Does internal resistance reveal battery capacity?
A study on rapid-test methods for stationary and automotive batteries

Isidor Buchmann
Cadex Electronics Inc.
isidor.buchmann@cadex.com
www.buchmann.ca
June 2004

During the last 20 years, three basic battery rapid test methods have emerged: DC load, AC conductance and multi-frequency electro-chemical impedance spectroscopy (EIS). All methods are resistance based, a characteristic that reveals the battery's ability to deliver load current. Internal resistance provides useful information in detecting problems and indicating when a battery should be replaced. However, resistance alone does not provide a linear correlation to the battery's capacity. The increase of cell resistance only relates to aging and provides some failure indications.

When measuring the internal resistance of brand new VRLA cells from the same batch, variations of 8% are common. The manufacturing process and materials used are only two of many possible variables contributing to this variance. Rather than relying on an absolute resistance reading, service technicians take a snapshot of the cell resistances when the battery is installed and then measure the subtle changes as the cells age. An increase in resistance of 25% over the baseline (100%) indicates a performance drop to about 80%. Battery manufacturers honor a warranty claim if the internal resistance increases by 50%.
Before analyzing the different test methods, let's briefly brush up on internal resistance and impedance, terms that are often used incorrectly when addressing the conductivity of a battery.

Resistance is purely resistive and has no reactance. There is no trailing phase shift because the voltage and current are in unison. A heating element is such a pure resistive load. It works equally well with direct current (DC) and alternating current (AC).

Most electrical loads, including the battery, contain a component of reactance. The reactive part of the load varies with frequency. For example, the capacitive reactance of a capacitor decreases with rising frequency. A capacitor is an insulator to DC and no current can pass through. The inductor, on the other hand, acts in the opposite way and its reactance increases with rising frequency. DC presents an electrical short. A battery combines ohmic resistance, as well as capacitive and inductive reactance. The term impedance represents all three types.

The battery may be viewed as a set of electrical elements. Figure 1 illustrates Randles' basic lead-acid battery model in terms of resistors and a capacitor (R1, R2 and C). The inductive reactance is commonly omitted because it plays a negligible role in a battery at low frequency.

Figure 1: Randles model of a lead acid battery. The overall battery resistance consists of pure ohmic resistance, as well as inductive and capacitive reactance. The values of these components are different for every battery tested.

Battery rapid test methods and how they work

Let's now look at the different battery test methods and evaluate their strengths and limitations. It is important to know that each method provides a different internal resistance reading when measured on the same battery. Neither reading is right or wrong. For example, a cell may read higher resistance readings with the DC load method than with a 1000-hertz AC signal. This simply implies that the battery performs better on an AC than DC load. Manufacturers accept all variations as long as the readings are taken with the same type of instrument.

DC load method: The pure ohmic measurement is one of the oldest and most reliable test methods. The instrument applies a load lasting a few seconds. The load current ranges from 25-70 amperes, depending on battery size. The drop in voltage divided by the current provides the resistance value. The readings are very accurate and repeatable. Manufacturers claim resistance readings in the 10 micro-ohm range. During the test, the unit heats up and some cooling will be needed between measurements on continuous use.

The DC load blends R1 and R2 of the Randles model into one combined resistor and ignores the capacitor. C is a very important component of a battery and represents 1.5 farads per 100 Ah cell capacity.

Figure 2: DC load method. The true integrity of the Randles model cannot be seen. R1 and R2 appear as one ohmic value.

AC conductance method: Instead of a DC load, the instrument injects an AC signal into the battery. A frequency of between 80-100 hertz is chosen to minimize the reactance. At this frequency, the inductive and capacitive reactance converge, resulting in a minimal voltage lag. Manufacturers of AC conductance equipment claim battery resistance readings to the 50 micro-ohm range. AC conductance gained momentum in 1992; the instruments are small and do not heat up during use.

The single frequency technology sees the components of the Randles model as one complex impedance, called the modulus of Z. The majority of the contribution is coming from the conductance of the first resistor.

Figure 3: AC conductance method. The individual components of the Randles model cannot be distinguished and appear as a blur.

Multi-frequency electro-chemical impedance spectroscopy (EIS): Cadex Electronics has developed a rapid-test method based on EIS. Called Spectro™, the instrument injects 24 excitation frequencies ranging from 20-2000 Hertz. The sinusoidal signals are regulated at 10mV/cell to remain within the thermal battery voltage of lead acid. This allows consistent readings for small and large batteries.

With multi-frequency impedance Spectroscopy, all three resistance values of the Randles model can be established.		Figure 4: Spectro™ method. R1, R2 and C can be measured separately, enabling the estimation of battery conductivity and capacity.
A patented process evaluates the fine nuances between each frequency to enable an in-depth battery analysis.

Spectro™ is the most complex of the three methods. The 30-second test processes 40 million transactions. The instrument is capable of reading to a very low micro-ohms level. More importantly, Spectro™ is capable of providing battery capacity in Ah, conductivity (CCA) and state-of-charge.

The EIS concept is not new. In the past, EIS systems were hooked up to dedicated computers and diverse laboratory equipment. Trained electrochemists were required to interpret the data. Advancements in data analysis automated this process and high-speed signal processors shrunk the technology into a handheld device.

Capacity measurements

DC load and AC conductance have one major limitation in that these methods cannot measure capacity. With the growing demand of auxiliary power on cars and trucks and the need to assess performance of stationary batteries non-invasively, testers are needed that can estimate battery capacity. Cadex has succeeded in doing this with car batteries. The company is working on applying this technology to stationary batteries.

Figure 5 reveals the reserve capacity (RC) readings of 24 car batteries, arranged from low to high on the horizontal axis. The batteries were first tested according to the SAE J537 standard, which includes a full charge,
a rest period and a 25A discharge to 1.75V/cell during which the reserve capacity was measured (black diamonds). The tests were then repeated with Spectro™ (purple squares) using battery-specific matrices. The derived results approach laboratory standards, as the chart reveals.

Figure 5: Reserve capacity of 24 batteries with a model-specific matrix. The black diamonds show capacity readings derived by a 25A discharge; the purple squares represent the Spectro™ readings.

Some people claim a close relationship between battery conductivity (ohmic values) and capacity. Others say that internal ohmic readings are of little practical use and have no relation to capacity. The truth lies somewhere in between. An analogy can be made with a doctor who not only takes the body temperature to determine the health of a patient but also observes blood pressure, glucose levels, and cholesterol readings. By taking more than just one measurement, better health assessments can be made.

To demonstrate the relationship between resistance and capacity, Cadex has carried out an extensive test involving 175 automotive batteries in which the cold cranking amps (CCA) were compared with the RC readings. CCA represents the conductivity of the battery and is related with the internal resistance. Figure 6 shows the test results. The CCA readings are plotted on the vertical Y-axis and the RC on the horizontal X-axis. For ease of reading, the batteries are plotted as a percentage of their nominal value and are arranged from low-to-high on the x-axis.

Figure 6: CCA as a function of reserve capacity (RC). Internal resistance (represented by CCA) and capacity do not follow the red line closely. Resistance values alone do not provide accurate capacity readings.

Figure 7: Spectro CA-12 automotive battery tester. The instrument displays CCA, reserve capacity and state-of-charge independently. A unit for stationary batteries is in development.

About the Author
Isidor Buchmann is the founder and CEO of Cadex Electronics Inc., in Vancouver BC. Mr. Buchmann has a background in radio communications and has studied the behavior of rechargeable batteries in practical, everyday applications for two decades. Award winning author of many articles and books on batteries, Mr. Buchmann has delivered technical papers around the world.

Cadex Electronics is a manufacturer of advanced battery chargers, battery analyzers and PC software. For product information please visit www.cadex.com.