Current Frequency:

At microwave frequency performance of the transistor is depends on its cut-off frequency rather than its gain.

$f_c=\text{cut off frequency=}\dfrac{1}{2πτ} \\ τ=\text{total transist time=}τ_c+τ_b+τ_c+τ_d \\ τ_0=\text{emitter base junction transit time} \\ τ_b=\text{Base transit time.} \\ τ_d+τ_c=\text{colector junction time.} \\ ∴f_{\max}=\sqrt{\dfrac{f_c}{8 \pi γ_b' C_c}} \\ γ_b'=\text{base resistance} \\ C_c=\text{collector capacitance}$

Power frequency limitation:-

It is been observed that with increase in frequency, power decreases due to following reasons.

• There is limitations to maximum velocity of charge carries.
• Also there is limitations to maximum field which can be applies to semiconductor.

Let $V_m = \text{Maximum applied vtg.} \\ L = \text{length of device} \\ I_m = \text{current corresponding to applied vtg.} \\ τ = \text{Total transit time of charge carriers}.$

WKT $f_c=\dfrac{1}{2 πτ} \\ \text{Multiply both sides by} V_m \\ ∴V_m f_c=\dfrac{V_m}{2πτ} \\ V_m f_c=\dfrac{V_m}{L} \times \dfrac{L}{2πτ}$

WKT, $V_d=\dfrac{L}{τ} \ \ \ \ \ and \dfrac{V_m}{L}=E_m=\text{Maximum electric field} \\ V_m f_c=\dfrac{E_m V_d}{2 π} \\ f_c=\dfrac{E_m V_d}{2 π}.\dfrac{1}{\sqrt{X_c b}.\sqrt{P_m}} ------ \text{(Xcb = collector base capacitor reactance)}$

We can say

$f_c∝ \dfrac{1}{\sqrt{P_m}}$

Gain of Microwave transistor:

• The gain of microwave transistor is given by,

  $Gain = G_{\max} = \bigg(\dfrac{fc}{f}\bigg) \dfrac{Z_{out}}{Z_{in}} \\ F_c = \text{Cut – off frequency} \\ F = \text{operating frequency} \\ Z_{out} = \text{o\p impedance} \\ Z_{in} = \text{i/p impedance}$