Question

Subject: Electrical Engineering 2.(a). Discuss about power output and efficiency of magnetron. (2pts) (b). Compare magnetron and reflex klystron. (2pts) (c). What is the Hartree condition in magnetron? Derive the equation for Hartree voltage of it. (2pts) 5.(a). Mathematically, give the analysis of a magnetron. (2pts) (b). What is the Hartree condition in magnetron? Derive the equation for Hartree voltage of it. (2pts) (c). A linear magnetron has following operating parameters. (2pts) Vo = 15 kV, lo = 1.2 A, f = 8 GHz,Bo = 0.015 Wb/m², d = 5 cm, h=2.77 cm. Calculate, Electron velocity at hub surface Phase velocity for synchronism Hartree anode voltage(5pts)

Answer 1

Ans: a. The power output and efficiency of a magnetron relies on the resonant structure and dc power supply: Figure below illustrates the equivalent circuit'' for a Yesbnator of a magnetron. You A BB va ac & Lid G. Bean Beam Resonator and Figure for unloaded - factor of a reso- The expression given as, nator is S U un Scanned with CamScanner

Where, wo - Angular resonant frequency = 214 1' e.- Capacitance at the tips of Vane G, - Resonator conductance. The expression for external Q- factor of the load Circuit is given as, Qeet - Gir die .......(3) Cooc Where , Hories G. - Load Conductant per resonator. The expression for loaded Ql-factor of a resonator Circuit is 0. resonator The expression for external conductance of a resonator is given by ... - Gext = G, 4G ...... (6) On Substituting equation (6) in (5), loaded Q-factor of a resonator circuit is obtained as , Scanned with CamScanner

The expression for Circuit, efficiency is given by, Me = Guit Gom ® Dino m it 1+ . On substituting equations (2) and (3) in (9), Circuit efficiency is obtained as, mes Woc + ext L !. I+WOCX Run hext Woc Scanned with CamScanner

. 1+ Run Text : . Circuit efficien The maximum efficiency the circuit is achieved, if the magnetron is heavily loaded" (G.>> Ge). But, in fews Cases , due to heavy loading, the Circuit becomes Sensitive to load. As a consequence, the ratio of all is selected Rext to compensate the needs of circuit with high efficiency and frequency stability " Electronic Codein Electronic t ritis efficiency is given by. Where, pigen – RF power generated in the Circuit Pac. - Dc power supply The expression for RF power generated in the circuit, is given by: .... Scanned with CamScanner

Pgen = Volo -Plost . ..(12) Where, 1. Vo - Anode Voltage Io – Anode Current Prost - Power lost in the circuit Power lost in the Circuit is given by. Plast = to meet above ......() Where ñ - Change - to - mass ratio of the electron A B – Phase constant Emas - Maximum electric field B - Magnetic flux density. On Substituting equation (3) in (12), Pgon is obtained as , Pegon = VI, -lo un .....(4) Maximum electric field is given by. Milvi ....(15) Where M, - Gap factor for the r - mode operation- Emax = 1 for Small S. Scanned with CamScanner

V-RF voltage across the resonator gap. We -- Center - to - Center Spacing of the tips of Vane. On. Substituting equation (14), RF power generated is obtained as, Pigen = { Nlul care lalhere, N - Number of Yesonators. ir NL20.C Again Simplifying equation (16), RE poloer generated, is obtained as, Pgen = 2M70 E max On Substituting equation (17) in (1), electronic efficiency is obtained as, NL2woC -..(1-1 12M? Qi Emas Eines - Volo NL260C 2M20 max Tal Electronic el V.I. Scanned with CamScanner

Ans:b. The comparison between magnetron and reflex klystron is given below Magnetron pri Reflex klystron 1. Magnetrons are Cross field Reflex klystron is a linear tubes as they have the microwave beam tube.. tubes, they have the elec- tric and magnetic fields perpendiculay' to each other. 2.1 These are also referred 2. These are also refferred to to as M-type tubes. L as o tubes or Original tubes. 3. The energy containing 3. The energy carrying electrons electrons interact with RF interacts the RF field for field for a long duration. I a short duration. H. The efficiency of magnetron H. The efficiency provided by is in the roues is in the range of Ho to reflex klystron is in the | range of to to 20% 5. The frequency range for 5. The frequency range of reflex magnetron is 500 MHZ Kylsbron is 4 to 200 GHz to iz GHz. 140% . Scanned with CamScanner

Magnetron Reflex klystron. 6. It has a Cathode, and its ** | 6. It has an electron gun (no- anode is divided into several thing but a filement Surrou- slots that act as cavities. nded by cathode) that gener- And the RF out is taken ates electron beam . And has out from one of the anode only two anode cavities, and the RF out is taken out cavity. of the anode cavity. A 7. In waveformi a permanent. 7. In reflex klystron a repeller magnet is used: Such that I electrode is used at the end it generates the magnetic in order to bounce back the electron beam. field perpendicular to electric th field. 8. The magnetrons are also 8. The main application of a used as oscillators, but reflex klystron is as a signal fixed frequency, continuous generator" (source) or as an Wove CCW) magnetrons oscillator in microwave radars or receiversi are used for industrial heating and microwave ovens." 9. The output power of magnet: 19. The output power of Reflex von is in the range of 2mW klystron is in the range of to 250 kW. " Im W to 2.5W. Scanned with CamScanner

. by using Ans: C. In a linear magnetron, the anode voltage or magnetic field strength required to get a non- zero anode Current in the absence of electromagnetic field is determined by using Hell.cut-off or Hartree condition. A linear magnetron with a hub of thickness 1. his placed in the Cathode - anodel interaction Space d as shown in figure below. mit d i Anodent -- Beom Twist beam boundary I a L zQt with boundary V cathode ! ↑ Figure: linear Model of Magnetron Hartree Resonance Condition In et mode of Operation, Hartree condition Scanned with CamScanner

Specifies an anode voltage that is required to synchron- Ize the electron Velocity with RF wave phase velocity. It is defined as, Vath = (bod - pe ntru Assuming the electron is moving in the positive y-direction then the velocity of electron' is given by..! itse Vy Bo Bo does its t ! : - ) Where; il .. .Ex. +. Electric field intensity in X--direction from Bo=B4 - The magnetic flux density in the positive 2- direction. V- Potential applied From the principle of energy conservation , kinetic energy of electron - Potential electron energy I m vj -eV -... 2) From equation (1) and equation (2), we get Scanned with CamScanner

The above equation can be rearranged as, . Integrating on both sides we get one >> T* - 3.49 * * * * fiatas) BIT+ CE Since, the constant of integration is eliminated for V:D at 2=0. Then, the potential with in the electron beam is given by ti toalett Vzebb x2 photo !! --.-..(4) The expression for potential and electric field at the hub surface are given by allo , V(h) - 2 m B h2 mobil wil .com E, - 0 - 8% + . . . Then, the anode potential is given by Scanned with CamScanner

Ese dx V = v(n) + B3 h (d-h) Substituting equation ®)} in above equation, we get Vo = bo tº the best h (d=-1); The Velocity of electron at the hub Surface is obtained from equation (1) and (6) as, to written Yy (h) - Bohol Boy - Vie) The phase Velocity of the slow wave structure is equal to the velocity of electron, V Lee Bohi. ....9 1. Then Substituting equation (6) in equation (7), the final anode potential for' T - mode is given by. Scanned with CamScanner

You ( ...) ...The above equation is called "Hartree response. Condition" or "Hartree anode voltage equation", which is the function of the magnetic flux density, Bo and of the Spacing between the cathode and anode, d. Scanned with CamScanner