Filter design steps and double pad T-type filter

Steps of microwave filter designing (insertion loss method)

 1. Specifications (fc, ripple, IL, Z0)
 2. Response type + order N
 3. Low-pass prototype g-values
 4. Scaling + LP->HP/BP/BS transform
 5. Lumped -> distributed (Richards,
    Kuroda, stepped-Z, coupled lines)
 6. Layout, simulate (EM), tune

1. Specifications: type (LP, HP, BP or BS), cut-off or centre frequency, passband ripple or insertion loss, stop-band attenuation and impedance R₀.
2. Response and order: choose Butterworth (PLR = 1 + k²(ω/ωc)²ᴺ) for a flat passband or Chebyshev (PLR = 1 + k²T_N²(ω/ωc)) for a sharper cut-off. Find N from attenuation charts.
3. Prototype: read g₁…g_N for a normalised LP ladder (R₀ = 1, ωc = 1).
4. Scaling and transformation: L_k = R₀g_k/ωc and C_k = g_k/(R₀ωc). Then convert to HP, BP or BS with the standard frequency transformations.
5. Distributed realisation: short high-Z lines for series L, short low-Z lines or open stubs for shunt C (stepped impedance), or Richards' λ/8 stubs with Kuroda identities.
6. Layout and verification: EM simulation, include discontinuities, and tune.

Double-pad T-type passive filter in microstrip

A T-section low-pass filter has a series inductor, a shunt capacitor and another series inductor. A "double-pad" T-type filter cascades two T-sections, giving two capacitive pads:

 Lumped:  --UUU--+--UUU--+--UUU--
            L1   |   L2  |   L3
                C1      C2
                 |       |
          -------+-------+-------

 Microstrip (top view):
        L1     pad C1    L2    pad C2    L3
 50 Ω ====____[######]____[######]____==== 50 Ω
        thin    wide    thin    wide    thin
       (hi Z)  (low Z) (hi Z)  (low Z) (hi Z)

• Thin lines (high Z₀, about 100–120 Ω, βl < 45°) act as the series inductors: βl = L·R₀/Z_h (L normalised).
• Wide pads (low Z₀, about 10–20 Ω) act as the shunt capacitors: βl = C·Z_ℓ/R₀.
• The 50 Ω feed lines connect at both ends, and the bottom side is a full ground plane.