Synthesize ladder-LC lowpass, highpass, bandpass, or bandstop filters with Butterworth or Chebyshev response. Component values are computed from the standard g-coefficient tables; |S₁₁| and |S₂₁| are simulated directly from the resulting network via ABCD-matrix cascade.
Component values are computed from standard lowpass-prototype g-coefficients:
Butterworth: g_k = 2·sin((2k−1)π / 2N)
Chebyshev: use Pozar's recursion with β = ln[coth(L_AR / 17.37)] and γ = sinh(β/2N); the load termination g_(N+1) equals 1 for odd N and coth²(β/4) for even N (i.e., even-order Chebyshev needs an unequal termination for ideal response).
Lowpass elements are denormalized with L = g_k·R₀/ω_c for series inductors and C = g_k/(R₀·ω_c) for shunt capacitors. Highpass swaps the kind (series L → series C, shunt C → shunt L) using 1/(g_k·ω_c) scaling. Bandpass and bandstop transformations resonate each prototype element at ω₀ = 2πf₀ with bandwidth BW.
Each branch's ABCD matrix is multiplied in cascade across the network, then converted to S-parameters at the specified source and load impedances. This is the actual response of the synthesized component network — not just the analytic prototype response — so any termination mismatch (e.g. equal terminations on an even-order Chebyshev) will show up as a return-loss bump.
By default components are ideal (infinite Q, no ESR). Enable Include finite component Q in the spec panel to model resistive losses: each inductor gets a series resistance R_L = ωL/Q_L, each capacitor R_C = 1/(ωC·Q_C). Typical chip-component Q values: inductors 30–80 (lower for small SMT, higher for wirewound / air-core), ceramic capacitors 300–2000. Parasitic capacitance, mutual coupling, and SRF effects are still not modeled — verify the final design in a full simulator (ADS, Qucs, ngspice, etc.) with measured component models before committing to a layout.
The topology dropdown picks between the two dual ladders: shunt-first (π-network for LPF, T-network for HPF) and series-first (the reverse). Magnitude response is identical for both — pick whichever gives more practical component values, fewer inductors (usually preferred at high frequency), or matches the impedance step you want at the input port.
D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, Chapter 8 (Microwave Filters).