Download iR Compensation tutorial

Version 1.11.0
NOVA iR compensation tutorial
1 – The uncompensated resistance
Potentiostats are instruments that are designed to control the potential of the
working electrode (WE) relative to a non-polarizable reference electrode (RE). In
order to achieve this potential control, the potentiostat will change the potential of
the counter (CE) relative to the WE (which is at virtual ground), in normal operating
conditions. The potential of the CE is set to the required voltage within the
compliance voltage limits in order to keep the potential difference between the RE
and the WE equal to the user-defined value.
For the following basic electrochemical cell (see Figure 1):
Figure 1 – An overview of an electrochemical cell (simplified)
RΩ corresponds to the solution resistance and Rp is the polarization resistance (also
known as the charge transfer resistance). In order to keep the potential of the WE
at +1 V relative to the RE, the CE is set to -1.1 V relative to the WE.
Note
A complete description of the working principle of a potentiostat can be found
in the Electrochemical Methods – Fundamentals and Applications handbook by
L. Faulkner and A. Bard, 2nd edition, Wiley, New York, 2000.
In practice, this means that the potentiostat will always compensate the solution
resistance, within the limits of the compliance voltage.
Unfortunately, in a real electrochemical cell, the reference electrode is always
located at a distance relative to the working electrode. This means that an additional
resistance, the uncompensated resistance, Ru, can never be avoided completely (see
Figure 2).
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Figure 2 – An overview of an electrochemical cell (complete)
The uncompensated resistance leads to an additional voltage drop, called the iR
drop, given by:
𝑉𝑉𝑖𝑖𝑖𝑖 = 𝑖𝑖 ∙ 𝑅𝑅𝑢𝑢
Therefore, whenever a current is passed through the circuit described in Figure 2,
there is always a potential control error due to the uncompensated resistance. If a
cathodic current flows, the true potential of the working electrode is less negative
than the specified potential. The opposite holds in the case of an anodic current.
Even with a very low uncompensated resistance value, the voltage drop can become
significant when the current is high 1.
1.1 – How to minimize the uncompensated resistance
Although iR drop cannot be avoided, it is possible to minimize its value. The
following strategies can be used:
1. Use a supporting electrolyte with high conductivity: this will reduce the total
resistance of the solution (and therefore also the uncompensated resistance).
2. Reduce the size of the working electrode: the total current depends on the
surface of the working electrode.
3. Use a Luggin capillary: this can be used to reduce the distance between the
reference electrode and the working electrode, therefore reducing the
uncompensated resistance.
1.2 – The iR compensation circuit
An additional strategy that can be used to reduce the effects of the uncompensated
resistance is to use the so-called positive feedback built into the Autolab
potentiostat in order to partially compensate the iR drop. The iR drop functionality
is available in the Autolab PGSTAT series 2.
In the Autolab PGSTAT, the iR compensation circuit is fitted with a DAC that can be
used to compensate the iR drop. The voltage range of the compensation circuit is 0
1
2
An Ru of 1 Ω with a current of 100 mA leads to a voltage drop of 100 mV.
The option is not available with the PGSTAT10 and the µAutolab II/III.
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– 2 V. This means that the resistance range than can be compensated through this
circuit is:
where 𝐶𝐶𝐶𝐶 is the current range.
𝑅𝑅𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 =
𝐷𝐷𝐷𝐷𝐷𝐷(𝑉𝑉)
𝐶𝐶𝐶𝐶
1.3 – Automatic current ranging restrictions
When the iR compensation circuit is used, the Automatic current ranging option
cannot be used. This restriction is verified during the validation process and an error
will be displayed by the procedure validation if this situation is detected (see Figure
3).
Figure 3 – Automatic current ranging is not possible when the iR compensation circuit is used
1.4 – Using the iR compensation circuit in NOVA
It is possible to define the value of the resistance to compensate using the iR
compensation circuit in the Autolab control interface. Using the Autolab control
command, it is possible to switch the iR compensation circuit on and off and to
specify the value of the resistance to compensate.
The Autolab control window displays the list of hardware settings for the
potentiostat/galvanostat. Using this interface, it is possible to set the current range
and switch the iR compensation On or Off (see Figure 4).
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Figure 4 – The Autolab control command can be used to switch the iR compensation circuit
On or Off
The iR compensation circuit can also be controlled using the Autolab display.
Clicking the iR-C label in the Autolab display switches the iR compensation circuit
On or Off (see Figure 5).
Figure 5 – Clicking the iR-C label in the Autolab control switches the iR compensation circuit
On or Off
The value of the resistance to compensate using the iR compensation circuit is also
specified through the Autolab control window (see Figure 6).
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Figure 6 – Defining the value of the compensated resistance
Note
The range of resistance values that can be compensated depends on the active
current range.
The value of the resistance to compensate can also be specified using the provided
slider (see Figure 7).
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Figure 7 – The compensated resistance can also be specified using the provided slider
Note
It is common practice to compensate about 90-95 % of the uncompensated
resistance.
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2 – Determination of the uncompensated resistance, Ru
In order to use the iR compensation circuit efficiently, the uncompensated resistance
value must be estimated. Several techniques can be used in order to determine this
value. The following methods are available in Nova:
•
i-Interrupt: the current interrupt method (i-Interrupt) is a quick method that
can be used to determine the uncompensated resistance value. The
technique involves switching off the current and measuring the decay of the
cell potential. As soon as the current is switched off, the potential difference
across the uncompensated resistance is zero and the charged double layer is
discharged. By extrapolating the measured voltage decay to the beginning
of the current interruption, the iR-drop can be calculated. Two i-Interrupt
methods are available in NOVA and a standard Autolab procedure is
available for both methods:
o i-Interrupt: in this case, the voltage decay is measured using the
ADC164 module.
o i-Interrupt high speed: measures the voltage decay using the fast
sampling ADC module (ADC10M or ADC750).
•
•
Positive feedback: the positive feedback technique is an interactive method
based on the measurement of current response following the application of
a potential pulse. The current response depends on the actual values of the
uncompensated resistance and the double layer capacitance. Compensation
of Ru results in a faster decay of the charging current. When the
compensation is near 100%, the measured current response will show
damped oscillation. This method is therefore based on a trial and error
approach. A standard Autolab procedure is provided for this method.
Impedance spectroscopy (FRA32M or FRA2 module required): the high
frequency limit of a typical electrochemical cell, as shown in Figure 2,
provides a direct and accurate measurement of the uncompensated
resistance value. Impedance spectroscopy (EIS) can thus also be used to
determine the value of Ru. The use of EIS for this purpose falls outside of the
scope of this tutorial. More information on impedance spectroscopy can be
found in the dedicated tutorial, available from the Help menu.
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2.1 – i-Interrupt 3
The default Autolab i-Interrupt procedure can be used to evaluate the
uncompensated resistance.
During the measurement, a DC potential is applied on the cell before the interrupt
circuit is triggered. This circuit interrupts the current flow in the cell and measures
the potential decay. From the measured potential decay, the uncompensated
resistance (Ru) value is determined.
Two values of the uncompensated resistance, Ru, are determined automatically at
the end of the measurement:
•
•
R u linear: this value is obtained from a linear regression performed on the
initial segment of the voltage decay.
R u exponential: this value is obtained from an exponential regression
performed on the initial segment of the voltage decay.
Proper determination of this value requires an accurate measurement of the current.
The measurements must therefore be carried out at a potential value where the
current is high enough to be measured properly and the current range must be
adjusted in accordance.
Note
For reliable measurements, the current should be at least in the order of 1 mA.
The accuracy of the determination also depends on the applied potential value
before the interrupt is triggered. The potential must be measured accurately in order
to calculate reliable values of Ru.
If a fast sampling ADC module is available, it is highly recommended to use the iInterrupt high speed procedure in order to obtain more reliable results (see Section
2.2). With the i-Interrupt procedure, the interval time is about 100 µs. The interval
time is reduced to 4 µs with the i-Interrupt high speed procedure.
The default procedure has the following parameters:
•
•
•
•
•
•
3
Pre interrupt potential: 0.9 V
Duration of interrupt: 10 ms
Start abscissa of linear regression: 0 s
Stop abscissa of linear regression: 0.0005 s
Start abscissa of exponential regression: 0 s
Stop abscissa of exponential regression: 0.005 s
This method is not available with the PGSTAT10 and the µAutolab type II/III.
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Figure 8 shows an overview of the i-Interrupt procedure.
Figure 8 – The Autolab i-Interrupt procedure
2.1.1 – Running the procedure on the dummy cell
The use of this procedure can be illustrated using the Autolab dummy cell. Connect
the potentiostat to the dummy cell as shown in Figure 9 and press the start button.
C1
1µF
R2
CE
100Ω
WE(+S)
(a)
R4
1MΩ
CE
C2
1µF
R1
RE
100Ω
R7
10kΩ
RE
1MΩ
C3
WE(+S)
(e)
WE(+S)
(b)
R3
R5
1µF
WE(+S)
(c)
1kΩ
WE
C4 R6
1µF 5kΩ
S
WE(+S)
(d)
DUMMY CELL2
Figure 9 – The Autolab dummy cell (c) can be used to test the i-Interrupt procedure
The Autolab will apply a potential of 0.9 V as specified in the procedure. Shortly
after the procedure starts, the i-Interrupt circuit is triggered and the potential decay
is measured.
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Figure 10 shows a measurement on the dummy cell (c) with the default Autolab iInterrupt procedure. The WE(1).Potential values are plotted versus the Time from
interrupt signal, which is a calculated time starting at the triggering of the i-Interrupt
circuit.
Figure 10 – Measured data obtained using the default Autolab i-Interrupt procedure on
dummy cell (c)
In Figure 10, the linear regression and exponential regressions fitted through the
measured potential values are shown. The linear regression is performed between
0 and 0.0005 s, as specified in the procedure. The exponential regression extends
further into the measured data points, from 0 to 0.002 seconds after the interrupt.
When the measurement is finished, the calculated values of Ru, obtained from the
regressions, are displayed in the Autolab display window (see Figure 11).
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Figure 11 – The Autolab display shows the fitted values of R u exponential and R u linear at the
end of the measurement
In the Autolab dummy cell, a 100 Ohm resistor is used to simulate the
uncompensated resistance. Both calculated Ru values are consistent with this value.
The linear regression provides a slightly higher value while the exponential
regression underestimates the resistance value.
Note
The calculated values strongly depend on the positions specified in the procedure
for the start and stop abscissa used for the linear and exponential regression. If
these positions are not adjusted properly, the calculated values can be
significantly different from the real uncompensated resistance.
It is possible to repeat the regression in the Analysis view once the data is saved.
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2.1.2 – Analyzing the measured data
The measured data is shown in the Analysis view, as shown in Figure 12.
Figure 12 – The data analysis can be refined in the Analysis view
Both the linear and the exponential regression data is displayed in the data explorer
frame as well as the calculated Ru linear and Ru exponential values (see Figure 13).
Figure 13 – The data explorer frame shows both fitted curves and the calculated Ru linear
and Ru exponential values
Clicking either one of the two measured curves in the data explorer frame displays
the measured data points and the corresponding regression line (see Figure 14 and
Figure 15).
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Figure 14 – Measured data obtained using the default Autolab i-Interrupt procedure on
dummy cell (c) and linear fit (green line)
Figure 15 - Measured data obtained using the default Autolab i-Interrupt procedure on
dummy cell (c) and exponential fit (red line)
Selecting either one of the curves displays the regression control panel on the right
hand side of the plot (see Figure 16).
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Figure 16 – The regression control panel is shown on the right-hand side of the plot
Using this control panel, it is possible to fine tune the regression. Select the
option in the regression control panel to adjust the regression manually (see Figure
17).
Figure 17 – Clicking the
option clears the calculated values
Click the plot area and, while holding the mouse button, drag the mouse pointer
across the range of potential values that have to be used in the fit. The selection will
appear in black, as shown in Figure 18.
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Figure 18 – Repeating the calculation with a new range of values (1/2)
Release the mouse button to finish the calculation. The regression calculation will
be repeated using the new range of values and the calculated curve and Ru values
will be shown in the plot area and in the data explorer frame, respectively (see Figure
19).
Figure 19 – Repeating the calculation with a new range of values (2/2)
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Note
If the shift key is pressed when the mouse button is released (as indicated by the
tooltip in Figure 18), a dedicated dialog box will appear on the plot, allowing you
to specify the start and stop X values to be used in the regression (see Figure 20).
Figure 20 – Holding the shift key before releasing the mouse button allows you to fine tune
the start and stop values used in the regression
For more information on the regression analysis tool, please refer to the User
Manual.
2.2 – i-Interrupt high speed
The default Autolab i-Interrupt high speed is similar to the i-Interrupt procedure.
The only difference is that in the high speed method, the fast sampling ADC module
(ADC10M or ADC750) is used to sample the potential decay. Since the number of
points measured using this method is larger than with the normal i-Interrupt
procedure, the Ru values will be more accurate.
It is therefore highly recommended to use the fast sampling ADC module to
determine the value of the uncompensated resistance, if it is available in the
instrument.
The i-Interrupt high speed procedure requires the fast sampling ADC module
(ADC10M or ADC750) to be installed in the Autolab. If this module is not available,
then the i-Interrupt procedure must be used instead (see Section 2.1)
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During the measurement, a DC potential is applied on the cell before the interrupt
circuit is triggered. This circuit interrupts the current flow in the cell and measures
the potential decay. From the measured potential decay, the uncompensated
resistance (Ru) value is determined.
Two values of the uncompensated resistance, Ru, are determined automatically at
the end of the measurement:
•
•
R u linear: this value is obtained from a linear regression performed on the
initial segment of the voltage decay.
R u exponential: this value is obtained from an exponential regression
performed on the initial segment of the voltage decay.
Proper determination of this value requires an accurate measurement of the current.
The measurements must therefore be carried out at a potential value where the
current is high enough to be measured properly and the current range must be
adjusted in accordance.
Note
For reliable measurements, the current should be at least in the order of 1 mA.
The accuracy of the determination also depends on the applied potential value
before the interrupt is triggered. The potential must be measured accurately in order
to calculate reliable values of Ru.
The default procedure has the following parameters:
•
•
•
•
•
•
Pre interrupt potential: 0.9 V
Duration of interrupt: 10 ms
Start abscissa of linear regression: 0 s
Stop abscissa of linear regression: 0.0005 s
Start abscissa of exponential regression: 0 s
Stop abscissa of exponential regression: 0.005 s
Figure 21 shows an overview of the i-Interrupt high speed procedure.
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Figure 21 – The Autolab i-Interrupt high speed procedure
2.2.1 – Running the procedure on the dummy cell
The use of this procedure can be illustrated using the Autolab dummy cell. Connect
the potentiostat to the dummy cell as shown in Figure 22 and press the start button.
C1
1µF
R2
CE
100Ω
WE(+S)
(a)
R4
1MΩ
CE
C2
1µF
R1
RE
100Ω
R7
10kΩ
RE
1MΩ
C3
WE(+S)
(e)
WE(+S)
(b)
R3
R5
1µF
WE(+S)
(c)
1kΩ
WE
C4 R6
1µF 5kΩ
S
WE(+S)
(d)
DUMMY CELL2
Figure 22 – The Autolab dummy cell (c) can be used to test the i-Interrupt high speed
procedure
The Autolab will apply a potential of 0.9 V as specified in the procedure. Shortly
after the procedure starts, the i-Interrupt circuit is triggered and the potential decay
is measured, using the high speed ADC. The interval time is 4 µs.
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Figure 23 shows a measurement on the dummy cell (c) with the default Autolab iInterrupt high speed procedure. The WE(1).Potential values are plotted versus the
Time from interrupt signal, which is set at t = 0 s. The high speed ADC module also
recorded data points that precede the triggering of the interrupt circuit. These
values are shown with negative time abscissa values.
Figure 23 – Measured data obtained using the default Autolab i-Interrupt high speed
procedure on dummy cell (c)
In Figure 23, the linear regression and exponential regressions fitted through the
measured potential values are shown. The linear regression is performed between
0 and 0.0005 s, as specified in the procedure. The exponential regression extends
further into the measured data points, from 0 to 0.002 seconds after the interrupt.
When the measurement is finished, the calculated values of Ru, obtained from the
regressions, are displayed in the Autolab display window (see Figure 24).
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Figure 24 – The Autolab display shows the fitted values of R u exponential and R u linear at the
end of the measurement
In the Autolab dummy cell, a 100 Ohm resistor is used to simulate the
uncompensated resistance. Both calculated Ru values are consistent with this value.
The linear regression provides a higher value while the exponential regression
provides a very accurate determination of the uncompensated resistance value.
The calculated values strongly depend on the positions specified in the procedure
for the start and stop abscissa used for the linear and exponential regression. If
these positions are not adjusted properly, the calculated values can be significantly
different from the real uncompensated resistance.
It is possible to repeat the regression in the Analysis view once the data is saved.
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2.2.2 – Analyzing the measured data
The measured data is shown in the Analysis view, as shown in Figure 25.
Figure 25 – The data analysis can be refined in the Analysis view
Both the linear and the exponential regression data is displayed in the data explorer
frame as well as the calculated Ru linear and Ru exponential values (see Figure 26).
Figure 26 – The data explorer frame shows both fitted curves and the calculated Ru linear
and Ru exponential values
Clicking either one of the two measured curves in the data explorer frame displays
the measured data points and the corresponding regression line (see Figure 27 and
Figure 28).
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Figure 27 – Measured data obtained using the default Autolab i-Interrupt high speed
procedure on dummy cell (c) and linear fit (green line)
Figure 28 - Measured data obtained using the default Autolab i-Interrupt high speed
procedure on dummy cell (c) and exponential fit (red line)
Selecting either one of the curves displays the regression control panel on the right
hand side of the plot (see Figure 29).
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Figure 29 – The regression control panel is shown on the right-hand side of the plot
Using this control panel, it is possible to fine tune the regression. Select the
option in the regression control panel to adjust the regression manually (see Figure
30).
Figure 30 – Clicking the
option clears the calculated values
Click the plot area and, while holding the mouse button, drag the mouse pointer
across the range of potential values that have to be used in the fit. The selection will
appear in black, as shown in Figure 31.
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Figure 31 – Repeating the calculation with a new range of values (1/2)
Note
Do not select the data points measured before the current interruption.
Release the mouse button to finish the calculation. The regression calculation will
be repeated using the new range of values and the calculated curve and Ru values
will be shown in the plot area and in the data explorer frame, respectively (see Figure
32).
Figure 32 – Repeating the calculation with a new range of values (2/2)
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Note
If the shift key is pressed when the mouse button is released (as indicated by the
tooltip in Figure 31), a dedicated dialog box will appear on the plot, allowing you
to specify the start and stop X values to be used in the regression (see Figure 33).
Figure 33 – Holding the shift key before releasing the mouse button allows you to fine tune
the start and stop values used in the regression
For more information on the regression analysis tool, please refer to the User
Manual.
2.3 – Positive feedback
Positive feedback is an alternative method that can be used to fine tune the value
of the uncompensated resistance. This method requires a trial and error approach.
Note: it is recommended to use the i-Interrupt or the i-Interrupt high speed
procedure in order to have an initial value of the uncompensated resistance, Ru, and
to start by using ~ 80% of this value in the positive feedback procedure.
By adjusting the value of the compensated resistance, the tipping point at which
the response of the cell starts to oscillate is detected. This critical value provides a
good approximation of the real uncompensated resistance, Ru.
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Note
The Positive feedback procedure cannot be used in combination with the
PGSTAT10 and the µAutolab type II/III.
The default procedure has the following parameters:
• Initial compensated resistance: 0 Ohm
• DC potential: 0 V
• Potential step 1: 0, duration 5 ms
• Potential step 2: 0.1 V, duration 5 ms
• Potential step 3: 0 V, duration 5 ms
Figure 34 shows an overview of the default Autolab positive feedback procedure.
The value of the resistance to compensate is set in the Autolab control command at
the beginning of the procedure. The default value is 0 Ohm. The value specified in
the Autolab control command is linked to an Input box at the beginning of the
procedure, which can be used to easily specify a resistance value.
Figure 34 – The Autolab Positive feedback procedure
Note
More information on the Autolab control command can be found in the Autolab
control tutorial, available from the Help – Tutorials menu.
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During this procedure, three consecutive potential steps are applied on the cell,
using the Chrono methods command. The DC potential, specified in the Set
potential command can be adjusted if necessary, depending on the experimental
conditions. When this potential value is adjusted, it is also necessary to adjust the
potential values of the steps involved in the Chrono methods measurement (see
Figure 35). The duration of each step can also be adjusted, if necessary.
Figure 35 – The steps used in the positive feedback procedure
Note
More information on the use of the chrono methods command can be found in
the chrono methods tutorial, available from the Help – Tutorials menu.
2.3.1 – Running the measurement on the dummy cell
The use of this procedure can be illustrated using the Autolab dummy cell. Connect
the potentiostat to the dummy cell as shown in Figure 36 and press the start button.
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C1
1µF
R2
CE
100Ω
WE(+S)
(a)
R4
1MΩ
CE
C2
1µF
R1
RE
100Ω
R7
10kΩ
RE
1MΩ
C3
WE(+S)
(e)
WE(+S)
(b)
R3
R5
1µF
WE(+S)
(c)
1kΩ
WE
C4 R6
1µF 5kΩ
S
WE(+S)
(d)
DUMMY CELL2
Figure 36 – The Autolab dummy cell (c) can be used to test the positive feedback procedure
An Input box is shown at the beginning of the procedure (see Figure 37).
Figure 37 – An input box is shown at the beginning of the measurement
Adjust the value of the resistance to compensate to 90 Ohm using the Input box
and press
to continue.
The measured potential profile will be displayed at the end of the experiment (see
Figure 38).
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Figure 38 – The potential profile measured during the positive feedback procedure
Note
Depending on the type of instrument used and on the dummy cell, the measured
potential can slightly overshoot the expected potential.
Figure 39 shows the response measured with four different compensated resistance
values: 0, 95, 99 and 101 Ohm. The response measured with a resistance of 0 Ohm
is normal. The values of 95 and 99 Ohm both introduce a damped oscillation around
the new potential value. The potential quickly settles to a stable value, similarly to
the data shown in Figure 38. Finally, the value of 101 Ohm introduces a ringing
oscillation that settles down after 5 ms.
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Figure 39 – Four different positive feedback experiment (plot 1 – green line: 0 Ohm, plot 2 –
blue line: 95 Ohm, plot 3 – orange line: 99 Ohm, plot 4 – red line: 101 Ohm)
The data shown in Figure 39 indicates that the exact value of the uncompensated
resistance is between 99 Ohm and 101 Ohm. Additional measurements can be
performed to further fine tune this value, but this is not a requirement since it is
recommended to set the compensation value at around 80-90 % of the
uncompensated resistance in order to achieve the best compromise between
compensation of the resistance and stability of potential control.
Warning
Over-compensating the iR drop leads to oscillation of the potentiostat circuit.
This is potentially hazardous for the working electrode or the electrochemical cell
and should be avoided if possible (see Figure 39).
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Figure 40 – A resistance of 103 Ohm drives the measurement on dummy cell (c) into
oscillation
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