1. Chemnitz – IWIS2012 – Tutorial 6, September 26, 2012 Electronics and Signals in Impedance Measurements by Mart Min by Mart Min min@elin.ttu.ee min@elin.ttu.ee Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology Tallinn, Estonia 1

2. Old Hansestadt Reval – Today’s Tallinn Tallinn / Reval was: - a member of the Hanseatic League (since 1285) -ruled under the Lübeck City Law (1248-1865) - capital of the Soviet Socialist Republic of Estonia within the Soviet Union (1940-1991) Tallinn is: -capital of the Republic of Estonia, EU member state since 2004 -currency: EURO since Jan 2011 2

3. The term was introduced by Oliver Heaviside, mathematician, physicist, and self- taught engineer: July 1886 - impedance Dec 1887 – admittanc e Ohm's law, published in 1826: Z = V/IZ = R + jX The concept of electrical impedance generalizes Ohm's law to AC circuit analysis. Unlike electrical resistance, the impedance of an electric circuit can be a complex number: Z = V/I, where Z = R + jX, and R is a real part and X is an imaginary part. Electrical impedance (or simply impedance) is a measure of opposition to sinusoidal electric current In 1893, Arthur Edwin Kennelly presented a paper “on impedance" to the American Institute of Electrical Engineers in which he discussed the first use of complex numbers as applied to Ohm's Law for AC What is impedance ? 3

4. Dynamic system identification is the final aim! 4

5. Goal: making the identification faster and simpler! 5

6. Both magnitude (amplitude) and phase are to be measured Both magnitude (amplitude) and phase are to be measured  Magnitude and phase measurement 6

7. Synchronous or phase sensitive detection (demodulation) suppresses additive noise and disturbances and gives the results (Re or Im) in Cartesian coordinates Synchronous or phase-sensitive detection phase lag Φ phase phase lag Φ lag Φ Synchronous detection 7

8. Two-phase (inphase and quadrature, I & Q) synchronous detection (the simpliest Fourier Transform) enables simultaneous measurement of Re and Im parts Two-phase or quadrature synchronous detection Fourier Transform 8

9. Impedance should be measured at several frequencies – a wide band spectral analysis is required. Impedance is dynamic - the spectra are time dependent. Examples: (a) cardiovascular system; (b) pulmonary system; (b) microfluidic device. Classical excitation – a sine wave – enables slow measurements. Excitation must be: 1) as short as possible to avoid significant changes during the spectrum analysis; 2) as long as possible to enlarge the excitation energy for achieving max signal-to- noise ratio. Which waveform is the best one? A unique property of chirp waveforms – scalability – enables to match the above expressed contradictory requirements (1) and (2) and the needs for spectrum bandwidth (BW), excitation time (T exc ), and signal-to-noise ratio (S/N). The questions to be answered: a. A chirp wave excitation contains typically hundreds and thousands of cycles, if the impedance changes slowly. What could be the lowest number of cycles applicable when fast changes take place? b. Are there any simpler rectangular waveforms to replace the sine waves and chirps in practical spectroscopy? Problems to be solved 9

10. Focus: finding the best excitation waveforms for the fast and wideband time dependent spectral analysis: intensity (Re & Im or M & φ) versus frequency ω and time t 10

11. freq: f 1 to f 2 Generation of excitation waveform Cross correlation C {V z (t),V r (t,τ)} Fourier Transform (DFT, FFT) gz(t)gz(t) S z (jω,t) time: t 1 to t 2 excitation, V exc response, V z Impedance spectrogram Ż Focus: finding the best excitation waveforms and signal processing methods for the fast and wideband, scalable, and time dependent spectral analysis: intensity (Re & Im or M & Φ) versus frequency ω and time t Signals and signal processing in wideband impedance spectroscopy A a – short rectangular pulse Crest factor CF = Peak / RMS A t1t1 t1t1 t2t2 b – chirp pulse (t 1 to t 2 ) covers BW (f 1 to f 2 ), scalable, acceptable CF=1.414 t1t1 t2t2 c – binary sequence (chirp pulse) from t 1 to t 2 covers BW from f 1 to f 2, scalable, ideal CF=1.0 A Δt Δt - very high CF (10 to 1000) - BW = 0 to 0.44(1/Δt), - low signal energy, - not scalable Excitation control reference, V r 11

12. Fast simultaneous measurement at the specific frequencies of interest! + Simultaneous measurement/analysis; + Frequencies can be chosen freely; +/- Signal-to-noise level is low but acceptable; − Both limited excitation energy and complicated signal processing restrict the number of different frequency components. Several sine waves simultaneously – Multisine excitation 12

13. Sine wave signals and synchronous sampling: multisite and multifrequency measurement Multisite (frequency distinction method, slightly different f 1 and f 2 ) Multifrequency (sum of very different frequency sine waves) 13

14. Multisine excitation: optimization (a sum of 4 equal level sine wave components – 1, 3, 5, 7f) Sum of 4 sine waves A i = 1, Φ i = 0, CF=2.08 Sum of 4 sine waves A i =1, Φ i = opt, CF=1.45 (the best possible case) Normalized to ∑A i = 1, Φ i = opt: Vrms i = 0.344, CF=1.45 Normalized to ∑A i = 1, Φ i = 0: Vrms i = 0.241, CF= 2.08 Sum of 4 sine waves A i =1, Φ i = 90 0, CF=2.83 (the worst possible case) RMS levels of sine wave components in the multisine signal the best case Φ i = opt; 0.344 Φ i = 0; 0.241 Sine waves: A=1, RMS = 0.707 Φ i = 90; 0.177 the worst case 14

15. Waveforms of wideband excitation signals Crest Factor CF = (max level) / RMS value ∫ ≈ ≥ ≤ ≈ ≈ ≈ 15

16. A. Scalability in frequency domain: bandwidth BW changes, T exc = const = 250 μs Texc = 250 μs t 2.24 mV/Hz 1/2 1.12 mV/Hz 1/2 1 mV / Hz 1/2 BW = 100 kHz BW = 400 kHz Texc = 1000 μs Excitation energy Eexc = 0.5V 2 ∙250 μs = 125 V 2 ∙μs Voltage Spectral Density @ 1 00 kHz = 2.2 4 mV / Hz 1/2 Voltage Spectral Density @ 4 00 kHz = 1.1 2 mV / Hz 1/2 Changes in the frequency span BW reflect in spectral density 48 cycles 12 cycles Excitation time Texc = 250 μs = const Scalable chirp signals: two chirplets 1 16

17. B. Scalability in time domain: duration T exc changes, BW = const = 100 kHz Texc = 250 μs Texc = 1000 μs 2.24 mV/Hz 1/2 4.48 mV/Hz 1/2 1 mV / Hz 1/2 BW = 100 kHz Energy E 250 μs = 125 V 2 ∙ μs Energy E 1000 μs = 500 V 2 ∙ μs Voltage Spectral Density @ 250μs = 2.24 mV / Hz 1/2 Voltage Spectral Density @ 1 000μs = 4.4 8 mV / Hz 1/2 Changes in the pulse duration T exc reflect in spectral density Bandwidth BW = 100 kHz = const 48 cycles 12 cycles Scalable chirp signals: two chirplets 2 17

18. - 40 dB/dec RMS spectral density (relative) 10 1 10 -1 10 -2 10 -3 10 -4 1k 10k 100k 1M f, Hz 2.26 mV / Hz 1/2 BW = 100 kHz Instant frequency,, rad/s - a linear frequency growth Current phase, rad; 100kHz T ch = 10 μs Texc = T ch = 10 μs, A very short Chirplet 3 - Half-cycle linear titlet Generated chirplet 18

19. Rectangular (binary) wave based impedance measurement 1 3 5 7 9 11 13 15 17 19 21 23 25 h t h = 1, 3, 5, 7, 9, 11,  A 1 9 11 13 15 17 1 A1A1 t A 1 = (4/π)A > A h = 1, 3, 5, 7, 9, 11,... A 3 = (4/3π)A tA A problem: sensitivity to all the odd higher harmonics ! contains the products of all odd higher harmonics in addition to the response to signal component A 1 A 5 = (4/5π)A 19

20. FIG. 2B Ternary signals – waveforms and spectra -11 1 reference excitation 7 th 11th 13th 17th 19th 23rd 3rd 5th 1st 9th 25th - coinciding spectral lines 20

21. Ternary signal processing – 3-positional synchronous switching 21

22. Generator of binary and ternary signals 22 Binary 2-level signals Ternary 3-level signals

23. Different rectangular waveforms (binary and ternary) of excitation signals (b)(b) (c)(c) (a)(a) ( a ) – binary (2-state) chirp, scalable ; ( b ) – binary pseudorandom (MLS), not scalable, waveform is quite similar to the multifrequency binary signal, see next slide ( c ) – ternary (3-state) chirp, scalable. 23

24. 00 18  30  Spectra and power of binary/ternary chirps Binary(0  ): P exc = 0.85P Ternary(18  ): P exc  0.93P Ternary( 30  ): P exc  0.92P Binary(0  ) Trinary(30  ) Trinary (21.2  ): P exc = 0.94P – max. possible! P exc – excitation power within (BW) exc =100kHz 100kHz 24

25. Synthesized multifrequency binary sequences (4 components – 1, 3, 5, 7f) Equal-level components Growing-level components ! Decreasing levels: usual case! A simple rectangular waveform 25

26. The spectrum contains 14 components at 1, 2, 4, 8f,..., until 8192 f with mean RMS value of 0.22 each. Max level deviation is +/- 3.5 %; 67 % of the total energy is concentrated onto desired frequencies A section of one binary wave sequence: 14 frequency components and 81920 samples While multisine signals concentrate all the energy into wanted spectral lines, the binary ones only about 60 to 85% Despite of losses (15 to 40%), the energy of the desired frequency components in binary sequences have greater value than the comparable components in multisine signals ! Example: optimized multifrequency binary sequence (14 binary rated components – 1, 2, 4, 8 f,...,8192 f) 26

27. Based on diamond transistor How to make a current sources C parasitic Based on current feedback is a problem C parasitic 27

28. Simple resistive V-to-I converter How to make passive current sources C parasitic Compensated resistive V-to-I converter is a problem 28

29. Tends to be unstable (both negative and positive feed-backs) Howland current source C parasitic is a problem 29

30. We designed a current source using differential difference amplifier. We got the output impedance: 250 kΩ. At higher frequencies a part of excitation current is flowing down through a parasitic capacitance 40pF. We added a voltage follower (more exactly, an amplifier with a gain 0.9) and reduced the parasitic capacitance about 10 times ! How to make the current excitation better and to couple the excitation signal with the impedance to be measured C parasitic 30

31. We added a trans-impedance amplifier for the measurement of excitation current. Result – degradation of the current source at higher frequencies can be taken into account How to make the excitation more accurate? C parasitic An alternative: voltage measurement on a shunt 31

32. How to measure voltage drop across the impedance Instrumentation amplifier (IA) Solution Good BW can be reached when the IA is constructed from separate high performance op-amps. Magnitude Phase Voltage aquisition amplifier 32

33. 1) Frequency stepping or sweeping together with multiplexing of traditional sine wave excitation is too time consuming, especially when the dynamic impedances are to be measured. 2) Simultaneous applying of several sine wave excitations with different frequencies (multisine) is a better, but more complicated solution. 3) We propose specific chirp based excitation signals as chirplets and titlets, also binary and ternary chirps and chirplets for carrying out the fast and wide band scalable spectroscopy of dynamic objects. 4) Also multi-sine binary and ternary (trinary) signals are proposed for excitations in impedance spectroscopy and tomography. 5) Synthesis of the above mentioned excitation signals enables to provide independent, time and frequency domain scalable spectroscopy, which is adaptable to given measurement situation (speed of impedance variations, frequency range, S/N level). 6) Use discrete and digital signal generation/processing methods as much as possible, but you can never avoid analog part of the measuring system. 7) Be careful with current sources, avoid if possible. 8) Using of field programmable gate arrays (FPGA) is challencing. Both, microcontrollers and signal processors, make troubles with synchronising and throughput speed. Summary Summary 33