tapered cosine window. Such window basically consists in a constant region around 0 and a cosine half-lobe tapered to a minimum threshold t next to it. In the proposed array the excitation current coëfficiënt are computed according to a Tukey window starting from the central uniformly illuminated region of the array and ending at the edge elements. The excitation coefficients in the outer portion consist of samples of the cosine and are computed according to the equation 2.2.1:

illustration not visible in this excerpt

where

illustration not visible in this excerpt

An example of Tukey window is shown in Figure 2.2.1.

An important parameter that allows ns to eonsider the effect of the ele­ment excitations current levels on the array is the dynamic range (mentioned several times in the previous section), which is defined as the ratio of the maximum level to the minimum valne, that is:

illustration not visible in this excerpt

Increasing it by reducing the edge taper t, reduces the side-lobes and de­creases the antenna gain. However there is a point beyond which decreasing it stops to be effective for the reduction of the side-lobe level: when the aper­ture illumination slope is such that the high-order spatial harmonics induced by the slope become large enough to produce a contribution to the side-lobes larger than that of the edge truncation.

A second very important parameter in antenna design, which is however less of concern for the present design, is the taper efficiency, which is defined as the ratio of the gain of the amplitude distribution over the aperture to the gain of an uniformly illuminated aperture:

illustration not visible in this excerpt

This páramete is directly linked to the antenna gain by:

illustration not visible in this excerpt

The main advantage of the Tukey-window illumination law is that it offers at the same time good control over the side-lobe level, via the interplay between the edge taper t and the maximum slope of the cosine roll-off controlled by (Rmax — Rfiat), as well as over the aperture efficiency, mainly governed by the radius of the central area Rflat, i.e, for an array of 244 elements (of which half are active) the illumination law, based on a Tukey window with a 5% tapering, offers a taper efficiency of about 65%.

In the hexagonal layout, each ring of elements outside the central region includes at least 2 excitation levels, with their number increasing with the radius of the ring. Still the total number of different levels is less than that of the square array despite the much higher edge taper.

Chapter 3 ADF-EMS 3D Antenna Modelling

3.1 Introduction

This Chapter presents the Computer Aided Design (CAD) software ADF- EMS and the numerieal tools available in support to the design of both the planar array and the meta-surfaee antenna.

The Antenna Design Framework and EleetroMagnetie Satellite (ADF- EMS) is a electromagnetic simulator software developed by IDS Ingegneria Dei Sistemi Spa, in collaboration with ESA, Università di Siena, Università di Firenze and Politecnico di Torino, Its development, started in early 1990s has been focused to achieve a complete and performant EDA tool for space antenna engineers. The main difference with respect to other commercial electromagnetic simulators is that its overall structure and computational algorithms have been specialised to space antenna needs, both in terms of general functionality and accuracy.

In such antenna workbench the user finds a suite of different modelling tools (multi-methods environment), both general purpose and specialised, which can be easily combined to form complex modelling procedures (com­bined methods procedures), ADF enables the analysis and design of anten­nas both in free-spaee and on their final platforms, making it possible to completely assess their perfomanee within a single homogenous environment hosting several electromagnetic modelling tools. In practice, the user can start with antennas and arrays design and then verify their performance on board the platforms, also using several different methods to gain eonfidenee in the aeeuraey and stability of the results obtained. At the same time the system offers the possibility to keep traek of the complete design process, since it automatically stores all previous versions of each antenna element and keeps traek of their relations to the simulations results obtained during the whole process.

The application eonsits of pre-eonfigured packages, tailored to particular applications (Single Antenna Design Package, Array Design Package, An­tenna Farm Package), The simulation environment brings together validated and sophisticated electromagnetic solvers that make it possible to produce highly accurate prediction of the electromagnetic performances of single an­tennas, arrays and complex antenna platforms. In comparison with many electromagnetic simulators ADF enables the full-wave analysis of arrays also on average computing platforms, with a weaker constraint on the maximum size and results accurate to very low field levels (usually around -30 dB with reference to the peak). Structures with thousands of mesh elements can be modelled in just a few minutes on standard PCs.

The innovative methods for fast and accurate full-wave analyses (SFX, Mo.M SIM. SM-AIM, multilayers Green Functions) allow the modelling of the whole array including inter-element coupling. Moreover, as just men­tioned, it is possible to build the global mesh of a platform on which the an­tenna is installed (Antenna Farm full wave modelling procedure IDS-MMMP, IDS-MMMP ext PO, IDS-MMMP ext. GTD and IDS-MMMP ext. SMW) and to evaluate the equivalent current distribution on the platform and the Xear Field or Far Field radiation, through the use of an active equivalent model of the array based on the Equivalence theorem. Full-wave models of complete satellites with up to 10 million elements can be run in a matter of hours on common-place 16-core computational servers, while more approx­imate solutions based on asymptotic methods, i.e, PO and GTD, can be obtained in a few minutes.

3.2 Antenna CAD

3.2.1 Modelling approach

A real world object, as an antenna or an array, reacts to some Stimuli (i.e. sig­nals or excitations applied to the antenna port) showing a certain behaviour. Sneh behaviour can be represented by measurable parameters, technically called Observables, that have an electromagnetic meaning (i.e. fields and currents).

In the computational world the physical-object is represented as an en­tity that collects all the data needed to describe the physical object, while the input category is an element that represents a translation of a corre­sponding element of the stimuli category in a format suitable for use in a mathematical/electromagnetic model.

The electromagnetic stimuli (model input) are applied to the antenna terminals (ports). The direction of incidence (or radiation) of a plane wave or an equivalent current distribution (impressed .sources) can be also considered as s port. This approach brings to the so called generalized .scattering matrix representation, which is often extended to far-field ports. Sneh stimulus may consequently have different forms: voltage/currents generator, guided waves, amplitude and phase of an incident plane wave or a spectrum of plane or spherical waves, modulus and phase of an impressed source.

The output parameters, that can be measured at the ports of the general­ized scattering matrix representing the antenna, cosisi in the computational model output. They are raw electromagnetic data from which processing performance parameters of the antenna can be derived.

ADF data categories start from the definition of the Physical Model, that collects data for the characterization of the real object under analysis. Sneh data are indipendent from the computational method and are represented by modelling information that defines the Geometry and the Terminals, The Tool Specific Model (TSM) is the first idealization of the PH Model that includes the selection of the modelling method. Finally the E.M. Model translates the TSM in the input to the selected e.m. solver. At this stage a meshing operation is performed. For our purpose the selected modelling method is the 3D AM (MoM).

Since, at an intermediate step, MoM based methods allow the calculation of a solution for the electromagnetic problem in form of modal currents, in ADF such solutions are indicated as Internal Models. Hence Internal Models are not a simulation output but they are useful to minimize the effort required for computing repeated output.

ADF data category for the Stimuli category of the real world is repre­sented by Excitations.

Observables represent the Behaviour of real world objects excited by the Stimuli, ADF 3DAM modelling procedure allows the evaluation of the an­tenna performance in terms of: S-parameters, Far-Field, Xear-Field scans, induced structure currents, antenna coupling coefficients, active impedance parameters such as input impedance/admittance (Z, Y), Return Loss, reflec­tion coefficient (Γ) and VSWR, Starting from these basic Observable calcu­lated by ADF, user can build-in his own processing procedures in MATLAB, in order to obtain specific outputs.

3.2.2 3D Antenna Modelling

The "31)Α.\Γ (3D Antenna Modelling) procedure is a double precision general purpose code based on the MoM (Method of Moment), It is suitable for modelling metallic, microstrip and slot antennas, also embedded in infinite dielectric multi-layers.

The Method of Moments (MoM) is an integral equation methods, working in the in the frequency domain, that divides the surfaces of conductors and the interfaces of dielectric layers into meshes. This approach is also known as full-wave analysis and consists in solving the complete set of Maxwelľs equa­tions without any simplifying assumptions. Basically the MoM consist in discretising Maxwelľs equations in integral form and finding the unknowns represented from sources (currents), Consequetely such procedure is very useful to solve radiation and scattering problems and is convenient especially for problems involving open volumes, where the surfaces that carry the cur­rents are relatively small.

Over FEM methods, MoM offers some advantages as a smaller (but full) matrix, lesser dimensionality and the possibility of treating arbitrary regions. Anyway, with MoM method, the cost of simulations increase in terms of computing time and memory as the number of conductors and dielectric layers increase.

The MoM is discussed in more detail in Section 3.4.

Antenna full-wave models (based on geometry discretization) of the ra­diating elements can be used for building an array antenna mesh (suitable for the array full-wave modelling procedure 3DAMxLAD, Section 3,3), As a faster but less accurate alternative it is possible to create a canonical equiva­lent antenna model, which consists in an antenna pattern for each port of the radiating element, suitable for the array synthetic modelling procedure (SM), which computes the overall array performance using the linear superposition taking also into account inter-element coupling if the scattering parameters of the whole structure are available.

In the analysis performed for the study of the radiating elements the frequencies have been selected in a range of about 200 MHz around the operating frequency (435 MHz), The typical sizing of the discretisation to be used for such analises is around λ/ιο corresponding to about 70 mm in the present case, clearly too large to properly model array element not larger than about 450mm, The final design was analised with a discretisation of about 10 mm for the patches, that corresponds to about 70 cells per wavelength, as some convergence tests shown such mesh to be necessary to obtain a stable prediction of the input impedance.

3.3 Array CAD

ADF-EMS includes the Graphical Array Layout Editor (GALE), a specific CAD for planar array modelling which allows the user to interactively create and modify the array layout. Through the GALE tool is possible creat­ing complex layouts and managing excitation laws, sequential rotation and “complex groups" of elements.

Array modelling in ADF implements both Full-Wave methods (that pro- vide for accurate array modelling) and synthetic methods (suitable for suit­able for fast prototyping and optimisation procedures). So, detailed design T (FW)2 and WARM (GAM/MOM), that allows the computation of inter-element coupling and array truncation effects.

According to ADF user manual, since the conceived array of patches displays the following features:

- it belongs to the group from medium to large arrays,
- it has regular grid and the layout exhibits symmetries,
- possible strong coupling among the array elements,
- high number of ports and vertical elements,

the simulations have been carried out with 3DAMxLAD (3D Antenna Mod­eller extended for Large Array Design) based on the technique SFX (Syn­thetic Functions expansion), a special algorithm that extend the application of the MoM to large and very large arrays, suitable to strong interactions among array cells.

3.4 Method of Moments

As mentioned above, the MoM is a method the objective of which is to find the unknown current density, induced on the surface of the radiator (seatterer), by solving an integral equation (IE), Having applied a boundary condition, to solve the integral equation the unknown current is approxi­mated by an expansion of X known function, usually referred as “basis", with unknown constant coefficients. The basis must be chosen to best represent the currents distribution. Therefore the IE is reduced to a set of X linearly indipendent algebrie equations that can be solved for the unknown coefficient by conventional matrix inversion techniques.

For time-harmonic electromagnetics the most common integral equations are the “electric-field integral equation" (EFIE) and the “magnetic field inte­gral equation" (MFIE), The first one enforces the boundary condition on the tangential component of the electric field and is valid both for open and close surfaces. The EFIE can be used both for radiation and scattering problems, in the first ease the most popular equations are the Poeklington Integral Equation and Hallen Integral Equation,

Poeklington’s integrodifferential equation is convenient to find the current distribution on conducting wires and is described below.

3.4.1 Pocklington’s Integral Equation

Assuming that an incident electric field Ei(r) hits on the surface of a conduct­ing wire of length l and radius a (or similarly the feed source of an antenna produces a radiating field that can be seen as an incident wave), part of the electromagnetic radiation induces a linear current density Js (A/m) which, in its turn, produces a scattered electric field Es(r). Therefore, at any point of the space the total electric field E1 (т) is given by the sum of incident and scattered field:

illustration not visible in this excerpt

On the surface of the wire (where т = a) the total tangential electric field is null, therefore the tangential component of 3,4,1 reduces to:

illustration not visible in this excerpt

The scattered field generated by an induced current, for observations at the surface of the wire can be write as:

illustration not visible in this excerpt

If the wire is very thin the current density Jz is not function of the azimuthal angle φ, hence

illustration not visible in this excerpt

where Iz (z') is an equivalent filament line-source current located at ra­ dial distance p = a from the z axis.

Given the symmetry of the scatterer, the observations are not function of φ, which can be neglected. Therefore the equation 3.4.4 reduces to:

illustration not visible in this excerpt

Thus for observations at the surface of the scatterer, the tangential compo­nent of the electric field can be expressed as:

illustration not visible in this excerpt

Finally the equation 3.4.7 can be rewrite as:

illustration not visible in this excerpt

referred to as Pocklington’s integral equation, which can be used to determine the current density on the wire by enforcing the boundary condition on the incident electric field.

3.4.2 Moment Method Solution

The equation 3,4,8 is expressed as:

illustration not visible in this excerpt

where F is a known integrodifferential operator, h is the known excita­tion function and g is the response function.

Thanks to the linearity of the operator F a numerical solution is possible and it can be achieved with the Method of Moments, According to the MoM the unknown response function must be written as combination of X terms:

illustration not visible in this excerpt

where each an is an unknown and each gn(zr) is a known basis function, which are chosen in order to evaluate conveniently each F (gn).

Therefore the equation 3,4,9 turns into an equation with X unknowns and alone is not sufficient to resolve them. Consequently it is necessary to have X linearly independent equations and this can be achieved by evaluating the equation at X different points, i.e, by applying the boundary conditions. This is referred to as point matching. Finally the 3,4,9 becomes:

illustration not visible in this excerpt

The unknowns can be found by conventional matrix inversion techniques:

illustration not visible in this excerpt

Chapter 4 Preliminary design of the array

4.1 Introduction

As described above, an acceptable baseline for the array layout was the start­ing point for the study and the following step consisted in finding an appro­priate radiating element for the array, i.e. one offering a good polarisation purity, dual-linear polarisation operation, an adequate input matching and compatible with the required spacing. The design effort implied verifying with a full-wave analysis that the corresponding array performances were satisfactory (using ADF-EMS/3DAM & 3DAMxLAD tools). This part of the overall antenna design process is called preliminary design, as it does not usually take into account all the issues related to the practical implementa­tion, e.g, mechanical design and manufaetoring, except at a rather simplified level. Several iteration were made to achieve a good design of the radiating element, in particular to satisfy the need of relatively small array element spacing.

Usually, in order to reduce the physical size of the radiating element, the most straightforward technique is to use a substrate with a high dielectric constant, however such approach leads to poor efficiency, narrow bandwidth and above all, with reference to the design of the Calibration Transponder Radar, it would increase the weight of the array, making the structure even more complex. Consequently, air has been chosen as dielectric for all the radiating elements assessd, moving the solution of the size issue on the type and the geometry of the antenna itself.

The array concept has been designed according to the following procedure. With regard to the project requirements the antenna must work on two different polarisations. Since a dual-polarised element needs a rather complex feeding network and it is prone to imbalances affecting its polarisation purity, it seemed to be preferable to select as starting point elements in which the two polarisations could be easily decoupled. The search has therefore been focused on a single polarisation small antenna to be placed in a dual polarised “sub-array” configuration, made of 4 elements rotated by 90° and coupled in pairs of two opposite ones, i.e, like two arms of a swiss cross, which arranged on the array laetiee constitute in effect two interleaved arrays each radiating a single polarisation. In this way the requirement on the polarisation is met and a fairly symmetrical radiation pattern is guaranteed. Figure 4,1,1 shows the three main levels of the array layout, precisely it is the first assessed array, presented in Subsections 4,2,1 and 4,2,2, Referring to Subsection 2.1.3. given

illustration not visible in this excerpt

Figure 4.1.1: An illustration of the first assessed array layout at the three main levels (Hexagonal array, central region hexagonal array, square sub­array).

a structure made of 61 sub-array in dual polarisation, each one contains 4 radiating elements, leading to a total number of 244 single-polarisation antennas, combined in 122 pairs. Such 4 elements sub-array is conceived to be the fundamental “cell” of both the uniformly illuminated central array (composed by 7 sub-arrays) and of the 54 elements outer and tapered region of the array, where the first one is also reference for the design of the hybrid solution (obtained by combining a set of equally excited elements with a modulated meta-surface).

Modelled arrays consist of PEC radiating elements on a PEC ground plane.

The first one radiating element studied has been a Planar Inverted-F Antenna, which is sufficiently light to be placed in a 4 m diameter array.

4.2 Planar Inverted-F Antenna

A PIFA offers performances similar to a patch antenna while having a smaller size. The name is due to the side view of this antenna which resembles a letter F with its face down. This type of antennas are usually implemented in mobile telephone handsets because of their compactness and low profile. The PIFA is effectively a quarter-wavelength shorted patch consisting of a shorted top radiator and a coaxial probe on a finite ground plane. The follow­ing resonant frequency equation has been empirically founded and published in the open literature (i.e, |10| and |7|):

illustration not visible in this excerpt

However the previous equation provides only a rough aproximation and does not cover all the significant parameters, such as the height, the feed position and the dimension of the ground plane, all relevant for the correct estimation of the working frequency and bandwidth.

A better equation that also includes the width of the shorting plate and is useful to understand its effects, is available and has been found by fitting experimental data:

illustration not visible in this excerpt

However this equation does not cover also some of the parameters affecting the resonant frequency.

As discussed in |10|, the width of the shorting plate strongly influences the resonance frequency: when it is larger than half the width of the patch ( Ws > y), the resonant currents on the patch are similar to that of the TM10 mode of a quarter-wavelength patch, while for a smaller shorting plate width (Ws < y) the patch resonates at higher frequency being the current distribution similar to the TM10 mode of half-wavelength patch. In both cases increasing the width of the shorting plate means increasing the resonance frequency, since the total length of the average current patch decreases implying the need of shorter wavelength of the exciting signal to achieve resonance and efficient radiation.

illustration not visible in this excerpt

Figure 4.2.1: Measured return loss for a PIFA by varying the shorting plate widths (Ws), er = 1 ,h = 4 mm, L = Lg = 30 mm, W = Wg = 40 mm (from |10|)

The radiation pattern of Εθ in the two principal planes is near omni­directional, moreover, since currents are most concentrated on the shorting plate for W = Ws, a peak of radiated power can be seen in the upper direc­tion.

In order to match the input impedance Zin to the 50 Ω coaxial probe needed to excite the patch, the feed point of such antennas has to be placed close to the shorting plate. As in a normal patch, a PIFA can be matched by adjusting the distance of the feed position d from the shorting plate while moving it along the symmetry plane. It is worth noting that, although 50 Ω is commonly assumed as reference in microwave design it is by no means a mandated value, in particular, in eases like the present one, in which the individual radiating elements need to be first combined in pairs and then connected to the array beam forming networks, there is quite some freedom in the selection of the optimum impedance at the various junctions. In prac­tice however a preliminary design based on a 50 Ω input impedance simplifies testing and it is therefore a reasonable starting point.

The size of the ground plane can be also a limiting factor, as long as it is smaller than about a wavelength: first, the resonant frequency decreases when the size of the ground plane increases, second the impedance band­width and the antenna gain increase by enlarging the ground plane. Both effects are linked to the resonances of currents flowing of the ground plane, including the radiation they excite along the edges parallel to their direc­tion, In addition, the edge diffraction resulting from the current slope in the proximity of the edges perpendicular to their flow introduces a relatively high cross-polarisation at angles that correspond to the width of the ground plane.

The bandwidth of a PIFA is determined by the antenna height and the dielectric constant of the substrate, and it is usually quite narrow. An in­crease of the impedance bandwidth can be obtained by increasing the height or using a substrate with smaller dielectric constant. However, as the an­tenna height h increases the resonant frequency decreases, since the overall electrical length increases. In the present case the bandwith is not a large concern, as the requirement is below 2%,

4.2.1 PIFA Design

An accurate design of an the radiating element through simulation analy­sis has then achieved using as reference the theory described so far. Some practical examples available in the literature mentioned before were the basis for several models that have been analysed and partially optimised until it

illustration not visible in this excerpt

The geometry of a general PIFA is illustrated in Fig. 4.2.2. Length, width and height of the radiating patch are, respectively, L, W and h. The 50 Ω coaxial probe fed is positioned in the centreline of the patch and its distance from the edge of the plate is d. The patch is assume to be made of a perfectly conducting material (PEC), a good approximation for copper or aluminium, and to be placed on an infinite ground plane also made of a PEC material. The antenna is assumed to be placed in free space (εΓ = 1), which fills also the gap between patch and ground plane. The shorting plate consists of a vertical PEC strip with dimensions Ws and //. for the preliminary design Ws = W has been chosen, due to implementation reasons. In fact, the shorting plate also constitutes the main support patch and in a ground antenna, i.e. the BCRTA, as the mechanical stability is fundamental to protect the structure against meteorologie adversities. The major design limitation introduced by such early choice is that a reduction of the antenna size would be obtained by reducing the shorting plate width (at expense of the mechanical stability of the structure), however the same effect can be achieved by a capacitive top loading (at expense of some additional complexity and weight of the structure) as mentioned in [10]. Nevertheless the shorting-plate width could be re-considered in the detailed phase once an overall array design is obtained and selected as the most appropriate solution.

In the analysis, the thickness of all the conductors is assumed to be in­finitesimal, which is quite reasonable considering that an implementation can be expected to use plates of about 1 mm thickness, i.e of the оrder of Λ/ιοοο, at least along their edges were thickness is most relevant for the electrical behaviour.

illustration not visible in this excerpt

Figure 4,2,3: A view of the first assessed element, a Planar Inverted-F An- 170 x 170 x 40mm), from ADF-EMS

The first antenna design achieving satisfactory performance had the fol­lowing parameters: L = W = 170 mm, h = 40 mm and d = 145 mm (Fig, 4,2,3), The model shows good input matching at the operating frequency (Zin = 50 — 6j, Γ = —25 dB) and a satisfactory peak directivity gain equal of about 4 dBi, However, as it can be observed in Fig, 4,2,4, the radiation pattern shows a behaviour similar to that of monopole antenna, due to the infiniteness of the ground plane.

A working bandwidth BW = 15 MHz was obtained through a simulation- based matching of the input impedance, performed by adjusting the feed point position and connecting a inductive load in series to the feeding line, to compensate for the small capacitive susceptance observed.

The general behavior of the input impedance was studied as a prelimi­nary step to achieve a proper input matching. As we can see in Figured,2,5 the basis for the study were a number of equivalent circuits of the antenna as seen from the input port, A planar inverted-F antenna is usually made to work near its second resonance frequency, where real and imaginary part

illustration not visible in this excerpt

Figure 4,2,4: Directivity gain (Etotal) of the first PIFA design (L = W = 170 mm, h = 40 mm and d = 145 mm)

have opposite trend (the first one is decreasing while the second one is in­creasing), this information has been used to search, by successive trials, for the geometrical configuration having an input impedance matched to the 50 Ω coaxial feed, i.e, Xin = 0 and Rin = 50 Ohm.

illustration not visible in this excerpt

Once a satisfactory element design was available, a four elements sub­array has been designed using the ADF-EMS CAD utility dedicated to pla­nar array layout (Graphical Array Layout Editor), described in Section 3.3. (Fig. 4.2.6).

A number of different configurations were studied looking for a compact arrangement fitting the desired array spacing, i.e. 480 mm, which is rather tight for 4 elments 170 x 170 mm each. Initially the elements were placed along the four sides of a square and oriented in such a way to make the layout invariant under rotations of 90° or integer multiples. Solutions with the shorting wall facing the adjacent element or opposite to it were tested and various spaeings, i.e. lengths of the side of the enclosing squaring, were attempted. Unfortunately, while the isolated sub-array would perform quite reasonably, the asymmetry of their arrangement in the whole array combined with the relatively strong coupling due to the small spacing between adjacent elements of opposite polarisations resulted in a very high cross-polar of the complete array, making all these arrangements unsuited for the purpose.

The only available option to obtain a better control of the cross-polar radiation, clearly leading to a large sub-array, was to arrange the 4 elements in a symmetric way within the array cell. A first attempt was made using a cross-shape layout with the arms at 45° with respect to array axes, the x axis being parallel to opposite sides of the hexagon. Although some improvement was achieved, also in this case the asymmetries and coupling effects were too strong. As a consequence, a final attempt was made using the most promising among the cross-shaped solutions, but with arms parallel to the array axes.

In the first configuration the distance between the centres of the collinear elements necessary to obtain a suitably low coupling was found to be 230 mm, which implies a spacing of 650 mm in the 61 elements array, increased by half compared with the optimum distance found in the preliminary analysis. The PIFAs are arranged along the x axis to generate the corresponding polarisa­tion and along y axis for the other, so as to satisfy the requirement of double linear polarisation. Co-polarised elements are rotated by 180° to each other, with the shorting wall placed towards the centre of the sub-array (Figure 4.2.6) in such a way to minimize the coupling among cross-polarised ele­ments pairs in each sub-array (knowing that the distance among such pairs of different sub-arrays would be larger thanks to the array layout). In order

illustration not visible in this excerpt

Figure 4.2.6: A view of the first assessed sub-array (spaeing of eollinear elements of 230 mm) from the GALE.

to assess the performanee of the sub-array on a single polarisation, copo­larised element have been fed with amplitude A = V and a phase shift Αφ = 180° to compensate for the physical rotation that makes the radiat­ing elements working in phase-opposition, A plot of the simulated currents shows a low coupling among the excited and passive patches. The directiv­ity diagram shows high side-lobe levels close to the horizon both for both co-polarisation and cross-polarisation, which are typical of patch antennas. However these side-lobes would be mitigated in the array configuration by the array factor associated to a tapered illumination. As a consequence this solution seemed suited to meet the requirements at the moment.

Nevertheless an element of such size was considered too large for the final use because it leads to an overall diameter higher than 5 m, which is not optimum from the side-lobe performance point of view. Consequently a design of the radiating element was deemed necessary to reduce its size, while maintaining as much as possible the proven good performanees. The new design optimisation exeereise was performed by tracing the effects of each parameter (length L, width W, height h, feed point position d) on the resonant frequency and thus on the impedance matching. The input resistance and reactance as a function of the investigated parameters are shown below.

As already discussed a fundamental performance parameter is the input impedance, which is directly linked to the reflection coefficient, therefore a further detailed assessment of the effects of each parameter on the return loss was made, to verify which margin existed for reducing the element size by a minimum of 20 %. As it can be seen in Figure 4,2,7, when the antenna height decreases the impedance curve moves to higher frequencies, as the length of the current line get shorter. Unfortunately the frequency of interest is in a region in which the impedance is highly variable, located between the anti-resonance and the secondary resonance, therefore height changes have a strong impact on the return loss, as we can observe in Fig, 4,2,8, Since the target height, h = 20mm, offers bad input perfomance, a manual sweep of the remaining geometrical parameters has been carried on, in order to match the input impedance.

The sides of the top radiating plate have different effects on Su'- according to the simulated input impendanee shown in Figure 4,2,9 real and imaginary part of the impedance curves flatten out on the x axis as the shorted side width W enlarges, while, as expected, the resonant side L strongly influences the resonance peak, moving it towards lower frequencies when the length increases (Fig, 4,2,10), Having fixed the dimensions of the PIFA, the feed point was adjusted to get a proper impedance matching. As shown in Figure 4,2,11, the position of the feed point d along the y axis has a strong effect on Zin, where it can be seen that the closer the probe is to the open-edge of the radiating patch the larger is the impedance.

At the end of the manual design refinement process the following ge­ometrical parameters were considered to offer the best compromise on re­turn loss (Γ = —15 dB) : L = 166 mm W = 172 mm h = 20 mm and d = 63 mm, A planar inverted-F antenna as the one obtained in the design

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Figure 4,2,7: PIFA input impedance by varying the height h

process shows excited current distribution similar to the TMW mode of the quarter-wavelength patch (Fig, 4,2,12), eonsequetely it can be observed that the maximum of the current distribution is close to the shorted edge, owing to the larger shorting plate width, while the distribution of the current is very low near the side edge of the upper radiating plate.

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Figure 4,2,8: Return Loss for different antenna heights

The radiation patterns of the proposed antenna in the prineipal planes are presented in Fig, 5,1,8 and 5,1,9, The radiated fields respect the typical profile of patch antennas: the slot formed by the radiating edge of the patch, opposite to the shorting wall, and the ground plane hosts the aperture field which can be modelled as a magnetic dipole oriented along the y axis. The directivity gain is about 2,5 dBi with a maximum at the horizon (θ = 90°) in correspondence to the aperture field.

The PIFA offer a 10 dB impedance bandwidth of about 20 MHz (4,5 %), calculated by considering a characteristic impedance of the feed line matched to the simulated input impedance at the resonance frequency, to compensate for the inductive susceptance observed. Both side lobes and erosspolar level at to the horizon seem to be high, however it has to be verified the effect of coupling among the elements inside the array configuration.

4.2.2 Design of array based on PIFAs

As explained in Chapter 4, in an array, as the proposed one required to sat­isfy rather demanding requirements, it is hard finding the best arrangement of the individual radiating elements because of the intrisie symmetries of the

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Figure 4.2.9: Input impedance for different lengths of the shorted side

desired radiation pattern, of the array and of the sub-arrays are easily at odds with each other. Such elements, clustered in groups of 4 and operating on two different polarisations, produce fields that add in Far-Field differently depending on the observed cut and inevitably eo-polar and cross-polar radia­tion patterns display uneven levels at the horizon depending on the observed φ. As a conseguence the inhomogeneitv of pattern levels at the horizon in- ereses, in certain eases with a variation range up to 10-20 dB, Therefore an overall solution can only be found by successive approximations, often go­ing back almost at the starting, with the sole advantage of the background knowledge and understanding of the behaviour of the whole structure ac­quired in the meantime. The impact of this process on the element design

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Figure 4.2.10: Input impedance by varying the length L of the PIFA (fixed W=172 mm, h=20 mm)

was described in previous Section, just giving a brief rational of the causes that lead to further exploration of its design space. The effects on the array are examined in the following.

After the initial design of the radiating element and the evaluation of an optimum spacing among the sub-arrays for it, we have to take into account

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the effect of their relative positions and orientation within the array, consider­ing the two separate sets working on the two polarisations. The eonseguenee of the lack of a global symmetry, which in fact can be seen as asymmetries

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Figure 4.2.12: Simulated currents distribution (dBA/m) on IDS Current Post Processor for the ultimate designed PIFA

in the structure, shows up especially on eo-polar side-lobe distribution and on the cross-polar radiation pattern, which are both characterised from ir­regular levels around the horizon and close to it, i.e, levels changing with the observed plane cut at constant φ angle. In any antenna with a relatively high directivity gain illuminated with uniform phase across its aperture (or length) the main lobe is only marginally affected by the local details. Such behaviour is a direct consequence of the Fourier-like relation between antenna aperture and far-held radiation, which is actually almost an exact Fourier re­lation for planar apertures and arrays. The main lobe is the portion of the spectrum of the aperture illumination close to a null spatial frequency, i.e, to its average and slow variations across its whole width, while side-lobes corresponds to variations of increasingly high spatial frequency moving from the antenna boresight to the horizon. Thus their levels are largely affected by details of increasingly local nature. The cross-polar radiation follows the same rule, with the only difference that it is usually expected to exhibit a very low level on the main beam axis and its surrounding since it arises from imbalances in the antenna design which typically have an odd symmetry and a mean dose to zero if the antenna is properly designed.

To achieve an overall satisfactory behaviour it was therefore necessary to study five different sub-array layouts. As mentioned before two were based on square cells and the last three had PIFAs aligned on two orthogonal axis placed either parallel to the array axes or at 45° to them.

The design of the array started by placing the optimised PIFA model into the first 4-elements sub-array layout (Fig, 4,2,6) presented in Subsec­tion 4,2,1, The analysis of this small array, working in a single polarisation, shows the presence of coupling effects among the radiating elements: an in­crease by 66% of the return loss at the centre frequency of work, mainly due to the decrease by 30% of the real part (ARin) of input impedance (while the reactance Xin improves by getting closer to 0), Such effected is to be expected when working with elements which are smaller than the wavelength and placed in close proximity and can be compensated by retuning the geo­metrical parameters of the element and possibly by adding or changing reac­tive elements placed at the feed point to compensate for residual reactances. The radiation pattern of the sub-array, excited on the vertical polarisation (φ = 90°), shows a main lobe with d0 = 5.8 dBi directivity gain in broad­side direction, which is in line with the expectations, i.e, about 3 dB higher than the single PIFA, with the difference gain caused by the coupling among them. Moreover, as it can be observed in Fig, 4,2,13a, the sidelobe levels are quite high at the horizon, however it has to be considered the effect in the overall array configuration combined with the tapering provided by the circularly symmetric illumination law. Figure 4,2,13b displays the directivity gain of the erosspolar component, which produces high radiation levels at the horizon (up to 5 dBi), probably due to imbalanced currents flowing on the external edge of the non-active elements, while it is very low (-20 dBi) in broadside direction. Performance are identical on horizonatal polarisation as the layout has the same symmetry with respect to the axis. Therefore, since the assessed sub-array shows critical coupling effects, the XPD and the SL performance have to be carefully evaluated during the design process in such a way to consider an alternative radiating element.

Next step consisted in modelling the array by placing 61 sub-array into

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the selected hexagonal layout (Fig, 4,2,16 ), Since the optimum distance estimated during the preliminary study is not compatible with the size of the sub-array, the spacing among the elements has been set as low as possible in order to control the coupling and verify its effects on the complete array, that is 525 mm. Then, with such information at hand, it was refined by computing analitieally the optimum value by considering the link between the array diameter and the position of the nulls between successive side-lobes at the proximity of the horizon, as explained in Section 6,2, finding a possibile optimum spacing to be about 535 mm. As expected the assessed arrays excited with the Tukey illumination taper, show a radiation pattern with very low side-lobe levels close to the horizon, up to 40 dB below the main lobe (Fig, 4,2,14), Nevertheless Figure 4,2,15 displays high erosspolar levels, up XPD = 25 dB in broadside direction. In other words it does not perform as required. However the design optimisation process proves that the selected spacing offers good SL performance at the horizon. The unequal levels of the eo-polar and especially cross-polar radiation patterns at the horizon, mentioned before, are clearly visible in those maps.

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Figure 4,2,14: Radiation pattern of hexagonal array composed by 61 square sub-arrays of PIFAs (H-POL)

Next a similar configuration obtained bv rotating each patch 90° coun­terclockwise around his central axis (so that the shorts were external in the 4 PIFA sub-array) has been assessed (Fig, 4,2,16b), It shows better results than the previous one, however the cross-polar levels remain too high for the requirements.

The bad performance of these two configurations are believed to be caused by the asymmetry of the structure, as proved by the currents excited on the non-active elements, which are indeed oriented to radiate the orthogonal polarisation, Consequentelv a 45° rotation has been applied to each PIFA to increase their distance and reduce the asymmetries in the overall layout

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(Fig. 4.2.16c). To better understand the latter point it is useful to observe in Figure 4.2.16 how in the previous two configurations (a,b) the two sets of elements with the same orientation were not symmetrically placed on the array nor were they complementary as it would be necessary to have a global symmetry.

As mentioned, the impact of the mutual disposition of the antennas on the radiation pattern can be assessed by comparing the simulated current distributions at the operating frequency. Given the modular composition of the array and the uniform illumination in the central region of the array, with an aperture tapering starting from the edge elements, hence observing the excited currents on the 7 central sub-arrays is sufficient to assess the coupling and the effects of the asymmetries. We can observe the comparison among the assessed layouts in Figures 4.2.16 (a,b,c). The analysis of current distributions excited on passive elements shows a better behaviour of the second array in comparison with the first one, while the last one, despite having a better symmetry, does not seem to provide a significant performance enhancement.

Furthermore the last solution does not allow an enhancement of the side- lobe performance without further increasing the spacing among adjacent sub­arrays, which already raised to 570 mm from of 525 mm of the two previous layouts. The overall diameter of the array would be too large and conse- quetely the Radar Transponder Antenna would become heavier and more

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Figure 4.2.16: Distrubution currents on main assessed central arrays layouts (V-POL), from left to right: cells with internal shorting wall, cells with external shorting wall and PIFAs alligned on orthogonal axis.

sensitive to wind. So, unless no better solution could be envisaged, the de­sign refinement process had to be continued.

The comparison among the overall performance of the central arrays can be assessed also by observing the corresponding radiation patterns over dif­ferent φ — cut : Figures 4,2,17 (a, b, c) show that the third layout compared to the first two (square sub-arrays) has higher erosspolar levels over the full pattern, as expected by observing the distribution currents on the non-active elements. The second layout, the one with the shorting walls of the PIFAs placed at the edge of the sub-array, shows better performance indeed. To­tal directivity patterns are not compared, since the side-lobe levels at the horizon change only by few dB.

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Figure 4.2.17: Comparison among the radiation patterns of the erosspolar component for different 7-elements array (V-POL), from left to right: cells with internal shorting wall, cells with external shorting wall and PIFAs al- ligned on orthogonal axis.

Clearly performance are slightly different on the orthogonal polarisation with respect to the vertical one, but there is no point to show them because such differences do not provide for an overall improvement.

All the findings, collected in the array design so far, pointed in the direc­tion of a smaller element that could allow for a further improvement in the array symmetry without impacting its overall size. The study of a smaller radiating element has then started.

Given that the simulated shorted-pateh and the related array layouts, although not meeting the requirements, display relatively good perfomanees and the behaviour of the radiating elements is not so far from the target, the logical following step seemed to be modifying the PIFA, addressing directly the problem to its excessive size.

Chapter 5 Advanced array design

5.1 Folded Planar Inverted-F Antenna

A folded version of the radiating element has been assessed to improve the sub-optimal design achieve with the PIFA, At this stage |11|, a paper pub­lished in 2004 by IEEE, has been the reference point to design the new an­tenna , The shorted patch antenna, also known as PIFA, originally designed as a variation upon the filar inverted-F antenna, can also be seen as obtained starting from a conventional patch antenna operating in the fundamental mode, observing that the electric field is zero in the middle of it and conse­quently shorting the radiating plate along its middle line, A folded planar inverted-F antenna can be obtained following the same logic by folding the top radiating plate together with the piece of the ground plane beneath it, which now serves as an upper patch, and clearly adding a new piece of ground plane to compensate for the part folded away (Fig, 5,1,1a, b, e). Finally, the folded patch can be reduced to a single layer, as shown in Fig, 5,1,Id, thus obtaining a structure which can also be seen as to overlapped PIFA fac­ing opposite directions, only one of them being fed. The whole development process of a folded PIFA, starting from a standard PIFA, is depicted in Fig, 5.1.1.

A folded shorted-pateh antenna still resonates at a quarter wavelength, since the currents path goes from the radiating aperture between the top and the middle patch, all around the latter and through its shorting plate till the

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Figure 5.1.1: Development of a folded PIFA as explained in Li & Tentzeris’s paper ( |11| )

ground plane, while its physical length is reduced by 50 %, from λ/4 (typical length of the PIFA) to λ/8 (length of the top radiating plate).

In Fig, 5,1,2 we can observe the 3-dimensional geometry of a folded PIFA, which basically consists in a stacked-shorted patch, looking like an S-antenna, The heigths, widths and lengths of the lower and upper patches are, respectively, hi, Wi; L1 and h2, W2, L2, where h2 is actually the distance between the lower and the upper plate. The distance of the feed point from the shorted side of the lower patch is d, while it is placed in the middle of the patch in x direction.

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Figure 5,1,2: Tridimensional geometry of a folded PIFA from [11]

According to theory, the resonant frequency of the folded shorted-pateh is about half of that for a conventional PIFA of the same dimensions. Actually it is tipieally slightly higher than this value. The main reason is the need of a small gap between the lower plate and the shorting wall of the upper pateh, in order to let the power flow from the probe to the radiating slot. Consequently the length Li of the lower patch is shorter than half the one of a standard PIFA working on the same frequency, making the total path length of the resonant currents twice as much shorter thus raising the resonant frequency.

The almost equivalent behaviour of the folded shorted patch compared to the unfolded one, is also explained in the literature by observing the electric field and surface current distributions at resonant frequencies of the two an­tennas, Simulations shown that the energy of the electric field is concentrated in the gap between the lower and upper patches of the folded shorted-pateh, just like the fringing field of the equivalent slot of the conventional PIFA, It has been also noticed that lower and upper surfaces of the lower patch of the folded PIFA correspond to the lower surface of the unfolded shorted-pateh and that the lower surface of the upper patch of the folded shorted patch corresponds to the part of the ground plane beneath the traditional PIFA, It is important also to mention that simulations shown that the energy of the electric-field resulted to be stored between the edge of the lower patch and the shorting wall of the upper one, this is is mainly due to electrostatic effects of the sharp edge of the lower plate combined with the short distance between the edge and the opposite shorting wall. Such electric-field con­centration may cause a reduction of the impedance bandwidth, therefore a careful control of the gap size is necessary.

5.1.1 Design of a Folded PIFA

A folded shorted-pateh is defined by almost the double of the geometrical parameters in comparison with the traditional PIFA, Thus, it is not easy to find an optimum combination of parameters by direct search. As mentioned previously, the design of the radiating element has started making reference to Tentzeris’s paper, hence the first model of the proposed folded PIFA has been sized proportionally to the one displayed in the article. Later, according to the theory, the resonant length Li has been set at slightly less than | together with the width of lower and upper patches, while the length of the upper patch has been set at In the analysis below, the thickness of the conductors is assumed to be much smaller than the heights, however it is much lower than the wavelength of resonance frequency, therefore its effect on the computational model can be ignored.

Since the reactance Xin is exclusively positive and never crosses the ж-axis, simulations show that impedance matching is hard to reach for the proposed antenna unless the reactance is compensated externally. In other words, as the input impedance is strictly inductive it is necessary to introduce a capacitive feeding to cancel it out.

Therefore a parameter study has been carried out through simulation in order to understand the behaviour of the input impedance by adjusting the undefined geometrical parameters (height h, feed point position d, distance between the plates, length and width of both patches), A second benefit of these analysis was the possibility to achieve a more accurate overall design of the folded PIFA, This part is described in the following Subsection (Subsec, 5.1.1.1).

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(L2 = W2 = 86 mm, h = 22 mm h1 = h2 = 11 mm Li = 84 mm d =17 mm and Wi = 86 mm)

A radiating element with the top radiating plate having L2 = W2 = 86 mm and thickness h = 22 mm has been then obtained (other parame­ters: h1 = h2 = 11 mm L1 = 84mm d = 17mm and W1 = 86mm). The obtained model consists in a folded PIFA positioned on a ground plane mea­suring 220 x 220 mm, with the axis of the top radiating patch aligned to the one of the ground plane and with z axis of the reference system. All the geometries are made of PEC and the whole model includes 1742 mesh patches with a length of 10 mm. The design of the folded shorted-pateh is depicted in Fig, 5,1,3 and Fig, 5.1.4.

The simulated input impedance at f0 = 435 MHz is Zin ~ 54 + 16 j Ω, with a return loss Γ = —17 dB . Clearly it is not an optimum matching but, as explained below, it is not simple matching the input impedance by finding the best combination among geometrical parameter, as it means varying one while freezing the others and each one has a different effect on the input per­formance, As a eonseguenee the bandwidth is not fully satisfactory, resulting to be B ~ 4.8 MHz (1.1 %) for Γ = —10 dB, while it increases up to 6,5 MHz (1,5 %) by considering a characteristic impedance matched to the simulated Zin (Zg = 54 — 16j). However both matching and bandwidth need to be meaningfully assessed in the array configuration, as the coupling over the whole structure, including all the elements and also the feeding network, has a strong impact on the performance of the single antenna. Therefore it makes sense to left the improvement of the design of the antenna together with a proper beam forming network, for the detailed design. Referring to Subsec­tion 4,2,1, a conventional PIFA shows an impedance bandwidth almost three times higher compared with that of the simulated folded shorted-pateh, that is 4,5 % against 1,5 %, this result is expected as the volume of the latter is reduced almost 4 times lesser.

5.1.1.1 Parameter study

As mentioned above the parameter study of the folded PIFA has been useful to understand the behaviour of input impedance Zin and therefore of the S-parameter and bandwidth. Such parameters are fundamental to assess the performance of any antenna at the resonance frequency.

Figure 5,1,5 displays how the input impedance changes by varying the width of the gap between the lower patch and the shorting wall of the upper patch. The length Li of the shorted patch has been slightly modified to control the gap width, which means that when the gap get wider Li gets shorter and consequently impedance curves move to higher frequency, as the resonant length decreases. Moreover shorter gaps provide also lower reactance, therefore are more recommended.

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Figure 5,1,4: Top view and side view of the antenna modeled with ADF-EMS CAD (L2 = W2 = 86 mm, h = 22 mm, hi = h2 = 11 mm, Li = 84 mm, d =17 mm and Wi = 86 mm)

As the conventional PIFA, a folded shorted-patch can be matched to 50 Ω by adjusting the distance d of the feed from the shorted wall of the lower patch. The behaviour of Zin for different feed position is shown in Figure 5,1,6; it can be seen that the input impedance increases as the the pin get closer to the edge side of radiating plate.

The parameter study, together with the assessment of a slightly tilt in the upper patch in the final design (Sec, 7,5), has been also useful to understand the main differences between measurements and simulations.

Referring to Subsections 4,2,1 and 5,1,1 a conventional PIFA show an impedance bandwidth almost three times higher compared with that of the simulated folded shorted-patch, that is 4,5 % against 1,5 %.

Figure 5,1,7 shows the simulated input impedance Zin against the thick­ness h = hi + h2 of the folded shorted-patch: in accordance with general antenna theory, the curves display a decrease of the resonance frequency when h increases because of the longer current path, moreover the results suggest that the height of the radiating element should be keep low so that the reactance is low as well. This can be explained by considering the folded PIFA as a shorted patch loaded by a capacitor. Below is touched on the

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Figure 5.1.5: Simulated real (Rin) and immaginary (Xin) part of input impedance for different distances between the lower plate and the shorted wall of the upper patch ( parameters of the folded PIFA: L2 = W2 = W1 = 86 mm, d =17 mm, h1 = h2 = 11 mm)

theoretical analysis that reveals the physical insight of the variation of the resonance characteristics for this antenna.

In literature has also been carried out a theoretical analysis of this antenna by associating it to an unfolded shorted-pateh configuration and modelling it with a transmission line. Assuming that both the total thickness h of the antenna |hi — h2\ are much shorter than the total patch length, the folded PIFA can be represented by an equivalent trasmission-line defined by analytical expressions. Starting from this, theoretical results and numerical simulations have been compared, showing a good agreement. Moreover it has been observed that effectively resonant frequency decreases as \h2/h1 \ decreases and it has been shown that the upper patch can be considered as

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Figure 5,1,6: Simulated real (Rin) and immaginary (Xin) part of input impedance for different feed position (parameters of the folded PIFA: L2 = W2 = W\ = 86 mm, L\ = 84 mm, h\ = h2 = 11 mm)

capacitive load connected between the radiating edge of the lower patch and the ground plane, A decrease in h2 is actually equivalent to an increase in the coupling capacitance between both patches, leading therefore to a decrease of the resonance frequency.

The radiation pattern at the resonant frequency for the proposed folded shorted-pateh is shown in Figure 5,1,8 where it is compared to the conven­tional PIFA simulated in Chapter 4, Note that for comparison, the radiating slots of both antennas are oriented to the negative y direction, are working on

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Figure 5,1,7: Simulated real (Rin) and immaginary (Xin) part of input impedance by varying the height of the patches hi = h2 (parameters of L2 = W2 = Wi = 86 mm, Li = 84 mm, d = 17 mm)

the same frequency (/0 = 435 MHz) and are positioned on a ground plane of the same size (220 x 220mm). Since both patches share the same radiating slots, they produce similar radiation pattern. Given that the electric size of the ground plane is the same for both antennas, while the electric size of one is twice that of the other, the folded PIFA has a higher directivity gain compared to the standard PIFA, about 4 dBi against 3 dBi. Observing the E-cut it can be noticed that both patterns (Εθ) show a peak slightly oriented to θ = —30°, corresponding to the shorting wall of the upper patch side, and a back-radiation peak oriented to θ = —150°, corresponding to the back of the probe.

The beamwidth (θ3άΒ) of the simulated folded PIFA is about 110° both on H-eut an E-cut, thus the folded shorted-pateh has a nearly omni-directional

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Figure 5.1.8: Simulated radiation pattern at 435 MHz of the Λ/8 folded-PIFA compared with a conventional quarter-wavelength PIFA on E-cut (up) and H-cut (down)

radiation pattern.

To a further comparison the models have been positioned on an infinite PEC ground plane. Simulations, exhibits in Figure 5.1.9, show that, under the same conditions, the radiation pattern of the folded-PIFA has effectively an higher directive gain in comparison with a shorted patch working at the same resonant frequency.

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Figure 5.1.9: Main cuts of the radiation pattern of a Folded PIFA and a conventional PIFA over an infinite ground plane

The radiation pattern of the designed radiating element has been also 3-D plotted and it is depicted in Figure 5.1.10. The diagram shows a nearly omni-directional pattern.

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Figure 5.1.10: 3-D radiation pattern of the Folded PIFA

Finally, Fig, 5,1,11 shows the eurrents distribution on the folded shorted- pateh as seen through the Current Post Proeessor of ADF, The post-proeessing eonfirmed the hypothesis made during the analysis.

As expected the eurrents are concentrated on the shorting walls of both patches. The combination with the equivalent magnetic current of the radi­ating slot between the two patches produces the observed radiation pattern of the antenna. Moreover the high eurrents distribution near the feed point could explain the orientation baek-lobe observed both in the simulations and in the measurements.

To conclude, it can be noticed that there is a also “folding" effect on the eurrents, in fact, starting from the edge of the upper patch, the eurrents flow to the shorting wall, then they go through the ground plane until they reach the shorting wall of the lower patch. Finally eurrents go up to the lower patch until they reach the edge. The path of the eurrents is clearly longer than λ/8 and it can be approximated to λ/2 by considering the sum of all the lengths covered by the currents ( three times λ/8 plus the heigths of the shorting walls). The path of the currents can also be seen as a loop, explaining therefore the purely inductive reactance shown above.

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Figure 5,1,11: Distribution currents on the simulated folded PIFA (dBA/m)

5.1.2 Design of an array concept based on folded PIFA

Since a folded PIFA offers reduced dimensions, the previous sub-array layout, the one with eo-polarised patches aligned on the same 45 degree-oriented axis (Fig, 4,2,6), has been re-assessed. This configuration with the smaller radiating element allows a higher distance between the folded PIFA and therefore lower cross-polarisation levels were expected (Fig, 5,1,12) even while bringing back the sub-array spacing to the desired value. As previously the array layout is hexagonal and it is composed by 61 sub-arrays, but cells (4 radiators) are now 330 mm in diameter and spaced by 480 mm, leading to an overall diameter of the Transponder Antenna close to 4.2 meters. Also in this case the illumination law is based on a Tukev window with a 5% edge tapering and the 7 central sub-arrays are excited with uniform amplitude, resulting in a dynamic range of 26 dB.

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Figure 5,1,12: Fundamental sub-array of the assessed arrays eomposed by folded planar inverted-F antennas

The radiation pattern of the 61 elements array, eomposed by folded PI­FAs aligned on two orthogonal axis placed at 45° to the array axis (sub-array elements oriented as in Fig, 5,1,12), shows satisfactory side-lobe levels and a lower cross-polar levels indeed, but not low enough to respond to the re­quirements (XPD = 20dB broadside), A similar configuration obtained by rotating 180° each element shows very low side-lobe levels at the hori­zon (about -55 dB below the directivity peak) but the cross-polar levels are unsatisfactory also for this configuration (XPD = 30 dB).

Finally a rotation of 45 degrees has been applied to all sub-arrays obtain­ing indeed a more electrically balanced configuration. The obtained layout is illustrated in Figure 5.1.15.

Results in the horizontal polarisation were encouraging: the radiation pattern shows a cross-polar peak directivity on axis nearly 80 dB lower than the co-polar component and the cross-polar also goes down to about —45 dB over the full pattern. Side-lobe levels at the horizon are everywhere lower than —45 dB below the peak (Fig, 5,1,17 and 5,1,18), The performances are slightly different in the horizontal polarisation, as the symmetry of the related 122 elements array is different from the one of the horizontally polarised one, but still satisfactory. To be more precise, in Fig, 5,1,14 and 5,1,13 it can

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be noticed that the horizontal polarisation offers higher eross-polar levels over the full pattern and also higher side-lobe in comparison to the vertical one. Moreover both configurations show side-lobes close to the horizon of about -20 dBi entering in the visible region over the upper hemisphere and secondary lobes at θ = ±20° of abo ut 0 dBi. Consequently, in the detailed design process it must be take into account also the different behaviour of the array in the two orthogonal polarisations, paying more attention for the horizontal one.

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The performance of the array can be can also explained by looking at distribution currents on the non-active radiating elements: as we can see in Figures 5,1,15 and 5,1,16, in vertical polarisation the non-exeited elements showing a higher coupling are concentrated at the edge of the array in the direction φ = ±90°, while in horizontal polarisation the same happens for φ = ±30° and symmetrically for φ = 150'°/φ = 210°, Therefore there is good agreement between the behaviour of the current distribution on the array elements and the corresponding radiation patterns. Moreover both polarisations show very low induced currents on the non-excited elements in the orthogonal polarisation aligned on the central row (or column) of the array (that is the largest one).

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Figure 5,1,15: Distribution currents on the array fed with a Tukey illumina­tion law (V-POL),

Therefore low back radiation is guaranteed by the chosen illumination law together with the selected spacing, which is now achievable (the overall diameter is about 4.16 m). Furthermore the half-size radiating elements offer some margin for a further optimisation of the sub-array spacing based on the full-wave analysis results, i.e, taking into full account the coupling effects at

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array level and the finiteness of the ground plane. This kind of optimisation is within the scope of the detailed design of such array as it can be meaningfully performed once some more details of the mechanical design are known, since for such a small element any slight modifications of the geometry can be expected to bring changes into its behaviour.

Figure 5.1.19 displays the 3-D radiation pattern of the array computed using a MATLAB code. The main lobe of the radiation pattern offers a 3 dB beamwidth of θ3αΒ = 13°, with about 25 dBi of directivity. The secondary lobes, oriented to 0 ±23°, have a maximum directivity peak of about 0 dBi.

The uniformly illuminated array composed by 7 sub-arrays has been

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also assessed for each one of the sub-array configuration studied. The array composed by sub-arrays with the radiating elements aligned on two orthog­onal axis, placed at 45° to the array axis (Fig, 5,1,12 outer shorting walls), displays an uneven distribution of the side-lobe levels all around the horizon and the array composed by elements aligned on two axis parallel to the array

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axis (eorresponding to array in Fig, 5,1,15) shows an irregular behaviour over the full radiation pattern as well. Surprisingly, the central array composed by radiating elements aligned on two orthogonal axis placed at 45° to the array axis, but rotated by 180° with respect to the previous configuration, that is with the shorting walls internal to the sub-array, is the one that offers the best performance in terms of radiation pattern, as we can observe in Fig, 5,1,20 cross-polar component is not higher than -10 dB over the full pattern and eo-polar levels close to the horizon are not higher than -10 dB, However, as discussed above, the corresponding 61-elements array did not confirmed the expected performance.

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Inter-elements coupling is critical in a structure as the one designed one, however is expected a lower effect in comparison to the arrays composed by PIFAs and discussed in Subsection 4,2,2, Nevertheless in the sub-array composed by folded PIFAs has been registered a relevant decrease of the resistance of about ΔΒ = 40% and also an increase of the reactance of about ΔΧίη = 35%, In order to have an accurate assessment of the bandwidth when the coupling affects the performance of the single antenna, the embedded radiating elements (within the sub-array) have been matched by setting the active input impedance of the excited elements within the sub-array ( Zin = 30 + 25j Ω) as characteristic impedance of the feed. In this wav the effects of the coupling have been balanced and the inductive reactance compensated. Observing the computed return loss on the excited ports (Fig, 5,1,21), the

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Figure 5,1,21: Return Loss (Zc = 30 + 25j Ω) of the active input impedance of a radiating element in the sub-array configuration (Port 1, 4)

sub-array shows a bandwidth of about 3 MHz (since the antenna is aimed for a Space Mission a return loss Γ = —20 dB has been considered as a reference, which corresponds to a VSWR = 1.22 and a reflection coefficient ρ = 0.1), Clearly this is not completely satisfactory, however an analysis of the behaviour indicates that the matching can be improved by a proper design of the power divider needed to feed each pair of elements and has therefore been left for the detailed design that shall deal with these additional elements. The narrow bandwidth can be also assessed by observing in the Smith chart

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Figure 5,1,22: Smith chart (Zc = 50 Ω) of the active input impedance of a radiating element in the sub-array configuration (Port 1, 4)

of the active impedance that the resonance loop is not around the centre of the chart and there is only a small part of the curve contained within the constant VSWR=1,22 circle, leading therefore to a lower bandwidth (Fig, 5.1.22).

Chapter 6 Potential optimisations

6.1 Array of 91 elements

A final test was made to verify the potential of a 91 elements array, which would be expected to have higher gain and somewhat lower side-lobe level at the horizon. The tested excitation is a tukey taper with 7 uniformly illuminated central elements and 32 dB taper.

The 61-elements array has been modified by adding a further ring of elements, thus obtaining an array of 91 sub-arrays (leading to a total number of 364 folded PIFAs), The radiating elements have been excited according to an illumination law based on a Tukey window, with a 2.5% edge tapering. The layout of the structure with the graphic representation of the excitations is displayed in Figure 6,1,1, where it is clearly visible that the number of excitation levels increased from 7 to 9 and the central region fed by excitations of the same amplitude is extented to the first ring, leading to a total number of 19 uniformly illuminated sub-arrays.

The performance of this design are displayed in Figure 6,1,2, As expected this solution offers larger margins on the performance of the array: the main lobe increases by 2 dB in broadside direction, reaching a maximum directivity gain of about 25 dBi, Also the margins on XPD and SL levels are better than the previous case, as the side-lobes at the horizon are lower than —55 dB below the directivity peak and the cross-polar levels are lower than —50 dB with respect to the boresight. Obviously the trade-off among the increase

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Figure 6,1,1: Excitations of 91 elements hexagonal array

of the overall size (about 5 m diameter), the added complexity in the feeding network and the improvement of the performance must be considered at system level.

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Figure 6.1.2: Radiation pattern of the 91 elements array H-POL (red eo- polar, blue cross-polar)

6.2 Optimum array element spacing

It is known that the spacing between two consecutive elements is a fundamen­tal parameter that affect the overall performance of an array. In particular, in array configuration the field from individual antennas interfere construc­tively in some directions and destructively in others, then we can direct the nulls of the pattern in a desired direction by setting an optimum spacing.

The proposed arrangement of antennas in an hexagonal array configura­tion provide for a directive far-field in broadside direction and low erosspolar levels; the performance in terms of side lobe levels at the horizon are good as well, anyway the element spacing selected at the beginning could be refined through the analysis of the array factor for different sub-array distances, in order to possibly obtain an improvement of array performance by lowering radiation levels at the horizon. Although such reduction does not appear nec­essary with the design achieved, it is to be considered that any manufacturing inaccuracies, especially in the feeding network, as well as any alterations of the actual array geometry due to temperature gradients or wind loads are bound to adversely affect such very low side-lobe loves and as a consequence the larger the margins the better.

The far-field pattern of a planar array is given by the product of the pattern of the single element, in presence of its neighbours, and the array factor, which is defined as below:

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where

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consequently, as long as element coupling can be assumed negligible, the array gain G{0, φ) is proportional to the gain of the array factor:

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Therefore it is possible to approximately place a null at the horizon by cal­culating the array factor for different distances (chosen in a range d\ — d2 around the spacing estimated initially) and selecting the optimum one (dopt), which minimize the maximum gain at the horizon. In other words the opti­misation procedure consist in minimizing the maximum of the absolute value of the arrav factor at the horizon:

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For optimisation purpose, since the fundamental cell of the proposed array can be seen as an equivalent directive antenna, the array is assumed to consist of 61 identical radiating elements in a hexagonal configuration, fed with a current of uniform magnitude In = Io = 1 A and uniform phase shift a0 = 0. The centre of the array is placed in the origin of the reference system and the n element has coord inates (xnyn) . Since we are looking for a spacing which provide for minimum radiation at the horizon, we must consider the array factor for θ = 90° hence the Equation 6.2.1 can be written:

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where the d dependence upon is embedded into the values of xn and yn. Hence, the array factor has been computed through a MATLAB code for a range of distances within which the optimum spacing can be chosen, therefore the maximum of its absolute value over the azimuth has been calculated and plotted in Figure 6.2.1. According to the plot the optimum distance appears to be slightly lower than the one chosen at the beginning of the design process. The curve has several minima in the parameter interval shown and others outside it, the general feature appears to be that their level inereases with inereasing spaeing, this however may be a nnmerieal artifact due to the sampling of the curve. The current design is based on d = 480 mm spacing which was selected based on a rotationallv symmetrical element pattern, while the plot above only includes the array factor. An improvement of about 2 dB appears to be possible by reducing the spacing to around 460 mm. Such minor reduction could be feasible with the folded-PIFA elements without heavily affecting the mutual coupling and consequently the cross-polar levels.

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Figure 6,2,1: Array factor maximum (absolute value) for different spacing among array elements

Moving to the next and apparently lower minimum around 360 mm is likely instead to adversely affect it, as shown moving in the opposite direction when using the quarter-wavelength PIFA elements.

In all cases an optimisation based on a full-wave analysis should be made before making any such change to the design. The associated gain reduction or increase in array complexity to maintain the same peak gain should also be considered.

An assessment of the improvement that could be achieved by reducing the spacing between adjacent sub-arrays to 440 mm has been carried out on the central uniformly illuminated array composed by 7 sub-array. The radiation patterns are compared in Figure 6,2,2 which shows that effectively the spacing computed analytically (440 mm) offers slightly lower side-lobe levels at the horizon than the optimum assessed in the preliminary analysis (480 mm). However this result shows a good agreement with the optimum spaeing found during the preliminary analysis. As expected the directivity peak is a bit higher for the larger spaeing.

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6.3 Bandwidth enhancement

Having observed that the performance of the radiating element is not fully satisfying in terms of bandwidth, as the shorted patch antenna has a very narrow band by its nature and reducing the length by half further reduces the bandwidth. From the theory of antennas we know that the bandwidth of a radiator can be represented as an equivalent circuit and thus characterized by the quality factor Q, defined as the ratio of the energy stored to the dissipated energy. Since the Q factor is inversely proportional to bandwidth, the latter can be enlarged by ineresing the power loss or by increasing the radiated power and thus reducing the energy stored.

Therefore it has been made an attempt to improve the performance by adding a small conductive strip, 3 mm thick, to each side of the patches and the shorting walls of the folded pifa except for the open edge of the lower patch. Figure 6,3,1 shows the numerical model of the modified antenna. The full-wave analysis of the antenna proved that the bandwidth increased indeed. As expected the addition of radiating elements to the structure

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Figure 6,3,1: Simulated folded PIFA with short patches added to each side

produce a detuning of the resonance frequency, however the bandwidth can be assessed by setting the characteristic impedance of the feed to the value of input impedance of the patch at the operating frequency. Figure 6,3,2 compares the reflection coëfficiënt of the conventional folded PIFA to that of the modified one: considering the anomalous peak of the return loss as a numerical artifact, the bandwidth at -20 dB is about 8 MHz, that corresponds to an increase of almost 800% with comparison to the antenna which have been discussed so far.

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Figure 6,3,2: Comparison between the return loss of the conventional folded PIFA (left) and of the modified one (right)

Hence, the bandwidth of the planar array can easily meet the require­ment by adding radiating components and therefore thickness to the array elements, which as a eonseguenee need to be appropriately retuned at the operating frequency.

Chapter 7 Antenna prototyping and testing

7.1 Prototyping of the radiating element

After the preliminary design proeess had been completed with satisfactory results, the prototyping proeess has started to verify the results obtained. The antenna prototype has been totally handmade in ESTEC.

The patches are made of copper sheet with a thickness of 0.25 mm. The ground plane consists of a duroid substrate the surfaces of which are both covered by a thin copper sheet, the total thickness is 2 mm and the size is 220 x 220 mm.

Figure 7.1.1a displays the raw materials: the square ground plane and the copper sheet, from which both upper and lower patches have been cut by using an appropriate pairs of scissors. Both patches have been manually bended and the outcome is shown in Fig. 7,1,1b.

Hence the SMA connector (a square flange jack receptacle with tab con­tact) has been attached to the ground plane with a set of fasteners and it has been connected to a copper pin with a diameter of 2 mm by welding the tab contact to the inner surface of the pin with a piece of tin wire.

Finally both radiating plates have been positioned on the ground plane, the axis of which is aligned with the vertical axis of the upper patch. As it can be seen in Figure 7,1,2 the shorting walls of the patches have been attached to the ground plane both by using two fasteners for each side and by weldeing tin wires in order to make electric contact. The top and side

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Figure 7,1,1: The raw material whereby the experimental antenna has been developed (left) and the obtained parts of the prototype (right)

view of the prototype after some adjustment is displayed in Fig, 7,3,6,

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Figure 7.1.2: The folded PIFA prototype

7.2 Antenna test

Experimental results are needed to validate theoretical data and to verify the antenna construction. Hence the antenna testing included the excecution of two activities:

1. S11 parameter measurement
2. Directivity Gain measurement and further evaluation of S parameter

Such measurements allow to characterize the performance of the prototype in comparison to the simulated model and have been carried out in the antenna ranges described below.

7.2.1 Antenna ranges

Pattern measurements can be conveniently performed with the test antenna in receiving mode, so that, if the antenna is reciprocal, performance in re­ceiving mode are identical to those in transmitting mode. Therefore the ideal condition to measure far-held parameters is having fields uniform in ampli­tude and phase near the test antenna, which means illuminating the antenna by plane waves. To approximate this condition the distance between source and test antenna must be longer than the inner boundary of the far-field region:

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Such condition can be easily respected in outdoor antenna ranges, however they are not protected against environmental conditions. Indoor ranges are limited by space restrictions (depending on the frequency range), however if well designed they are more convenient than outdoor ranges.

The measurements described above have been then earrried out in two different test facilities:

1. the Compact Antenna Test Range facility (CATR) of the European Space Research and Technology Centre, in Noordwijk (Netherlands)
2. the Starlab of Microwave Vision Italy facilities, in Pomezia (Rome, Italy)

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Figure 7.2.1: A view of the CATR facility hosted by ESA/ESTEC

Both of them are basically ane.c.hoic chambers supplied with specific test­ing instrumentation. The purpose of an ane.c.hoic chamber is to screen the indoor environment against external eleetromagnetieal radiation by minimiz­ing electromagnetic interference, absorbing signals and preventing unwanted reflections. For this aim the chambers where testing is performed have walls that are covered with radiofrequency absorbers, i.e, pyramid-shaped ane.c.hoic. foam. Generally the thickness of RF absorbing material is proportional to the wavelength of the lower operating frequency. An anechoic chamber de­sign is based on geometrical optics techniques and two basic configurations ea be identified: the rectangular and the tapered chamber. The first one is aimed to maximize the volume of the quiet zone and minimizing the re­flections by using high quality absorbers, however significant reflections can occur, i.e, at large incidence angles. The latter type is pyramidal horn-like with a source properly placed in the apex in such a way that reflections from the sidewalls occur near the antenna under test add in phase; as operating frequency increases is necessary to improve the absorbing performance of the side-walls, in order to compensate for the higher level of phase difference among reflected and direct rays.

Microwave measurements are often performed in compact range in order to achieve a nearly planar wavefront on the test antenna. In comparison with the minimum 2D2/λ required, a compact antenna test range allows to generates a nearly plane wave illumination condition in very short distance. Generally a CATR is supplied with one or two collimating reflector antennas designed in such a way to produce a planar wavefront with minimal perturba­tions in the near field of the antenna under test, emulating therefore a far-field condition. The region where a nearly plane wave illumination is produced and that is therefore usable for the antenna testing is commonly referred to as quiet zone. Clearly such approximation is not a perfect plane wave, eonsequentely the imperfections of the fields in the quiet zone are usually represented as phase and amplitude ripples and taper amplitude component. Also in this case undesirable reflections are minimized by placing the test range within an aneehoie chamber.

ESTEC’s CATR is dedicated to testing small to medium size antennas, up to 1 m diameter and it essentially consists in a dual reflector antenna (with serrated edge) hosted by a rectangular aneehoie chamber supplied with stan­dard instrumentation that covers the frequency range from 4 to 110 GHz. The merit of the CATR are listed in Table 7,1, SATIMO’s StarLab is a eom-

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Table 7.1: CATR specifications

pact portable solution suitable for pattern measurements of small antennas in very short distances. The system is composed by a mast in the centre of an arch supplied with two interleaved sets of dual polarised wideband probe array (15 probes and 1 reference channel from 0,8 to 6 GHz), that are embed­ded in multi-layer conformal absorbers. The spherical scanning of the near field of the radiator under test is carried out by positioning the Antenna Under Test (AUT) on top of a mast and performing a 180° azimuth rotation (φ) while the probe array provide for a contemporary electronic scanning in elevation (θ), acting as a recorder over the full 3D sphere. Hence the samples of the near field are proeessed by the system in order to obtain the far-field pattern.

If needed the system perform an Oversampling by a meehanieal rotation of the probe array in elevation, leading therefore to an inereased number of samples, A small aneehoie ehamber, whieh walls are totally covered with pyramid absorbers, is also provided for the StarLab in order to reduce the effects of stray signals.

StarLab uses a Switching Unit to switch between passive and active mea­surement RF instrumentation. For passive measurements a Vector Network Analyzer is used as transmitter and receiver for the antenna test, while for active measurements, the test is perfomed through up to three different Radio Communication Testers.

StarLaRs specifications are listed in Table 7.2.

The methods used by StarLab to perform the pattern measurements are described in more detail in Section 7.4.

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Table 7.2: StarLab specifications

7.3 Impedance measurements

It is known that an antenna is characterized by a self and a mutual impedance. In a controlled enviroment, where the antenna can be nearly seen as an iso­lated radiating element into an unbounded medium, the mutual impedance can be ignored, as there is no coupling with other antennas or surrounding obstacles, therefore the input impedance of the antenna is its self-impedanee. In a system composed by a source (T/R), a trasmission line and an antenna the mismatch, that determines the amount of reflected power at the antenna input terminal, is referred to as reflection coefficient (Γ, return loss in dB) and is a function of the input impedance and of the characteristic impedance of the line. As the coupling is negligible the reflection coefficient is also equal to An, therefore to assess the input performance of the radiator it is neces­sary to connect a source to the input terminals of the antenna and measure the reflected power at the port.

The S-paramenters have been then measured with a vector network an­alyzer (VXA), used as transmitter and receiver for the antenna test. The sequence of preliminary operations before the network analysis is commonly known as set-up and is summarized in the following steps:

1. Selection of measurement parameters including start and stop frequen­cies, number of samples in the frequency domain and source power
2. Calibration of the VX A by measuring its response to a number of cali­bration standards supplied in a calibration kit (i.e, open circuit, short circuit and an impedance-matched termination) in order to guarantee accurate measurements
3. Connession of the antenna to the test cables and performance of the measurements

The better explain the second step, calibration is needed to compensate for any residual undesired component (i.e, frequency response, power loss, impedance mismatch) in the VXA and in the trasmission line. The instru­ment compares the measured data with the nominal values of each calibra­tion standard, then it computes a correction factor for each frequency point through a set of calibration equations by using measured and nominal values. Later these correction factors are applied by the VXA to the measurements of the S-parameters, To sum-up a typical calibration mathematically removes the offset data from the calibration data in order to give a 'zero' reference point at the connector, moving the reference plane to the end of the test cables. Consequently the phase reference is shifted at the input terminals of the antenna and the amplitude reference is compensated for the losses of the cable, leading to an equivalent circuit where the antenna input impedance is directly connected to the output of the network analyser.

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Figure 7,3,1: The prototype inside the CATR neehoie ehamber

7.3.1 Return loss measurements

This stage has been earried out in the Compact Antenna Test Range (de­scribed in Sub, 7,2,1) facility that has been exploited only for its absorptive properties, in order to improve as far as possible the quality of the return loss measurements. Therefore, besides a standard VXA, the CATR instru­mentation has not been exploited but it would be properly used in our ease if antenna patterns were measured.

First of all the VXA has been calibrated following a standard procedure (described in 7,3) to ensure accurate measurements. Then the reflection coefficient has been sampled at s = 250 KHz steps in a frequency range of 300 — 500 MHz, which means having 801 samples available, with an input power of Pin = 0 dBm.

Since the anechoic chamber is not fully adequate for 435 MHz, the mea­sured An parameter shows some anomalies:

- a periodic ripple of the curve that makes the return loss positive, as displayed in Figure 7,3,2
- a secondary minimum close to the resonance peak
- lowering of resonance frequency, from f0 = 435 MHz to fm = 411 MHz with Γ0 = —13 dB minimum peak, resulting in a 4.6% frequency shift

The irregularities of the Sn are most likely due to measurement artifacts, as evidenced by the oscillation of the curve. Its frequency period is about 12.2 MHz which corresponds to Г = 82 ns time period, that is around 2r = 24 m in distance, consequetelv surrounding objects within r =12 m inside the aneehoie chamber, could be the origin of a periodic single or mul­tiple reflection, most likely the CATR reflectors. Because of its strong de­pendence on the environment, measurement was repeated after changing the orientation of the antenna without obtaining any improvement.

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Figure 7.3.2: Raw return loss Γ as measured in the CATR

Consequently a Fourier analysis has been carried out in order to get a clean curve of the S-parameteras, as in time domain the delays due to the reflections at the input port of the antenna can be easily distinguished from the others due to the ground plane edge diffraction and to the scattering from the environment. Figure 7.3.4 illustrates the block diagram of the post­processing process.

The procedure is explained below. First of all the frequency domain was extended down to 0 Hz and up to 1 GHz by adding a zero-padding to the beginning and to the end of Sn sequence of complex samples, in order to increase the sampling rate in the time domain. In this way the sequence Sn(k) defined by 801 frequency samples becomes a N = 4004 samples sequence the and spectral magnitude plot of the 4004-point DFT of Sn(k) is therefore more detailed (the frequency-domain sampling has increased by a factor of 5 (4004/801),

Then the complex sequence in the frequency domain has been inverse Fourier-transformed bv:

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The time-domain samples t are multiples of the sampling period T = 4 μβ (corresponding to 250 KHz).

The absolute value of the time response obtained is shown in Fig, 7,3,3a has been filtered through a symmetrical Tukev window tapering (t = 0% edge tapering, Rßat = 40) defined in Section 2,2, to remove the spurious reflections.

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Finally the fourier transform has been applied to obtain again the se­quence Sn(k) in the frequency domain, according to:

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Figure 7.3.4: Measured SII post-processing block diagram.

The filtered return loss curve is displayed in Fig. 7.3.5. The results obtained clearly show that it is quite likely that the performance of the antenna is quite close to the predicted one, beside a shift in the resonance frequency, which is however typical for this kind of antennas and can be traced back to the unavoidable approximations of the computational model. The good agreement between the raw return loss and the filtered one can be observed in Fig. 7.5.4.

In the transition from simulations to the real prototype, many reasons for the discrepancy between simulated and measured S paramenters can be identified. Some of these can be identified below:

Some physical components are not well modeled in CAD session, while they could have an effect on the performance:

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Figure 7.3.5: Return loss obtained by filtering the time response through a tukey window

- the SMA connector, which has not been simulated in the model
- the copper PIN, which is thicker than the one simulated
- the size and the material of the ground plane, that at the beginning has been set in ADF-EMS as infinite PEC ground plane
- the material of which the folded shorted patch and the feed are made, which at the beginning has been set as PEC in the solver

The following full-wave analysis shown that, as expected, the ground plane has strong impact on the bandwidth and on the radiation pattern, but it does not affect the resonance frequency. The material of which all the geometries of the antenna are made has slight effect on the input impedance, in fact by replacing the PEC with copper the resonance frequency decreases of about 2 MHz, A thicker probe has been also simulated in the computational model, but it does not seem to affect the performance of the folded PIFA, Therefore the approximations of the physical model are clearly not the causes of the mismatch between the simulations and the measurements.

Since the physical prototype is completely handmade, it is not perfectly shaped. Actually is relatively far form perfection, thus showing that the lack of an accurate manufacturing has definitely an impact on the antenna performance. Some features of the object that are visible to the naked eye:

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Figure 7.3.6: Top and side view of the prototype

- due to the welding, the contact of the patches over the ground plane seems to be not fully appropriate, leading eventually to a change of the path of the currents
- the shape of the horizontal patches that are not entirely flat (Fig, 7.3.6b)
- the transition from the patches to their related shorting wall is not properly 90° degree shaped

To assess the effects of the inaccurate manifaeturing, further simulations have been made. The results are discussed in Section 7.5.

7.4 Radiation patterns measurements

The radiation pattern of the prototype has been calculated by the MVTs StarLab.

As mentioned in Subsection 7,2,1, the StarLab enables a full spherical scanning and exctracts the amplitude and phase data in order to perform the transformation from near-field to far-field (Sub, 7,4,1), The sampling criteria is performed by the array of probes and is based on the need of determine the contributions of all the spherical modes.

The set-up for passive mode measurements of antennas started by con­necting the system to a VXA, in order to measure amplitude and phase signals, either being transmitted and received by the AUT, The near field is then sampled by the probe array and later the acquisition data are transmit­ted to the control unit which provides for the processing.

At the end of the process both the partial directivities Όθ(θ,φ) and Όφ{θ, φ) have been found in a wide range of frequencies (410 - 460 MHz), as the fast probe array technology allows measurements at a large number of fre­quency points. The total directivity is given by: Ό(θ, φ) = Όφ(θ, φ)+Όθ(θ, φ)

7.4.1 Near-field to far-field methods

As we know the spatial distribution of the fields radiated by an antenna evolves with increasing distance from the antenna. Three spatial regions around a radiating element can be recognized and are classified according to the amplitude (or phase) pattern. The region closer than:

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where D is the largest dimension of the antenna

is known as “reactive near field" as it is characterised by predominant reactive energy and therefore the electric field component does not propagate radially. The space between this region and the far-field region, is also known as “near-field region". In near-field as the distance increases the propagation vector gradually becomes radial, but the contributions from all parts of the antenna to the total radiated field at any observation point do not have mutual identical phases.

Through analytical methods the measured radiating near field can be transformed to the far-field radiation pattern, therefore this methods, also known as “near-field to far-field" methods (XF/FF), allow the reduction of the size of a test range. The method consists in sampling with a set of measuring probes the amplitude and the phase of the tangential electric field components radiated by the Antenna Under Test (AUT) at predetermined points over a geometrical surface in the near field, i.e, planar cylindrical and spherical. Then an angular spectrum of basis functions (plane, cylindrical, or spherical) is generated from the measured data, according to the principle of modal expansion. The far-held radiation patterns (E,H) can be computed from the total field of the antenna expressed in terms of modal expansion, using vector waves functions (Mmn, Nmn ) orthogonal to the scanning surface. Hence, according to the spherical-wave expansion, both electric and magnetic fields for R > Ri can be expressed as summations of spherical-wave functions (Ludwig’s definition):

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where amn, bmn are the coefficients of the wave functions that can be de­rived from the tangential electric field on the surface of the sphere of radius R1 in near field. Therefore such coefficients are computed from the data extrapolated with the spherical scanning performed by the StarLab,

7.4.2 Directivity and Gain measurements

The directivity can he computed using the measurements of the antenna radiation pattern. The most accurate method is based on the definition of directivity:

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The radiation pattern is measured by sampling the field over a sphere of radius r in at wo-dimensional plane cuts with φ^ constant and θ variable, or vice versa. In our ease it has been used the radiation pattern obtained by transforming the near-field samples,

7.4.2.1 Directivity Gain of the prototype

Finally the antenna prototype has been tested in MVTs Starlab, where Re­turn Loss and Directivity Gain measurements have been carried out.

For active measurements the VX A (Agilent PXA X5230A) has been cal­ibrated according to the procedure explained in Sub, 7,3 (calibration kit Rosenberger RPC-2,92), then some tricks have been used to remedy the manufaetoring imperfections of the prototype. Such tricks consisted in weld­ing again the patches to the ground plane and adding two strips of copper tape (Fig, 7,3,6a), as there were some points where the contact was faulty. Moreover it was also made an attempt to straighten the lower and the up­per patches of the antenna by inserting some spacers made of cardboard and using paper adhesive tape. Then the Sn has been measured with a frequency step of 833,333 KHz, in order to check its proper operations as well as the possible presence of spurious reflections would heavily affect the radiation pattern measurement. As we can observe in Figure 7,4,1 the an­tenna shows a resonance frequency shifted to f0 = 417 MHz, with return loss Γ ~ —19 dB, slightly better performance than those measured in ESTEC’s CATR and consistent with the “cleaned" version of them.

The impedance bandwidth results to be B = 7 MHz a! Sn = —10 dB and it is in line with expectations since the prototype does not include any com­pensation of the reactance. It is also higher than the simulated impedance bandwidth of the folded PIFA, as the copper of which the patches are made introduces some power losses and therefore increases the bandwidth by re­ducing the Q factor.

Finally the directivity gain has been measured as described above. Fig-

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Figure 7,4,1: Measured return loss in SATIMO’s Starlab

lires 7,4,3 and 7,4,2 display the eomparison among the measured patterns and the simulated ones on the main planes, A very good agreement ean be noted, in fact the E — cut and H — cut of the prototype’s pattern are almost similar to those of the numerical model: the difference in broadside direction, where the simulated directivity have a peak of about 4.3 dBi, is abo ut 0.4 dBi on both cuts, while patterns on the E — cut show variations for different point over θ up tо 0.7 dBi. It can be noted that the main lobe on the E — cut is oriented to about 60°, which corresponds to the side of the shorting wall of the upper patch, this is in line both for simulated and measured patterns as the shorting wall is where an higher currents distribution has been observed.

The beamwidth {03dB) of the prototype of folded PIFA is about 120° on the H-cut and is about 110° on the E-cut, therefore results of the mesurements compared with the simulations are more than acceptable. Fig, 7,4,3 shows that the beamwidths of the E-cut patterns have a difference of about 10° and, as mentioned above, the peak of the measured pattern is a bit lower than the simulated one. However those differences can be also imputed to simple measurement artifacts.

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Figure 7.4.2: Polar representation of simulated and measured radiation pat­terns (directivity gain, dBi) over the full sphere (left E-cut, right H-cut)

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The main cuts of the radiation pattern over the upper hemisphere are displayed in Fig, 7,4,4, which shows a nearly-omnidirectional pattern of the folded shorted-patch.

The directivity has been also assessed within a range of frequencies corre­sponding to the 10% of the centre frequency, that is the resonance frequency. As expected form a patch antenna, the radiation pattern of the radiating element shows a low sensitivity to the frequency, as the directivity is rather constant in the assessed band.

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Figure 7.4.4: Main cuts of the measured radiation pattern over the upper hemisphere.(Etotoi, Directivity Gain)

7.4.2.2 Assessment of the Gain

With regard to the antenna gain the most commonly used method to perform the measuremets is the gain-transfer method that consists in using the gain of a standard antenna to determine absolute gain. First of all the relative gain is measured than it is compared with the standard gain.

Since it has not been possible to measure the relative gain by comparison with a standard gain antenna, an estimation of the antenna gain G has been performed by assessing the antenna losses and after that the antenna efficiency. The total antenna efficiency e0 takes into account losses at the input terminal and within the antenna. According to Equation 7,4,6, such losses may be due to the mismatch between the transmission line and the antenna (reflection loss) and 12R losses (conduction and dielectric):

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where

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It is known that the gain reference is the power accepted (input) by the antenna (Pin). The total radiated power (Prad) is related to the total input power by:

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where ecd = eced is the antenna radiation efficiency. Then we can calculate the gain using the following equation:

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where Ό(θ,φ) is the measured directivity. With regard to the proposed antenna, since the dielectric is not present ed can be ignored, hence the only loss sizeable is due to the SMA connector since the conduction lossess in the copper used for the radiating part are inherently negligible for an antenna of this size. The connector welded on the ground plane of the folded shorted-pateh is a common square flange jack receptacle with tab contact of the SMA type, which insertion loss is estimated to be about:

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Consequently, given that ai = 0.026 dB at 435 MHz, the conduction effi­ciency results to be:

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To take into account the reflection losses represented in Eq 7,4,6, we have to consider the absolute gain Gabs, that can be written:

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Since ecd = 1, we have only have to calculate er to estimate e0. For the proposed folded-PIFA the mismatch efficiency at f0 = 435 MHz is er = 0.5327, while at fm = 417.5 Mhz it is ab о ut 98.7%, Referring to the Figure 7,4,5the antenna gain G at the resonance frequency fm = 417.5MHz is about 0,4 dB lower than the directivity gain, while it is reduced by half at the operating frequency f0 = 435 MHz. The maximum absolute gain in the first case is G0 ~ 3.9 dB while in the second is reduced to about 1 dB.

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Figure 7.4.5: E-cut and H-cut of the antenna absolute Gain (dB), estimated by calculating the efficiency of antenna.

7.5 Sensitivity analysis

Having observed a different behaviour of the antenna prototype in terms of input impedance, a sensitivity analysis has been performed in order to understand if the unexpected results can be appointed to the level of accuracy of the manufaetoring process. Therefore to assess the effects on the output in terms of return loss at the resonance frequency, some input of the numerical model has been changed by modifying the geometry of the physical model. Having already studied the effects of the main geometrical parameters of the antenna in Subsection 5.1.1.1, in this Section the impact of the tilt angle of the upper and lower patch and the gap between the edge of the lower plate and the shorting wall of the upper are discussed.

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Figure 7,5,1: Return loss for different tilt angles ( Ut) of the upper patch (the green curve is the ideal situation).

Figure 7,5,1 shows the return loss for different tilt angles of the upper patch selected in a range of ±1°: the resonance frequency is strongly affected by this parameter, in fact it shifts in a range of about 22 MHz, The same experiment was made by tilting the lower patch with angles selected within a range of ±1°: as we can see in Fig, 7,5,2 the results are rather similar to the previous case, in fact the resonance frequency shifts in a range of about 27 MHz, By observing the input impedance, it seems that in both cases the tilt angles produce a wide shift of resistance and reactance curves along the frequency axis, while the effects along the y axis are very weak. Therefore tilting the patches can be seen as an increase or a decrease of the currents path, depending on the tilt angle, to be more precise, both a negative angle for the upper patch and a positive angle for the lower extend the path of the currents.

Therefore the results show that it is sufficient even a little tilt angle of the horizontal patches to shift the resonance frequency up to 5 or 10 MHz and the combination of different effects could have even worst eonseguenees, hence these parameters are very critical in the manufacturing process and it is very important to conform as much as possible to the physical model.

The effects of the width of the gap on the input impedance (as the length of the lower patch changes) have already been discussed in Section 5,1,1,1, however it was also investigated the impact of the position of the lower patch respect to the upper as one moves relative to the other, with a fixed size of

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Figure 7,5,2: Return loss for different tilt angles (Lt) of the lower patch (the green curve is the ideal situation)

the patches, increasing thus the gap between the lower plate and the short­ing wall of the upper patch. The comparison between the return loss for different gaps is shown in Fig, 7,5,3 and points out that small changes of the distance between the edge of the lower patch and the shorting wall of the upper plate have a weak impact on the resonance frequency, as the main feature when the gap get wider is a slight increase of the input reactance due to a reduced capacitive effect. Given the different behavior of the prototype

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Figure 7,5,3: Reflection coefficient (dB) by varying the width of the gap

from that of the simulated model, a further parametric study of the antenna was performed and the results attributed such differences to the imperfec­tions of the manufaet, Next performance of a numerical model reproducing the major features of the imperfect geometry of the folded-PIFA prototype has been assessed. The prototype model provides for —1°/ + 1° tilt in upper and lower patch respectively, established by measurements on the real an­tenna, therefore according to the above simulations a strong lowering of the resonance frequency is plausible, as both a negative tilt angle of the upper and a positive tilt angle of the lower reduce the operative frequency.

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Figure 7,5,4: Comparison among measured (CATR and Starlab), filtered (CATR) and simulated return loss (ADF-EMS) of the prototype and return loss of the simulated folded PIFA.

The comparison of S-parameters appears to provide a further proof of the conclusions reached with available data. The curves of return loss obtained by the measurements in the CATR of ESTEC (raw and filtered) and in the partially-aneehoie chamber of MVI (Starlab) are displayed In Figure 7,5,4, along with the simulated return loss of the prototype-like model (simulated prototype) and of the first performing model (simulated folded PIFA): it can be observed that simulated return loss of the prototype-like model and the measured are very close, this is especially true for filtered return loss (measured in CATR), So we can say that the prototype antenna differs from the model mainly because of the inclination of both the horizontal patches, while the attempt made at MVI to straighten the two plates and to further improve the electrical contact with the ground plane has led only to a slight improvement of the reflection coëfficiënt.

Chapter 8 Conclusions

The analysis and the design of two similar radiating elements have been carried out. The folded PIFA offers the same radiative perfomanee as the conventional shorted patch with a size reduced by half. Different layouts for the array based both on PIFAs and on folded PIFAs have been assessed.

The final concept of the planar array meets the most critical requirements, namely the cross-polar and the side lobes levels. The solution offers a high modularity thanks to repetition of a simple folded PIFA radiating element all over the array and the selected elements are quite simple and completely metallic, thus easy to manufacture.

However the bandwidth achieved at element level is slightly lower than the required value. Still there are several techniques available to increase the bandwidth at sub-array level that can be relied upon to improve the matching at this level in the subsequent detailed-design phase of the project. In the first place a combined matching of the F-PIFA pairs and the power division network connecting them, which including an 180° phase shift has an inherent flexibility in compensating the element reactances if all remain­ing parameters are properly adjusted. The reduction of mutual coupling by arranging slots among the radiating elements is another possible option. Therefore the design also offers significant room for improvement.

Different feeding schemes can be considered for the full array, either with a single level beam forming network for each polarisation or with two level, one for the radiating element and the other for the 61 elements. The power splitting within the BFX has no criticalities in both cases.

The radiating element shows some critical parameters, i.e. the tilt angle of the patches, therefore a proper design must be achieved by strictly adapting the physical radiator to the numerical model of the antenna and eventually taking advantage of some spacers in other to block the horizontal plates of the folded PIFA.

Finally the assessment of the hybrid solution may show that such solution would be better and simpler than the array, while the effort made to design it would have been useful to provide both a sound reference for performance comparison as well as a robust design for the 7-element central array to be used to excite the meta-surfaee.

Bibliography

|1| ESA, ASTRIUM, BIOMASS P-band Transponder Study Executive Summary, April 2013
|2| ESA SP-1324/1, “Report for Mission Selection: Biomass", ESA Com­munication Production Office, May 2012
|3| European Space Agency, “Earth Explorer 7 Candidate Mission Biomass: Addendum to the Report for Mission Selection", January 2013
|4| Computational Electromagnetics, Anders Bondeson,Thomas Rylan- der,Pär Ingelström, Springer, 2005
|5| The Method of Moments in Electromagnetics, Walton C, Gibson, Chap­man & Hall/CRC, 2008
|6| M, Sabbadini, G, Minatti, “Biomass CRTA", 26/03/2013
|7| H, T, Chattha, Yi Hnang, M, k, Ishfaq, S, J, Boyes, “A Comprehensive Parametric Study of Planar Inverted-F Antenna", Wireless Engineering and Technology, 2012
|8| J, W, He, K, S, Chnng, Design considerations of Planar Inverted-F An­tenna (PIFA) on a Finite Ground Plane", APCC, 1987
|9| R, Garg, P, Bhartia, I, Bahl, A, Ittipiboon, “Mierostrip Antenna Design Handbook", Arteeh House, 2001
|10| H. M. Chen, Y. F. Lin, P. S. Cheng, H. H. Lin, C. T. P. Song and P. S, Hall, “Parametric Study on the Charaeter-isties of Planar Inverted-F Antenna", IEEE Proceeding of Microwave Antennas and Propagation, Voi. 152, Xo. 6, 2005.
|11| G. De Jean, R. Li, M. M. Tentzeris, and J. Laskar, “Development and Analysis of a Folded Shorted-Pateh Antenna With Reduced Size", IEEE Transactions on Antennas and Propagation, Voi. 52, Xo. 2, February 2004
|12| Satimo, StarLab product sheet, 2010
|13| L. J. Foged, A. Seannavinni, Efficient Testing of Wireless Devices from 800 MHz to 18 GHz, 2009
|14| R. C. Johnson, H. A. Ecker, J. S. Hollis, Determination of Far-Field Antenna Patterns from Xear-Field Measurements, Proceedings of the IEEE, Voi. 61, Xo. 12, December 1973
|15| C. A. Balanis, Antenna Theory Analysis and Design (third edition), John Wiley & Sons, 2005
|16| C.A. Balanis, Modern antenna handbook, John Wiley and Sons, 2008
|17| IDS Ingegneria Dei Sistemi S.p.A., ADF-EMS v, 05.00 - User manual, 2012

Appendix A

Fundamental parameters and definitions for antennas

The performance of the radiating elements have been described referring to definitions of different parameters that are given in this appendix. The most of parameters are defined in IEEE Standard Definitions of Terms for Antennas (IEEE Std 145-1983),

A.l Radiation pattern

The radiation pattern of an antenna is defined as “a mathematical function or a graphical representation of the antenna radiation properties as a function of space coordinates,The radiation pattern is often determined in the far-field region and is represented as a function of the directional coordinates,"

The 2D or 3D radiation distribution radiation is mostly expressed as a function of the observer’s position along a surface of constant radius. The conventional set of coordinates is the spherical coordinates system shown in Figure A.1.1.

The radiation pattern can represent both the spatial variation of electric and magnetic fields and the power density. Pattern can be plotted both in linear scale and in decibels (dB).

Different “lobes" can be identified as parts of the radiation pattern, which can be subelassified in main, side and back lobes, A radiation lobe is defined

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Figure A,1,1: Spherical coordinates system as defined in |15|

as “a portion of the radiation pattern bounded by regions of relatively weak radiation intensity (nulls)". The main lobe is the “radiation lobe that contains the direction of maximum radiation", while a side-lobe is a “radiation lobe in any direction other than the intended lobe". Finally a back lobe is “a radiation lobe contained in the opposite emisphere with respect to the desired beam of an antenna,"

For a linearly polarised antenna, performance is often described in terms of its principal E-cut and H-eut patterns. The E-cut is defined as “the plane containing the electric field vector and the direction of maximum radiation" while the H-plane is “the plane containing the magnetic-field vector and the direction of maximum radiation."

The beamwidth is a parameter of the radiation pattern that is defined as “the angular separation between two identical points on opposite side of the pattern maximum". One of the most common definition is the Half-Power Beamwidth (BW3dB), which is defined by IEEE as “the angle between two directions in which the radiation intensity is the half valne of the maximum beam".

A.2 Directivity

The directivity of an antenna is defined as “the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions". The average radiation intensity is equal to the total radiated power (Prad) divided by 4π. If the direction is not specified, the directivity is referred to as the maximum directivity and is exspressed as:

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where Imax is the maximum radiation intensity (W/unit solid angle)

A.3 Antenna Gain

The antenna gain is defined as “the ratio of the intensity in a given direction to the radiation intensity that would be obtained if the input power at the terminals of the antenna were radiated isotropically". Therefore the gain can be expressed as:

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Often we deal wiht relative gain, which is defined as “the ratio of the power gain in a given direction to the power gain of a reference antenna in its referenced direction". The reference antenna is usually a dipole or a horn, whose gain is well known. The power input must be the same for both antennas.

The relation between the antenna gain and the directivity is matter of Subseetion7.4.2.l.

A.4 Bandwidth

The bandwidth of an antenna is defined as “the range of frequencies within which the performance of the antenna conforms to a specified standard". It can be considered as the range of frequencies centred in a frequency, i.e. the resonance frequency, where the characteristics of the antenna (i.e. input impedance, beamwidth, polarisation, side-lobe level, directivity, radiation efficiency) are within an acceptable value of those at centre frequency.

Since some antenna parameters may be more or less sensitive to the fre­quency, the bandwidth is usually characterized as pattern bandwidth and impedance bandwidth. The first definition is associated with pattern pa­rameters, i.e, beamwidth, gain and side-lobe levels, while the impedance bandwidth is related input impedance and radiation efficiency.

For narrow-band radiators the bandwidth is expressed as a percentage:

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where f0 is the resonance frequency.

A. 5 Polarisation

The polarisation of an antenna in a given direction is defined as the “polari­sation of the radiated wave in the direction of maximum gain (if the direction is not stated)". In practice the polarisation varies with the direction from the center of the antenna so that the radiated fields can have different polar­isation over the full pattern.

The polarisation of the radiated wave is defined as “the property of an electromagnetic wave that describes the time-varying direction and relative magnitude of the electric field vector". In practice the polarisation is the curve traced by the end point of the instantaneous electric field vector, that can be written as:

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The linear polarisation is characterised by a time-phase difference between the two components:

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At each point on the radiation sphere the polarisation is usually is dis­tinguished into a pair of orthogonal polarisations, the co-polarisation and the cross-polarisation. The first one is the polarisation that the antenna is intended to radiate or receive while the latter represents the polarisation orthogonal to the co-polarisation. Therefore the co-polarisation must be specified at each point on the radiation sphere.

A.6 Cross Polarisation Discrimination

The cross-polarisation discrimination (XPD) is defined as “the ratio of the peak of the co-polarisation gain to the cross-polarised gain of the antenna in the given direction", therefore it is given by:

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This parameter quantifies the isolation between two channels that are trans­mitting id different polarisations. The larger the XPD, the less is the coupling between the channels.

The XPD can be alternatively assessed by calculating the ratio of the eo-polarised maximum gain to the maximum cross-polarised radiated power.

Clearly in an array configuration the XPD decreases by increasing dis­tance among the radiating elements.

A.7 Input impedance

The input impedance is defined as “the impedance presented by an antenna at its terminals, that is the ratio of the voltage to current at a pair of terminals with no load attached". Therefore the antenna impedance can be expressed as:

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In general the resistive part is the sum of two components:

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Having assumed that the antenna is connected to a generator with internal impedance:

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the antenna and the generator can be represented by an equivalent circuit where a part of the power is delivered to Rr for radiation and the other part is dissipated as heat in RLand in Rg. The maximum power is delivered to the antenna as the conjugate matching between antenna and generator is obtained, that is when:

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Considering an equivalent circuit consisting of an antenna terminated to a load, the voltage reflection coefficient at the input terminals (return loss if expressed in dB) of the antenna is therefore given by:

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where Zl is the impedance of the load.

The ratio of reflected power to the incident power at the input terminals of the antenna is given by |Γ|2,

Appendix В Array

An array is an antenna composed by several radiating elements arranged in an electrical and geometrical configuration. The aim of an array is to increase the electrical size of an antenna, to achieve a very high gain without increas­ing the size of the individual elements. The total far-field is determined by the vector addition of the radiation patterns of the individual elements, as the coupling is neglected and the current is assumed the same in each element. Consequently, to produce directive patterns, the fields must add construc­tively in the desired direction and interfere destructively in the remaining space. The parameters that control the shape of the overall pattern of the antenna are mainly:

- the geometrical configuration
- the relative spacing between adjacent elements
- the excitation amplitude and phase of the individual elements
- the relative pattern of the individual elements

Some of the parameters listed above are included in the definition of Array Factor:

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which is a function of the number of elements A, the constant spacing d, the amplitude In and the excitation phase β. By varying the geometry and the excitations, the radiation pattern in direction ψ can be controlled according to the “pattern multiplication" theorem, given by:

E (total) = [E (single element at reference point)] x [array factor] (B.0.2)

For an linear array with progressive excitation phase β = ad and uniform amplitude In = I0, the Array Factor is given by:

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where u = k0dcosif and u0 = ad The maximum value is for u = —u0, that is AF = (N + 1)I0, which means that the total field has a gain N+l times higher than the individual element in the direction of the main lobe. To have a maximum in broadside direction all the elements must have the same phase excitation a = 0, Since |u| < k0d, on the upper hemisphere can be defined a “visible region” related to the physically observable angle θ and given by:

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therefore the number of side-lobes within this region can be increased or reduced by varying the spacing d. The minimum levels of the side-lobe at the horizon can be also determined by observing the outer limits of the visible region and therefore the radiation pattern close to the horizon. Consequently the desired SL levels can be positioned toward the desired observation point by assessing the radiation pattern for different spaeings.

For a planar array the Array Factor is given by the multiplication of the Array Factor of a single row of radiators and the Array Factor of an array composed by rows of radiators.

Appendix C Meta-surface antenna

The design of a radiating element can result from the integration of com­plex printed elements covering a grounded dielectric layer. Having defined the geometry, the materials and the excitation of the structure of interest it is possible to satisfy the requirements in terms of radiation pattern by implementing a proper punctual boundary condition on the surface of the structure. Such boundary condition can be interpreted by introducing the concept of “Surface Impedance” Zs.

In other words, the electromagnetic surface wave propagation TM0 can be controlled by accurately shaping the metallic patches, thus leading to the con­trol over the radiation from surface currents on metallic bodies and obtaining then a modulated “meta-surface”. In fact the antenna consists of an artifi­cial impedance surface that is implemented as an array of sub-wavelength metallic patches on a grounded dielectric substrate. The effective impedance over the surface can be modulated by varying the size of the metallic patches and the gap among them, obtaining then the transformation of a known in­put wave into a desired output wave. Furthermore the polarisation can be also controlled by creating an anisotropic surface that offers specific tensor impedance properties.

The studies on the effects of leaky waves on modulated impedance surfaces have been started OlineFs comprehensive analysis, in which he describes how the propagation and radiation of surface waves are controlled by the magnitude, the modulation depth and the period of the surface impedance.

The meta-surface antenna considered in the preliminary analysis consists a flat dish (very thin at microwave frequencies) consisting of a dielectric slab covered by a dense texture of small metallic patches. The modulation size of such patches produces the desired antenna radiation pattern by giving peculiar scattering properties to the antenna surface. The feeder is placed at centre of the dish and eonsits of an exciter that can be a single radiating element or have a different design, i.e, a simple cross dipole. The structure is excited by the surface wave launched by the exciter.

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Figure C.0,1: Central array (composed by 28 folded PIFAs) surrounded by a meta-surfaee

The meta-surfaee solution for the Biomass Transponder Antenna, men­tioned in Chapter 4, has been assessed providing an edge taper of about 20 dB and shown a baek-lobe 25 dB lower than the peak (due to the presence of residual power in the surface wave that excites the structure). However it is possible to improve its performance in the same way as it has been shown to be feasible for an array. The baek-radiation can be reduced by increasing the edge taper of the illumination, thanks to the combined effect of a reduced the edge scattering of the radiated field and a lower residual power in the surface wave. Unfortunately this is not easy to achieve with simple means since an accurate control of the illumination law can only be achieved by an optimisation process based on full-wave analysis of the complete antenna.

If necessary the field levels at the edge can be further reduced by closing the structure edge, which is probably a recommended choice to improve the mechanical behaviour of the antenna in any case, or implementing surface wave traps in the ground plane, but they also require full-wave modelling for their design and assessment. Finally the pure meta-surface solutions requires special care to be designed for dual-linear polarisation operations.

Having achieved an acceptable solution for the preliminary design of an antenna for the Biomass Calibration Transponder Radar, the central region uniformly illuminated array, composed by 7 sub-arrays of folded shorted- patch aligned on xy axis (assessed in Sec, 5,1,2) has been selected as feed for a meta-surface surrounding area which should guarantee the tapering effect produced by the Tukey illumination and described so far. This alternative design, as mentioned in Subsection 2,1, is proposed as a “hybrid solution" and is illustrated in Figure C.0.1.