JEE Main & Advanced Physics Semiconducting Devices Different Gains in CE/CB Amplifiers

(1) Transistor as CB amplifier

(i) ac current gain \[{{\alpha }_{ac}}=\frac{\text{Small change in collector current (}\Delta {{i}_{c}})}{\text{Small change in collector current (}\Delta {{i}_{e}})}\] \[{{V}_{B}}\] (constant)

(ii) dc current gain \[{{\alpha }_{dc}}\text{(or}\alpha \text{)}=\frac{\text{Collector current(}{{i}_{c}}\text{)}}{\text{Emitter current (}{{i}_{e}})}\]      valve of \[{{\alpha }_{dc}}\] lies between 0.95 to 0.99

(iii)  Voltage gain  \[{{A}_{v}}=\frac{\text{Change in output voltage(}\Delta {{V}_{o}})}{\text{Change in input voltage (}\Delta {{V}_{i}})}\] \[\Rightarrow \] \[{{A}_{v}}={{\alpha }_{ac}}\times \] Resistance gain

(iv)  \[\text{Power gain}=\frac{\text{Change in output power(}\Delta {{P}_{o}})}{\text{Change in input power(}\Delta {{P}_{c}})}\] \[\Rightarrow \text{Power gain}=\alpha _{\text{ac}}^{\text{2}}\times \text{Resistance  gain}\]

(2) Transistor as CE amplifier

(i) ac current gain \[{{\beta }_{ac}}=\left( \frac{\Delta {{i}_{c}}}{\Delta {{i}_{b}}} \right)\,\]\[{{V}_{CE}}=\]constant

(ii) dc current gain \[{{\beta }_{dc}}=\frac{{{i}_{c}}}{{{i}_{b}}}\]

(iii) Voltage gain :  \[{{A}_{v}}=\frac{\Delta {{V}_{o}}}{\Delta {{V}_{i}}}={{\beta }_{ac}}\times \text{Resistance gain}\]

(iv)  \[\text{Power gain}=\frac{\Delta {{\text{P}}_{\text{o}}}}{\Delta {{\text{P}}_{\text{i}}}}=\beta _{ac}^{2}\times \text{Resistance gain}\]

(v) Trans conductance \[({{q}_{m}})\] : The ratio of the change in collector current to the change in emitter base voltage is called trans conductance. i.e. \[{{g}_{m}}=\frac{\Delta {{i}_{c}}}{\Delta {{V}_{EB}}}\].

Also\[{{g}_{m}}=\frac{{{A}_{V}}}{{{R}_{L}}}\]; \[{{R}_{L}}=\] Load resistance

(3) Relation between \[\alpha \]and \[\beta \] : \[\beta =\frac{\alpha }{1-\alpha }\] or \[\alpha =\frac{\beta }{1+\beta }\]