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# Note for Microwave Engineering - ME by Pandu Manepalli

• Microwave Engineering - ME
• Note
• RISEKRISHNASAIGANDHIGROUPOFINSTIUTIONS - RGAN
• Electronics and Communication Engineering
• B.Tech
• 2 Topics
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Microwave Engineering The space present between the anode and cathode is called as Interaction space. The electric field is present radially while the magnetic field is present axially in the cavity magnetron. This magnetic field is produced by a permanent magnet, which is placed such that the magnetic lines are parallel to cathode and perpendicular to the electric field present between the anode and the cathode. The following figures show the constructional details of a cavity magnetron and the magnetic lines of flux present, axially. This Cavity Magnetron has 8 cavities tightly coupled to each other. An N-cavity magnetron has N modes of operations. These operations depend upon the frequency and the phase of oscillations. The total phase shift around the ring of this cavity resonators should be 2nπ where n is an integer. If ! represents the relative phase change of the AC electric field across adjacent cavities, then ! & & ' ' Where n = 0, ±1, ±2, ± ( ( 1), ± =" 2#\$ % Which means that N/2 mode of resonance can exist if N is an even number. If, & ""\$ = " ""*+,\$"" ' ! = "# !" =0 This mode of resonance is called as π-mode. """\$ = 0""*+,\$""" This is called as the Zero mode, because there will be no RF electric field between the anode and the cathode. This is also called as Fringing Field and this mode is not used in magnetrons. 71

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Microwave Engineering Operation of Cavity Magnetron When the Cavity Klystron is under operation, we have different cases to consider. Let us go through them in detail. Case 1 If the magnetic field is absent, i.e. B=0, then the behavior of electrons can be observed in the following figure. Considering an example, where electron a directly goes to anode under radial electric force. Case 2 If there is an increase in the magnetic field, a lateral force acts on the electrons. This can be observed in the following figure, considering electron b which takes a curved path, while both forces are acting on it. 72

#### Text from page-4

Microwave Engineering Radius of this path is calculated as - =" ./ ,3 It varies proportionally with the velocity of the electron and it is inversely proportional to the magnetic field strength. Case 3 If the magnetic field B is further increased, the electron follows a path such as the electron c, just grazing the anode surface and making the anode current zero. This is called as “Critical magnetic field” (34 ), which is the cut-off magnetic field. Refer the following figure for better understanding. Case 4 If the magnetic field is made greater than the critical field, 3 > " 34 Then the electrons follow a path as electron d, where the electron jumps back to the cathode, without going to the anode. This causes “back heating” of the cathode. Refer the following figure. 73

#### Text from page-5

Microwave Engineering This is achieved by cutting off the electric supply once the oscillation begins. If this is continued, the emitting efficiency of the cathode gets affected. Operation of Cavity Magnetron with Active RF Field We have discussed so far the operation of cavity magnetron where the RF field is absent in the cavities of the magnetron (static case). Let us now discuss its operation when we have an active RF field. As in TWT, let us assume that initial RF oscillations are present, due to some noise transient. The oscillations are sustained by the operation of the device. There are three kinds of electrons emitted in this process, whose actions are understood as electrons a, b and c, in three different cases. Case 1 When oscillations are present, an electron a, slows down transferring energy to oscillate. Such electrons that transfer their energy to the oscillations are called as favored electrons. These electrons are responsible for bunching effect. Case 2 In this case, another electron, say b, takes energy from the oscillations and increases its velocity. As and when this is done, · It bends more sharply. · It spends little time in interaction space. · It returns to the cathode. These electrons are called as unfavored electrons. They don’t participate in the bunching effect. Also, these electrons are harmful as they cause “back heating”. Case 3 74