Notch Filter Frequency⚠ unverified
Electrical / Filters · Compute the centre frequency of a Twin-T notch filter
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| R | R | — | 1.0 | Resistance |
| C | C | F | 1.0 | Capacitance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | f0 | Hz | Notch centre frequency, in hertz (Hz) |
The science & history
Understanding the Parameters
-
$R$, $C$ — the Twin‑T uses matched resistors and capacitors (one arm $R,R,2C$; the other $C,C,R/2$). The single $R,C$ here parameterises that matched set.
-
$f_0$ — where the two arms' outputs are equal in magnitude and opposite in phase, so they cancel.
Derivation (Approaching a Proof)
A Twin‑T splits the signal into a low‑pass T ($R$–$R$ series, $2C$ to ground) and a high‑pass T ($C$–$C$ series, $R/2$ to ground) whose outputs are summed. At low frequency the signal passes through the low‑pass arm; at high frequency through the high‑pass arm; at one special frequency the two arms deliver equal and anti‑phase contributions that cancel exactly. Solving the network for that cancellation condition gives
$$f_0 = \frac{1}{2\pi R C},$$
the same $1/(2\pi RC)$ corner as a simple RC section, but here it marks a rejection null rather than a pass‑band edge. The depth of the null depends on how precisely the components are matched.
History
The Twin‑T notch was widely used from the mid‑20th century in instrumentation and audio to suppress mains hum and unwanted carriers, and (with feedback) to build sharp band‑reject and oscillator circuits. Modern designs often replace it with active or switched‑capacitor equivalents for tunability and depth.
Related Concepts: RC Low-Pass Cutoff, Q Factor, Rlc Bandwidth, Impedance Capacitor
Notes: Registry calculator notch-filter-frequency (unverified; R mislabelled dimensionless — should
be ohms). Assumes an ideal, perfectly matched Twin‑T.