Design, calibration and tests of versatile low frequency impedance analyser based on ARM microcontroller

Accepted Manuscript Design, calibration and tests of versatile low frequency impedance analyser based on ARM microcontroller Tomasz Piasecki, Konrad Chabowski, Karol Nitsch PII: DOI: Reference:

S0263-2241(16)30214-7 http://dx.doi.org/10.1016/j.measurement.2016.05.057 MEASUR 4073

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

7 October 2015 4 May 2016 13 May 2016

Please cite this article as: T. Piasecki, K. Chabowski, K. Nitsch, Design, calibration and tests of versatile low frequency impedance analyser based on ARM microcontroller, Measurement (2016), doi: http://dx.doi.org/10.1016/ j.measurement.2016.05.057

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Design, calibration and tests of versatile low frequency impedance analyser based on ARM microcontroller

Tomasz Piasecki, Konrad Chabowski, Karol Nitsch Faculty of Microsystem Electronics and Photonics, Wroclaw University of Technology, Z. Janiszewskiego 11/17, 50-372 Wroclaw, Poland

Abstract

Numerous simple impedance analysers based on the microcontroller (µC) and dedicated impedance converter integrated circuits (IC) were reported recently. In many applications sophisticated analogue circuitry has to be appended to enhance the measurement possibilities or to circumvent the limitations. In this paper the impedance analyser IMP-STM32 based solely on the µC and general purpose operational and instrumentation ampliers is presented. It uses the internal DAC and ADCs in the µC to generate the excitation and to measure the response of the measured object. It also uses the external analogue circuits to condition the excitation signal and measure voltage and current. The magnitudes and phase shifts of voltage and current are evaluated using the three parameter sine tting algorithm allowing for fast low-frequency impedance measurements. The calibration procedure of completed device is presented as well as the tests of its accuracy. The device allowed for measurements at frequency range between 1 mHz and 100 kHz in 1 Ω to 1 GΩ impedance range with 1% accuracy. IMP-STM32 was also compared to the Agilent 4294A precision impedance analyser. In the middle of the impedance ranges (1 Ω to 300 kΩ) the discrepancies between the two were less than 0.2%. Keywords:

impedance, three parameter sine t, embedded system

Email address:

[email protected] (Tomasz Piasecki)

Preprint submitted to Measurement

May 4, 2016

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1. Introduction

Impedance spectroscopy is a technique based on the measurement of the electric impedance of an object in wide range of frequencies - the impedance spectrum[1]. It nds its applications in various areas such as in investigation of the solar cells [2, 3], in the electrochemistry [4, 5], fuel cells characterization [6, 7], improved batteries [4, 8] and supercapacitors design [9] or in the biosensors [1021]. One of the most common method for obtaining the impedance spectrum is to measure the impedance during the linear or logarithmic sweep at a number of discrete frequency points using sinusoidal excitation[1]. The impedance itself is a measure of the relation of magnitudes and phase shifts of voltage (U , ϕU ) and current (I , ϕI ) owing through the measured object:

Z= 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

U j(ϕU −ϕI ) e I

(1)

Impedance spectra are usually measured using impedance analysers or advanced RLC bridges which are commercially available laboratory devices. However, there are specic application elds where it is necessary to use a simple and small device which may be embedded in portable measurement system. Such devices may exhibit the limited frequency or impedance ranges or may lack another features typical to the laboratory impedance analysers such as the wide range of excitation signal magnitudes, measurement with DC bias etc. Numerous inexpensive custom-built impedance analysers have been reported recently [1013, 1619, 2225]. Most of these devices utilize the dedicated impedance converter integrated circuit AD5933 [26] (Analog Devices) controlled by the embedded microprocessor (microcontroller, µC). In some applications that do not require wide range of frequencies or impedances that setup is sucient and may be successfully used [1013, 27, 28]. Otherwise the device requires external circuitry such as the variable clock generator [16, 22, 24], excitation signal correcting circuits [1618, 2325], external current-to-voltage converter (CVC) with selectable conversion ratios [16, 19, 22, 24, 25], four terminal-sensing capability [1719, 22, 23], etc., to overcome its limitations and drawbacks as well as to widen the impedance and frequency ranges increasing the circuit complexity. That necessity was the motivation for the research that lead to the construction of impedance measurement system IMP-STM32, presented in this 2

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paper. The IMP-STM32 does not contain any dedicated impedance converter integrated circuits. It is based solely on the DAC and ADCs integrated in the µC and controlled by the rmware cooperating directly with analogue circuitry composed of general purpose operational and instrumentation ampliers.

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2. Impedance measurement system IMP-STM32

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The IMP-STM32 is designed as a simple, small and versatile impedance analyser aimed to the measurement of two-electrode impedimetric biosensors. Basing on the own experience in that eld [20, 21] and taking into account the possible hardware limitations its design assumptions are as follows: the excitation frequency range from at least 100 mHz to 100 kHz, the impedance range from at least 10 Ω to 10 MΩ measured the accuracy not worse than 1% using the typical excitation signal level of 25 mVRMS as biosensors most often use electrodes directly exposed to the liquid medium which limits the excitation signal level to several tens of milivolts to avoid the electrolysis. The IMP-STM32 is based on the STM32F405RG µC. This is the inexpensive and powerful µC based on the ARM Cortex-M4 core with 168 MHz maximum clock frequency, built-in DAC and ADCs, 192 kB of SRAM and single-precision Floating-Point Unit (FPU), which is convenient for fast signal processing. The simplied block diagram of the system is presented in Figure 1. The DAC in the µC is the source of the excitation signal which is ltered, attenuated and fed to one of the four terminals (HC, HP, LP, LC in Figure 1) through which the device under test (DUT) is connected. The voltage at the DUT and current owing through the DUT are measured and their instantaneous values are simultaneously sampled by two ADCs in the µC. Sampled data are then analysed by signal processing algorithms in the µC. The IMP-STM32 system is designed in a way in which three of the most signicant shortcomings of the impedance meters based on the AD5933 are eliminated:

− the lack of the built-in possibility of the actual DUT voltage measurement which in AD5933 based systems may be solved by switching [23] or dual impedance converter [22] conguration, − diculty of using the anti-aliasing lters the lack of which causes signicant errors in case of capacitive DUTs [24], 3

Figure 1: Block diagram of the IMP-STM32 impedance measurement system. Marked are the internals of the STM32F405RG µC and analogue circuitry responsible for excitation voltage of the device under test (DUT), voltage and current measurement.

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− long duration of the low frequency impedance measurements caused by the limitations of the impedance evaluation algorithms [22, 24, 26] .

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Parts of the IMP-STM32 system are described in following subsections.

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2.1. Excitation signal generator

The excitation signal in In IMP-STM32 is generated using software implemented direct digital synthesis (DDS) method. The lookup table (LUT) contains 32k of 12-bit samples of the sinusoidal wave to fully utilize the resolution of the DAC. Allocation of the LUT in the SRAM allows the amplitude of generated signal to be adjusted by changing LUT content however decreasing the amplitude also decreases the utilization of the DAC dynamic range. The DDS tuning word is 32 bit long therefore the resolution of the excitation signal frequency is 1 MHz/232 ∼ = 0.23 mHz. The bandwidth, although theoretically wider, is arbitrary limited to the 1 mHz - 100 kHz range. Generated waveform is ltered with 4th order Butterworth low-pass antialiasing lter, designed to exhibit 3 dB attenuation at 100 kHz (maximal excitation signal frequency) and 80 dB attenuation at 1 MHz (DDS generator 4

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frequency). All operational ampliers used in the IMP-STM32 are MCP6022 (precision, low voltage, rail-to-rail operational ampliers, GBP=10 MHz, VOS ≤ ±500 µV, eN = 8.7 nVHz−0.5 at 10 kHz or 2.9 µVPP ). The sinusoidal excitation signal has the DC oset of 1.65 V which is half of the supply voltage of the µC. For convenience the voltage shifter is used to remove that oset. In that way all voltages at the DUT are referred to the ground while the the DAC and ADCs in the µC operate at their full voltage ranges. The amplitude of the voltage generated by the DAC is up to 3 VPP . To meed the design assumptions the signal is attenuated 25 times to reduce the amplitude of the voltage applied to the DUT to the range from 5 to 42 mVRMS . Such range is convenient for measurements of the biological sensors which were the main eld of application for the IMP-STM32. Attenuated voltage is fed through the HC terminal to the DUT. 2.2. Voltage measurement

IMP-STM32 allows direct, simultaneous measurement of both voltage and current at the DUT. The voltage is measured between the HP and LP terminals using the instrumentation amplier (INA331, 2 MHz bandwidth at 5× gain, VOS < ±250 µV , eN = 46 nVHz−0.5 at 1 kHz or 7 µVPP ) and amplied back 25 times. Level shifter is used to transform the measured voltage into the µC operational range. Up to 16k samples of instantaneous values of the voltage are converted by the 12 bit ADC in the µC and stored in preallocated buer by means of the DMA channel. The sampling frequency fs is adjusted according to the measurement frequency fm based on the following user-selectable parameters: the desired number of samples per measurement n, (32 ≤ n ≤ 16384) and the minimum number of excitation periods per measurement k, (0.1 ≤ k ≤ 10):

fs = 113 114 115 116 117 118 119

n fm k

(2)

The value calculated from (2) may be higher than 1 MHz which was assumed as the highest sample rate of the ADC. For example, if fm = 10 kHz, n = 1024 and k = 1 the sampling frequency would be over 10 MHz. In that case the sampling frequency is limited to 1 MHz, the total number of samples n remains unchanged but the measurement would last for a greater number of excitation periods than k . In practice this is not inconvenient as the real need for low values of k is during the low frequency impedance measurements [29]. 5

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2.3. Current measurement

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The current owing through the DUT is measured at the LC terminal using the current-to-voltage converter (CVC). The ranges of the CVC are switched by changing the resistors in the feedback loop Rf by means of electronic switches (ADG712). Our system is able to measure current at one of 7 ranges for which the Rf b changes from 10 Ω to 10 MΩ. Capacitors parallel to the range resistors improve the stability of the CVC and lower the noise level at high impedance measurements at cost of the frequency range. Values of feedback components used in IMP-STM32 are presented in Table 1. The output voltage from the CVC is amplied 25 times and sampled using the same sampling rate as the DUT voltage.

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2.4. Signal processing

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During the acquisition phase of the measurement the instantaneous values of voltages which corresponded to the voltage and current at the DUT are sampled, converted in ADC and stored in the buers. The magnitudes (AU , AI ) and phases (ϕU , ϕI ) of sinusoidal voltage and current waveforms are determined using three parameters sine tting (TPSF) algorithm [30]. The TPSF algorithm has several advantages over the most commonly used discrete Fourier transform (DFT). In DFT samples have to be windowed, for example using the rectangular window which width was the closest integer number of excitation periods, to avoid spectral leakage. Additionally, apart of the possibility for the number of the sampled periods k (2) to be a noninteger number, the TPSF allows to reduce it below 1 which means that the measurement of the impedance may be done in time shorter than the period of the excitation signal [29].

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2.5. Interfaces and measurement control

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The IMP-STM32 is equipped with the LCD and buttons which allow to change the measurement parameters manually. The result of the measurement is also displayed on the LCD. The IMP-STM32 is designed to be able to be controlled from the personal computer (PC) with dedicated software which controls the impedance spectra measurements. The USB 2.0 controller in the µC which is congured and programmed to work as a USB Communications Device Class (CDC) device [31]. The exchange of commands with the PC occurrs through the virtual serial port. Commands are compatible with Standard Commands for Programmable Instruments (SCPI-99) [32]. 6

(a)

(b)

Figure 2: The general view of the IMP-STM32 impedance measurement system (a) and the digital and analogue modules inside (b).

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Measurement system is built as a compact device contained inside the 100 x 106 x 42 mm housing (Figure 2a). It consists of two PCBs, one containing the µC, display, keyboard and power supply, second one contains whole analogue circuitry (Figure 2b). The IMP-STM32 rmware allows to control the following parameters of the impedance measurement: the measurement frequency, the amplitude of the voltage excitation, type of the CVC range switching (automatic or manual), the desired number of samples per measurement, the minimal number of excitation signal periods per measurement, continuous or one-shot triggering and the delay between measurement triggering and start of the sampling.

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3. Calibration of the measurement system

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Presented impedance measurement system IMP-STM32 required the calibration to determine the exact values of the CVC conversion ratios as well as the frequency characteristic of the analogue circuitry.

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3.1. Preparation of the reference resistors

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Set of 11 resistors was used as the reference in calibration and tests of the measurement accuracy. It consisted of 9 metal lm resistors covering the range from 100 mΩ to 10 MΩ and 2 carbon composition resistors for 100 MΩ and 1 GΩ. They were precisely measured to evaluate their resistance and parasitic components. 7

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True values of the resistances R were measured using Keithley 2001 7.5 digit multimeter with 4-wire connection for resistors below 1 kΩ, the same meter but 2-wire connection for resistors between 1 kΩ and 10 MΩ and Keithley 6512 electrometer for 100 MΩ and 1 GΩ resistors. The parasitic series inductance Ls and parallel capacitance Cp of the reference resistors inuence the impedance of reference resistors at higher frequencies. They were determined basing on the impedance spectra measured with Agilent 4294A precision impedance analyser in frequency range from 40 Hz to 1 MHz and equivalent circuit modelling using Scribner ZView2 [33]. Knowing the resistance and parasitic elements of each of the reference resistors their impedance Zref may be calculated for any radial frequency ω basing on the formula:   R ωR2 Cp Zref (ω) = + j ωLs − (3) 1 + (ωRCp )2 1 + (ωRCp )2

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which is the impedance of the resistor R with series inductance Ls and parallel capacitance Cp . Results of the measurement and simulation of the reference resistors are shown in Figure 3. Good agreement between the measurement and simulations was achieved. The impedance spectra for resistors below 1 Ω were truncated because of the insucient precision of the Agilent 4294A at low impedances and low end of its frequency range [34]. These measurements allowed also to determine the maximum useful frequency at which these resistors may be used as the reference, even taking into account the fact that the values of the parasitic elements are known and the characteristics may be simulated for whole frequency spectrum. It was arbitrarily established that the 10 MΩ, 100 MΩ and 1 GΩ resistors may be used as reference up to 10 kHz, 1 kHz and 100 Hz, respectively. Remaining resistors may be used at whole frequency range of the IMP-STM32.

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3.2. Calibration procedure

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The precision of the impedance measurement relays on the transmittance of the components used in the analogue front-end of the IMP-STM32 (Figure 1). For example, the 25× voltage amplier at the 100 kHz frequency introduces about 6◦ of the phase shift despite actually being split into two 5× stages built using operational ampliers with 10 MHz gain-bandwidth product (GBP). Such phase shift would aect the impedance argument measurement signicantly if it was not properly compensated. 8

1G 100M 10M 1M

|Z| (

)

100k 10k 1k 100 10 1 100m 100

1k

10k

100k

1M

frequency (Hz)

Figure 3: The measured using Agilent 4294A precision impedance analyser (dots) and simulated (lines) impedance modulus of the reference resistors.

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The uncalibrated impedance Znc was dened as the ratio between the direct results of the TPSF applied to the voltage (AU , ϕU ) and current (AI , ϕI ) samples, expressed in arbitrary units, without taking into account the conversion factor of the CVC:

Znc = 214 215 216 217 218 219 220

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AU ϕU −ϕI e AI

(4)

The calibration procedure relied on the measurement of the Znc using the reference resistors as the DUT, whose impedance at any frequency was known (3). Measurement was repeated at each of the CVC ranges using the reference resistor of the nominal value equal to the feedback resistor in the CVC. Results of the Znc measurements were shown in Figure 4 as dots. The measured frequency characteristic were then approximated with polynomials: Znc 2 (5) Zref = m0 + m1 · fm + m2 · fm   Znc 2 arg = a1 · f m + a2 · f m (6) Zref where mi were the magnitude calibration parameters and ai were the argument calibration parameters. The results of the calibration procedure were shown in Figure 4 as lines. Proposed approximation with second order polynomials was sucient to achieve good t quality (reduced χ2 < 10−4 ) if the t was done in the frequency range at which the argument of uncalibrated impedance was less than 15◦ . Calibration data were used to compensate for the frequency characteristics of the measurement system according to the transformed (5) and (6) in which the Zref was substituted with the unknown impedance Zx of the DUT: |Znc | |Zx | = (7) 2 m0 + m1 · fm + m2 · fm
2 arg(Zx ) = arg(Znc ) − a1 · fm + a2 · fm (8) The analysis of the approximation data also allowed to determine the maximum measurement frequencies at each of the ranges which was resulting from the 15◦ limit on the uncalibrated impedance argument. The maximum measurement frequencies of IMP-STM32 are shown in Table 1. 10

(a) modulus

(b) argument 15° values of R

fb

10

1.1

100

) arg (Z

values of R

|Z

fb

0.9

10

100

1 k

10 k

100 k

1 M

1 k 10 k 100 k

nc

1.0

nc

| (a.u.)

10°

1 M 10 M

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10 M

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100m

1

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100m

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1

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1k

10k

100k

frequency (Hz)

frequency (Hz)

Figure 4: Illustration of the impedance measurement calibration of (a) modulus and (b) argument. Dots represent the measured value, lines the approximated frequency characteristics at each of the ranges 238

4. Performance tests

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To test the accuracy of the calibrated IMP-STM32 the performance tests were conducted.

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4.1. Evaluation of the measurement system accuracy

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The impedance spectra of the reference resistors were measured using IMP-STM32 in the frequency range from 1 mHz to 100 kHz using 25 mVRMS excitation. The measured impedance Zm was compared with the reference (3) and relative error of impedance modulus δmod (9) and absolute error of argument ∆arg were calculated and presented in form of the contour maps in Figures 5a and 5b, respectively. |Zref | − |Zm | δmod = (9) |Zref | The modulus accuracy plot revealed that in full range of frequencies the impedance between 100 Ω and 1 kΩ and at frequencies below 1 kHz the impedances from 10 Ω to 100 kΩ are measured with very good, 0.1% modulus accuracy and 0.01◦ argument accuracy. The still useful 1% relative modulus 11

Table 1: CVC ranges: the nominal values of feedback resistance Rf b and capacitance Cf b and the maximum measurement frequency fmax . range Rf b Cf b fmax 0 10 Ω 10 nF 100 kHz 1 100 Ω 1 nF 100 kHz 2 1 kΩ 100 pF 100 kHz 3 10 kΩ 47 pF 80 kHz 4 100 kΩ 47 pF 8 kHz 5 1 MΩ 47 pF 800 Hz 6 10 MΩ 47 pF 80 Hz

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measurement error and 0.1◦ argument error was obtained for impedances covering the range from 1 Ω to 100 MΩ except from the area which was limited by the frequency characteristics of the CVC. It is important to note that this investigation covered only the accuracy of the proposed measurement method and the quality of the analogue circuitry. It did not include the errors introduced due to the thermal nor time drift of the components used in that circuit. To verify the sensitivity to the temperature changes the system was placed in the temperature controlled chamber and similar measurements were performed at 10◦ C and 40◦ C and the maximal values of errors evaluated in the same way as before were shown in Figure 6. As may be observed from the comparison beween Figures 5 and 6 the temperature inuenced mainly the modulus measurement error. That allows to conclude that the main factor contributing to that increase was the temperature drift of the resistive elements which determine the gain, mainly at the CVC feedback loop. At low impedance ranges the temperature coecient of resistance (TCR) of the electronic switch used for range switching was dominant whereas the medium and high impedance ranges were mostly inuenced by the TCR of the resistors. The change of the argument measurement error was much smaller however it also increased.

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4.2. Measurements of the RC networks

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The test objects were used: 6.6 nF and 220 nF foil capacitors and a RC network consisting of the 100 nF foil capacitor with 30 Ω series and 3.3 kΩ parallel resistance. The impedance spectra of the test objects were measured using Agilent 4294A precision impedance analyser and IMP-STM32. In both 12

(a) modulus 1G

(b) argument 1G

3%

1%

100M 0.3%

10M

0.1%

3°

100k )

10k

|Z| (

)

0.1°

1M

100k |Z| (

0.3°

10M

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1k

0.03%

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10k 0.01°

1k 100

10 0.1%

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100k

1°

0.1° 3°

0.3°

1m

10m 100m

frequency (Hz)

1

10

100

1k

10k

100k

frequency (Hz)

Figure 5: The dependence of the experimentally established measurement accuracy of the impedance modulus (a) and argument (b) on the measurement frequency and the modulus of the measured impedance.

(a) modulus

(b) argument 1G

1G

3%

1°

100M

100M 10M

10M

0.3%

10k

)

0.1%

1k

|Z| (

)

0.03°

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100k |Z| (

0.1°

1M

1M

0.3%

10k 0.01°

1k 100

100 10

10

1% 3%

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3°

1%

10%

1m

10m 100m

1

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0.03°

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frequency (Hz)

100m

1m

10m 100m

1°

0.1°

0.3°

3°

1

10

100

1k

10k

100k

frequency (Hz)

Figure 6: The experimentally established measurement accuracy of the impedance modulus (a) and argument (b) over the extended temperature range between 10◦ C and 40◦ C

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1k 6n6

220n

frequency (Hz)

10k

100k

RC

100k

6n6

1% 0.1% 0.01%

|Z|

100

220n RC

10k

6n6 ref

|Z| (

)

220n ref RC ref

1k 100 10 100

1k

10k

100k

frequency (Hz)

Figure 7: Comparison of measured (dots) and reference (lines) impedance modulus of the 6.6 nF and 220 nF foil capacitors and a test RC network. The bars represent the relative dierence between measurement and reference. 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291

cases the frequencies were the same ranging from 100 Hz to 100 kHz. Tests objects were selected in a way that provided that the Agilent 4294A measured them with the accuracy better than 0.3% with the excitation signal of 0.5 VRMS [34]. The excitation signal amplitude in IMP-STM32 measurement was 25 mVRMS . The results obtained using Agilent 4294A were treated as the reference values and the relative dierences of the two were calculated and presented in Figure 7 together with the impedance modulus spectra. The comparison of the impedance modulus measured using the IMPSTM32 and the reference impedance analysers revealed good correlation between the two. Despite possible additional errors introduced by our system the relative error between the measurements generally did not exceed 0.2%. The 0.3% discrepancy was observed only for the worst-case combination of the highest frequency (100 kHz) and lowest impedance magnitude (about 8 Ω) amongst all measured samples but even though it was not greater than 14

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the declared measurement error for the Agilent 4294A precision impedance analyser.

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5. Conclusions

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The designed, constructed and tested IMP-STM32 proved to be able to measure the impedance precisely, in wide range of frequencies and impedance magnitudes, exceeding the initial design assumptions and making it a versatile low frequency impedance analyser. The usable frequency range was from 1 mHz to 100 kHz. While measuring standards that were used for the calibration the measurement error of impedance modulus and argument reached 0.03% and 0.01◦ , respectively, and were better than 1% and 0.1◦ for impedances from 1 Ω to 10 MΩ. In comparison with the advanced impedance analysers based on the AD5933 exhibiting similar measurement capabilites [1619, 2224] our system has following advantages:

− simultaneous voltage and current measurement, − no need for variable frequency clock source to cover wide range of frequencies, − constant DDS clock frequency which allows to use single, xed frequency anti-aliasing signal generation lter, − three-parameter sine tting algorithm used to evaluate magnitudes and phases of voltage and current which allows fast low frequency impedance measurements, − possibility to implement advanced signal processing and impedance evaluating algorithms, − full control over the measurement process. Acknowledgments

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Presented research was supported by the Wroclaw University of Technology statutory grant.

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References

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Highlights

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Versatile impedance analyser based on the ARM microcontroller is presented Frequency range 1 mHz to 100 kHz, impedance range 1 Ω to 1 GΩ Base accuracy 0.03% Discrepancy with Agilent 4294A less than 0.2% for impedances 1 Ω to 300 kΩ

Graphical Abstract