# Dynamic-Load Circuit Determines a Battery's Internal Resistance

## Analog Devices LT1077 LTC1150 LTC1798 LTC6943

The simplest model of a battery comprises an ideal voltage source that connects in series with a resistance whose value – often a few milliohms – depends on the battery's electrochemical condition and construction. If you attempt to use an ordinary ac milliohmmeter containing a kilohertz-range ac excitation source to measure a battery's internal resistance, you get erroneous results due to capacitive effects, which introduce losses. A more realistic battery model includes a resistive divider that a capacitor partially shunts (Figure 1). In addition, a battery's no-load internal resistances may differ significantly from their values under a full load. Thus, for greatest accuracy, you must measure internal resistance under full load at or near dc.

 Figure 1. An elementary model of a battery’s internal impedance includes resistive and capacitive elements, but the capacitive elements introduce errors in ac-based impedance measurements. For improved accuracy, analyze the battery’s voltage drop at a frequency near dc.

The circuit in Figure 2 meets these requirements and accurately measures internal resistance over a range of 0.001 to 1 Ω at battery voltages as high as 13 V. One section of an LTC6943 analog switch, IC2A, alternately applies 0.110 and 0.010 V derived from 2.5 V voltage reference IC3 and resistive divider R2, R3, and R4 to IC1's input.

 Figure 2. This circuit determines a battery’s internal resistance by repetitively applying a calibrated discharge current and measuring the resultant voltage drop across the battery’s terminals.

Amplifier IC1, power MOSFET Q1, and associated components form a closed-loop current sink that provides an active load for the battery under test via Q1's drain. Diode D1 provides reversed-battery protection. The voltage at amplifier IC1's positive input and the voltage drop across R1 determine the load applied to the battery. In operation, the circuit applies a constant-current load comprising a 1 A, 0.5-Hz square wave biased at 100 mA to the battery.

The battery's internal resistance develops a 0.5-Hz amplitude-modulated square-wave signal at the Kelvin connections attached to the battery. A synchronous demodulator comprising analog switches S3 and S4 in IC2B and chopper-stabilized amplifier IC5 processes the sensed signal and delivers a 0 to 1 V analog output that corresponds to a battery-resistance range of 0 to 1 Ω.

Via transistor Q2, amplifier IC5's internal approximately 1-kHz clock drives CMOS binary divider CD4040, IC4, which supplies a 0.5-Hz square-wave clock drive for the switches in IC2. In addition, a 500-Hz output from IC4 powers a charge-pump circuit that delivers approximately –7 V to IC5's negative power-supply input and thus enables IC5's output to swing to 0 V.

The complete circuit consumes approximately 230 µA, allowing nearly 3000 hours of operation from a 9 V alkaline-battery power supply. The circuit operates at a supply voltage as low as 4 V with less than 1-mV output variation and provides an output accuracy of 3%. The circuit accommodates a battery-under-test voltage range of 0.9 to 13 V, but you can easily alter discharge current and repetition rate to observe battery resistance under a variety of conditions.

EDN