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

Different Gains in CE/CB Amplifiers

Category : JEE Main & Advanced

(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 $\alpha =\frac{\beta }{1+\beta }$

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