RF filters and attenuators

LC filters

The normalised low-pass prototype values come from the standard formulas (Matthaei, Young and Jones; Zverev): Butterworth gₖ = 2·sin((2k − 1)π/2n), and the Chebyshev recursion for the chosen ripple. They are scaled to your impedance and cut-off, and transformed for high-pass (L ↔ C) and band-pass (each element becomes a series or parallel resonator at the centre frequency).

Give a stop-band requirement and the tool works out the minimum order. The insertion-loss plot is computed from the actual component values, so it doubles as a check of the design. The Butterworth cut-off is the −3 dB point; the Chebyshev cut-off is the edge of the ripple band. Even-order Chebyshev filters need unequal terminations — use an odd order between two 50 Ω ends.

Typical use: a 5-pole Chebyshev low-pass after a transmitter to suppress harmonics.

Attenuator pads

With K = 10^(dB/20):

Pi: shunt = Z₀(K + 1)/(K − 1), series = Z₀(K² − 1)/(2K)
T: series = Z₀(K − 1)/(K + 1), shunt = 2Z₀K/(K² − 1)
Bridged-T: arms = Z₀, bridge = Z₀(K − 1), shunt = Z₀/(K − 1)
Minimum-loss pad between unequal impedances: series √(Z₁(Z₁ − Z₂)) on the high side and shunt Z₂·√(Z₁/(Z₁ − Z₂)) on the low side.

A 3 dB Pi pad in 50 Ω is 292.4 Ω shunt and 17.6 Ω series; 75 to 50 Ω minimum loss is 43.3 Ω and 86.6 Ω for 5.72 dB. The tool shows the power in each resistor and the nearest E24 or E96 value.