Battery Fuel Gauge and Coulomb Counting Design

A fuel gauge answers a simple question that is surprisingly difficult to measure: how much energy is left in the battery. The cell voltage moves with load and temperature, the capacity changes as the battery ages, and the current that has to be counted ranges over several orders of magnitude. A usable gauge combines several methods and compensates for the conditions it can measure.

What a Fuel Gauge Reports

state of charge is the remaining capacity expressed as a percentage of the capacity the battery can deliver under the conditions of use. It is not a fixed property of the cell, because capacity falls with temperature and with age, so a gauge that reports a percentage without compensating for those effects will become optimistic as the battery gets older.

Some systems report a simpler quantity instead: the remaining charge in milliampere hours, or the time remaining at the present load. Each has its place. Time remaining is the most useful figure for a user but the hardest to estimate, because it depends on the load, which the gauge does not control and which may change without warning.

Accuracy expectations matter as much as accuracy itself. A gauge that is within a few percent over most of the range and less accurate near the extremes is usually acceptable, while one that jumps from twenty percent to zero without warning is not, even if the average error over a full cycle is small. The behaviour near empty is what users notice.

Coulomb Counting and Its Errors

coulomb counting integrates the current over time, which gives the charge that has entered or left the battery. The measurement is conceptually simple and works over the whole range, including during charging, but its errors accumulate because the integration never resets itself. A small offset in the current measurement becomes a growing error in the reported charge.

The offset is the dominant error. A current sense amplifier with an offset of a few microvolts, referred to a sense resistor of one milliohm, corresponds to a few milliamperes of apparent current. Over a day of standby operation that error can accumulate to a significant fraction of the battery capacity, which is exactly the situation in which the gauge is relied upon.

Full charge and full discharge events provide the correction. A gauge that knows when the battery is full can reset its count to the known capacity, and one that knows when the battery is empty can reset to zero. Both events have to be detected reliably, which usually means monitoring the voltage and the current together rather than relying on a single threshold.

Open Circuit Voltage and Impedance Methods

open circuit voltage is a direct indication of state of charge, provided the battery has rested long enough for the terminal voltage to equal the internal voltage. After a rest of a few hours the relationship is repeatable, which makes it useful for a gauge that spends most of its life idle, such as in a sensor node.

The difficulty is the relaxation time. A battery that has just been discharged needs minutes to hours to settle, and during that period the terminal voltage is not a reliable indicator. An equivalent circuit model can shorten the wait by estimating the internal voltage from the terminal voltage and the recent current history, at the cost of some accuracy.

battery impedance changes with state of charge and with temperature, and it can be measured by applying a small current step or a small alternating signal and observing the response. The measurement is informative because the impedance rises sharply as the battery approaches empty, but it requires a controllable load and careful signal processing.

Combining the Methods

A practical fuel gauge uses coulomb counting as the primary method and the voltage measurements as a correction. The voltage is used when the battery is at rest to correct the accumulated count, and the coulomb count carries the reading through the periods when the voltage is uninformative because of load and relaxation.

The combination is usually implemented as a model that runs in the background. It tracks the open circuit voltage, the internal resistance and the counted charge, and it weights the three according to how long the battery has been resting and how large the current has been. The result is a state of charge that follows the truth more closely than any single method.

Battery impedance is the third input, and it is most useful at the end of the discharge, where it changes quickly. Some gauges use it to decide when to declare the battery empty, which avoids the sudden drop from a few percent to zero that a pure coulomb count can produce when the count is running ahead of reality.

Sense Resistor and Layout

The current sense resistor is the component that sets the accuracy of the whole gauge, and it deserves more attention than the integrated circuit. A one milliohm resistor carrying five amperes dissipates twenty five milliwatts, which is manageable, but the same resistor at fifty amperes dissipates two and a half watts and will warm up by tens of degrees unless the copper is sized for it. The width required for a given current is covered in our guide to trace width and current.

A four terminal resistor removes the effect of the solder joints and the trace resistance from the measurement, and it should be used wherever the accuracy requirement justifies the cost. Where a two terminal part is used, the sense connections must be taken from inside the current path and symmetrically on both sides, because an asymmetric tap produces a gain error rather than a common mode shift.

Keep the sense traces short, matched and routed as a pair to the gauge input. They carry a signal of tens of microvolts, so any copper that also carries load current will add an error that varies with the load. Returning the sense pair to the gauge input over a path that is separate from the power return is the single most important layout decision in the channel.

Temperature, Ageing and Cell Matching

The capacity of a lithium cell falls noticeably at low temperature, and the internal resistance rises. A gauge that does not account for temperature will report a state of charge that is too high in the cold, which is the dangerous direction because the user may then rely on capacity that is not there. Reading a temperature sensor mounted on the cell and scaling the estimated capacity is the usual correction.

Ageing reduces capacity and increases resistance, and it happens gradually over hundreds of cycles. The gauge can track the effect by comparing the charge it counts between a full and an empty event with the capacity it expected. A persistent difference indicates that the capacity estimate needs to be adjusted, and the adjustment should be slow so that a single unusual cycle does not corrupt the model.

Cell matching matters in a pack with several cells in series. The weakest cell determines when the pack is empty, so the gauge has to track the pack rather than an average of the cells. Monitoring individual cell voltages and using the lowest one for the end of discharge decision keeps the reported range consistent with what the pack can actually deliver.

Verification in the Product

Verification begins with a controlled discharge at a known temperature, recording the current, the voltage and the reported state of charge. Comparing the reported value with the charge actually delivered gives the error directly, and the shape of the error curve shows which method is drifting and in which direction.

Repeat the test at the temperature extremes and after a period of accelerated ageing. A gauge that is accurate when new and inaccurate after a few hundred cycles has a capacity tracking problem, while one that is inaccurate at low temperature has a compensation problem. Both are correctable, but only if the test reveals them before the product ships.

The last check is behavioural rather than numerical. Run the product through its normal use until the battery is empty and observe whether the reported value falls smoothly or drops abruptly. A smooth fall with a small final error is a good gauge, whatever its average accuracy, while an abrupt drop near the end indicates that the end of discharge detection needs attention. The measurement techniques used to verify these channels are the ones described in mixed signal board design for precision analogue front ends, and the same manufacturing considerations described in board quality characteristics apply to the sense resistor assembly.

FAQ

How accurate can a fuel gauge be? A well compensated gauge is typically within a few percent over the middle of the range, with larger errors at the extremes where the voltage curve is flat and the model is least certain.

Can I estimate state of charge from voltage alone? Only when the battery has rested. Under load the terminal voltage depends on the current and on the internal resistance, so a voltage only gauge is unreliable during use.

Why does my gauge read twenty percent and then shut down? Either the coulomb count is running ahead of reality, or the end of discharge threshold is set too low. Check the current offset first, then review the impedance based end of discharge detection.