--- title: "Magnetron with 45° phase shift as power amplifier" subject: "RF and Microwave Engineering" chapter: 5 key: "semester_7/rf_and_microwave_engineering:magnetron-45-degree-amplifier" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/magnetron-45-degree-amplifier site: BCT Engineering --- # Magnetron with 45° phase shift as power amplifier RF and Microwave Engineering · Chapter 5: Microwave Generators - Asked in: 2080 Baisakh, 6+2 marks - Video: [Magnetron Oscillator (Basics, Structure, Working, Equivalent Circuit & Applications) Explained](https://www.youtube.com/watch?v=8u_OXXB7LNE) — Engineering Funda - 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/magnetron-45-degree-amplifier - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-5 ## Question Sketch a cross-sectional view of a magnetron having 45 degrees of phase shifts among the adjacent cavities, and explain its functioning as a power amplifier. Explain the bunching effect. ## Short answer An 8-cavity magnetron with 45° phase shift (n=1 mode) employs radial E and axial B for E×B drift. Injected RF propagates via cavity coupling, and Hartree synchronism ensures phase focusing forms a rotating spoke that amplifies the wave; a drift section prevents oscillation. Bunching is density modulation by velocity modulation and drift. ## Answer #### Cross-section of a magnetron with 45° between adjacent cavities In mode n, the phase difference between adjacent cavities of an N-cavity anode is φ = 2πn/N. For φ = 45°, N = 8n, so an **8-cavity anode in the n = 1 mode** gives 45°. The pattern repeats every 8 cavities, so there is **one rotating spoke**. (A 16-cavity anode with n = 2 gives two spokes.) ```text 8 cavities, phase of each cavity's RF field 0° 315° _/ \_ 45° / \ 270° | (cathode) | 90° B0 axial \ spoke / E radial 225° \_ _/ 135° 180° RF in -> cavity 0° RF out <- cavity 315° ``` #### Functioning as a power amplifier A magnetron is normally an oscillator. It works as a **power amplifier** (as in a **cross-field amplifier**, amplitron type) when an RF input is injected into the cavity chain and the drive conditions are set so that it does not oscillate by itself. 1. **Fields:** a heated cathode at the centre and the anode block give a radial DC field E (anode voltage V₀). A magnet gives an axial field B₀, slightly above the Hull cut-off B₀c = √(8mV₀/e) / [b(1 − a²/b²)]. Electrons drift around the cathode at the E × B speed. 2. **Input:** the weak RF signal is coupled into one cavity. The cavities are coupled through the interaction space, so the signal moves from cavity to cavity with a 45° phase step. This forms a slow wave that rotates around the cathode at angular velocity ω/n. 3. **Synchronism:** V₀ and B₀ are adjusted (Hartree condition) so that the electron drift velocity equals the wave's phase velocity. 4. **Phase focusing and energy transfer:** electrons in the retarding phase of the RF field give potential energy to the wave and move toward the anode. Electrons in the accelerating phase gain energy and return to the cathode. The useful electrons form a spoke that stays locked to the wave and keeps giving it energy. 5. **Growth and output:** the wave grows as it travels from the input cavity to the output cavity. The amplified signal is coupled out with a loop. A **drift section** (or a non-resonant gap) between output and input stops the amplified signal from reaching the input again, so no self-oscillation occurs. **Performance:** efficiency of about 40–70%, gain of about 10–20 dB, bandwidth of about 10%, high peak power. Used in radar transmitters. #### Bunching effect **Bunching** is the grouping of electrons into dense packets at regular intervals. In O-type tubes (klystron, TWT) it comes from **velocity modulation** followed by drift: fast electrons catch up with slow ones. In magnetrons the same idea appears as **phase focusing**. Electrons in favourable (retarding) RF phase stay in the interaction, while unfavourable ones are removed, so electrons gather into spokes. The bunched electrons give energy to the RF field in step with it. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Using phi = 2*pi*n/N, which anode gives 45 degrees between adjacent cavities in the n = 1 mode? A. 16 cavities B. 4 cavities C. 8 cavities D. 2 cavities Answer: C. 45° = 360°·n/N gives N = 8n, so n = 1 needs 8 cavities and gives one spoke. (Key point: Cavities for 45 degrees) 2. What does the Hartree condition require in the magnetron amplifier? A. Electron drift velocity equals the phase velocity of the RF wave B. Anode voltage equals the cathode voltage C. The magnetic field is zero D. The cavity Q is infinite Answer: A. V0 and B0 are set so electrons drift around the cathode in step with the rotating RF wave, so they stay in a favourable phase. (Key point: Hartree condition) 3. What happens to electrons in the retarding phase of the RF field? A. They gain energy and return to the cathode B. They give potential energy to the wave and move to the anode, forming the spoke C. They are reflected back to the input D. They stop moving Answer: B. Electrons in the retarding phase give energy to the wave and stay in the interaction; accelerating-phase electrons return to the cathode and are removed. (Key point: Phase focusing) 4. Why is a drift section placed between the output and input cavities of the amplifier version? A. To raise the efficiency to 100% B. To cool the anode C. To provide the DC field D. To stop the amplified signal from feeding back to the input so it does not self-oscillate Answer: D. Breaking the coupling between output and input prevents feedback, so the device amplifies rather than oscillates. 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