# JEE Main & Advanced Physics Semiconducting Devices Triode as an Amplifiers

## Triode as an Amplifiers

Category : JEE Main & Advanced

Amplifier is a device by which the amplitude of variation of ac signal voltage / current/ power can be increased

(1) The signal to be amplified $({{V}_{i}})$ is applied in the grid circuit and amplified output is obtained from the plate circuit

(2) The voltage at grid is the sum of signal ${{V}_{i}}$ and grid bias ${{V}_{gg}}$. ${{V}_{g}}={{V}_{gg}}+{{V}_{i}}$

(3) Small change in grid voltage results in a large change in plate current so results in a large change in voltage across ${{R}_{L}}\,({{V}_{0}}={{i}_{p}}{{R}_{L}}\,\Rightarrow \,\Delta {{V}_{0}}=\Delta {{i}_{p}}{{R}_{L}})$

(4) The linear portion of the mutual characteristic with maximum slope is chosen for amplification without distortion.

(i) For the positive half cycle of input voltage $({{V}_{i}})$ : ${{V}_{g}}$ becomes less negative, so ${{i}_{p}}$ increases

(ii) For the negative half cycle of input voltage $({{V}_{i}})$ : ${{V}_{g}}$ becomes more negative, so ${{i}_{p}}$ decreases

(iii) The phase difference between the output signal and input signal is ${{180}^{o}}$ (or $\pi$)

(5) Voltage amplification

Current through the load resistance is given by ${{i}_{p}}=-\frac{\mu {{V}_{i}}}{{{r}_{p}}+{{R}_{L}}}\,$ $\Rightarrow \,{{V}_{0}}={{i}_{p}}{{R}_{L}}=\frac{-\,\mu {{V}_{i}}{{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}$  $\Rightarrow$ Voltage gain $=\frac{{{V}_{0}}}{{{V}_{i}}}=-\frac{\mu {{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}$ Numerically $A=\frac{\mu {{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}=\frac{\mu }{1+\frac{{{r}_{p}}}{{{R}_{L}}}}$

(i) If ${{R}_{L}}=\,\,\infty \,\,\Rightarrow A$ will be maximum and ${{A}_{\max }}=\mu$ (Practically $A<\mu$)

(ii) If ${{r}_{p}}={{R}_{L}}\Rightarrow A=\frac{\mu }{2}$

(iii) Power at load resistance $P={{i}_{p}}{{V}_{0}}=i_{p}^{2}{{R}_{L}}$

Condition for maximum power ${{R}_{L}}={{r}_{p}}$ $\therefore$ ${{P}_{\max }}={{\left( \frac{\mu {{V}_{i}}}{{{R}_{L}}+{{R}_{L}}} \right)}^{2}}\times {{R}_{L}}=\frac{{{\mu }^{2}}V_{i}^{2}}{4{{R}_{L}}}$

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