Proceedings of the 2009 ASEE North Midwest Sectional Conference

A Method to measure battery Impedance using operational amplifier

circuit in electrical engineering lab curriculum Prakash Ranganathan1, Saleh Faruque2, Richard Schultz3

Department of Electrical Engineering, University of North Dakota, Grand Forks

email: prakashranganathan@mail.und.edu

Abstract – The paper introduces a novel circuit to measure and study the battery

impedance (Zbatt) behaviour of the commercially available AA batteries. The frequency

response of the battery under test is analyzed over several kilohertz. This paper studies

the construction and analysis of an instrument that will measure the impedance of a

battery (Zbatt) as a function of frequency (Hz). A standard 1.5 volt (AA) and 9 volt battery

will be tested. The proposed instrument allows us to model and measure the battery

impedance (Zbatt) mathematically to better understand its properties over time.

1- Introduction

Battery is a complex electrochemical device. The performance of battery and its lifetime

can be extended and improved by studying the characteristics of its impedance. At

present, there are two simple ways of measuring impedance of the battery: cause a signal

to be generated in the battery by “pulse” thereby discharging the battery or by applying

an AC current signal [1]. The proposed instrument calculates the cell impedance by

measuring the AC root-mean square (rms) voltage drops due to a measured ac rms

current signal.

II- Experimental setup:

Step I

The first step of the experiment set-up involves the construction of an instrument, as

shown in the following Figure.1. The instrument will be constructed using the

TL071(Typical 741) operational amplifier (Figure.2) powered by a 12 volts and with

two matching resistors R1=R2=1k . A DC battery will then be connected in series with

R1. A multimeter can then be connected across R1 to measure the AC voltage across R1.

In addition to existing meter, an another multimeter (voltmeter) can be placed

across the battery in order to measure the AC voltage across the battery. It is important to

makesure that the multimeter isin AC mode to measure the root mean square (RMS)

voltage.

Finally, an input sinusoidal signal (Vin ) is applied to the proposed circuit.

Proceedings of the 2009 ASEE North Midwest Sectional Conference

R11.0k

R2

1.0k

U1

OPAMP_5T_VIRTUAL

V1ac

1 V

1kHz

0Deg

V2ac1.5 V

XMM1

Vbatt

XMM2

Figure 1:The Impedance Measurement Circuit

Figure 2: TL 071 Pinout Diagram

Theory

The above operational amplifier circuit uses the following equation to calculate the

battery impedance.

1

1

2

)(R

V

VZ

batt……………………… (1)

where.,

V2= voltage across the battery under „test‟

V1= voltage across the resistor R1

Z(batt) = Impedance of the battery under “test”

The above equation was utilized throughout the paper to calculate its impedance (Zbatt) of

the battery at given frequencies

Step II

The second step of the proposed instrument set-up, includes the actual measurement of

the impedance(Zmeas) of a battery. The input voltage Vin should be setto 5Vp-p at a

Proceedings of the 2009 ASEE North Midwest Sectional Conference

frequency of 1kHz to measure the AC voltage across the resistor (V1) and the AC voltage

across the battery (V2) should be measured. Using these measured values, the battery

impedance (Zbatt) can then be calculated using equation 1. This process should be

repeated for frequencies of 1kHz, 2kHz, 4kHz, 8kHz, 16kHz. A plot can then be

constructed showing the impedance of the battery as a function of frequency.

Step III Results

The commercial batteries are tested over a wide range of frequencies and its response is

plotted using the data in the following table:

Table 1: Duracell 1.5V (AA) Measurements

Table 2: Rayovac 9-volt battery Measurements

Figure 3: 1.5 V Battery Impedance vs.frequency

Frequenc

y (kHz)

V1p-p

(Vrms)

V2p-p

(mVrms)

Zbatt

( )

1 1.789

6

.94 .526

2 1.786 .85 .476

4 1.786 .82 .4591

8 1.787 .80 .4476

16 1.788 .77 .4306

Frequency

(kHz)

V1p-p

(V-

rms)

V2p-p

(mVrms)

Zbatt

( )

1 1.05 3.10 2.95

2 1.05 2.72 2.59

4 1.044 2.34 2.24

8 1.043 2.04 1.96

16 1.045 1.81 1.773

1 .5 V o lt Du r a c e ll Ba t te r y

0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 5 1 0 1 5 2 0

Fr e q u e n c y

Ba

tte

ry I

mp

ed

an

ce

Proceedings of the 2009 ASEE North Midwest Sectional Conference

Figure 4: Impedance Vs frequency - 9V Battery

III. Impedance as an indicator:

Measure of impedance could be an indicator for battery aging. Battery cells are

categorized as weak, abnormal and normal based on their percentage change in its

impedance over its life period. IEEE defines that all battery cells must deliver 90% of

rated capacity upon delivery unless otherwise specified to account for this [2].

Conclusion: Promising Investigation into multiple frequency testing of battery

impedance has been underway for sometime now. This approach requires a relatively

accurate model of a cell and should be able to indicate what areas of the battery

construction and chemical processes are varying over time. By knowing these

parameters, it is expected to learn what processes are showing signs of aging, defect,

overstress or damage. To aid this analysis, this paper illustrates one such model for

measuring the impedance of the battery.

The behavior of commercially available AA batteries are studied by measuring the

battery impedance under test using the proposed op-amp circuit and its response over

wide frequencies has been analyzed. The proposed circuit can be transformed into an

battery measuring instrument.

Acknowledgement: The author(s) would like to thank the students in the EE 309 Junior

Laboratory of Spring 2008 semester for collecting the data, since the data illustrated in

the Table 1 and 2 are the averaged response gathered by them, as part of a exploration of

a new lab added in EE 309 Junior Laboratory at University of North Dakota, Grand

Forks, ND.

9 V o lt Ra y o v a c Ba t te r y

0

0 .5

1

1 .5

2

2 .5

3

3 .5

0 5 1 0 1 5 2 0

Fr e q u e n c y

Ba

tte

ry I

mp

ed

an

ce

Proceedings of the 2009 ASEE North Midwest Sectional Conference

REFERENCES:

1. Willihnganz and Rohner, “Battery Impedance :Farads, Milliohms, Microhenrys”,

AIEE Chemical Industry Committee, Paper #59-823, 1959.

2. IEEE, “IEEE -485 Recommended practice for sizing Lead acid batteries for

Stationary applications”, 1995.

BIOGRAPHICAL INFORMATION PRAKASH RANGANATHAN- is currently a faculty member in the Department of Electrical Engineering

at the University of North Dakota - Grand Forks. Ranganathan‟s research area and teaching interests are in

Electric Circuits, Sensor Networks and Engineering Education.

RICHARD SCHULTZ - is currently the Professor and Chair and Associate Professor in the Department of

Electrical Engineering at UND. His research interest are in Unmanned Aerial Vehicles (UAVs), Digital Signal and Image Processing, Embedded Systems, and Engineering Entrepreneurship.

Saleh Faruque – is currently an Associate professor in the Department of Electrical Engineering at UND.

His research interests are in Electronics and Communication Engineering.