Voltage Divider Accuracy Design

A voltage divider is two resistors and a ratio, and it appears in almost every analog circuit. Its accuracy is usually worse than the designer expects, because the errors that matter are the ratio errors and the loading, not the absolute values.

The Ratio and Its Tolerances

The output is the input multiplied by the ratio of the lower resistor to the sum. The absolute values do not matter for the ratio, and the tolerances of the two resistors do not add directly either.

For a divider with two resistors of the same tolerance, the worst case ratio error is approximately the tolerance multiplied by the ratio of the two values. A pair of one percent resistors in a ten to one divider gives a ratio error much better than one percent, which is why dividers are more accurate than the individual parts suggest.

Matched networks exploit this. A pair of resistors on one substrate with a ratio tolerance of a few parts per million is available, and it is the component to use whenever the ratio is what matters.

temperature coefficient and Tracking

The temperature coefficient of the ratio is the difference between the coefficients of the two resistors, not the coefficient of either one. Two resistors with the same coefficient track and the ratio stays constant as the temperature changes.

A network in one package tracks well because the two elements are on the same substrate. Two separate resistors of the same type from the same batch track reasonably and not perfectly.

Where the divider is used to scale a signal for a converter, the tracking matters more than the absolute accuracy. A ratio that is stable over temperature gives a scale factor that a calibration at one temperature can remove.

loading error

The output of a divider is a voltage source with an impedance equal to the parallel combination of the two resistors. Anything connected to it draws current and reduces the output.

loading error is the drop caused by that current, and it is proportional to the load. A divider with a source impedance of ten kiloohms feeding an input with a resistance of a megohm has a loading error of about one percent.

A buffer amplifier after the divider removes the loading, at the cost of its own offset and drift. Where the load is a converter with a sampling capacitor, the loading is a transient and the settling behaviour matters as much as the resistance.

input impedance and Source Loading

The divider also loads whatever drives it. A sensor with a high output impedance connected to a low resistance divider is attenuated by the divider input impedance as well as by the ratio.

input impedance of the divider is the sum of the two resistors, and it should be high compared with the source impedance if the source impedance is known and stable. Where it is not known, a buffer is placed in front of the divider.

The choice of resistance is a compromise between the loading on the source and the loading by the load, and the two pull in opposite directions. A high resistance divider is not a solution, because it is more sensitive to leakage and to the bias current of the following stage.

Leakage and Board Effects

At a high resistance the board itself becomes part of the divider. Surface leakage and flux residue add a resistance in parallel with the lower element, and the effect is worse in humid conditions.

Cleaning and coating the board removes most of it, and the practices are the same as for any high impedance node, described in our guide to conformal coating board protection. For a divider above a megohm, a guard ring is the next step.

Leakage through the input protection diodes of a following stage also loads the divider. A diode with a leakage of a nanoamp is negligible at a low resistance and significant at a high one.

Dividers in Measurement

A resistive divider scaling a high voltage for a converter is the classic application, and here the ratio accuracy and the voltage coefficient both matter. A resistor whose value changes with the applied voltage introduces a non linearity.

High value resistors have a voltage coefficient, and a divider made of two such parts is non linear at the top of its range. The effect is specified in parts per million per volt and it is the reason a divider is calibrated at the voltage it will be used at.

The divider for a high voltage also has to withstand the voltage, which means a resistor rated for it and a creepage distance along the board. A divider that works on the bench and flashes over in a damp environment is a common field failure.

Practical Layout

Place the two resistors close together so that they share a temperature. A gradient across the board changes the ratio if the two have different coefficients, and the effect is small and real.

Keep the output node short and away from switching circuits. The node has a moderate impedance and it is the point at which the signal is most easily disturbed.

Return the divider to the analog ground rather than to the nearest ground, which is often the digital ground of a converter. The current in the divider is small and the noise on a digital ground is large compared with the signal.

Verification and Faults

Verify the divider by measuring the input and the output at the same time with two instruments, and calculating the ratio. A single measurement of the output does not separate a divider error from an input error.

Check the ratio at two temperatures if the accuracy is critical. A change in the ratio indicates a mismatch of the temperature coefficients.

Check the output with the following stage connected and disconnected. A difference between the two readings is the loading error, and it is the most common reason a divider reads low. The release checks that keep such a divider consistent are collected in our PCB design release checklist, and the assembly points in judging PCB quality.

Process Control and Verification

On a design of this kind, voltage divider is the item that decides how the rest of the board is arranged. Reviewing the design before the data is released is cheaper than correcting it after the panel is in the tank, because every step downstream inherits the decision made at the front end. Documenting the assumption is part of the design work, and a short note on the drawing prevents a question that would otherwise arrive a day later and cost a day of schedule.

Process Control and Verification

On a design of this kind, voltage divider is the item that decides how the rest of the board is arranged. Reviewing the design before the data is released is cheaper than correcting it after the panel is in the tank, because every step downstream inherits the decision made at the front end. Documenting the assumption is part of the design work, and a short note on the drawing prevents a question that would otherwise arrive a day later and cost a day of schedule.

FAQ

Does the resistor tolerance add in a divider? Not directly. What matters is the ratio tolerance and the tracking of the two parts over temperature.

Why does my divider read low? Loading. The following stage draws current and the source impedance of the divider drops the voltage.

Can I use a divider for a high voltage measurement? Yes, with resistors rated for the voltage, a ratio calibration and enough creepage on the board.