Short note: Design procedures of microwave filters

Microwave filters are normally designed by the insertion loss method, which gives exact control of the passband and stopband.

Procedure:

1. Specifications: filter type (LP, HP, BP, BS), cut-off or centre frequency, bandwidth, ripple, stopband attenuation, R0.
2. Choose the response from the power loss ratio PLR = 1/(1 − |Γ|²):
   • Butterworth: PLR = 1 + k²(ω/ωc)^(2N), flat passband.
   • Chebyshev: PLR = 1 + k²TN²(ω/ωc), equal ripple, sharp cut-off.
   • Linear phase: flat group delay.
3. Order N from the stopband attenuation (graphs or formula).
4. Low-pass prototype: g-values from tables for R0 = 1 Ω, ωc = 1 rad/s.
5. Scaling and transformation: L = gR0/ωc, C = g/(R0ωc); LP → HP (ω → −ωc/ω), BP and BS using ω0 and fractional bandwidth.
6. Implementation: Richards' transformation (L → short stub, C → open stub), Kuroda identities, stepped-impedance lines, coupled-line or resonator filters.
7. Simulation, tuning and measurement (S21, S11 on a network analyzer).

Specs → Response → N → g-values → Scale/
Transform → Line realisation → Simulate → Build

Example: Butterworth N = 3 LPF at 2 GHz, 50 Ω → C = 1.59 pF, L = 7.96 nH, C = 1.59 pF.