Twin-T Filter

Combine two balanced RC T networks to cancel a selected frequency without an inductor.

Schematic and stimulus

V1 on the left supplies an AC analysis magnitude of 1 V and phase of 0°. The upper T has R1 = R2 = 10 kΩ and a 20 nF shunt capacitor C3. The lower T has C1 = C2 = 10 nF and a 5 kΩ shunt resistor R3. Both T networks share the same input and output; their local ground symbols share the source return.

Vin is green, Vout is red and Iin is blue. Current is positive from the source into the network.

Expected response

With $s=j2\pi f$ and $H=V_{\mathrm{out}}/V_{\mathrm{in}}$:

$$H(s)=\frac{1+(sRC)^2}{1+4sRC+(sRC)^2}$$

Use $R=10\,\mathrm{k\Omega}$ and $C=10\,\mathrm{nF}$ in the expression below. The balance ratios are R1 = R2 = 2R3 and C1 = C2 = C3/2. The two paths cancel at the notch frequency.

$$f_0=\frac{1}{2\pi RC}=1.5915\,\mathrm{kHz}$$

The ideal unloaded network has Q = 0.25, giving a broad rejection region. At the exact center, Vout is zero and phase is undefined. The 100 points/decade sweep samples nearby frequencies, so the displayed minimum is finite. Input current need not be small when the output cancels.

Read the Bode chart

The saved AC sweep runs from 100 Hz to 10 kHz, with 100 points per decade. Voltage magnitude and phase are shown separately. Current is hidden from the default chart to keep the voltage-gain scale readable; enable Iin in the chart series controls and expand the magnitude-axis range to plot it. Open Table for all 201 frequency samples and the same probe order. Because the input is 1 V, output voltage in dBV has the same numeric value as voltage gain in dB. Current magnitude is in dBA referenced to 1 A, so it is not a voltage gain.

$$G_{\mathrm{dB}}=20\log_{10}|H|,\qquad \phi=\arg(H)$$

AC sweep computes a sinusoidal steady state at every frequency; it does not show startup. AC analysis magnitude and AC analysis phase control this sweep. The source's Frequency and Peak voltage properties apply to transient simulation instead.

Try two changes

1. Double C1 and C2 → Capacitance from 10n to 20n, and C3 from 20n to 40n. Run again: the notch halves to 795.77 Hz and the balance ratios are preserved. Restore 10n, 10n, 20n.
2. Double R1 and R2 → Resistance from 10k to 20k, and R3 from 5k to 10k. Run again: the notch also halves. Restore 10k, 10k, 5k.

Changing just one of these three matching values breaks the balance and reduces notch depth.

Click Run simulation after each change. Keep V1's AC analysis magnitude at 1 and phase at 0, then restore all component values above to return to the saved response.

Model limits

The transfer function assumes a zero-impedance source and no output load. A real load changes the response. Resistor/capacitor tolerances and leakage limit achievable notch depth. No amplifier or positive feedback is used.