Solution:

The quality factor of the resonator. The following are the definitions associated with quality factor $(g)$ of resonator:

Unloaded (Q०)

$Q_0=2 \pi \frac{\text { Energy stored in the cavity }}{\text { Energy lost per cycle in the cavity }}$

So is the selectivity factor, dependent on the geometrical portion of the cavity.

• Loaded $Q_L$:

$Q_1=\frac{f_0}{\Delta f}=\frac{\text { Resonant Frequenuy }}{3 d B \text { Bondwidth. }}$

• External QE:

$Q_E=2 \pi \frac{\text { Energy stored in the cavity}}{\text { Energy lost per cycle in the cavity }}$

Slotted-Lime measurement of Q:

It is used to measure the Q of a reflection type cavity which is normally used in a microwave tube, through VSWR measurement or through measurement of the shift in the position of standing wave minima as the generator beg is varied The measurement setup is as shown in figure

(a) If $Z_{1 n}=R+j X$ is the input impedance of the cavity in the vicinity of resonance frequency and $z_0$ is the,

VSWR $=\frac{\left|z_{i n}+z_0\right|+\left|z_{1 i}-z_0\right|}{\left|z_{1 n}+z_0\right|-\left|z_{i n}-z_0\right|}$

at resonance $x=0$

$ \begin{aligned}\\ S_R=\operatorname{VS\omega R}(R) & =R / Z_0 \text { if } R\gtZ_0 \\\\ & =z_0 / R \text { if } R\ltZ_0\\ \end{aligned} $

at half power points,

once the VSWR at half power point is calculated, Change the klystron freq. so that the VSWR meter indicates $S_{H p}$.

$Q$ is Calculated as $Q=f_0 /\left(f_1-f_2\right)$.