--- title: "Why insertion loss; double-section shunt-arm LPF" subject: "RF and Microwave Engineering" chapter: 6 key: "semester_7/rf_and_microwave_engineering:insertion-loss-shunt-arm-lpf" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/insertion-loss-shunt-arm-lpf site: BCT Engineering --- # Why insertion loss; double-section shunt-arm LPF RF and Microwave Engineering · Chapter 6: RF Design Practices - Asked in: 2080 Baisakh, 3+5 marks - Video: [Design Steps for RF filter using Insertion Loss Method #RFDesign #Microwave #RFcircuit](https://www.youtube.com/watch?v=eV_d3_0MwU4) — We The Engineers - 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/insertion-loss-shunt-arm-lpf - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-6 ## Question Explain why insertion loss technique is used to design microwave filters. With proper labeling sketch microwave double-section shunt-arm types microwave LPF using micro strips. ## Short answer The insertion loss method specifies the complete frequency response exactly and enables systematic design from prototype tables. A double-section shunt-arm microstrip LPF uses narrow high-impedance line sections as series inductors and two open-circuited stubs as shunt capacitors. ## Answer #### Why the insertion loss technique is used The **insertion loss method** designs a filter from a chosen **power loss ratio**: ```text PLR = 1 / (1 − |Γ(ω)|²) = 1 + M(ω²)/N(ω²) Butterworth: PLR = 1 + k²(ω/ωc)^(2N) Chebyshev : PLR = 1 + k² T_N²(ω/ωc) ``` It is preferred over the older image-parameter method because: - the **complete response** (passband ripple, cut-off sharpness, phase) is specified and achieved exactly, - the design is **systematic**: g-value tables, then scaling, then transformation, with no trial and error, - the order N gives a clear trade-off between performance and size or loss, - one LP prototype can be turned into HP, BP or BS filters and then into microstrip (Richards, Kuroda, stepped-impedance). #### Double-section shunt-arm microwave LPF in microstrip In a **shunt-arm** LPF, the shunt capacitors are made as **open-circuited stubs** (or wide pads) connected across the line, and the series inductors are short high-impedance line sections. A double-section filter has **two shunt arms**. ```text Lumped: o--UUU--+--UUU--+--UUU--o L1 | L2 | L3 C1 C2 | | o-------+-------+-------o Microstrip (top view): stub C1 stub C2 | | | | open end | | l_s | | (λ/8 at fc) 50 Ω ====+----+-+----+-----+-+----+==== 50 Ω feed L1 (hi-Z) L2 (hi-Z) L3 feed -------- ground plane below ------ ``` **Labels** - **50 Ω feed lines** at input and output. - **L₁, L₂, L₃:** narrow high-impedance (about 100–120 Ω) line sections, βl = L·R₀/Z_h (normalised L), acting as series inductors. With Richards and Kuroda design, these are λ/8 unit elements. - **C₁, C₂:** open-circuited shunt stubs. From Richards' transformation each is λ/8 long at fc with Z₀ = R₀/g_k. (Wide low-impedance pads can be used instead.) - Substrate with εr and height h, and a full ground plane underneath. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the insertion loss method preferred over the image-parameter method? A. It needs no prototype B. The complete response can be specified and achieved exactly in a systematic design C. It uses fewer components always D. It ignores terminations Answer: B. It starts from a chosen power loss ratio and uses tables, scaling and transformation, giving an exact, systematic design. (Key point: Why insertion loss) 2. What is the power loss ratio (PLR)? A. 1/(1 − |Γ|²), the available over delivered power B. |Γ|² C. |S21| D. 1 − |Γ| Answer: A. PLR = P_available/P_delivered = 1/(1 − |Γ(ω)|²). (Key point: Power loss ratio) 3. In the microstrip shunt-arm LPF, what forms the shunt capacitors and series inductors? A. Shorted stubs and wide lines B. Open-circuited stubs (or wide pads) and short high-impedance lines C. Gaps and vias D. Coupled lines and gaps Answer: B. Shunt C = open stubs (λ/8 at fc, Z0 = R0/g), series L = narrow high-Z line sections. (Key point: Shunt-arm realisation) ## Related in RF and Microwave Engineering - [Single-section series arm BPF and insertion loss](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Abpf-microstrip-insertion-loss) — RF and Microwave Engineering, chapter 6 - [Double-section series-arm microstrip filter](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adouble-section-series-arm-filter) — RF and Microwave Engineering, chapter 6 - [Insertion loss method and microstrip LPF](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Ainsertion-loss-lpf-microstrip) — RF and Microwave Engineering, chapter 6 - [Insertion loss design of given LC ladder filter](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Afilter-ladder-insertion-loss-microstrip) — RF and Microwave Engineering, chapter 6 - [Butterworth LPF prototyping by insertion loss](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Abutterworth-lpf-prototyping) — RF and Microwave Engineering, chapter 6 - [Short note: Strip-lines against micro-strips](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Astriplines-vs-microstrips-note) — RF and Microwave Engineering, chapter 2 ## Related in other subjects - [Insertion gain/loss, design steps, active vs passive](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Ainsertion-loss-steps-active-passive) — Filter Design, chapter 1 - [Define αmax, αmin, insertion loss and gain](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Adefine-amax-amin-insertion-loss) — Filter Design, chapter 1, asked 2× - [Insertion gain/loss and element scaling equations](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Afilter-insertion-gain-scaling) — Filter Design, chapter 1