Chebyshev Low-Pass Filter Calculator
A Chebyshev low-pass filter allows a fixed amount of passband ripple in exchange for a steeper cutoff than a Butterworth filter. Enter the order, cutoff frequency, impedance and ripple to get the component values of two LC ladder circuits, together with the frequency response and a zoomed view of the passband ripple. It suits transmitters that need strong rejection of nearby harmonics.
How to use
- Enter the order n (1–9, odd only). Raise the order or the ripple for a steeper cutoff.
- Enter the cutoff frequency fc (MHz, passband edge), the system impedance Zo (usually 50 Ω) and the passband ripple (dB).
- Click Calculate. The table lists capacitors (pF) and inductors (nH) for both Type 1 and Type 2 circuits.
- Choose one topology from the circuit diagram, select the nearest standard parts and tune while measuring S21/S11 with a network analyzer.
Theory and formulas
The prototype values gk of a Chebyshev filter are set by the order n and the ripple Lr (dB):
γ = sinh( β / 2n )
ak = sin( (2k − 1)π / 2n ) bk = γ² + sin²( kπ / n )
g1 = 2a1 / γ gk = 4ak−1ak / ( bk−1 · gk−1 ), k = 2 … n
They are then scaled to real components with the usual low-pass transformation:
C = gk / (Zo · ωc) L = gk · Zo / ωc
How to choose the ripple
The response is |H(f)|² = 1 / (1 + ε²Tn²(f/fc)) with ε² = 10Lr/10 − 1. The ripple also sets the worst passband reflection: return loss RL = −10·log10(1 − 10−Lr/10). For example, 0.1 dB ripple corresponds to about 16.4 dB return loss (VSWR ≈ 1.36) and 0.5 dB to about 9.6 dB. RF circuits usually use 0.01–0.1 dB to balance matching and roll-off.
Why odd orders only?
An even-order Chebyshev prototype has a load impedance different from the source impedance (gn+1 ≠ 1) and would need extra matching in a 50 Ω system. Odd orders are terminated in Zo at both ends and can be used directly, so this tool offers odd orders only.
Design tips
- At RF, use high-Q, low-ESR C0G/NP0 capacitors and wire-wound or high-Q multilayer inductors. The self-resonant frequency of every part must be well above fc.
- Chebyshev element values are more sensitive to tolerance. Use capacitors and inductors of ±2% or better and leave pads for tuning.
- PCB traces add parasitic inductance and capacitance. Keep components close together and connect them with 50 Ω microstrip (see our Microstrip Line Calculator).
- For PA harmonic suppression, set fc above the operating frequency with some margin so that the carrier sits in the ripple region and the second harmonic falls in the stopband.
- If you need a perfectly flat passband or better phase linearity, use the Butterworth low-pass instead.
FAQ
- Chebyshev or Butterworth low-pass?
- At the same order a Chebyshev filter has a steeper cutoff and more stopband attenuation, but it has passband ripple and more group-delay variation. A Butterworth passband is flat. If ripple such as 0.1 dB is acceptable, a Chebyshev design can often save one or two components.
- Is a smaller ripple always better?
- Smaller ripple behaves more like a Butterworth filter: better matching but a gentler cutoff. 0.01–0.1 dB is the usual RF range; 0.5 dB or more gives noticeable reflection and is rarely used in 50 Ω RF chains.
- Why is fc not the −3 dB point?
- This tool uses the ripple-bandwidth definition: fc is where the attenuation equals the ripple. The actual −3 dB point is slightly above fc, and the difference grows as the ripple gets smaller.
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