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LC bandpass filter calculator

Where the practical limit lies

A bandpass filter comes from a low-pass prototype by replacing each element with a tuned circuit. The mathematics is simple, but there is a hard practical limit: the narrower the band, the larger the component values and the more coil Q spoils the response. At around 5 % fractional bandwidth an LC filter gives up, and crystal territory begins.

A series inductor turns into a series resonant circuit, a shunt capacitor into a parallel one
Response
Prototype order
Lower band edge (MHz)
Upper band edge (MHz)
System impedance (Ω)
Topology

📐 The formulas​

f₀ = √(f1 · f2)              Δ = (f2 − f1) / f₀

Bandpass transformation of the prototype:

from a series L:  L = g·R₀/(Δ·ω₀),   C = Δ/(g·R₀·ω₀)     ← a series tuned circuit
from a shunt C:   C = g/(Δ·R₀·ω₀),   L = Δ·R₀/(g·ω₀)     ← a parallel tuned circuit

Every prototype element becomes a tuned circuit, so the part count doubles.

Where this calculator stops:
  • Below about 5 % fractional bandwidth the component values become unrealistic and coil losses dominate. The calculator warns you
  • Coil Q is not accounted for: in a narrowband filter it eats both the passband loss and the shape of the skirts
  • An even-order Chebyshev needs different input and output impedances
  • Coupling between adjacent coils is not accounted for: in a dense layout it changes the response

🎯 In practice​

  • A receiver band filter (a preselector) — typically 3–10 % wide.
  • A filter after the mixer, ahead of the IF amplifier.
  • A transmitter bandpass filter, to suppress harmonics and subharmonics at once.
Practical advice:
  1. For bandwidths below 5 % use a crystal filter — an LC one loses on every count there.
  2. Mount the coils at right angles to each other or screen them: stray coupling spoils the shape.
  3. Tune each circuit separately with the neighbours shorted out, or tuning is impossible.
  4. The passband loss of a three-pole filter with Q = 200 is about 1–2 dB; allow for it in your budget.

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UR3PKI. «LC bandpass filter calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/lc_bandpass (licence CC BY-NC-SA 4.0).

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