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LC low-pass and high-pass filter calculator

What actually matters here

For a transmitter's harmonic filter the cutoff frequency is not the goal but the means. The goal is a given attenuation at the second harmonic. So the important part of this calculator is not the component values but the stopband table: that is what the filter order gets chosen from.

Rsrc 50 ΩRload 50 Ω
Low-pass: series inductors, shunt capacitors
Response
Filter type
Order (number of elements)
Cutoff frequency (MHz)
System impedance (Ω)
Topology

📐 The formulas​

Butterworth — analytically, with no tables:

g_k = 2 · sin( (2k − 1)·π / (2n) ),   k = 1…n
g₀ = g(n+1) = 1

Chebyshev with a ripple of Ar:

β = ln( cth( Ar / 17.37 ) )
γ = sh( β / 2n )
a_k = sin( (2k−1)π / 2n )
b_k = γ² + sin²( kπ / n )

g₁ = 2·a₁ / γ
g_k = 4·a(k−1)·a_k / ( b(k−1) · g(k−1) )
g(n+1) = 1 (odd n) or coth²(β/4) (even)

Denormalising, low-pass:

series coil:      L = g · R₀ / ω_c
shunt capacitor:  C = g / (R₀ · ω_c)

For a high-pass, swap the element types.

Stopband attenuation:

Butterworth: A = 10·log10( 1 + (f/f_c)^(2n) )
Chebyshev:   A = 10·log10( 1 + ε²·T_n²(f/f_c) )
Where this calculator stops:
  • An even-order Chebyshev cannot be matched to equal terminations — the calculator warns you and shows what output impedance it needs
  • Coil Q is not accounted for: a real filter has higher loss and a slightly different skirt
  • Coil self-capacitance is not accounted for, and it spoils the attenuation at high frequencies
  • The E12 values are shown for guidance: with them the response shifts, so recompute the filter for the parts you actually have

🎯 In practice​

  • A transmitter harmonic filter. Put the cutoff a little above the band and look at the attenuation at 2·f.
  • A filter after a DDS — to remove images and spurs.
  • A receiver input high-pass — to cut off the strong broadcast stations below the band.
Practical advice:
  1. A fifth-order Chebyshev with 0.1 dB ripple is the workhorse choice for an HF transmitter.
  2. The pi topology uses fewer coils, and it is the coils that contribute most of the loss.
  3. Trim a coil by spreading its turns and a capacitor with a parallel trimmer.
  4. Check the finished filter on an analyser: stray capacitance already shows at 28 MHz.

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

How to cite this calculator
UR3PKI. «LC low-pass and high-pass filter calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/lc_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.

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