Printed-Resistor Twin-T Filters: Keep Component Mismatch Out of the Notch

System boundary

Two parallel passive T branches, external capacitors, source and receiver. The printed resistor relationships contribute to cancellation but do not alone establish installed rejection.

Integration interfaces

Integration risks

Label the two parallel T branches explicitly

Connect one branch from input to output through two series resistors, each nominally R, with a capacitor of 2C from their midpoint to the signal reference. Connect the second branch through two series capacitors, each nominally C, with a resistor of R/2 from their midpoint to the same reference. These are two complete T networks in parallel, not two independent filters whose outputs can be tested separately and then assumed to cancel.

The calculations here use a low-impedance voltage source, an unloaded output and a fixed reference. Buffers, finite source resistance or an active feedback connection change the implementation. A ceramic thick-film network can supply the resistive elements, but the capacitors and connected active circuit remain necessary parts of the filter requirement. State exactly which components are included in the supplied assembly.

Separate the cancellation frequency from the width of rejection

For the ideal balanced passive network, the null frequency is f0 = 1/(2 pi RC). R is the nominal series resistance in ohms, C is the nominal series capacitance in farads and f0 is in hertz. At that frequency the ideal output cancels. This ideal zero is a mathematical property, not a promise of infinite rejection in a physical module.

The passive network has a broad surrounding response. Active feedback can change the rejection bandwidth, but it introduces an additional circuit and its stability requirements. A narrow notch and a deep notch are not interchangeable descriptions. State how much attenuation is required at the unwanted frequency and how much loss is permitted at nearby useful signal frequencies before deciding whether this topology fits the application.

Calculate the nominal values and common-scale movement

Assume a passive network with two 10 kilohm series resistors, a 5 kilohm shunt resistor, two 330 nF series capacitors and a 660 nF shunt capacitor. Its nominal ideal null is approximately 48.2288 Hz. These are illustrative values selected to expose the calculation, not a proposed solution for a particular mains frequency or a released component specification.

If all three resistors increase by two percent together while the capacitor values remain unchanged, the resistor relationships remain balanced. The ideal null moves to approximately 47.2831 Hz. Matching alone therefore does not keep rejection centered on a fixed interference frequency. Conversely, keeping one RC product correct does not establish the other relationships required for cancellation. Record both absolute values and relevant ratios.

Evaluate residual output when one balance element changes

Keep the illustrative series resistors and all capacitors nominal, but increase only the shunt resistor from 5 kilohms to 5.1 kilohms. Solving the three internal/output node equations at the original 48.2288 Hz gives an output-to-input amplitude ratio of approximately 0.003509, or about minus 49.10 dB. A 1 V input at that frequency would leave approximately 3.51 mV in this ideal passive mismatch model.

This result is evaluated at the specified original frequency; it does not assert that the new minimum lies there. Sweep the response to locate that minimum separately. The result also excludes buffer error, parasitic coupling and capacitor loss. It demonstrates why accepting a resistor solely because its individual value is close to nominal cannot replace a functional rejection allocation for the complete balanced network.

Match the resistors to the capacitors actually used

The two series capacitances and doubled shunt capacitance participate directly in cancellation. Their relationships can change with component selection and operating conditions. Request the actual capacitor family and relevant tolerance or measured values instead of allocating the entire rejection target to printed resistor matching. A resistor network cannot correct an unspecified external capacitor set automatically.

If components are selected or adjusted as an assembled set, preserve that association in the manufacturing and repair records. Replacing one capacitor with an arbitrary nominal equivalent can disturb the accepted null. Likewise, achieving a deep null with one selected set does not establish interchangeability across the full allowed component population. Decide whether production acceptance is based on component relationships, assembled functional testing or both.

Use a rejection specification that cannot be satisfied at the wrong frequency

Consider an illustrative customer requirement of at least 60 dB rejection at a named frequency. A minus 49.10 dB result at that frequency fails even if the frequency sweep shows a deeper dip elsewhere. Conversely, a deep dip at the right frequency can still remove too much nearby useful signal. Keep the required response envelope visible during adjustment.

Verify that the measured residual belongs to the filter

Deep rejection makes the measurement setup part of the problem. Generator distortion can put harmonics outside the notch even while the fundamental is strongly rejected. A broadband output RMS reading can therefore be dominated by those harmonics or by noise. Use a method that distinguishes the required fundamental residual from other frequency components, and retain the bandwidth and detector settings.

Check direct input-to-output coupling through cables, fixtures and the instrument before assigning a residual entirely to component mismatch. Maintain a stable reference connection for both T branches. Record the actual source amplitude at the filter input and avoid receiver loading that changes the circuit. A measured floor limited by the setup should be reported as a bound, not as the filter's exact minimum amplitude.

Deliver a balanced-network requirement and a reproducible sweep

For a ChipSimple printed-resistor enquiry, provide all resistor and capacitor connections, the desired interference band and the allowed nearby signal loss. Identify any permitted adjustment and its direction. An adjustment that improves one frequency point can move the notch or change another response requirement, so preserve the complete accepted sweep rather than only the final meter minimum.

Include source impedance, receiver loading, buffers, temperature range and any component-set association used during tuning. Keep the resistor-network acceptance distinct from the complete module response while ensuring they refer to the same circuit revision. The resulting specification describes a practical rejection function whose limits can be checked, rather than an ideal cancellation diagram interpreted as guaranteed suppression.