--- title: "Lumped vs distributed analysis, applications, protocols" subject: "RF and Microwave Engineering" chapter: 1 key: "semester_7/rf_and_microwave_engineering:lumped-distributed-protocols" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/lumped-distributed-protocols site: BCT Engineering --- # Lumped vs distributed analysis, applications, protocols RF and Microwave Engineering · Chapter 1: Introduction - Asked in: 2080 Bhadra, 3+3+4 marks - Video: [Lumped and Distributed Elements](https://www.youtube.com/watch?v=PLzCIZdnTBw) — Neso Academy - 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/lumped-distributed-protocols - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-1 ## Question Differentiate between lumped and distributed circuit analysis. List out the areas of application of microwave system. Provide detail protocols of two microwave communication systems. ## Short answer Lumped analysis treats R, L, C as point elements valid when circuit size is much smaller than wavelength; distributed analysis uses per-unit-length R, L, G, C and wave equations when size is comparable to wavelength. Applications include communication, radar, navigation, heating, medical, and radio astronomy. Two protocols: Wi-Fi (2.4/5 GHz, OFDM, CSMA/CA) and satellite (C/Ku/Ka bands, transponders, FDMA/TDMA/CDMA). ## Answer #### Lumped vs distributed circuit analysis **Lumped analysis** treats R, L and C as concentrated at points connected by ideal wires. It is valid when the circuit size is much smaller than λ (a rule of thumb is l < λ/10). **Distributed analysis** treats R, L, G and C as spread along the line per unit length. Voltage and current then vary with position, which is needed when the size is about λ or larger. | Lumped | Distributed | |---|---| | Size ≪ λ | Size ≥ λ/10 | | Elements are discrete R, L, C | R′, L′, G′, C′ per unit length | | V and I are the same along a wire | V and I vary with z (waves) | | No propagation delay | Phase delay βz | | KVL/KCL, ordinary ODEs | Telegrapher's equations (PDEs in z, t) | | Example: a 50 Hz power circuit | Example: a 10 GHz microstrip line | ```text Distributed model of a length Δz of line: o--R'Δz--L'Δz--+------o | G'Δz C'Δz | o--------------+------o ``` #### Areas of application of microwave systems Communication (terrestrial links, satellite, cellular, Wi-Fi), radar (ATC, weather, military, automotive), navigation (GPS), broadcasting (DTH TV), remote sensing, industrial and domestic heating (2.45 GHz ovens), medical (diathermy, hyperthermia), and radio astronomy. #### Detailed protocols of two microwave communication systems **1. Wi-Fi (IEEE 802.11 WLAN)** - Bands: 2.4 GHz ISM (2.400–2.4835 GHz), 5 GHz (5.15–5.85 GHz), and 6 GHz for Wi-Fi 6E. - Channels: 20/40/80/160 MHz wide. At 2.4 GHz there are 13 channels 5 MHz apart, and only 1, 6 and 11 do not overlap. - Modulation: OFDM with BPSK up to 1024-QAM (802.11ax). 802.11b used DSSS/CCK. - Access: CSMA/CA with optional RTS/CTS. Duplexing is TDD. - Rates: 11 Mbps (b), 54 Mbps (a/g), 600 Mbps (n, MIMO), about 9.6 Gbps (ax). - Security: WPA2/WPA3 (AES). **2. Satellite communication** - Geostationary orbit at 35,786 km. The ground-to-satellite delay is about 120 ms, so one hop (up and down) takes about 240 ms. - Bands: C band (uplink 5.925–6.425 GHz, downlink 3.7–4.2 GHz, written 6/4 GHz), Ku band (14/12 GHz), Ka band (30/20 GHz). - A transponder receives the uplink, translates the frequency down, amplifies with a TWTA or SSPA, and retransmits. Typical transponder bandwidth is 36 MHz. - Access: FDMA, TDMA, CDMA. Example: VSAT networks with QPSK/8PSK and DVB-S2. - Uplink is at the higher frequency because the ground station can afford more power to overcome the greater loss. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the rule of thumb for lumped analysis to be valid? A. Circuit size l greater than lambda B. Circuit size l less than lambda/10 C. Circuit size equal to 10 lambda D. Frequency above 1 GHz Answer: B. Lumped analysis requires l much smaller than lambda, roughly l < lambda/10. (Key point: Lumped validity) 2. Which governs distributed analysis? A. KVL and KCL as ordinary ODEs B. Telegrapher's equations (PDEs in z and t) C. Ohm's law only D. Norton's theorem Answer: B. With R', L', G', C' per unit length, V and I satisfy telegrapher's equations. (Key point: Distributed equations) 3. What differs about delay in distributed circuits? A. Delay is ignored B. Phase delay beta*z matters C. Delay is always zero D. Delay is independent of length Answer: B. Voltage and current vary with position through phase delay. (Key point: Delay) 4. In satellite links, why is the uplink at the higher frequency than the downlink (e.g. 6/4 GHz)? A. The satellite has more power to spare than the ground station B. Higher frequency suffers less loss, so it suits the satellite receiver C. The ground station can afford more power to overcome the greater loss D. The transponder can only amplify higher frequencies Answer: C. Path loss rises with frequency; the ground station has abundant power, whereas the satellite is power-limited, so the higher-loss band is used for the uplink. 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