A radar has a maximum range of 120 km. The maximum allowable pulse repetition frequency for unambiguous reception is

The operation of magnetron is based on interaction of electromagnetic fields with electrons moving in static electric and magnetic fields oriented at 90° with respect to each other.

In a magnetron three forces act on electron viz. force due to electric field (equal to - eE), force due to magnetic field [equal to - e (v x B)] and centrifugal force (equal to mv²/r).

The path of the electron can be found by balancing these three forces. Magnetron can be of three types i.e., negative resistance device, cyclotron frequency device and travelling wave or cavity device.

In negative resistance magnetron use is made of the negative resistance between two anode segments.

It has low efficiency and is used at frequencies less than 0.5 GHz.

In cyclotron magnetron a synchronism exists between ac component of electric field and periodic oscillation of electrons in a direction parallel to the field.

It is used for frequencies higher than 100 MHz.

A cavity magnetron has a number of cylindrical cavities in the interaction region.

The cavity magnetron is the most common type of magnetron. Its features are :

1. Frequency range - 500 MHz to 10 GHz

2. Power output - 250 kW (pulses)

3. Efficiency - about 50%

It is used in radar systems, industrial heating systems and microwave ovens.

Some applications require dual polarization capability. Circular waveguide has this capability.

These analysis uses cylindrical coordinates.

In circular waveguide TE₁₁ mode has the lowest cut off frequency and is the dominant mode.

If D is diameter of waveguide

?_c = 1.706 D for TE₁₁ mode

?_c = 1.029 D for TE₂₁ mode

?_c = 0.82 D for TE₀₁ mode

?_c = 1.306 D for TM₀₁ mode.