Development of a low-power-signal acquisition device for signals lower than 25 Hz


Diploma Thesis, 2012
58 Pages, Grade: 2.0 bzw."B"

Excerpt

Content

1. Assignment

2. Concepts
2.1 Using the sound board of a personal computer
2.2 Using the USB-Interface

3. Low-pass-filter
3.1 Motivation to use a low-pass-filter before digitizing
3.2 Kinds of low-pass-filters
3.3 Development of Butterworth-low-pass filters in general
3.4 Designing a Butterworth low-pass filter of 6th order
3.4.1 Measurement results

4. Digitising and preparation of the signal
4.1 Sampling
4.2 Quantization
4.3 Coding
4.4 Requirements for digitising ELF-signals
4.4.1 Anti-aliasing filter
4.4.2 Sample frequency
4.4.3 Resolution
4.5 Microcontroller and adapting circuits
4.5.1 Sigma-Delta-ADC

5. Data exchange
5.1 The SPI-Bus in general
5.2 Initialization of SPI with the MSP430F2013 microcontroller

6. USB-Interface
6.1 Requirements to transfer the data into the compute
6.2 The IO-Warrior56 (IOW56)
6.2.1 Normal mode function
6.2.2 Special mode function

7. Interaction

8. Power supply

9. Software

10. Appendix
10.1 Circuit diagram
10.2 Board, layout and bill of material
10.3 Used formulaic symbols
10.4 Used equipment
10.5 List of sources

1. Assignment

The assignement is, to develop a device for data aquisition of signals with in the frequency range between

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with f is the frequency. This frequency range is usually named in short form "ELF", which means "Extremely Low Frequency".

The amplitude of the signals is weak. The absolute value is not known. The system must be sufficient sensitive.

With the delivered data of the system it should be possible to show the signal independent from the form of the curve.

It is planned to do measurements at many places at the same time. The hardware should be easy to build and cheap. Moreover it must work with any standard personal computer. Most PCs work with MS-Windows operating systems. So the program must run under Windows.

2. Concepts

Today data will be saved and calculated in digital form. So the analog input signal must be digitised. Before the digitalisation can be done, an amplification and a low pass filtering is necessary. The amplification is necessary because of the fact, that the system must be able to receive very weak signals.

Filtering is necessary, to keep away signals with higher frequencies than 25 Hz from the analogue to digital converter. This has different advantages.

Because of the Shannon criteria it applies: the lower the upper limit frequency, the smaller can be the sampling frequency.

Moreover this, the less signal components above 25 Hz are in the signal, the more dynamic range from the analog-digital-converter is available for the desired signal. Details to this can be seen in chapter 3.

After filtering, two different meaningful ways are possible for digitizing the signal and save it on a disk:

1) Digitizing under using the sound-board and the A/D converter on it, which is in each personal computer available.
2) Digitizing under using an external A/D-Converter and transfering the data through the USB-interface into the computer.

2.1 Using the sound board of a personal computer

A solution in the way similar to 1) is described in8.

The problem in this case is, that it is not sure, whether the sound board in a personal computer can process signals in the ELF range. Typically this sound boards are designed for audio signals like music or speech. So, before the sound board of a computer can be used for recording of ELF-signals, it is necessary to measure the transfer characteristic. With this data an adaption must be designed with hardware or software. This has to be done for each computer which is used for ELF-recording. This is uncomfortable and result easy to errors.

On the other hand, commercial sound boards in personal computers have a 16-Bit-Analog- Digital-converter already implemented. This makes the handling easy.

To solve the problem with the unknown frequency characteristics of the sound board a modulation can be used. For example an AM-signal with a carrier-frequency which lies in the middle of the audio range can be used. It is very likely, that in the middle of the audio range the transfer characteristic of an audio sound board is straight.

The block diagram for this solution is shown in figure 2.1. The modulated signal, which goes to the sound board is shown in figure 2.2.

Assumption: In the surrounding of 200 Hz, each standard sound card has a linear frequency response. According to9, the bandwidth B of an AM-signal is:

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Whereby fmax is the highest frequency which modulates the carrier. So here it is

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So the used band starts at 175 Hz and it stops at 225 Hz. It can be assumed that any standard soundboard has a linear frequency response in this range. With this concept there is no limit of the low frequencies.

Details to the AM-modulation can be found in9.

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Fig. 2.1: Concept under using the sound board of an personal computer

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Fig. 2.2: Amplitude modulated (AM) signal. The carrier is modulated with the ELF-Signal.

Test with this concept has been made. A complete system is described in8. Figure 2.5 shows the used board. A real disadvantage is the fact, that through the modulation, the dynamic range is restricted. The dynamic range results from the allowed modulation factor m. The modulation index is defined as the ratio, between the highest and the lowest amplitude value of the (upper) envelope of the AM-signal.

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Theoretically m can go from 0 to 100 % (see9 ). In practice it is necessary to have a good distance from 100%. Otherwise there is a danger of over-modulation and resulting signal- distortion. The signal-noise-ratio depends also on the amplitude of the carrier. The higher the amplitude, the more better is the signal-noise-ratio on the transmission way. However there is a limit, because most commercial sound boards can only handle input voltages of 2 Vss. To make sure, that any sound board can be used, without signal distortion, the amplitude of the carrier should not exceed 1 Vss.

Of course, in the computer the data must be demodulated by software. In8 is a very simple way described with which ELF-signals can be demodulated without Hilbert transformation. However, this requires that the sampling frequency is at least 5 times higher than after Shannon necessary (see Eq. {4.1}).

For those in8 described methods of "peak tracking", an amplitude error is present. In the worst case, the peak value occurs exact between two samples. In figure 2.3, one can see, that the peak value of a 2π-function occurs at π /2. The maximum error appears, if the next sample value is 1/2 fS before or after the peak value. For the relative value of the error one can write:

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Fig. 2.3: Estimation of the maximum possible error, with demodulation through peak tracking. With constant carrier frequency, the used sample frequency is crucial factor for the error.

The declaration of the formula-statement will be more clear with the help of the diagram in figure 2.4. As expected, the error is as smaller, the higher the sampling rate is and/or the lower the carrier frequency is. The minimum value of the carrier frequency is in turn determined by the behavior of the transmission channel in general or specific case and the expected frequency of the desired signal. The 1%- accuracy-line can be calculated as follows:

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The sine value 0.99 exists also for an argument which is smaller than pi / 2 - i.e. before the maximum of the function. The result of the above equation, therefore, leads to a negative frequency-ratio. Because of the symmetry around the point pi / 2 one can also write the following:

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Assuming a carrier frequency fC of 200 Hz, the sampling frequency fS must therefore be at least:

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Then, the maximum error which is caused by the demodulation, is less than 1%. According to the Shannon-criteria (see chapter 4 and equation 4.1), that could be used for frequencies up to

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If the demodulated signal will be used not only for signal processing, but also must be presented graphically, then the frequency of the measured signal cannot be much larger than:

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Under using a sampling rate of 96 kHz, could thus be used a carrier frequency of 4360 Hz. This corresponds to a maximum signal frequency of approximately 2180 Hz, or for graphic representation then only about 218 Hz. See chapter 4 for details.

However standard sound boards offer not more than 48 KHz sample rate. This results in round about 109 Hz for graphical representation.

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Fig. 2.4: Connection between the carrier frequency, sampling rate and possible error of the presented example.

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Fig. 2.5: Test board for acquire ELF-signals with the help of AM-modulation.OTA = Operational Transconductance Amplifier. SC = Switched Capacitor.

2.2 Using the USB-Interface

On the first view, the advantage of the second concept is, that no modulation which restricts the dynamic range of the system, is needed. Also, no demodulation is necessary which causes an error. Beyond this, there is no unknown component in the transfer path.

The digitization happens outside from the computer. After digitization, the signal goes through the USB-interface to a personal computer. There it can be analysed and saved on a hard disk.

So the complete concept looks like the sketch in figure 2.4.

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Figure 2.4: block diagram of the complete hardware.

To record all frequencies f > 0, it is necessary, that all components let pass DC-voltage. 16- Bit-resolution should be possible for analog-to-digital-conversion. This allows a large dynamic range for the desired signal.

Pre amplifier and low pass filter are designed with operational amplifiers. This is similar to the first concept. Analog-to-digital conversion is done with an MSP430F2013 microcontroller, which has a 16-Bit-Sigma-Delta ADC on the chip. The USB-Interface is realized with an IO-Warrior56-Chip.

The using of a microcontroller with includes the AD-converter, allows to extend the system e.g. as a data logger. For that, the microcontroller must be connected to a flash memory and it needs a software extension. But, this is not a topic of this work.

This concept is used in the following.

3. Analogue lowpass filter of 6th order for aquisition of signals with extremely low frequencies (ELF)

3.1 Motivation to use a low-pass-filter before digitizing

Today, filtering of signals is realized in the digital way. However there are applications,

which needs the filtering before the analogue-to-digital-converter. One of this application is the aquisition of ELF-signals (ELF = Extremely Low Frequency), how it is described e.g. in 1 and2. Would the signal, which is coming from the antenna, digitized without filtering, then, almost the whole dynamic range of the A/D-converter must be used for the 50-Hz-hum of the main power supply. For the relevant ELF-signal only a few bits at the end of the scale (near the LSB) can be used. This results in a very poor signal-noise-relation. The frequency- diagram in figure 3.1 shows this clearly. This diagram results from a measurement inside of a house. The 50-Hz-hum from the power supply is in this case round about 41 dB stronger than the ELF-signals below this frequency.

The solution of this problem offers a analogue low-pass-filter with strong slope. The cut-off- frequency must be placed with enough distance to the 50-Hz-hum. With this configuration, teh 50-Hz-hum-signal is suppressed and only the ELF-signals goes to the A/D-converter. So much more of the dynamic range of the A/D-converter can be used for digitalization the ELF- signals.

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Figure 3.1: The difference in the dynamic range between the 50-Hz-hum of the power supply and the ELF-signals (left of the 50-Hz-Peak) is round about 41 dB.

3.2 Types of lowpass filters

The question is, which characteristics the filter must have. To be sure, that no signals will missed, it would be good, if the filter can pass all frequencies until close to 25 Hz. However, the 50-Hz-hum of the power supply must be surpressed very strong. To do this, a low-pass- filter with high slope is necessary.

However, especially steep filter, like the Chebychev-type, causes errors - depending on the design - in the passband or stopband. Also, after this steep filter, a meaningful analysis of the time signal is not longer possible. The reason for that is, the fact, that chebyshev-filters have a marked non-linear group delay and so, an extremly non-linear phase-characteristic. If the signal must be analysed also in the time domain, only the bessel-filter can deliver a relevant result. This kind of filter is optimised for constant group delay. However, the transfer characteristic from the pass-band too the stop-band is comparatively width. So, steep-edge filters with Bessel-characteristic require a high filter-order, what increases the effort. The compromise is the filter with butterworth-characteristic. Just as the chebyshev-filter, it has not a constant group delay, but it causes no error in the passband - and has relatively strong steepness anyway. If it is planned, to make the analysis preferably in the frequency range, the butterworth-filter is the right selection.

As closer the cut-off frequency should be placed to 50 Hz, as more steepness is needed from the passband to the stopband. In general applies for the steepness of the transfer characteristics depending from the filter-order:

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Figure 3.2 shows the transfer characteristic of optimized lowpass filters. The optimization is relevant for the range around of the cut off frequency. Of course, in width-band-view, equation 3.1 is relevant.

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Figure 3.2: Qualitative comparison of the transfer characteristics of optimized filters 4. order: 1 Bessel, 2 Butterworth, 3 Chebycev.

3.3 Development of Butterworth-low-pass filters in general

To optimize a filter it must be at least of the order 2. Otherwise the for the optimization necessary degrees of freedom are missing.

Second-order Low pass filters of type Butterworth can be designed like described in 3. In this book is described the design of filters based on the "Sallen-Key-Concept". Each filter just needs one operational amplifier, two resistors and two capacitors. The following comes from this publication.

Higher order filters can be constructed through series circuits. Two filters of second order in series delivers a filter of fourth order. Three filters of second order in series delivers a filter of sixth order. When dimensioning must be noted, however, that the individual filter curves multiplied together gives the total transfer-characteristic. Two low pass filters with the cutoff frequency fc in series delivers a low pass filter with a cutoff frequency which is lower than fc. A filter higher order, which is constructed from several single filters, requires therefore a certain dimensioning of the whole filter.

The transfer characteristic of a Butterworth low-pass filter of sixth order is calculated in generally:

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The variable s stands for the frequency-dependence. If a filter of sixth order is builded from three filter of second order, the characteristic of each filter is:

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Now a circuit must be found, which allows to realize the corresponding curves. The easiest way to create a low pass filter of second order, offers the Sallen-Key-Filter corresponding to Figure 3.3.

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Fig. 3.3: Sallen-Key low pass filter of second order.

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The component values can be calculated by comparing coefficients with Eq. {3.3}.

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To obtain real values, the condition must be fulfilled. Therefore, at first the capacitors are to be chosen. Subsequently, the calculation of the resistors can be done.

By skilful choice of cutoff frequencies, a filter of 6th order can be designed by three filter of 2nd order, which are serially connected. The overall transfer function is the result from the product of the single transfer functions of each filter.

To make the calculation easier, one can use a worksheet like it is described in3.

Alternatively a special filter-calculation-program can be used. An example for that is the program “Filter Pro” from Texas Instruments (fig. 3.4, http://www.ti.com/tool/filterpro). After selecting the filter-type and entering of the parameters, the program offers a circuit diagram and the transfer-characteristic. As one can see, in this case, the transmission curve (green curve) is not completely flat - although, the type "Butterworth" was selected. It has a slight increase just before the bend - a sign that it is an optimized filter - not a perfect one. Optimisation is always a compromise. It may not be exactly as desired. But, the greatest uncertainty-effect is caused from the standardized components (from the standard lines E6, E12). These can represent a calculated value only approximately.

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Fig. 3.4: Filter design with the program "Filter Pro" from Texas Instruments (above) and the result (left, see text). Green: transfer characteristic Red: phase response

Black: group delay

3.4 Designing a Butterworth low-pass filter of 6th order

According to equation {3.1}, the steepness of a filter of 6th order is 36 dB/Octave. If the cutoff frequency is 25 Hz, the 50 Hz hum of the power network, which bother the measurement, is reduced by 36 dB. Based on the task to filter out ELF-signals just before the line frequency and under considering of Figure 3.1, is the result compared to the unfiltered A/D conversion, a dynamic improvement of these 36 dB.

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If the cutoff frequency is 20 Hz, the 50-Hz-hum is even reduced to 46 dB (see Fig. 3.4),

which is equivalent to an attenuation-factor of nearly 200. However, in this case, the ELFsignals are transferred then only until nearly 20 Hz without damping - what means error free in the frequency range. This cutoff frequency (20 Hz) was selected, because for the intensity of the 50-Hz-hum, the damping of 36 dB is not enough. The fact, that this filter reduces the 25 Hz about 11 dB, must be considered if necessary.

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Fig. 3.5 shows the circuit diagram of the designed Butterworth-Low Pass filter of 6th order with a cutoff frequency of 20 Hz. It is build up with three filters of 2nd order. The first operational amplifier (OP1.1) is just for preamplification of the incoming signal to the factor:

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The filter itself is designed with the operational amplifiers from OP1.2 to OP1.4. The selected type OPA4227 from Texas Instruments has the advantage of an extrem low offset-voltage and its minimal temperature dependance. Maybe even C7 can be leaved out, so that the let- through range begins with 0 Hz (DC). This can certain be made with adding an offset adjustment (not in the circuit diagram), which must be connected at OP1.4. In figure 3.6 one can find a proposal for the PCB-layout (this is for wired components). C5 was built from three capacitors with 3,3 F in parallel circuit. These are more handy and easier to buy, comparison to one capacitor with 10 F.

Fig. 3.5: Circuit diagram of the low pass filter of 6th order designed according to Sallen-Key (see3 ). The first operational amplifier (OP1.1) is for separating and input-amplification. The real filter is designed with the operational amplifiers OP1.2, OP1.3 and OP1.4.

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Excerpt out of 58 pages

Details

Title
Development of a low-power-signal acquisition device for signals lower than 25 Hz
College
The Slovak Technical University  (Faculty of electrical engineering and information technology)
Grade
2.0 bzw."B"
Author
Year
2012
Pages
58
Catalog Number
V196879
ISBN (eBook)
9783656230175
ISBN (Book)
9783656231660
File size
2703 KB
Language
English
Notes
Design a signal detection device for detection and digitization of weak signals with frequencies up to 25 Hz before their transmission into a personal computer (PC). The device should contain an input low-pass filter with a cutoff frequency of 25 Hz, a preamplifier, microcontroller MSP430F2013 for digitization and preparation of the digitized signals for transmission into the PC via USB interface.
Tags
development
Quote paper
Dipl.-Ing. Franz Peter Zantis (Author), 2012, Development of a low-power-signal acquisition device for signals lower than 25 Hz, Munich, GRIN Verlag, https://www.grin.com/document/196879

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