Checking Active Filter Pole Frequency Against Component Tolerance

A filter designed for a particular cutoff frequency does not necessarily retain that response after preferred component values, production tolerances, and temperature changes are included. The useful review separates movement of the poles from changes in damping. A single nominal frequency calculation cannot establish both.

Identify which values set the response

Write the equations for the actual circuit topology and identify the resistors and capacitors controlling frequency and Q. The Analog Devices AD8295 data sheet illustrates a Sallen Key section whose capacitor relationship affects Q while resistor and capacitor tolerances affect pole frequency. The particular equations belong to the illustrated connection.

Use the fitted values rather than the unrounded design values. A substitution to the nearest stocked capacitor can change the response before manufacturing variation is considered.

Distinguish common shifts from mismatch

If all frequency setting capacitors change together, the response may principally move along the frequency axis. If their ratio changes, its shape can change as well. Evaluate both types of variation instead of applying one percentage to the final cutoff.

For a simple isolated RC pole, frequency is inversely proportional to the product RC. If both R and C increase by 5 percent, that product increases by 10.25 percent and the pole falls by about 9.3 percent. This example does not describe every second order circuit, but it shows why adding percentages is only an approximation.

Translate response variation into a requirement

Check gain at the highest required signal frequency and attenuation at the lowest unwanted frequency. Also inspect peaking and step response if the signal contains transients. A shifted cutoff may be acceptable while increased ringing is not.

Include temperature coefficients, relevant capacitor bias effects, and loading only where they apply to the selected parts and connection. Avoid treating the tolerance printed on a component as a complete lifetime error budget.

Verify representative assemblies

Measure the transfer function with known source and load impedances. Record actual component values when investigating a response near the limit. This separates an assembly value error from a predictable tolerance effect.

Save the nominal calculation, evaluated variation cases, measured response, and acceptance frequencies. If parts are selected or trimmed, document which relationship is controlled and how it is checked. A useful release criterion states the permitted gain, attenuation, and transient behavior of the assembled filter. Merely requiring its nominal cutoff to equal the design target leaves important changes in response shape unaddressed.