## Introduction

Battery internal resistance is a critical performance parameter that determines the runtime, power delivery, current capabilities, efficiency and health of a battery. Measuring the internal resistance allows you to analyze battery characteristics and performance for design optimization, production testing or periodic maintenance.

This article provides a comprehensive guide on techniques to measure the internal resistance of different battery types along with the required test circuits and calculations. We will cover:

- Importance of battery internal resistance
- Factors affecting internal resistance
- DC measurement methods
- Voltage drop method
- Discharge test method

- AC measurement methods
- Impedance spectroscopy
- AC conductance method

- Calculations and formulae
- Measurement errors and accuracy

Understanding suitable methods to determine the internal resistance will help you characterize battery performance for your application or properly evaluate battery condition during field use.

## Why Measure a Battery’s Internal Resistance?

The internal resistance represents the resistive elements within a battery including the electrolyte, electrodes, active materials, interconnects and separators. The key aspects influenced by the battery internal resistance include:

- Voltage drop under load – Higher internal resistance causes larger voltage drops during discharge. This reduces the usable capacity at higher current draws.
- Power delivery – Internal resistance dissipates power as heat during operation, reducing battery efficiency.
- Runtime – Increased internal resistance shortens battery life before voltage cutoff.
- Effective capacity – Usable capacity is decreased due to voltage drops across internal resistance at higher discharge currents.
- Current capabilities – Internal resistance limits the maximum continuous or pulse discharge currents.
- State of health – Increase in internal resistance over time indicates battery aging or damage. Periodic measurement can gauge battery health.
- Design factors – Internal resistance determines required cell configurations to meet voltage, current and runtime targets.
- Safety – High internal resistance can lead to battery overheating during operation.

Measuring internal resistance at production or periodically during service life is critical to evaluate these battery performance factors.

## What Impacts a Battery’s Internal Resistance?

Many design, material, operational and environmental factors influence the internal resistance of a battery. Understanding these effects allows interpreting resistance measurements and correlating to battery performance.

### Battery Design Factors

- Electrochemistry – Internal resistance varies significantly between battery chemistries.
- Physical construction – Cell structure, electrode thickness, surface area, separator materials impact resistance.
- Internal connections – Welds, interconnects between cell elements contribute resistance.
- Form factor – Cylindrical, prismatic or pouch cell designs influence resistance.

### Materials Used

- Electrodes – Electrode materials, surface area, porosity and thickness affect resistance.
- Electrolyte – Type of electrolyte solution determines ionic conductivity impacting resistance.
- Separators – Porosity and thickness of separators introduce resistance.

### Manufacturing Variances

- Production inconsistencies – Resistance deviations across batches and manufacturers.
- Assembly alignment – Improper winding alignment increases resistance.
- Interconnect welds – Weak welds between electrodes and terminals increase resistance.

### Operating Conditions

- Temperature – Elevated temperatures reduce electrolyte resistance.
- Discharge current – Internal resistance can increase at very high discharge currents due to electrochemical effects.
- SOC level – Resistance generally increases at very high and very low state of charge.
- Cell aging – Gradual increase in resistance due to physical and chemical changes.

### Environmental Factors

- Extreme temperatures – High or low temperatures increase resistance.
- Mechanical damage – Cracks, dents, cause internal disconnects increasing resistance.
- Improper storage – Environmental exposure can accelerate aging and resistance rise.

By measuring resistance under controlled conditions, the impact of these factors can be evaluated.

## DC Measurement Methods

Internal resistance has a complex behavior based on electrochemical factors. However, it can be approximated by DC measurements under specific conditions using Ohm’s law.

### Voltage Drop Method

This simple test involves passing a DC current through the battery and measuring the voltage drop which manifests due to the internal resistance.

#### Test Circuit

The battery is discharged at a low steady current ITest. A voltmeter measures the terminal voltage V1 without load and V2 under the test current drain.

#### Calculations

The internal resistance is calculated using Ohm’s law:

The test current should be low enough such that the voltage drop is less than 10% of the battery’s open circuit voltage. Typically 10-50mA per Ah capacity is appropriate.

**Pros**

- Simple and fast to implement
- Minimal equipment required

**Cons**

- Only valid at low currents due to nonlinearity
- Poor resistance resolution

### Discharge Test Method

This test determines internal resistance based on the battery’s runtime under load to a discharge cutoff voltage.

#### Test Circuit

A constant discharge current load is applied to drain the battery till a cutoff voltage level. The discharge time to reach the cutoff voltage is measured.

#### Calculations

The battery’s theoretical capacity without internal resistance is:

$$Capacity_{Theoretical} = I_{Test} x t$$

Where ITest = Discharge current in Amps

t = Time to cutoff in hours

The actual deliverable capacity considering resistance is:

$$Capacity_{Actual} = \int I :dt$$

The internal resistance is then:

$$R_{internal} = \frac{V_{cutoff}}{I_{Test}} – \frac{Capacity_{Actual}}{Capacity_{Theoretical}}$$

Where Vcutoff is the voltage cutoff level

**Pros**

- Accounts for nonlinear battery behavior
- Provides average internal resistance

**Cons**

- Time consuming test
- Requires accurate current and timing measurements

## AC Measurement Methods

AC techniques help overcome some limitations of DC methods and provide more detailed resistance analysis.

### Electrochemical Impedance Spectroscopy

This method measures the battery‘s complex impedance over a range of AC excitation frequencies.

An AC signal with varying frequency is applied to the battery and the current response is measured to determine impedance. The real part of impedance provides resistance while the imaginary part reflects reactive effects.

Measuring the impedance spectrum allows separating resistance contributions from different sources:

- High frequency region correlates to electrolyte resistance
- Mid-frequency region indicates charge transfer resistance
- Low frequency impedance represents total internal resistance

An electrochemical impedance analyzer instrument is required for such measurements.

**Pros**

- Provides frequency-dependent resistance behavior
- Measures electrolyte, charge transfer and total resistances

**Cons**

- Requires expensive test equipment
- Complex testing and data analysis

### AC Conductance Method

This method involves applying an AC current signal to the battery and measuring the conductance response to determine resistance.

An AC current of fixed amplitude and frequency is passed through the battery while measuring the AC voltage response. The conductance is calculated as:

$$Conductance = \frac{I_{acRMS}}{V_{acRMS}}$$

The internal resistance is the inverse of conductance:

$$R_{internal} = \frac{1}{Conductance}$$

Typically a 1kHz AC excitation signal is used since it correlates well with the DC resistance.

**Pros**

- Simpler testing than full impedance spectroscopy
- Good approximation of DC resistance

**Cons**

- Still requires AC source and measurement capability
- Limited frequency-dependent data

## Test Procedure Guidelines

Follow these guidelines for reliable internal resistance measurements:

- Discharge battery to 50% SOC before testing for best results.
- Allow battery to stabilize at room temperature of 25°C ±2°C.
- Securely connect test leads to minimize contact resistance.
- Apply test currents for sufficient time duration for readings to settle.
- For DC methods, use low currents (~50mA/Ah) to avoid nonlinearity.
- Take average of multiple measurements for more consistent results.
- Size test currents based on battery capacity rating.
- Compare similar measurement conditions when tracking resistance over time.

## Typical Internal Resistance Values

The table below provides typical internal resistance values for common battery types to provide a reference:

Battery Chemistry | Typical Internal Resistance Range |
---|---|

Lithium-ion (Li-ion) | 50 – 150 mΩ |

Nickel-metal hydride (NiMH) | 100 – 300 mΩ |

Lead-acid | 1 – 6 mΩ |

Alkaline (primary) | 150 – 300 mΩ |

However, factors like cell size, construction, quality and operating conditions impact the resistance. Consult manufacturer’s datasheets for expected resistance values.

## Measurement Limitations and Accuracy

Consider these key limitations when measuring battery internal resistance:

- All methods provide an approximation based on certain assumptions.
- Resistance varies nonlinearly with operating conditions.
- Measurements have inherent errors from equipment accuracy and tolerances.
- Contact resistances and connections add uncertainties.
- AC methods measure slightly lower than true DC resistance due to absence of electrochemical effects.
- Temperature changes during testing can skew results.

Typical measurement accuracy levels for different methods:

- Voltage drop method: ±3% to ±10%
- Discharge test: ±5% to ±15%
- AC conductance: ±2% to ±5%
- Impedance spectroscopy: ±2% to ±5%

Improving measurement consistency and using calibrated equipment enhances accuracy. Periodically cross-validate methods for better reliability.

## Internal Resistance Measurement Applications

Measuring internal resistance is useful in the following battery applications:

### Design and Development

- Comparing internal resistances of different cell chemistries and constructions
- Determining cell configurations to meet voltage and current requirements
- Estimating effective capacities, runtimes and voltage drops
- Thermal modeling using I2R heating rates
- Developing battery fuel gauges and state of charge estimators

### Production Testing

- Incoming quality assurance checks of cells and battery packs
- Process control and batch acceptance testing
- Benchmarking resistance across manufacturers
- Detecting manufacturing defects

### Maintenance and Service

- Identifying battery aging and determining end of life
- Diagnosing cell damage or deterioration
- Verifying battery health after storage, transportation or cycling
- Ensuring specifications are still met during service life

## Internal Resistance Measurement FAQs

### Q: What is the easiest and cheapest way to measure battery internal resistance?

The voltage drop method provides the simplest approach using just a voltmeter and DC load. But it only works at low currents. For a basic measurement, a purpose-built resistance meter is reasonably affordable and simple to operate.

### Q: Which provides more accurate resistance measurement – DC or AC methods?

AC techniques like impedance spectroscopy generally provide more accurate and repeatable measurements. However, DC methods can also achieve good accuracy if properly implemented.

### Q: How often should I measure battery internal resistance?

For new batteries, measure initial internal resistance as a baseline. Then re-measure periodically during service, such as every 6 months or after certain cycle counts. Check resistance more frequently for batteries exposed to high-stress conditions.

### Q: How do I calculate power loss from internal resistance?

Power loss due to internal resistance is calculated using:

$$P_{loss} = I^2R_{internal}$$

Where I is the discharge current and Rinternal is the internal resistance value. This gives power loss in Watts.

### Q: What is a normal internal resistance change as a battery ages?

It’s typical for internal resistance to increase up to 2x over a battery’s lifespan. For example, a Li-ion cell resistance may rise from 50mΩ to 100mΩ. Drastic or sudden resistance increases likely indicate a fault or battery failure.

## Conclusion and Summary

Key points to remember:

- Battery internal resistance determines runtime, capacity, efficiency and discharge capabilities.
- DC methods like voltage drop and discharge testing provide simple resistance measurement but have limitations.
- AC techniques like impedance spectroscopy give detailed frequency-based resistance analysis.
- Test conditions like SOC, temperature, connections and currents impact results.
- Compare measured resistance values to manufacturer’s datasheets.
- Monitor resistance change over time to identify aging and detect battery faults.

Determining the internal resistance by suitable DC or AC methods allows fully characterizing battery performance to meet application requirements.