Chemnitz – IWIS2012 – Tutorial 6, September 26, 2012Chemnitz – IWIS2012 – Tutorial 6, September 26, 2012

Electronics and Signals Electronics and Signals in Impedance Measurementsin Impedance Measurements

byby Mart Min Mart Min min@elin.ttu.eemin@elin.ttu.ee

Thomas Johann Seebeck Department of Electronics, Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology Tallinn University of Technology

Tallinn, EstoniaTallinn, Estonia

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Old Hansestadt Reval – Today’s TallinnOld 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

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____________________________________________________________________________________________________________________________________________________________

The term was introduced by

Oliver Heaviside, mathematician, physicist, and self-taught engineer:

July 1886 - impedance

Dec 1887 – admittance

Ohm's law, published in 1826:

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/IZ = V/I, where Z = R + jXZ = 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 ? What is impedance ?

33

Dynamic system identification is the final aim!Dynamic system identification is the final aim!

44

Goal: making theGoal: making the identification faster and simpler! identification faster and simpler!

55

Both magnitude Both magnitude (amplitude) (amplitude) and phase are to be measuredand phase are to be measured

Excitation generator (sine wave)

Amplitude

meter

Phase meter

V/ I

Amplifier .

Z

.

Vz’ Vexc

Iexc

_

Vz

_

Φz

. phase lag Φz

.

Vz

Re Ż = R Re Ż

Im Ż

Im Ż = X

Ż

Ż = R + j X

Ż = R + j X

Magnitude and phase measurement

66

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 detectionSynchronous or phase-sensitive detection

Excitation generator (sine wave)

LPF (filter)

V/ I

.

Z

.

Vz Vexc

Iexc

_

Vz · cos (Φ – φ )

Phase shifter

φ

Multiplyer

×

Phase lag Φz

- φ

Re Ż = R Re Ż

Im Ż

Im Ż = X

Ż

Ż = R + jX

phase lag Φphasephase lag Φ lag Φ

Synchronousdetection

77

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 detectionTwo-phase or quadrature synchronous detection

Excitation generator (sine wave)

V/ I

.

Z

Vexc

Iexc

.

Vz

Phase shifter

90º

LPF (filter)

Multiplyer

×

LPF (filter)

Multiplyer

×

_

Vz · cos (Φ ) = Re Ż = R _________

Re Ż

_________

Im Ż

_

Vz · sin (Φ ) = Im Ż = X

p h a se la g Φ

Vexc · sin (ω t)

Vexc · cos (ω t)

Fourier Transform

88

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 (Texc), 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?

Excitation current

Response voltage

Excit. Z(t)

Problems to be solvedProblems to be solved

99

. response Vz

1) excitation amplitude is strictly limited ! 2) excitation time is limited !

|Ż (f )|

(f )

Short-time DFT or FFT: directly or via binary transforms (Walsh, Hadamard)

Frequency: f 1 to f n

Timing/synchro: t 1 to t 2 Measurement time, Tm

. Response Vz(t)

Generator of excitation current Iexc(t)

|Z (ω,t)| Φ(ω,t) ReŻ (ω,t) ImŻ (ω,t)

Ż(t)

internal noise, a time-variant

nonlinear system

Results as

Spectrograms

outer noise

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

freq: f1 to f2

Generation ofexcitationwaveform

Cross

correlation

CVz(t),Vr(t,τ)

Fourier Transform

(DFT, FFT)

gz(t) Sz (jω,t) time: t1 to t2

excitation, Vexc response, Vz

Impedance

spectrogram

Ż

Focus:Focus: finding the bestfinding the best excitation waveforms excitation waveforms and signal processing methods and signal processing methods ffor the fast or the fast and wideband, scalable, and and wideband, scalable, and time dependent spectral analysistime dependent spectral analysis: :

intensity ( intensity (ReRe & & ImIm oror M M & & ΦΦ) versus frequency ) versus frequency ωω andand time time tt

Signals and signal processing Signals and signal processing in wideband impedance spectroscopyin wideband impedance spectroscopy

A

a – short rectangular pulse

Crest factor CF = Peak / RMS

A

t1t1t2

b – chirp pulse (t1 to t2)

covers BW (f1 to f2), scalable, acceptable CF=1.414

t1 t2

c – binary sequence (chirp pulse) from t1 to t2 covers BW from f1 to f2 , scalable, ideal CF=1.0

A

Δt

- very high CF (10 to 1000) - BW = 0 to 0.44(1/Δt), - low signal energy, - not scalable

Excitation

control

reference, Vr

1111

Fast simultaneous measurementat 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 Several sine waves simultaneously – Multisine excitation

1212

Sine wave signals and synchronous sampling: Sine wave signals and synchronous sampling: multisite and multifrequency measurementmultisite and multifrequency measurement

MultisiteMultisite (frequency distinction method, (frequency distinction method, slightly different slightly different ff11 and and ff22))

Multifrequency Multifrequency (sum of very different frequency sine waves)(sum of very different frequency sine waves)

1313

Multisine excitation: optimization (a sum of 4 equal level sine wave components – 1, 3, 5, 7f)

Sum of 4 sine waves Ai = 1, Φi = 0, CF=2.08

Sum of 4 sine waves Ai =1, Φi = opt, CF=1.45(the best possible case)

Normalized to ∑Ai = 1, Φi = opt: Vrmsi = 0.344, CF=1.45Normalized to ∑Ai = 1, Φi = 0: Vrmsi = 0.241, CF= 2.08

Sum of 4 sine waves Ai =1, Φi = 900, CF=2.83 (the worst possible case)

RMS levels of sine wave components in the multisine signal

the best caseΦi = opt; 0.344 Φi = 0; 0.241

Sine waves: A=1, RMS = 0.707

Φi = 90; 0.177 the worst case

14

Waveforms of wideband excitation signalsCrest Factor CF = (max level) / RMS value

Multisine waveform: Σsin

Chirp, chirplet / titlet: ch(t)

Binary sequences (BS)

A

Tch

+V

-V

0

T s

+ V

-V

0

Σsin = Σ Ai sin(ωi t), discrete spectrum

Ai V/ n, i = 2 to n max P 0.5 V2 max RMS 0.707 V CF = 1.38 to (2n)½

max Pexc = max P 0.5V2

Ideal signal-to-disturb. ratio S/ D (no disturbances)

ch(t) = A sin [ ω(t)dt], continuous spectrum

A = V, ω(t) = var, ω1 to ω2

P = 0.5 V2 RMS = 0.707 V CF 1.41

Pexc P = (0.4…0.5) V2

Good S/ D, complicated signal processing

- multifrequency binary sequence (MFBS), discrete spectrum, as signΣAisin(ωit); - binary chirp, cont. spectrum, as sign ch (t); - binary random, cont. spectrum, as MLS

P =1.0 V2 ( the highest possible level ! ) RMS =1.0 V

CF = 1 (the best possible value!)

Pexc < P = (0.6…0.9)V2

Lower S/ D, complicated processing, plenty of disturbing components

A1

T2 T1

+ V

- V

0

A2

∫

≈

≥

≤

≈

≈

≈

15

A. Scalability in frequency domain: bandwidth BW changes, Texc = const = 250 μs 1.0

-1.0

-0.8

-0.5

-0.2

0.0

0.2

0.5

0.8

250u0 25u 50u 75u 100u 125u 150u 175u 200u 225u

Texc = 250 μs

t

100m

1u

10u

100u

1m

10m

10M1k 10k 100k 1M

2.24 mV/Hz1/2

1.12 mV/Hz1/2

1 mV / Hz1/2

BW = 100 kHz

BW = 400 kHz

Texc = 1000 μs

Excitation energy Eexc = 0.5V2 ∙250 μs = 125 V2∙μs

Voltage Spectral Density @ 100 kHz = 2.24 mV/Hz1/2

Voltage Spectral Density @ 400 kHz = 1.12 mV/Hz1/2

Changes in the frequency span BW reflect in spectral density

48 cycles 12 cycles

Excitation time Texc = 250 μs = const

Scalable chirp signals:Scalable chirp signals: two chirplets 1 two chirplets 1

1616

B. Scalability in time domain: duration Texc changes, BW = const = 100 kHz 1.0

-1.0

-0.8

-0.5

-0.2

0.0

0.2

0.5

0.8

1m0 100u 200u 300u 400u 500u 600u 700u 800u 900u

Texc = 250 μs

Texc = 1000 μs

100m

1u

10u

100u

1m

10m

10M1k 10k 100k 1M

2.24 mV/Hz1/2

4.48 mV/Hz1/2

1 mV / Hz1/2

BW = 100 kHz

Energy E250μs = 125 V2∙μs Energy E1000μs = 500 V2∙μs

Voltage Spectral Density @ 250μs = 2.24 mV/ Hz1/2 Voltage Spectral Density @ 1000μs = 4.48 mV/ Hz1/2

Changes in the pulse duration Texc

reflect in spectral density

Bandwidth BW = 100 kHz = const

48 cycles 12 cycles

Scalable chirp signals:Scalable chirp signals: two chirplets 2 two chirplets 2

1717

10

100u

1m

10m

100m

1

10M1k 10k 100k 1M

-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/Hz1/2

BW = 100 kHz

Instant frequency , , rad/s - a linear frequency growth chfin Ttfdt

tdt /2

)(

Current phase , rad; chfin Ttfdttt 2/2)( 2

100kHzTch = 10 μs

Texc = Tch = 10 μs,

A very short Chirplet 3 - Half-cycle linear titlet A very short Chirplet 3 - Half-cycle linear titlet

chfin Ttfdttt 2/2)(sinsin 2Generated chirplet 1818

Rectangular (binary) wave based impedance measurementRectangular (binary) wave based impedance measurement

Clock

The current switch operates as a multiplier!

V-to-I

Vin

S1

I –

I+ I

Driving Flip-Flop

transor

S2

+

–

Vout

I-to-V

1 3 5 7 9 11 13 15 17 19 21 23 25 ht h = 1, 3, 5, 7, 9, 11,A1

9 11 13 15 17 1

A1 t

A1 = (4/π)A > A

h = 1, 3, 5, 7, 9, 11, ...

A3 = (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 A1

A5 = (4/5π)A

1919

Ż

Ternary SD

reference signal excitation signal

response

+1 -1

0 +1 -1

0

1.0

-1.0

-0.5

0.0

0.5

1.00.0 0.2 0.4 0.6 0.8

1.0

0.0

0.2

0.4

0.6

0.8

260 5 10 15 20FIG. 2B

Ternary signals – waveforms and spectraTernary signals – waveforms and spectra

-111 reference

excitation

7th 11th

13th

17th

19th

23rd

3rd 5th

1st

9th 25th

- coinciding spectral lines

2020

+1

-1

Ternary SD

reference

0 -1

+1

0 response

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

2121

Generator of binary and ternary signals

22

QQ

C ____

CE QQ

CE QI

C ____

QI

RG

CLOCK

FFQ

FFI

OR

XOR

"1"

"0"

D1 Q 1

Q 2

Q 3

Q 4

Q 5

RG Q 6

Q 7 C

Q 8

Q 9

Q10

Q11

Q12

Q13

D14 Q14

0°

6°

12°

18°

24°

30°

36°

42°

48°

54°

60°

66°

72°

78°

84°

90°

NAND

Binary 2-level signals

Ternary3-level signals

Different rectangular waveforms (binary and ternary) of excitation signals

(b)

(c)

(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

0

18

30

Spectra and power of binary/ternary chirpsSpectra and power of binary/ternary chirps

Binary(0): Pexc= 0.85P Ternary(18): Pexc 0.93P

Ternary(30): Pexc 0.92P

Binary(0)

Trinary(30)

Trinary (21.2): Pexc= 0.94P – max. possible!

Pexc – excitation powerwithin (BW)exc=100kHz

100kHz

2424

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

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)

2626

Based on diamond transistor

How to make a current sourcesHow to make a current sources

Cparasitic

Based on current feedback

is a problemCparasitic

2727

Simple resistive V-to-I converter

How to make passive current sourcesHow to make passive current sources

Cparasitic

Compensated resistive V-to-I converter

is a problem

2828

Tends to be unstable (both negative and positive feed-backs)

Howland current sourceHowland current source

Cparasitic is a problem

2929

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 !

Dual differential amplifier

AC

0.9XZ

Instru-mentationamplifier

0.9X U:Uz

+

-

+

-

Shunt

How to make the current excitation better and to couple the How to make the current excitation better and to couple the excitation signal with the impedance to be measuredexcitation signal with the impedance to be measured

Cparasitic

3030

Dual differential amplifier

AC

0.9X

Trans- impedance

amplifier

ZInstru-

mentationamplifier

0.9

X U:Uz

U:Iz

+

-

+

-

+

-

Shunt

Programmableshunt

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?How to make the excitation more accurate?

Cparasitic

An alternative: voltage measurement on a shunt

3131

How to measure voltage drop across the impedanceHow to measure voltage drop across the impedance

Instrumentation amplifier (IA)SolutionGood BW can be reached when the IA is constructed from separate high performance op-amps.

Magnitude

Phase

Voltage aquisition amplifier

3232

1) 1) Frequency stepping or sweeping Frequency stepping or sweeping together withtogether with multiplexing of multiplexing of traditional traditional sine wave sine wave excitation is excitation is tootoo time consuming, especially when time consuming, especially when the the dynamic impedances dynamic impedances are to be are to be measured.measured.

2) 2) Simultaneous applying of several sine wave Simultaneous applying of several sine wave excitationsexcitations with different frequencies with different frequencies ((multisinemultisine) ) is a better, but more complicatedis a better, but more complicated solution. solution.

3) 3) We propose specific chirp based excitation signals as We propose specific chirp based excitation signals as chirpletschirplets and and titletstitlets, also , also binary and ternary chirpsbinary and ternary chirps and chirplets and chirplets for carrying out the fast and wide band for carrying out the fast and wide band scalable scalable spectroscopyspectroscopy of dynamic objects. of dynamic objects.

4) 4) Also Also multi-sine binary and ternary multi-sine binary and ternary (trinary) (trinary) signalssignals are proposed for excitationsare proposed for excitationsin impedance spectroscopy and tomography.in impedance spectroscopy and tomography.

5) 5) Synthesis of the above mentioned excitation signals enables to provide independentSynthesis of the above mentioned excitation signals enables to provide independent,, time and frequency domain scalable spectroscopytime and frequency domain scalable spectroscopy, , which is which is adaptadaptableable to given to given measurement situation (speed of impedance variations, frequency range, measurement situation (speed of impedance variations, frequency range, S/NS/N level level).).

6) Use discrete and digital signal generation/processing methods as much as possible, 6) Use discrete and digital signal generation/processing methods as much as possible, but you can never avoid analog part of the measuring system.but you can never avoid analog part of the measuring system.

7) Be careful with current sources, avoid if possible.7) Be careful with current sources, avoid if possible.

8) Using of field programmable gate arrays (FPGA) is challencing. Both, microcontrollers 8) Using of field programmable gate arrays (FPGA) is challencing. Both, microcontrollers and signal processors, make troubles with synchronising and throughput speed.and signal processors, make troubles with synchronising and throughput speed.

SummarySummary

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