m_pulse - ZAHNER

m_pulse  - ZAHNER
High Current Interrupt Measurement ´HCI´
© Zahner 06/2011
Pulse
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Pulse
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1. Introduction _______________________________ 4
2. Hardware Setup ____________________________ 4
3. Software __________________________________ 5
3.1 Setup of the Current Transient ....................................................6
3.2 Setup of the Potentiostat Default State .......................................7
3.3 Setup of Trigger Parameters ........................................................8
3.4 Setup of Pulse Probe Attenuation ...............................................8
3.5 Evaluation Control ........................................................................9
3.6 Initiate an HCI measurement ......................................................10
3.7 Export of the Transient ...............................................................11
3.8 Analysis of HCI measurements..................................................11
3.9 Saving HCI measurements .........................................................12
Pulse
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1. Introduction
This manual describes the necessary steps to set up an HCI experiment by means of the Zahner HCI
instrumentation. The first part explains how to connect the hardware. Then is described, how the
PULSE and the TRC software are to configure, in order to enable and perform HCI measurements.
Finally the user is informed about the immediate Ohmic drop determination and how to save and
export the data for further analysis.
For a deeper inside into the basics and the technique of HCI, please refer to the attached extract from
our El.Apps. issue 1/2002, p. 1-6.
2. Hardware Setup
Besides of the system under test (A, in the example below sketched as a fuel cell) the experimental
setup consists of a Zahner slave potentiostat unit (B), usually an electronic load from the Zahner ELseries. An electrochemical workstation Zennium or IM6, C (operated by a PC, not part of the scheme)
acts as a controller and as data procession unit. C is equipped with an EPC42 slave potentiostat
controller. The first channel connector of the EPC should be wired to the slave potentiostat used. C
Pulse
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also carries a TR8M transient recorder module, which has to collect the pulse transient data with high
time resolution.
The signals from the cell under test are not connected directly to the TR8M. In order to scale down the
pulse signals to a level appropriate for the TR8M, a Pulse Probe, D, is wired between measuring
object and the CH0 input. The pulse probe also provides galvanic isolation and protects the TR8M
from hazardous high energy EMP interferences, typically accompanying HCI measurements.
The slave potentiostat has to establish the default conditions at the cell under test. For potentiostatic
control, both the power feeding lines as well as the voltage sensing lines have to be connected, like
indicated in the drawing. In a galvanostatic experiment the voltage sensing lines may be omitted in
principle, but one should to use the complete wiring for a better control and security.
Electrode
of sample
Positive
Negative
Color of current
leading wires EL
Red
Blue
Color of sense cable
BNC socket of Pulse
Probe
EL
Pulse Probe
Black
Black
Shielding
Blue
Blue
Center pin
Due to the unipolar range of an EL slave potentiostat, the cell MUST be connected in a way, that the
positive polarity electrode (cathode, the O2-side of a fuel cell) is connected to the lower (+), and the
negative polarity electrode (anode, the H2-side of a fuel cell) is connected to the upper (-) outlet of the
EL (for more details, please refer to the EL manual). This wiring corresponds to a positive load current
and a negative rest potential measured.
Although the pulse probe provides AC-coupling it should be connected as shown in the picture and
table above. Otherwise sign of the transients will swap and the trigger presets in the software will not
match.
3. Software
Please enter the PULSE software after activating the “time domain” pop-up menu in the Thales shell:
After a successful installation of the HCI hardware arrangement, the PULSE menu is used to trigger a
measurement, evaluate the Ohmic drop contribution and save the data for further analysis.
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3.1 Setup of the Current Transient
The device and current used for the transient is set by using the control potentiostat button of the
Pulse software. Choose the device for the current transient, here EL300 as device 1, and the current,
here 10 A. There are two possible default states of the potentiostat. If the potentiostat is switched off,
as shown in the picture below, the Pulse software will switch the potentiostat automatically on for a
settling time given in the Pulse setup before recording the current interrupt. The other option is to have
the potentiostat switched on as default state and only switch it off shortly for the transient
measurement. The setting made in the testsampling must correspond to the setup of the pulse as
described in chapter 3.2.
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3.2 Setup of the Potentiostat Default State
The pulse setup must be configured to match the default state of the potentiostat set in the
testsampling. To enter the pulse setup click the setup button in the Pulse main screen.
Toggle between the default states by clicking on the on/off button. In case the real state does not
match the actually selected one, the HCI-trigger-button “shoot” is disabled.
ON
The potentiostat is off for the duration time period of the current
interrupt (≈0.2s). Before and after the pulse it is active (on). This is
usually the
Default state for fuel cell HCI measurements.
OFF
The potentiostat is on only during a settling time period just before
the current interrupt measurement and is switched off for the rest of
the time. This is usually the
Default state for battery HCI measurements.
The settling time period, active in the “default potentiostat state = off” mode, should normally be
chosen just long enough to allow electronic settling (between 0.5s up to some s).
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3.3 Setup of Trigger Parameters
Before an HCI measurement can be “shot”, the user should complete the necessary settings of the
transient recorder to prepare the instrument for a correct triggering capability. Use the “TRC” entry to
enter the transient recorder menu. Please refer to the TRC manual for more details about TRC.
Entering PULSE will pre-configure the transient recorder due to the requirements of
HCI, but apart from some triggering adjustments: The optimum triggering conditions
usually change with the object under test, with the load conditions and the
adjustments of the pulse probe. Therefore the corresponding settings of the transient
recorder have to be adjusted accordingly, but:
Do not change any settings in the TRC menu, except trigger level and polarity!
For a correctly connected cell under test, controlled by an EL slave potentiostat, the load current is
always positive. An interrupt will therefore cause a current transient into negative direction (from the
steady state mean value down to zero). This is accompanied by a potential transient into negative
direction. Therefore a negative trigger level as well as a negative trigger slope has to be chosen.
The selection of the level value is not very critical, but nevertheless a little bit more tricky than slope
and polarity: for best case accuracy, it should be between 20% to 50% of the Ohmic drop step height
expected. Too low (absolutely) level selected may cause spontaneous triggering on noise, too high
(absolutely) level will prevent triggering. If you are uncertain, perform some test-shots to find out the
best value.
In order to check or change the steady state conditions, one may use the
“control potentiostat” entries from both the PULSE as well as the TRC menu.
In a typical HCI measurement condition, the mean (steady state) current should
be at least 5 A or higher. The height of the potential pulse one may expect, is
the product between the current at the interrupt time (in a fuel cell system
usually identical with the steady state current) and the Ohmic contribution. Take
25% of this value as trigger level.
3.4 Setup of Pulse Probe Attenuation
The direct input of the transient recorder allows a dynamic range of ±2V. The really observed pulse
may have a much higher initial amplitude due to overshot and ringing, depending on the parasitic
inductance of the current carrying circuit. This can overload or even damage the inputs of the TR8M.
Therefore the pulse probe provides galvanic isolation and attenuation between the sample and the
inputs of the TR8M.
In the HCI setup menu the user can select the sensitivity range for the pulse
response. Use the more sensitive ranges (for instance /2) for lower current and
lower Ohmic drop, for instance state “/2” for single cell fuel cells. Use the less
sensitive ranges for instance in fuel cell stack measurements. Otherwise
nonlinear clipping of the initial pulse response may reduce the accuracy of the
result.
The software cannot check, if the physical state of the attenuator selector fits the state of the HCI
setup, therefore:
Be sure, that the HCI setup fits the physical state of the pulse probe!
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The signal amplitude is attenuated to the dynamic range of the TR8M in the following manner:
Direct input to TR8M, no attenuation
Dynamic range: ±2 V, no galvanic isolation.
Only for testing purposes!
Input through Pulse Probe, divisor 2
Dynamic range: ±4 V, galvanic isolation
Input through Pulse Probe, divisor 8
Dynamic range: ±16 V, galvanic isolation
Input through Pulse Probe, divisor 32
Dynamic range: ±64 V, galvanic isolation
After changes of the probe sensivity in the HCI setup it is recommended to control the trigger level.
3.5 Evaluation Control
The HCI measurement setup provides the possibility to edit the parameters for the automatic Ohmic
drop calculation. In this process, the frequency range between the “lower frequency limit “ and the
“upper frequency limit “ is analysed. The minimum value of the impedance modulus is taken then as
the Ohmic share estimate. Besides this, for the calculation of the scalar impedance spectrum and for
the reverse ZHIT transformation (see addendum), leading to a phase angle course approximation,
different smoothing operations are used. Normally it is not necessary to change the pre-configured
widths of 0.5 and 2 respectively. For very noisy measurements, take “wider” smoothing parameters
(according a wide Gaussian weighting window).
When leaving the HCI setup page, the setup data are stored, besides the trigger adjustment
information for the transient recorder. The settings will be recalled again after a restart of Thales.
Pulse
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3.6 Initiate an HCI measurement
If all conditions of an HCI measurement are met, the SHOOT button gets active. Trigger the HCI
measurement by clicking on this button.
If the SHOOT button is not active check:
• State of the potentiostat in testsampling and default state Pulse setup match.
• In case of default on the current is more than 2 A.
Starting conditions not met
Starting conditions met
Start interrupt measurement
The TRC panel will pop up, displaying an empty graph data section (initially), or the last shot curve
graph. The PULSE software will interrupt the cell current for about 0.2s, while the transient recorder
waits for a triggering signal. If a wiring problem exists or if the trigger condition settings are not
selected properly, no trigger event will take place. A message will pop up, giving a suggestion for the
correct trigger level.
Please note this suggestion relies on the correct wiring as described in chapter 2. Otherwise the
suggestion will not be correct. After checking the wiring and the trigger settings try another shot from
the pulse main screen.
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After a successful shot, the resulting curve displayed should exhibit a negative going step function,
with the step (trigger event) located around 30 µs.
Now the transient can be viewed, zoomed, exported etc. in the usual way like described in the TRC
manual. By means of the “file operations” menu, the transient raw data can be saved for later analysis.
The most effective way for analysis is getting back to the PULSE menu by leaving the TRC panel.
3.7 Export of the Transient
Using the outputs button the transient can be exported either as ASCII text or as graphics. The ASCII
text can either be saved on disk as a file, copied to the clipboard or pasted directly to the Thales
editor.
3.8 Analysis of HCI measurements
The PULSE menu provides the possibility for an instant analysis. For details of
the analysis process, please refer to the addendum. The evaluation is based on
the reconstruction of an impedance spectrum, belonging to the actual pulse
response. Assumed, that previously performed calibration measurements are
representative for the (un-observed) actual current course within a certain
accuracy, the (scalar) impedance spectrum can be calculated from the fourier
transform of the observed voltage pulse, divided by the fourier transform of the
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normalized current response available from the calibration results. The quotient is then scaled by the
current measured at the time just before the interrupt.
The spectrum found is examined for the impedance minimum within the frequency range, selected in
the setup. This minimum value is then displayed as the Ohmic share estimate.
Scalar impedance spectrum, together with the reconstructed phase angle, found by an inverse
ZHIT approximation. The yellow line within the dotted black lines of the frequency limit marks
the location of the impedance modulus minimum.
3.9 Saving HCI measurements
An even more precise analysis can be done, if the resulting spectrum is passed to the SIM equivalent
circuit simulation and fitting software.
For that, click this button and call the file manager. The calculated
impedance spectrum data can be saved. Later on it can be loaded in the
usual way into the SIM software for further analysis.
Current Interrupt Technique Measuring low impedances at high frequencies
F. Richter, Siemens AG, KWU, Erlangen, Germany, [email protected]
C.-A. Schiller, Zahner-elektrik, Kronach, Germany, [email protected]
N. Wagner, DLR, Stuttgart, Germany, [email protected]
- imaginary part
If a power generating device is examined, its
dynamic electrical equivalence generally will appear
as a network which represents anode, cathode,
membrane, electrolyte, and connectors.
The specific losses of every partial impedance of
the network contribute to the overall efficiency of the
device. The porous layers of anode and cathode,
responsible for the charge transfer reaction,
normally play a major role. Other contributions seem
to be much less important. There is the resistance of
the electrolyte or the membrane as well as the
resistance of contacts and connectors. A dynamic
part is added by the inductance of the body and the
connectors.
anode
c o n n e c to r
re s is ta n c e
anode
F a ra d a y ic
p ro c e s s
in s id e th e
p o ro u s
s y s te m
*
m e m b ra n e +
e le c tro ly te
re s is ta n c e
anode
d o u b le la y e r
c a p a c ita n c e
*
anode side
porous
distributed
impedance
c a th o d e
d o u b le la y e r
c a p a c ita n c e
*
cathode side
porous
distributed
impedance
total
total
inductive Ohmic
share
loss
L
R
.
Fig. 2: The appearance of ohmic share and stray
inductance in a fuel cell spectrum
EIS allows to separate all contributions and to
determine the ohmic part in the high frequency
region of a spectrum, where the impedance curve
intersects the real axis. The inductance is shown at
successive higher frequencies in the diagram. But
there is one great restriction: Measuring impedance
always means to measure two signals, current and
voltage.
*
∼
Z=
∼
to ta l
in d u c tiv e
s h a re
*
real part
to ta l
o h m ic
lo s s
e q u iv a le n c e
b u lk
in d u c ta n c e
c a th o d e
F a ra d a y ic
p ro c e s s
in s id e th e
p o ro u s
s y s te m
a n o d e s id e
p o ro u s
d is trib u te d
im p e d a n c e
L⋅ ω
R
*
anode
c o n n e c to r
in d u c ta n c e
anode arc
*
Nevertheless,
the
ohmic
part
(electrolyte,
membrane, connectors) plays an important role
regarding the performance of the device and
accounts sometimes for the main part of the overall
losses. It is very sensitive to degradation caused by
corrosion and thermal stress.
cathode arc
E
∼
I
I
c a th o d e s id e
p o ro u s
d is trib u te d
im p e d a n c e
∼
E
c a th o d e
c o n n e c to r
re s is ta n c e
c a th o d e
c o n n e c to r
in d u c ta n c e
Fig. 1: Simplified electrical equivalent circuit of a typical
electrochemical power source device
Z
Current
E noise ∝
∼
ω , x, y, z, I
Interfering
Potential
Enoise1
Magn.
Coupl.
Z
Interesting
Potential
Current Flow
In applications with dynamic load changes the
inductive parts, for example in a laptop computer
battery or in electromotive applications, are limiting
the maximum pulse load available.
= Impedance of the Object of Interest
W ith the Extensions in Space x, y, z.
Measured
Potential
Interfering
Potential
Enoise2
Fig. 3: Basic impedance measurement circuit – principle
(top) and detail (bottom)
A closer look at the circuit in figure 3 shows that the
potential information does not only contain the
interesting part from the site of the connecting
terminals. It is rather contaminated by dynamically
induced error voltages. These errors are caused by
unavoidable mutual induction from the magnetic
field of the current circuit.
The interference increases with increasing
frequency and with the strength of the magnetic field
of the current. It depends on the geometry and
grows with the dimensions of the object. For the
investigation of power sources this means: The
more you scale up, the lower is the available upper
frequency limit (fg). Finally, there is a limit for the EIS
at low ohmic objects. At a rough estimation you can
calculate with:
the interruption results in a breakdown of the current
to at least small values within a short time. In this
case, the potential will be disturbed much less by
mutual induction compared with an EIS
measurement.
In theory, the ohmic contribution to the overall
impedance can be easily seen from the height of the
fast rectangular step of the potential. For the
evaluation a linear step model is commonly used.
T im e / µ s
E /m V
0
-5 0
-1 0 0
fg ≈ 1 MHz * |Z|min / Ohm
As a consequence, the window for getting an Ohmic
resistance information by means of the EIS gets
smaller for bigger cells. For certain systems, the
window will be closed.
What can be done to complement the EIS under
these conditions? The question is answered by the
well known current interrupt technique, which does
not need the knowledge of two signals
simultaneously. The principle is depicted in figure 4
and explained in the following:
-1 5 0
-2 0 0
0
E /m V
200
400
600
800
T im e / µ s
0
-5 0
-1 0 0
e le c tro n ic s w itc h
p o te n tia l
m e a s u re m e n t
-1 5 0
-2 0 0
10
lo a d
20
Fig. 5: Typical current interrupt potential step response.
Long (top) and short (bottom) term response of a single
cell PEM fuel cell at 80 A.
o b je c t
s te a d y s ta te
c u rre n t I
ze ro c u rre n t
lin e a r
s te p ∆ E
p o te n tia l
u n d e r lo a d
O h m ic s h a re =
∆ E
tim e o f
in te rru p tio n
15
T im e
I
Fig. 4: Principle of current interrupt technique to determine
the ohmic share
A steady-state current is interrupted by a switch.
The step response of the potential is sampled and
analysed assuming that the current drops
instantaneously from its stationary value to zero.
In practice, the settling time depends on the
electromagnetic energy stored in the parasitic
capacity and inductivity of the cell arrangement on
the one hand and the damping process on the other
hand. Provided that the set-up is built appropriate,
But this evaluation suffers from the fact that the
analysis of the time domain data is interfered by the
“ringing” in the signal as a result of the parasitic
resonance. In addition, the early phase of the
response is characterized by a non-linear behavior
due to the imperfect characteristics of the electronic
switch. Furthermore, the response of both doublelayers may follow soon after the interruption when
the concentrations of the involved species turn from
their steady state values to new ones without load.
All these effects bend and distort the expected ideal
shape of the potential step. Therefore, the automatic
analysis of pulse measurements by means of a
simple fit to a linear step model often leads to
inaccurate results.
Our aim was to improve the method in order to get
results of comparable reliability to the EIS. The
basic idea is not to evaluate the distorted step
function in the time domain. Instead, after a
transformation of the data into the frequency
domain, the resulting spectrum and all parasitic
effects can be analysed by means of EIS methods.
total
porous
distributed
impedance
to the modulus of the impedance of the unknown
object.
total
damped
inductive
share
total
Ohmic
share
L
R
Rdmp
Rsw
|impedance| / Ω
*
10m
Csw
f0
f1
1m
Csw,R sw: Capacitance and resistance of the electronic switch.
Rdmp: Damping of the inductive share due to spatial distribution.
Zmin
Fig. 6: Approximate equivalent circuit for a complete high
current
interrupt
measurement
set-up
of
an
electrochemical power source device.
100u
1K
In figure 6, a simplified equivalent circuit for a
complete HCI measurement set-up of a power cell is
shown. It contains the impedance of the active cell
part (circle), the integral inductance (L) and
resistance (R) and the parasitic effects of the switch
circuit. The resonance circuit is mainly built of the
series inductance, the double layer capacity and the
capacity of the electronic switch. It is responsible for
the overshot and “ringing” in the pulse response
signal.
T im e
I
E
E (t)
fro m
c a lib ra tio n
p ro c e d u re
I0
I(t)
0
E0
H a n n in g W in d o w
f(t) = E (t) ⋅ H (t)
h ig h p re c is io n
c o a x ia l re s is to r
Z o o m -F F T
G ( j ω ) = F (f(t))
R e fe re n c e
S p e c tru m
fre q u e n c y
fre q u e n c y
im pedance
A m p litu d e
S p e c tru m
S c a la r Im p e d a n c e
S p e c tru m
10K
100K
1M
8M
frequency / Hz
Fig. 8: Automatic evaluation of the ohmic share from the
scalar impedance function.
This scalar impedance spectrum can be used to
evaluate the ohmic share in a simple, automated
way: The user selects a reliable frequency range for
analysis, which excludes the parasitic resonance at
the high frequency end. The impedance minimum
within this range represents the ohmic share with an
acceptable accuracy of about 1 to 3%.
If you want to evaluate the response spectrum with
the standard methods of the EIS, beside the
impedance, the phase data will be necessary: For
this calculation a relation between impedance and
phase for all two pole impedance objects of
minimum phase can be used. The ZHIT1 relation
allows to calculate the modulus of the impedance
course from the course of the phase angle. It will
also be able to perform the inverse application, if
one uses the ZHIT in an iterative numeric way. This
is the way, our analysis software obtains a complete
spectrum.
The complex spectrum can now be analyzed in the
usual way, for instance, by means of simulation and
fitting of the equivalent circuit. According to our
experience, the ohmic share can be determined in
this way, with typically the double or triple accuracy
compared to the automatic minimum detection in
the scalar impedance function.
fre q u e n c y
Fig. 7: Principle scheme of the Zahner high current
interrupt data processing.
Figure 7 illustrates the essential steps for the
transformation of the time domain data into the
frequency domain. The potential response signal E
is sampled by a transient recorder. The numeric
algorithms use discrete Fourier transform methods
to achieve an effective analysis. In order to minimize
the errors caused by their application on single
events, a weighing function has to be applied. At
least, a Zoom FFT calculates the amplitude
spectrum in the frequency domain. A similar
procedure using a reference resistor was done for
calibration. The quotient of both spectra finally leads
Figure 10 is a sketch of the practical set-up of our
high current interrupt measurement arrangement of
a fuel cell. The electrochemical cell (A) is supplied
by means of an electronic load (B) or another type
of high power potentiostat to force the steady state
load conditions. Additionally, the potentiostat acts as
fast electronic switch for the current interruption.
1
W. Ehm, R. Kaus, C.-A. Schiller, W. Strunz: ZHIT - a
simple relation between impedance modulus and phase
angle... Electrochemical Society Proceedings 2000-24, 1
|im pedance| / Ω
10m
1m
100u
1K
10K
100K
1M
8M
frequency / Hz
⇓
ln | Z (η) | ≈ const. +
2
η
π η∫
0
π dϕ
ϕ (ω )d lnω − ⋅
(η)
6 d ln ω
⇓
Fig. 10: Practical set-up of a high current interrupt fuel cell
measurement arrangement
phase ο
90
45
0
-45
-90
1K
10K
100K
1M
8M
frequency / Hz
Fig. 9: Calculation of the phase angle from the impedance
1
modulus by means of the inverse application of the ZHIT
transform. The ZHIT equation shows that the impedance
modulus at the frequency η can be calculated from the
integral of the phase angle course ϕ(ω) within limited
frequency boundaries (η0 to η). A correction term
proportional to dϕ/dlnω enhances the accuracy.
The potentiostat is controlled by an electrochemical
workstation (D) including a high resolution transient
recorder. The recorder input is connected to the
potential sense lines of the cell along a so called
pulse probe (C). The main task of the pulse probe is
the galvanic isolation of the potential sense circuit
from the instrument in order to minimize
electromagnetic interference. On the other hand, it
is responsible for the protection of the instrument
input by means of an energy consuming clipping
circuit.
After a short ‘sampling shot’ during the interrupt, the
instrument switches on the current again, in order to
re-establish the steady state and to avoid potential
damage of the cell. The pulse response is analyzed
then by the software of the workstation as described
before.
A lot of test experiments under controlled conditions
have been done. The major experience is that,
compared with the standard EIS, the HCI is much
less sensitive to mutual induction artefacts. This is
illustrated by the example depicted in figure 11.
Here, we made test measurements at resistors
using two different, intentionally non-optimized
connection geometries. As you can see, the strong
in-phase mutual induction of the above example
leads to an inductive component which seems
unrealistically high in the case of the standard EIS.
The HCI method, however, leads to the almost
exact value.
With the other example, which shows a strong outof-phase mutual induction, one obtains almost the
same impedance functions, which has been omitted
here. Yet, the phase diagram shows paradox
behaviour for the standard EIS curve: The course
indicates capacitive characteristics! The phase
curve of the HCI experiment shows the correct sign
due to its origin from the ZHIT transform.
We also found that the HCI worked fine with power
generating devices. As an example, the results of
an EIS and a HCI experiment at a high temperature
fuel cell are depicted in figure 12. The cell has been
driven with air and humidified hydrogen and
generated more than four Amperes at a potential
exceeding 0.73 Volts. In both experiments the best
case wiring was used to reduce the mutual induction
contribution.
The original HCI potential step response is plotted
on top of figure 12. At the bottom, the transformed
impedance (circles) as well as a comparative
impedance measurement (rhombi) are drawn. As
one can see, the methods complement each other
for the different frequency ranges. In this special
case, the frequency limit for the EIS experiment to
get accurate information on the ohmic share is not
exceeded. Therefore, both methods deliver the
correct results.
impedance
100m
10m Ω
T im e / µ s
E /m V
Ω
0
-5 0
30m
A
A
-1 0 0
10m
B
-1 5 0
10
1K
100K
-2 0 0
frequency / Hz
Current load lines
0
2 0 0
4 0 0
6 0 0
8 0 0
Potential sense lines
im p e d a n c e
phase ο
Ω
3 m
10m Ω
45
C
0
B
D
1 m
-45
3 0 0 u
1 0 0 m
10
1K
100K
1 0
1 K
1 0 0 K
fre q u e n c y / H z
frequency / Hz
Fig. 11: Results of test measurements at reference
resistors incl. mutual induction (MI) components.
A: In phase MI leads to a high inductive response in the
case of EIS (full dots) whereas the HCI spectrum (squares)
matches the theory.
B: Out-of-phase MI causes paradox capacitive (-) EIS
phase courses (squares) while the HCI phase course
shows the correct phase sign for inductance (+).
T im e / µ s
E /m V
100
0
-1 0 0
-2 0 0
0
200
im p e d a n c e
400
600
800
Ω
100m
30m
10m
100m
10
1K
100K
fre q u e n c y / H z
Fig. 12: High current interrupt measurement of a single
solid oxide fuel cell at 866°C.
EIS: 100 mHz – 100 kHz (rhombi)
HIC: 1 kHz – 800 kHz (circles)
The last example demonstrates that the dominating
error from the unavoidable mutual induction falsifies
the result of standard EIS measurements at very low
impedance objects. In the experiments depicted in
figure 13, a HCI measurement (top) as well as a
comparative EIS measurement (bottom, triangles)
Fig. 13: High current interrupt measurement of a single
PEM fuel cell at 85° C and 80 A. The resulting spectrum
(C) is compared with a standard EIS (D).
on a big PEM fuel cell at a current of 80 A were
performed. The shift of the increase of the
impedance for the transformed HCI-data (circles) to
higher frequencies indicates the smaller sensitivity
of the HCI measurement against the mutual
induction.
In our opinion, the missing correspondence between
the EIS- and the HCI-data at the low frequency end
of 1.1 KHz results from a non-linear component in
the long term pulse response signal. HCI analysis
has to rely on the rule of linearity. The transient
changes of about -10 mV within the 0.85milliseconds-analysis-interval may be enough to
violate this rule.
Conclusion
1. EIS capabilities are basically limited by mutual
induction at the high-frequency low-impedance
edge. This falsifies significantly the results for ohmic
and inductive share.
2. The HCI capability is limited by the magnetic
energy stored in the load circuit.
3. The HCI analysis can be automatically analyzed
reliably by transforming the time data into the
frequency domain.
4. According to our experience, HCI can extend the
available frequency range about a factor of three to
ten in a carefully optimized experimental set-up.
5. HCI data interpretation should not be extended to
the low frequency response. The unavoidable
violation of the EIS linearity rule after a certain
interruption time may lead to misinterpretations.
6. Thus, an arrangement which performs both, the
standard EIS and the HCI measurement within one
set-up, is the best choice for the challenges of
electrochemical power source device testing.
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