Download Complex Impedance Measurement Device for Alkaline Batteries

Complex Impedance Measurement Device for Alkaline Batteries
Including Constant Current Discharge Unit
1. Introduction
One of the most important battery parameters is the internal impedance
measured in ohms (Ω). The internal impedance determines the runtime of a
battery. The battery is restricted to deliver instantaneous peak currents with
high internal impedance. Having low impedance is becoming more vital
nowadays because unlike analog circuits that draw a steady current, digital
circuits require severe current spikes. The voltage of batteries with high internal
impedance suffers from fluctuations when high currents are applied. These
fluctuations push the battery voltage towards the end of the discharge voltage
(cut-off voltage), which eventuates in premature cut-off.
Measuring the internal impedance of a battery is also crucial. Internal impedance
of the battery changes with respect to the state of charge (SoC), battery capacity
and also the battery chemistry. The impedance of modern lead acid (PbA) and
Lithium-ion (Li-ion) batteries remain mostly flat over their SoC whereas for
alkaline and nickel based battery chemistries, this is not the case. The internal
impedance also changes with respect to the cycle count, which is a good
indication of the state of health (SoH) [1]. It is known that the internal
impedance is also indirectly proportional with temperature [2]. The internal
impedance of a non-rechargeable AA battery can be as high as an ohm at -40 °C
and decrease to about 0.15 Ω at room temperature. Evaluating of the difference
in impedance over time can be a useful tool in approximating the SoC and the
SoH of a battery.
The internal impedance of the battery consists of two components. The first
component is electrical impedance that is related with the materials such as
metal contacts, the internal components and the quality of connection between
them. Its effect on total effective impedance can be seen in milliseconds after the
battery is connected to a load. Furthermore, ionic impedance is the second
component that is related to electrochemical factors like ion mobility, electrode
surface area and electrolyte conductivity. Ionic impedance can be observed after
a few milliseconds of connecting the battery to a load, which is the result of the
polarization effects [3].
Electrical Impedance Spectroscopy (EIS) is often used to capture accurate
impedance data of an electrochemical system. EIS is done by perturbing the
electrochemistry of a battery by applying a sinusoidal voltage (AC voltage) at
fixed-frequencies to the battery terminals [4]. The measured data is often
represented by a Bode plot or a Nyquist plot. A battery is a complex system,
therefore; the impedance has resistive, inductive and capacitive elements.
However, the inductive element is commonly ignored due to its negligible effect.
The equivalent circuit of a battery (parallel network of R-C elements connected
in series) may be estimated by measuring the complex impedance over a
spectrum of frequencies.
2. Aims & Objectives
A constant current discharge unit will be designed including a protection circuit
in order to avoid overdischarging the battery. In addition to this, Analog Devices
EVAL-AD5933 evaluation board will be used to measure the internal impedance
spectrum of the battery. However, EVAL-AD5933 is designed to measure
impedances from 1 kΩ to 10 MΩ [5]. The measurement range must be from
0.1 to 1 Ω to examine the impedance spectrum of an alkaline battery.
Furthermore, EVAL-AD5933 can only measure impedances that do not inject
current to the evaluation board. Batteries can supply current which may be
damaging to the board. In this case, external circuitry should be designed to
adjust the measurement range and protect the board from battery’s current
injection.
3. Methods
3.1. Constant Current Discharge Unit
The internal impedance is often measured and recorded against state of charge.
As a result, a constant current discharge unit is required to discharge the battery
with specific C rates. C rate is the rate that battery is charged or discharged
according to its capacity. The typical capacity for AAA and AA batteries are
~1200mAh and ~2700mAh respectively. The discharge unit is specified to be
able to discharge the batteries with 1C rare. This indicates that the unit must be
able to draw ~2.7A. In addition to this, the battery should be discharged until it
reaches to the cut off voltage, otherwise overdischarging may cause cell damage.
The cutoff voltage for alkaline batteries is generally around 0.8V – 1V. The
constant current discharge unit needs to be designed consisting a window
comparator circuit to control voltage discharge range. It is therefore decided to
limit the operation voltage range of circuit from 0.8 to 1.5 Volts. Window
comparator circuit consists of various resistors to adjust the limit voltages and
two op-amps to stop the constant current discharging. The schematic and the
waveform of the circuit can be seen in figure 1.
Figure 1: Schematic and waveform of window comparator circuit.
In Figure 1, it can be seen that Vout is only high when Vref(lower) < Vin < Vref(upper)
where Vin is the voltage of the battery. Furthermore, this circuit should then be
connected to the discharging circuit that is consisting of an op-amp, a transistor
and a power resistor. This circuit can be seen in figure 2.
Figure 2: Constant current discharge circuit.
A constant discharge is possible from the battery with respect to the applied
V_ref voltage. This relation can be explained by the formula 1 below.
𝐼=
𝑣−
𝑅
=
𝑉𝑟𝑒𝑓
𝑅
[1]
A 1 Ω power resistor is used with the combination of IRF510 n-channel MOSFET
to discharge the battery. A potentiometer is used to adjust the discharging
current. The MOSFET generally gets hot as dissipating high power therefore a
heat sink is used to transfer the excess heat from the transistor. The circuit is
constructed with the window comparator and constant current section that can
be seen in figure 3 below.
Figure 3: Constant current discharge unit constructed on a matrix board.
3.2. Complex Impedance Measurement
It is decided that EVAL-AD5933EBZ will be used to perform impedance
spectroscopy on the alkaline battery. This board involves an AD5933 chip that is
the impedance converter system and an AD8606 chip that has low noise precise
op-amps. The AD5933 is a high precision system that combines an adjustable
frequency generator with a 12-bit, 1 megasamples/second (MSPS) analogue-todigital converter (ADC) [5]. A known frequency selected by the user is used to
excite the unknown impedance in test with the help of a frequency generator.
The analogue response signal received from the impedance is then converted to
digital by an analogue to digital converter (ADC). This signal is then sampled by a
discrete Fourier transform (DFT) and the complex impedance is displayed by the
software in the form of R (real) and I (imaginary) impedance [6]. The schematic
of EVAL-AD5933EBZ is shown in figure 4 below.
Figure 4: Circuit diagram of EVAL-AD5933EBZ from Analogue Devices.
It is stated that the EVAL-AD5933EBZ is capable of measuring the impedances
from 100 to 1kΩ with additional circuitry [5]. Furthermore, AD5933 chip has a
programmable output peak-to-peak excitation voltage to a maximum frequency
of 100 kHz. Generally a 1 kHz impedance test is used to represent alkaline
battery impedance. Despite using 1 kHz is common, a portion of the ionic
resistance could not be measured fully because of the speed of the test, therefore
an impedance measurement across a broader range of frequencies is useful [7].
The board has a system accuracy of 0.5% once it is correctly calibrated. To
calibrate the board, a calibration impedance of a midvalue between the limits of
the unknown impedance must be selected. For example, if the unknown
impedance is expected to have a value 180 kΩ < unknown impedance < 220 kΩ
and the interested frequency range is from 30 to 32 kHz, the calibration
impedance should be 200 kΩ with gain setting resistor of (RFB) 200kΩ should be
used to create a unity gain condition at the receive side of the amplifier, and a
calibration frequency of 31 kHz (midpoint frequency) should be used. It is also
important to adjust the system clock frequency that is applied to MCLK pin.
AD5933 has an internal clock with a frequency of 16.776 MHz however it is also
possible to provide a high accuracy external crystal oscillator through the MCLK
(Pin 8). The system clock value should be reduced if the excitation frequency is <
5kHz that is further explained in the datasheet [8].
If the user requires measuring small impedances such as alkaline battery
impedance (~0.1 to ~1 Ω), the current flowing through the unknown impedance
for a fixed excitation voltage increases according to Ohm’s law. In this case, the
transmit side amplifier at Vout (seen in figure 4) may not be capable of providing
enough current through the impedance. To solve this issue, an external current
amplifier is required to attenuate the peak-to-peak excitation voltage, thereby
reducing the signal current flowing through the unknown impedance.
Figure 5: Current amplifier circuit.
The circuit shown in figure 5 above can be used to attenuate the excitation peakto-peak voltage by connecting node A to Vout pin and Node A’ to the unknown
impedance pin with suitable R1 and R2 selection. The ratio of attenuation can be
adjusted by the equation (2) below.
𝑉𝑜𝑢𝑡 =
𝑅1
𝑅2
(2)
The excitation peak-to-peak voltage on the receive side of the board is then
improved by increasing the value of the gain setting resistor (RFB) by multiplying
the value with the inverse of the attenuation ratio. For example, if the excitation
peak-to-peak voltage is attenuated by a factor of 2, the RFB value must be
doubled so that the signal presented to the ADC stays the same. Furthermore, the
receive side of the EVAL-AD5933EBZ is hard-biased about VDD/2 (VDD = 3.3V)
by the manufacturer. It is important to apply VDD/2 Volts to the non-inverting
input of the external amplifier, to prevent it saturating the receive side amplifiers
of the EVAL-AD5933EBZ.
On the other hand, EVAL-AD5933EBZ needs another ingenuity to be able to
measure battery impedances. Generally alkaline batteries can supply current to
the rest of the circuit at around ~1.5V that can also be considered as a voltage
source. Not only measuring the battery impedance accurately, but also
protecting the measurement device requires another external circuit. The
battery’s current flow must be blocked or directed to a ground while the peak-topeak excitation voltage still passes through the battery. It is decided that
grounding the battery with an external circuit and measuring the voltage drop
with a sense resistor can solve the problem. This circuit can be seen in figure 6
below.
Figure 6: Grounded impedance measurement circuit including AC coupling.
The output peak-to-peak excitation voltage therefore flows through the series
connected RSENSE and the grounded battery. The current flowing through the
battery causes a voltage difference across RSENSE, and this voltage drop is
measured by the instrumental amplifier. The measured voltage drop is then
amplified to the original peak-to-peak excitation voltage value by the
instrumentation amplifier. After this process, AC coupling is applied to the signal
to remove any DC components that may distort the amplified AC sine wave. The
AC coupled signal is then connected to a series resistor (10kΩ is used in figure 6
because the user was testing a ~10kΩ unknown impedance) in conjunction with
the gain setting resistor, RFB, to create an inverted unity gain buffer for the
receive side amplifier of EVAL-AD5933EBZ [9].
Instrumentation amplifier is not readily available in the university stores
therefore it is decided to be constructed by other available op-amps. This circuit
is illustrated in figure 7.
Figure 7: Instrumentation amplifier circuit.
Instrumentation amplifier is capable of boosting the voltage difference supplied
to the non-inverting legs of the op-amps. This relation for this circuit can be
explained with equation (3).
𝐺𝑎𝑖𝑛 =
𝑉𝑜𝑢𝑡
𝑉𝑏 −𝑉𝑎
= (1 +
2𝑅1
𝑅𝐺𝑎𝑖𝑛
).
𝑅3
(3)
𝑅2
The full external circuitry required to measure the impedance of an alkaline
battery is illustrated in figure 8. The Node A is connected to the Vout of the EVALAD5933EBZ whereas Node B is connected to the ZUNKNOWN pin.
Figure 8: Current amplifier and grounded impedance measurement circuit.
4. Challenges/Discussion
4.1. Constant Current Discharge Unit
Constant current discharge unit is built and tested. It is found that the circuit is
capable of discharging various constant currents over the specified voltage
rating of the battery (0.8V to 1.5V). The circuit is tested to a maximum of 1A
constant discharge as the test power supply had a max current rating of 1A. The
temperature of the transistor and discharging resistor was acceptable after
continuous testing.
4.2. Complex Impedance Measurement
The grounded impedance measurement circuit is constructed and tested. At this
part, the testing is carried our with a 10 kΩ resistor. The EVAL-5933EBZ is
calibrated using a 10 kΩ resistor and the external circuit is connected
afterwards. Different values of sense resistors were used and the measured
impedance is recorded. These values are represented in table 1.
Sense Resistor (Ω)
100
1000
5000
Real value (Ω)
10000
10000
10000
Measured Value (Ω)
9999
10010
10500
Phase Degree
25
0
0
Table 1: Impedance measurement results with different RSENSE values.
The gain of the instrumentation amplifier is adjusted according to each RSENSE
value. For example, while testing a 10 kΩ resistor with 1 kΩ RSENSE the voltage
across the RSENSE is 1/11th of the original peak-to-peak excitation voltage (simple
voltage divider behavior), therefore the gain of the instrumentation amplifier
must be 11 (𝑅1 = 𝑅2 = 𝑅3 = 10𝑘Ω and 𝑅𝐺𝑎𝑖𝑛 = 2𝑘Ω is used according to
equation 3). The results show that a 100Ω RSENSE introduced an imaginary value
while measuring a resistor value of 10 kΩ whereas resistors do not have
imaginary impedance values. This might be caused by the high gain requirement
(~101) of the instrumentation amplifier as output signal had a huge phase delay
compared to the input signal. This value is therefore ignored at the remaining
tests. As a result, 1 kΩ RSENSE value seemed to be the most accurate. Furthermore,
from 47nF to 0.3𝜇𝐹 of coupling capacitor is used and found out that as the value
increases, the measurement accuracy increased by several ohms.
Several testing frequencies are used and the comparison of the measurement
error is displayed in figure 9. At this test, the ground of the external circuit and
the analog ground of EVAL-AD5933EBZ were connected together as advised in
the manual of the board.
Figure 9: Measurement error against test frequency with common ground connection.
The EVAL-AD5933EBZ is calibrated using a 10 kΩ without having any external
circuitry connected. It is found that at lower test frequencies the measurement
error decreases. It can be seen that the measurement error is minimum for all
the frequencies at calibration impedance. The measurement error is as small as
0.1% at 1kHz test frequency at the calibration impedance and 4.4% at 6.8 kΩ.
Then it is decided to remove the common ground connection. The test results are
displayed in figure 10.
Figure 10: Measurement error against test frequency without common ground connection.
When the common ground connection is removed, the measurement error at
calibration impedance is <0.1% at 1kHz test frequency and 0.74% at 6.8 kΩ.
Although the reason of this improvement is unclear, it might be possible that one
of the grounds may be not be virtual zero. Finally the board is calibrated (10 kΩ)
when the external circuit is connected and the measurement error decreases to
0.01% at calibration impedance and 0.53% at 6.8 kΩ.
The current amplifier circuit is also constructed and tested at 10 kΩ. It is
observed that the measurement error increased slightly because of adding more
components to the external circuit. A more careful gain adjustment is required to
increase the measurement accuracy for testing impedances lower than 10 kΩ.
This is because the current amplification circuit would attenuate the voltage and
a combination of careful adjustments would be required at the instrumentation
amplifier and the gain setting resistor, RFB.
Using a high precision instrumentation amplifier and low tolerance resistor
could increase the measurement accuracy. Although high precision
instrumentation amplifiers are available in the market e.g. Analogue Devices
AD8220, they are costly and had to be ordered in advance because of limited
project time.
5. Conclusions/Next Steps
The constant current discharge unit is constructed and tested. The circuit works
well up to a current value of 1A. It is possible to increase the power rating of the
discharge resistor and use a higher current rating power supply unit to push the
circuit to its limit. Then the temperature of the transistor can be measured again
and a larger heat sink can be adjusted if required.
The impedance measurement for grounded impedances with EVAL-AD5933EBZ
is possible however it is limited. The measurement accuracy decreases as the
measured impedance is smaller/higher than the calibration impedance. To
accurately calibrate the circuit with the current amplifier for lower impedance
measurement, it is suggested to use high precision components. It is strongly
suggested to use a readily available instrumentation amplifier. The AC coupling
value can be increased to understand if it has more effect on lower impedances.
The range of RSENSE and the test frequency should be increased to check if
different values might increase the accuracy. The value of RFB might be increased
while the gain of the instrumentation amplifier kept same when implementing
the current amplifier circuit. This might help having a better resolution signal at
the receive side of the board. Furthermore, there is an on board temperature
sensor that can measure the temperature on board. The effect of the
temperature might be investigated to understand if it can improve the
measuring accuracy. Constructing the external circuitry professionally might
also help decreasing the measurement error.
6. References
[1] Batteryuniversity.com. (2016). How to Measure Internal Resistance. [online]
Available at:
http://batteryuniversity.com/learn/article/how_to_measure_internal_resistance
[Accessed 2 Jun. 2016].
[2] Batteryuniversity.com. (2016). Does Internal Resistance Affect Performance?. [online]
Available at:
http://batteryuniversity.com/learn/article/how_does_internal_resistance_affect_perfor
mance [Accessed 2 Jun. 2016].
[3] www.energizer.com. (2016). Battery Internal Resistance. [online] Available at:
http://data.energizer.com/PDFs/BatteryIR.pdf [Accessed 2 Jun. 2016].
[4] Gould, C. (2014). Alternative Energy Storage, Energy Storage Management. University
of Sheffield.
[5] Analog.com. (2016). EVAL-AD5933 Evaluation Board | Analog Devices. [online]
Available at: http://www.analog.com/en/design-center/evaluation-hardware-andsoftware/evaluation-boards-kits/eval-ad5933.html#eb-documentation [Accessed 2 Jun.
2016].
[6] Chabowski, K., Piasecki, T., Dzierka, A. and Nitsch, K. (2015). Simple Wide Frequency
Range Impedance Meter Based on AD5933 Integrated Circuit. Metrology and
Measurement Systems, 22(1).
[7] www.energizer.com. (n.d.). [online] Available at:
http://data.energizer.com/PDFs/BatteryIR.pdf [Accessed 6 Jun. 2016].
[8] www.analog.com. (2016). [online] Available at:
http://www.analog.com/media/en/technical-documentation/evaluationdocumentation/537700023EVAL_AD5933EB.pdf [Accessed 6 Jun. 2016].
[9] Brennan, S. (n.d.). [online] www.analog.com. Available at:
http://www.analog.com/media/en/technical-documentation/application-notes/AN847.pdf [Accessed 6 Jun. 2016].