1.

The Q-factor of a waveguide resonator is given by (ω0 is resonant frequency, U is energy storage and ωL is power loss)1. \(Q = \frac{{{\omega _0}U}}{{{\omega _L}}}\)2. \(Q = \frac{{{\omega _0}{\omega _L}}}{U}\)3. Q = ω0UωL4. \(Q = \frac{{U{\omega _L}}}{{{\omega _0}}}\)

Answer» Correct Answer - Option 1 : \(Q = \frac{{{\omega _0}U}}{{{\omega _L}}}\)

Concept:

The quality factor is in general a measure of the ability of a resonator to store energy in relation to time-average power dissipation.

Specifically, the Q of a resonator is defined as:

\(Q=2\pi\frac{Maximum \ energy \ stored}{Energy \ dissipated \ per \ cycle}\)

In the case of resonators, the Quality factor is given by:

\(Q=\frac{ω_0W}{P_l}\)  ---(1)

Where,

ω0 = Resonant frequency

W = Total Energy

Pl = Power loss in the cavity.

Calculation:

Given:

Pl = ωL

ω0 = resonant frequency

W = U

Putting the above values in equation (1) we get the Quality factor as:

\(Q = \frac{{{\omega _0}U}}{{{\omega _L}}}\)

Hence option (1) is the correct answer.

  • Microwave resonators are tunable circuits used in microwave oscillators, filters, and frequency meters. 
  • The operation of microwave resonators is very similar to that of the lumped-element resonators (such as parallel and series RLC resonant circuits) of circuit theory. 
  • A cavity resonator is not a waveguide. It is a metallic enclosure that confines the electromagnetic energy within itself.
  • If excited properly, oscillations take place inside of it.
  • It is used as a tuned circuit at high frequencies.


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