Reviewing Thermal Noise When Scaling Analog Resistor Values

Increasing every resistor in an analog network can preserve its nominal gain while changing its noise, loading and sensitivity to leakage. Review the electrical consequences before accepting resistor scaling as a simple power-saving change. Matching the original ratio is only one part of the comparison.

Calculate the resistance seen by the signal

TI’s thermal-noise explanation relates a resistor’s voltage-noise density to resistance and absolute temperature. The square-root relationship means a tenfold resistance increase produces approximately 3.16 times the ideal thermal voltage-noise density at unchanged temperature.

Identify the equivalent resistance relevant to each node. In a divider driven by an ideal voltage source, both resistors influence the output’s noise and source impedance. In an amplifier, each resistor’s contribution follows its own path to the output. Do not add resistor values simply because they appear near one another.

Compare the complete signal chain

Keep the signal bandwidth and gain fixed while comparing candidate networks. Calculate the resulting output-noise contribution, then refer it to the input if that matches the product requirement. Include the amplifier’s current-noise interaction with the changed source impedance.

For illustration, scaling a divider from 10 kilohms and 10 kilohms to 100 kilohms and 100 kilohms leaves its ideal ratio unchanged. It also raises its Thevenin resistance from 5 kilohms to 50 kilohms. That new impedance is relevant to noise, input bias effects and any sampling load attached to the divider.

Look beyond the ideal resistor model

Check input leakage, bias current, protection-device leakage and contamination sensitivity at the new impedance. Review settling after a switched input or ADC acquisition event. Keep these error mechanisms distinct from thermal noise so the eventual test can identify which one changed.

Consider the power and temperature of the resistor network itself. Use the expected operating temperature in the noise estimate and assess whether the selected component technology has other noise behavior relevant to the application. Do not treat an ideal thermal-noise calculation as a complete component characterization.

Verify the reason for the change

Measure the actual power saving and the resulting measurement uncertainty using the same bandwidth as the original design. Test settling and DC error separately. Include the intended sensor or a representative source, because an ideal laboratory source can conceal impedance-related interactions.

Retain the old and new network values, calculated contributions and test results. Approve the scaling only when the power benefit and measurement performance both meet their assigned requirements. This keeps a convenient ratio-preserving edit from silently changing the behavior of a precision channel.