Chebyshev Band-Pass Filter Calculator

A Chebyshev band-pass filter accepts a small equal ripple in the passband in exchange for steeper skirts than a Butterworth design. Enter the center frequency, bandwidth and ripple to get the series and parallel LC resonator values instantly, with the frequency response plotted – ideal for receiver front-end selectivity and image or noise rejection.

Equal ripple, steep skirtsOdd order 1–9Type 1 / Type 2 topologiesL in nH · C in pF

① Input Parameters

Order n (resonators)1–9Center frequency f0MHzBandwidth BWMHzImpedance ZoΩPassband rippledB

This tool designs for equal source and load impedance, so n must be odd; an even entry is automatically increased by 1. BW is the ripple bandwidth (passband edges).

② Results

#	Type 1		Type 2
#	L (nH)	C (pF)	L (nH)	C (pF)
1
2
3
4
5
6
7
8
9

Each row is one resonator (L and C both resonate at f0). Type 1: odd rows = shunt parallel LC, even rows = series-arm series LC; Type 2 is the reverse. Only the first n rows are shown.

Circuit Diagram

Type 1: odd sections are parallel LC resonators to ground (high impedance at f0, so they do not load the line); even sections are series LC resonators in the series arm (nearly a short at f0, passing the signal). Type 2 is the reverse. For even n the last section is the other resonator type.

Frequency Response (current inputs)

Inductor LCapacitor CGroundCenter frequency f0Band edges

Ideal response: A(Ω) = 10·log[1 + ε²·T_n²(Ω)], ε² = 10^ripple/10 − 1; Ω = (f/f0 − f0/f) · f0/BW. The passband (between the orange lines) has equal ripple.

How to Use

Enter the order n (number of resonators, odd 1–9). A higher order gives steeper skirts.
Enter the center frequency f0 and bandwidth BW in MHz, and the system impedance Zo (usually 50 Ω).
Enter the passband ripple in dB, typically 0.1–0.5 dB. More ripple gives steeper skirts but poorer passband match.
Click Calculate. The table lists L (nH) and C (pF) for every resonator of Type 1 and Type 2; pick one topology from the diagram, build it and tune by measurement.

Theory & Formulas

First the Chebyshev low-pass prototype values g_k are computed from the ripple and order:

β = ln[ coth( L_Ar / 17.37 ) ], γ = sinh( β / 2n )
a_k = sin( (2k − 1)π / 2n ), b_k = γ² + sin²( kπ / n )
g₁ = 2a₁ / γ, g_k = 4a_k−1a_k / ( b_k−1 · g_k−1 )

The low-pass to band-pass transformation then turns each series inductor into a series LC resonator in the series arm and each shunt capacitor into a parallel LC resonator to ground:

ω₀ = 2π · f₀, Δω = 2π · BW
Series-arm series resonator: L = g_k·Z_o / Δω　C = Δω / ( g_k·Z_o·ω₀² )
Shunt parallel resonator: L = Δω·Z_o / ( g_k·ω₀² )　C = g_k / ( Δω·Z_o )

Ripple and return loss

Passband ripple L_Ar sets the worst-case return loss RL = −10·log(1 − 10^−L_Ar/10): about 16.4 dB for 0.1 dB and 9.6 dB for 0.5 dB. Every resonator satisfies L·C = 1/ω₀², i.e. resonates at f0.

Design Tips

The narrower the fractional bandwidth (BW/f0), the larger the series inductors and the smaller the shunt inductors, and component Q losses rise sharply; for bandwidths of only a few percent consider coupled-resonator, dielectric, SAW or ceramic filters.
At RF use C0G/NP0 capacitors and high-Q inductors, and make sure every part has a self-resonant frequency well above f0.
In Type 1 the shunt inductors short DC to ground, and in Type 2 the series capacitors block DC – keep this in mind if a DC bias must pass.
Keep components close together and connect them with 50 Ω lines (see the Microstrip Line Calculator); finally measure S21/S11 on a network analyzer and trim the capacitors to center the response.

FAQ

How does Chebyshev differ from Butterworth?: Chebyshev has equal ripple in the passband in exchange for steeper skirts at the same order; the Butterworth (maximally flat) BPF has the flattest passband and smoother group delay.
Why must the order be odd?: With equal source and load impedance, a Chebyshev prototype ends in Zo only for odd orders; even orders need an impedance transformation, so this tool adds 1 to an even entry.
Is f0 the arithmetic or geometric center?: The tool works with ω₀, so the band edges satisfy f₁·f₂ = f0² (geometric symmetry). For narrow bandwidths the two are almost identical.

Related Design Tools

Maximally Flat (Butterworth) BPF Chebyshev Band-Stop Filter Chebyshev Low-Pass Filter Chebyshev High-Pass Filter Microstrip Line Impedance All 28 design tools ›

Designing an RF product? WENSHING supplies RF transceiver modules, LoRa modules, SMD ceramic antennas, directional antennas and UHF RFID readers, and offers custom RF circuit design support.

Contact an Engineer