--- title: "Filter design steps and triple-pad HPF" subject: "RF and Microwave Engineering" chapter: 6 key: "semester_7/rf_and_microwave_engineering:triple-pad-hpf-microstrip" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/triple-pad-hpf-microstrip site: BCT Engineering --- # Filter design steps and triple-pad HPF RF and Microwave Engineering · Chapter 6: RF Design Practices - Asked in: 2082 Baisakh, 7+3 marks - Video: [Basic of microwave filter design and its lumped equivalent circuit](https://www.youtube.com/watch?v=SizslnJy6Gg) — RF Design Basics - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/triple-pad-hpf-microstrip - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-6 ## Question Mention the details of microwave filter designing steps. Provide a sketch of triple-pad series-arm type HPF using micro strips. ## Short answer Design by insertion-loss method: specify fc, ripple, Z0; choose response and order; get g-values; scale and transform LP to HP; realize with distributed elements; layout and tune. A triple-pad series-arm HPF uses three gap-coupled pads as series capacitors and thin high-impedance lines with vias as shunt inductors. ## Answer #### Microwave filter designing steps (insertion loss method) ```text 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. ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the LP to HP transformation, what do series L and shunt C become? A. Series L becomes shunt C; shunt C becomes series L B. Series L becomes series C; shunt C becomes shunt L C. Both stay the same D. Series L becomes shunt L Answer: B. A high-pass ladder has series capacitors and shunt inductors. (Key point: LP to HP transformation) 2. How are the series capacitors realised in the triple-pad HPF? A. As gap-coupled pads (or interdigital capacitors) along the main line B. As short-circuited stubs C. As wide shunt pads D. As via holes Answer: A. The gap width and pad overlap set the capacitance, and interdigital fingers give larger C. (Key point: Series capacitors in microstrip) 3. How are the shunt inductors L2 and L4 made? A. Open-circuited wide stubs B. Thin high-impedance lines shorted to ground through vias C. Gap-coupled pads D. Lumped resistors Answer: B. Narrow lines (Z0 about 100-120 Ω, βl < 45°) or λ/8 short-circuited stubs ending in vias act as inductors. (Key point: Shunt inductors) 4. After the low-pass prototype g-values, what comes next? A. Scaling and LP to HP/BP/BS transformation, then distributed realisation B. Layout directly C. Choosing the response D. Adding bias Answer: A. Specifications, response and order, and prototype come first. Scaling and transformation come next, followed by realisation and tuning. 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