How it works
The Twin-T network consists of two T-sections: one with two capacitors and a centre resistor of R/2, another with two resistors and a centre capacitor of 2C. At f_notch = 1/(2πRC), the two paths provide equal amplitude but opposite phase outputs that cancel completely — infinite theoretical attenuation. The passive Twin-T has a broad notch (low Q ≈ 0.25); placing it in the negative feedback loop of a non-inverting op-amp narrows the notch dramatically. Feedback fraction β_notch → 0 at the notch frequency, forcing the op-amp gain → infinity compensation to maintain the virtual short, which translates to a deep null in the overall transfer function.
Key points to remember
For a perfect null at f_notch, component matching is critical: the two resistors must be equal to within 0.1% and the two capacitors must match similarly — 1% components give only about −40 dB rejection instead of the theoretical −∞ dB. The 3 dB bandwidth of the notch is BW = f_notch / Q. In medical equipment, a 50 Hz notch filter is mandatory per IEC 60601-1 standards. An alternative implementation uses the state-variable filter architecture where the notch output is HP + LP summed — this allows independent electronic tuning of notch frequency by changing the same clock signal to both integrators.
Exam tip
The examiner always asks you to explain why the Twin-T passive network alone gives a low-Q broad notch while placing it in the op-amp feedback loop gives a high-Q sharp notch — the key is that the loop gain approaches zero at f_notch, making the op-amp compensate by driving its output hard to maintain the virtual short.