$2($a$)$ A two$-$cavity amplifier klystron has the following parameters:

Beam voltage: $.$

$V_{}=900V$

$I_0=30mA$

$f=8GHz$

Beam current:

Frequency:

Gap spacing in either cavity:

$d=$imm

Spacing between centres of cavities:

$L=4cm$

Effective shunt impedance:

$R_{sh}=40kO$

Determine the following:

$($i$)$ The electron velocity

$($ii$)$ The dc electron transit time

$($iii$)$ The input voltage for maximum output voltage

$($iv$)$ The voltage gains in decibels.