--- title: "Transit time effect and 45° magnetron" subject: "RF and Microwave Engineering" chapter: 5 key: "semester_7/rf_and_microwave_engineering:transit-time-magnetron-45" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/transit-time-magnetron-45 site: BCT Engineering --- # Transit time effect and 45° magnetron RF and Microwave Engineering · Chapter 5: Microwave Generators - Asked in: 2077 Chaitra, 2+6 marks - Video: [Conventional tubes at microwave frequencies | Transit time Effect | Microwave Engineering | Lec-81](https://www.youtube.com/watch?v=43DcDNFQ-2U) — Education 4u - 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/transit-time-magnetron-45 - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-5 ## Question What is transit time effect? State the working principles of a magnetron having phase difference of 45° of adjacent cavities. ## Short answer Transit time is the electron travel time between electrodes; when comparable to the RF period, it causes phase lag and input loading. In an 8-cavity magnetron with 45° phase shift (mode n=1), crossed radial E and axial B fields cause electron drift; under Hartree synchronism, phase-focused electrons form a rotating spoke that delivers energy to cavities, sustaining oscillation. ## Answer #### Transit time effect **Transit time** is the time an electron needs to travel between two electrodes: τ = d/v. At low frequencies τ is much shorter than the signal period and can be ignored. At microwave frequencies τ is comparable to the period, so the electrode voltage changes while the electron is still travelling. In conventional tubes this causes phase lag, loading of the input (input conductance ∝ ω²τ²) and lower gain and efficiency. Microwave tubes such as klystrons and magnetrons **use** transit time on purpose to bunch electrons. #### Magnetron with 45° phase difference between adjacent cavities For N cavities in mode n, the phase difference is φ = 2πn/N. For 45°, N = 8n: an **8-cavity anode in mode n = 1** (one spoke), or a 16-cavity anode in mode n = 2 (two spokes). ```text 8-cavity anode, phase of each cavity 0° 315° _/ \_ 45° / \ 270° | (cathode) | 90° B0 axial \ spoke / E radial 225° \_ _/ 135° 180° ``` **Working principles** 1. **Cross fields:** the cathode is at the centre and the anode block (8 cavities) around it. The anode voltage gives a radial E, and a magnet gives an axial B₀ above the Hull cut-off, B₀c = √(8mV₀/e) / [b(1 − a²/b²)]. Without RF, electrons curve back to the cathode. 2. **RF pattern:** noise starts oscillation in the cavities. In this mode each cavity's slot field lags its neighbour by 45°, so the RF fields in the interaction space form a wave rotating around the cathode once per n RF cycles. Its angular velocity is ω/n. 3. **Synchronism (Hartree condition):** V₀ and B₀ are set so that the E × B drift of electrons around the cathode matches the angular velocity of the wave. 4. **Phase focusing:** electrons in the retarding phase of the tangential RF field give energy to the wave and move outward to the anode. Electrons in the accelerating phase take energy, return to the cathode and are removed. 5. **Spokes and output:** the useful electrons form n rotating spokes (one for 8 cavities). These keep giving energy to the cavities in step, which sustains the oscillation. Power is coupled out by a loop in one cavity. 6. **Mode control:** because this is not the π-mode (180°), the mode must be chosen by the anode design. Strapping favours π-mode, so a non-π mode like this needs suitable coupling or an injected signal to hold it. **Uses:** pulsed radar transmitters, industrial heating and, in amplifier form (cross-field amplifier), radar power stages. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. When does transit time become a problem in a conventional tube? A. When the electrode spacing is zero B. When the electron transit time is comparable to the RF period C. When the frequency is very low D. When the beam is very narrow Answer: B. At microwaves the voltage changes while the electron is still crossing, causing phase lag and input loading. (Key point: Transit time effect) 2. How many cavities give a 45° phase difference in the n = 1 mode? A. 8 B. 4 C. 16 D. 2 Answer: A. phi = 2*pi*n/N gives N = 8n; n = 1 gives 8 cavities and one spoke. (Key point: Cavities for 45 degrees) 3. What does a magnetic field above the Hull cut-off do in the magnetron without RF? A. Electrons reach the anode directly B. Electrons stop being emitted C. Electrons curve back to the cathode without reaching the anode D. The anode voltage collapses Answer: C. Above cut-off, electrons curve back; only RF-driven phase focusing lets favourable electrons reach the anode. (Key point: Hull cut-off) 4. Why is mode control needed for the 45° (non-pi) mode? A. It has no spokes B. Non-pi modes lie close in frequency to others, so the design must hold the wanted mode C. It needs no magnet D. Strapping favours it Answer: B. Strapping favours the pi-mode, so a non-pi mode needs suitable coupling or design to avoid mode jumping. 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