Question

Find the values of r_p, µ and g_m of a triode operating at plate voltage 200 V and grid voltage −6. The plate characteristics are shown in the figure.

Answer 1

Dynamic plate resistance,
$r_p=\left(\frac{{\mathrm{\delta V}}_p}{{\mathrm{\delta I}}_p}\right)$ , at constant grid voltage
We need to find the slope of the graph for a particular value of grid voltage, i.e. V_g = −6 V.

Consider two points for the plot of V_g = −6 V:
$$\begin{gathered} r_{\mathrm{p}}=\frac{(240-160)\mathrm{V}}{(13-3)\times {10}^{-3}\mathrm{A}} \\ {r}_{\mathrm{p}}=\frac{80}{10}\times {10}^3\mathrm{\Omega } \\ {r}_{\mathrm{p}}=8\mathrm{K\Omega } \\ {g}_{\mathrm{m}}={\left(\frac{\delta I_p}{\delta V_g}\right)}_{V_{\mathrm{P}}=\mathrm{constant}(200\mathrm{V})} \end{gathered}$$

Consider two points on the 200 V line:
$$\begin{gathered} g_{\mathrm{m}}=\frac{(13-3)\times {10}^{-3}}{\left[\right(-4)-(-8\left)\right]}\mathrm{A} \\ {g}_{\mathrm{m}}=\frac{10\times {10}^{-3}}{4}=2.5\mathrm{mili}\mathrm{mho} \end{gathered}$$
Amplification factor, $\mu =-{\left(\frac{∆V_{\mathrm{P}}}{∆V_{\mathrm{G}}}\right)}_{i_{\mathrm{P}}=\mathrm{constant}}$
$$\begin{gathered} \mu =-\frac{100-180}{-6-(-10)} \\ \mu =\frac{80}{4}=20 \end{gathered}$$