Filter design steps and triple-pad HPF

Microwave filter designing steps (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: cut-off frequency fc, passband insertion loss or ripple, stop-band attenuation at a given frequency, and the terminating impedance R₀ (usually 50 Ω).
2. Choose the response: Butterworth (maximally flat, PLR = 1 + k²(ω/ωc)²ᴺ), Chebyshev (equal ripple, PLR = 1 + k²T_N²(ω/ωc)), elliptic, or linear phase. Find the order N from attenuation charts.
3. Low-pass prototype: read the normalised element values g₁…g_N (R₀ = 1, ωc = 1) from tables. For example, Butterworth N = 3 gives g = 1, 2, 1.
4. Scaling and transformation:
   • Impedance scaling: L' = R₀L, C' = C/R₀.
   • Frequency scaling and type change. For a high-pass filter, each series L_k becomes a series C'_k = 1/(R₀ωc g_k), and each shunt C_k becomes a shunt L'_k = R₀/(ωc g_k).
   • Band-pass and band-stop use series and parallel LC resonators.
5. Distributed realisation: Richards' transformation (L → short stub, C → open stub, λ/8 long), Kuroda identities, stepped-impedance lines, gap or interdigital capacitors, or coupled-line sections.
6. Layout and verification: include discontinuity effects (gaps, steps, T-junctions, vias), simulate, and tune the lengths and gaps.

Triple-pad series-arm HPF in microstrip

A high-pass ladder has series capacitors in the series arm and shunt inductors. In a triple-pad series-arm layout, the three series capacitors C₁, C₃, C₅ are made as gap-coupled pads (or interdigital capacitors) along the main line. The shunt inductors L₂, L₄ are thin high-impedance lines shorted to ground through via holes.

 50 Ω    C1          C3          C5     50 Ω
 ====| |[pad1]|  |[pad2]|  |[pad3]| |====
       gap  |     gap |     gap
            |  L2     |  L4
           (thin)    (thin)
            |         |
           [via]     [via]  -> ground plane

• Pads and gaps: the capacitance of each series arm is set by the gap width and the pad overlap. Interdigital fingers are used when larger C is needed.
• Shunt inductors: narrow lines (Z₀ about 100–120 Ω, βl < 45°) or λ/8 short-circuited stubs from Richards' transformation, ending in vias to the ground plane.
• Everything is printed on one substrate. Wide 50 Ω lines connect the input and output.