Matched Resistor Pairs in Instrumentation Amplifiers: Input Bias Currents Still Matter

System boundary

The printed input and gain resistors, sensor source impedances and instrumentation-amplifier inputs are analysed as one signal interface. Complete instrument accuracy and electrical protection remain system-level responsibilities.

Integration interfaces

Integration risks

Identify which resistors actually carry the current

Start at each amplifier input pin and trace the direct-current return to its source reference. Include a sensor winding or bridge output resistance, a series protection element, a closed switch and any intentional filter resistor. A resistor in a separate gain-setting connection is not automatically part of this path. Drawing the two equivalent source resistances prevents a common purchasing error: specifying exceptional matching for the wrong pair of resistors.

For a powered linear source, use its small-signal output resistance at the operating point when that model is justified. A protection clamp, switched source or disconnected sensor may not have one fixed resistance. Analyse those states separately. This page addresses bias-current voltage drops in a functioning input path; it does not replace the amplifier's input common-mode, output-swing or supply-sequencing checks.

Keep current direction and voltage polarity explicit

Define both bias currents as positive when flowing from the source into the amplifier. With ideal source voltages held fixed, the positive input falls by Iplus times Rplus and the negative input falls by Iminus times Rminus. Their difference therefore changes by minus Iplus times Rplus plus Iminus times Rminus. Reversing a current direction reverses its contribution; an unsigned maximum-current table cannot predict a signed cancellation.

The output contribution is the input error multiplied by the differential gain while the amplifier remains linear. This calculation excludes the amplifier's own input offset voltage, reference-terminal error, common-mode conversion and thermoelectric voltages. Keep those as separate budget entries so that one measured output offset is not assigned entirely to the ceramic resistor network.

A matched gain ratio can coexist with substantial offset

Consider an illustrative channel with gain 100, positive-input current 20 nA and negative-input current 18 nA. Let the total source resistances be 10 kilohms and 1 kilohm respectively. The input drops are 200 microvolts and 18 microvolts. The resulting differential error is minus 182 microvolts, producing minus 18.2 millivolts at the output. These assumed values demonstrate the arithmetic; they are not specifications for a supplied circuit.

Now make both source resistances 10 kilohms without changing the currents. The residual input error becomes minus 20 microvolts, or minus 2 millivolts at the output. Balancing the resistance reduces the contribution, but the current mismatch remains. Perfect matching of a gain-setting pair would not eliminate either result because it does not remove the input-current voltage drops.

Separate resistance imbalance from current imbalance

Write the mean input current as Iaverage and the signed current difference as Idifference. Likewise, write the mean source resistance as Raverage and the positive-minus-negative resistance difference as Rdifference. The same input error becomes minus Iaverage times Rdifference minus Idifference times Raverage. This form makes the design choices visible: resistance balance addresses the first term, while lower absolute resistance or lower offset current addresses the second.

Do not assume independent extremes cancel in production. A typical current value is not a guaranteed limit, and two individual maximum specifications do not establish the sign correlation of their errors. Use the amplifier manufacturer's applicable bias-current and offset-current limits across the actual temperature range. Where a required limit is unavailable, record the uncertainty and obtain characterization rather than treating nominal matching as a guarantee.

Build an input-state resistance table

The resistance budget belongs to a state, not just a schematic revision. A sensor multiplexer can add different switch resistances to the two inputs. A source with an open cable may lose its direct-current return entirely. A filter capacitor can look open at steady state yet dominate an acquisition transient. Do not mix those transient effects into the static bias-current calculation.

Verify the model by changing resistance deliberately

A useful low-energy bench comparison holds the differential source voltage and common-mode voltage constant while a known resistance is added to only one input path. Repeat at the other input. The changes in output offset should follow the signed current-resistance model if this is the dominant mechanism. Measure the actual source voltage at the relevant boundary so that generator loading does not masquerade as a bias-current effect.

Repeat with balanced added resistances to expose the residual current-difference contribution. Keep the source, amplifier and test fixtures thermally stable; touching connectors can create thermoelectric offsets comparable with small signals. A disagreement is a reason to investigate leakage, common-mode limits or source-model errors, not a reason to adjust the printed resistor ratio until one room-temperature measurement happens to pass.

Balance resistance without hiding other costs

Adding a balancing resistor may reduce one offset term while increasing thermal noise, leakage sensitivity or settling time. It can also alter an input filter pole and its differential response. Evaluate those changes using the actual bandwidth and acquisition requirements. A lower-current amplifier may be a better system decision than adding resistance, but its noise, protection behaviour and operating limits also need review.

For a custom thick-film network, identify whether the requested control is ratio matching, absolute resistance or thermal tracking. They answer different questions. Keep an element intended for gain setting distinct from a series input-protection element, even if both occupy one substrate. The drawing should preserve the circuit function of each element and the conditions under which its resistance is measured.

Deliver an offset budget that can survive integration

The completed record identifies the input state, resistance boundary, current sign convention, amplifier limits, gain and resulting output contribution. Attach the controlled-imbalance measurements and identify any term not explained by the model. A successful resistance comparison supports the circuit analysis; it does not qualify unrelated temperature, humidity or overload behaviour.

When the sensor or amplifier changes, recalculate the input-current terms before reusing the previous network acceptance limit. Keeping this budget with the channel design lets the network supplier control the requested resistors while the electronics owner retains responsibility for the complete measurement error.