# JEE Main & Advanced Physics Semiconducting Devices Constants of Triode Valve

Constants of Triode Valve

Category : JEE Main & Advanced

(1) Plate or dynamic resistance $({{r}_{P}})$

(i) The slope of plate characteristic curve is equal to $\frac{1}{\text{plate}\,\text{resistance}}$ or It is the ratio of small change in plate voltage to the change in plate current produced by it, the grid voltage remaining constant. That is, ${{r}_{p}}=\frac{\Delta {{V}_{\text{p}}}}{\Delta {{i}_{p}}},{{V}_{G}}=\text{constant}$.

(ii) It is expressed in kilo ohms $(K\Omega )$. Typically, it ranges from $8K\Omega$ to$40K\Omega$. The ${{r}_{P}}$ can be determined from plate characteristics. It represents the reciprocal of the slope of the plate characteristic curve. (iii) If the distance between plate and cathode is increased the ${{r}_{P}}$ increases. The value of ${{r}_{P}}$ is infinity in the state of cut off bias or saturation state.

(2) Mutual conductance (or trans conductance) $({{g}_{m}})$

(i) It is defined as the ratio of small change in plate current $(\Delta {{i}_{p}})$ to the corresponding small change in grid potential $(\Delta {{V}_{g}})$ when plate potential ${{V}_{p}}$ is kept constant i.e. ${{g}_{m}}={{\left( \frac{\Delta {{i}_{p}}}{\Delta {{V}_{g}}} \right)}_{{{V}_{p\,}}\text{is}\,\text{constant}}}$

(ii) The value of ${{g}_{m}}$ is equal to the slope of mutual characteristics of triode.

(iii) The value of ${{g}_{m}}$ depends upon the separation between grid and cathode. The smaller is this separation, the larger is the value of ${{g}_{m}}$ and vice versa. (iv) In the saturation state, the value of $\Delta {{i}_{p}}=0$, ${{g}_{m}}=0$

(3) Amplification factor $(\mu )$ : It is defined as the ratio of change in plate potential $(\Delta {{V}_{p}})$ to produce certain change in plate current $(\Delta {{i}_{p}})$ to the change in grid potential $(\Delta {{V}_{g}})$ for the same change in plate current $(\Delta {{i}_{p}})$i.e. $\mu =-\,{{\left( \frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}} \right)}_{\Delta {{I}_{p}}=\,\text{a constant }}}$; negative sign indicates that ${{V}_{p}}$ and ${{V}_{g}}$ are in opposite phase. (i) Amplification factor depends upon the distance between plate and cathode $({{d}_{pk}}),$ plate and grid ${{d}_{pg}}$ and grid and cathode $({{d}_{gk}})$. i.e. $\mu \,\propto \,{{d}_{pg}}\propto \,{{d}_{pk}}\propto \frac{1}{{{d}_{gk}}}$ (ii) The value of $\mu$ is greater than one. (iii) Amplification factor is unitless and dimensionless.

(4) Relation between triode constants : The triode constants are not independent of each other. They are related by the relation $\mu ={{r}_{p}}\times {{g}_{m}}$ The ${{r}_{p}}$ and ${{g}_{m}}$ depends on ${{i}_{p}}$ in the following manner ${{r}_{p}}\propto {{i}_{p}}^{-1/3}$, ${{g}_{m}}\propto {{i}_{p}}^{1/3}$, $\mu$ does not depend on ${{i}_{p}}$.

Above three constants may be determined from any one set of characteristic curves.

${{r}_{p}}=\frac{{{V}_{P1}}-{{V}_{P2}}}{{{I}_{PA}}-{{I}_{PB}}}$, ${{g}_{m}}=\frac{{{I}_{PA}}-{{I}_{PB}}}{{{V}_{G1}}-{{V}_{G2}}}$, $\mu =-\frac{{{V}_{P1}}-{{V}_{P2}}}{{{V}_{G2}}-{{V}_{G1}}}$

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