Skip to main content

Notch filter calculator

The depth comes down to the coil

A notch filter is a tuned circuit that, at its own frequency, either shorts the signal to ground or blocks its path. The resonance formula is trivial, but the depth of the notch depends entirely on coil Q: the capacitor has nothing to do with it. So the real question is not “what L and C” but “is there enough Q”.

LC
A series circuit across the line: at resonance its impedance drops almost to zero
Circuit
What you set
Notch frequency (MHz)
Tank reactance X (Ω)
Coil Q
System impedance (Ω)
Result
Notch frequency
Inductance
Capacitance
Tank reactance
Impedance of the circuit at resonance
Notch depth

📐 The formulas​

A series LC across the signal path:

f₀ = 1 / (2π·√(L·C))
X  = 2π·f₀·L
r  = X / Q                       ← the circuit's resistance at resonance
Depth: A[dB] = 20·log10( 1 + Z₀/(2·r) )

A parallel LC in series with the path:

R_res = Q · X
Depth: A[dB] = 20·log10( 1 + R_res/(2·Z₀) )

The notch width is worked out not “at −3 dB from the peak” but more honestly: over what span the attenuation still exceeds a chosen level.

series arrangement:  BW = f₀ · |X_required| / X

How much Q it takes:​

DepthCircuit resistance in a 50 Ω path
20 dB2.8 Ω
30 dB0.81 Ω
40 dB0.25 Ω
Where this calculator stops:
  • The depth assumes an ideal capacitor: a real one with poor temperature coefficient and losses gives less
  • Coil self-capacitance is not accounted for, and it creates a second, spurious resonance higher up
  • The deeper the notch the narrower it is — a narrow notch easily drifts off the interference
  • For −40 dB you need a Q of several hundred: an air-cored coil on HF gives 150–250

🎯 In practice​

  • Rejecting a local FM transmitter at the input of an HF receiver.
  • Cutting off a neighbouring band when two stations are operating at once.
  • Removing interference from a switch-mode supply at one particular frequency.
Practical advice:
  1. For −40 dB an air-cored coil is usually not enough — use a helical resonator.
  2. The circuit reactance is a free parameter: a lower X gives a wider notch, a higher one a deeper notch.
  3. Tune on an analyser rather than to the calculation: stray capacitance moves the frequency by percent.
  4. Two series circuits on slightly different frequencies give a wider, flatter notch than one deep one.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Notch filter calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/notch_filter (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

Last updated on