The triode amplifier of Fig. 4-30 utilizes cathode bias to eliminate the need for a grid power supply. The very large resistance R_G provides a path to ground for stray charge collected by the grid; this current is so small, however, that the voltage drop across R_G is negligible. It follows that the grid is maintained at a negative bias, so
v_G = -R_K i_P (1)
A plot of (1) on the plate characteristics is called the grid bias line, and its intersection with the dc load line determines the Q point. Let R_L = 11.6 k \Omega, R_K = 400 \Omega, R_G=1 M \Omega \text {, and } V_{P P} = 300 \text{V}. If the plate characteristics of the triode are given by Fig. 4-31, (a) draw the dc load line, (b) sketch the grid bias line, and (c) determine the Q-point quantities.
(a) The dc load line has horizontal intercept V_{PP} = 300 \text{V} and vertical intercept
\frac{V_{P P}}{R_{ dc }} = \frac{V_{P P}}{R_L + R_K} = \frac{300}{(11.6 + 0.4) \times 10^3} = 25 \text{mA}
as shown on the plate characteristics of Fig. 4-31.
(b) Points for the plot of (1) are found by selecting values of i_P and calculating the corresponding values of v_G. For example, if i_P = 5 \text{mA}, then v_G = -400 (5 \times 10^3) = -2 \text{V}, which plots as point 1 of the dashed grid bias line in Fig. 4-31. Note that this is not a straight line.
(c) From the intersection of the grid bias line with the dc load line, I_{PQ} = 10 \text{mA}, V_{PQ} = 180 \text{V}, and V_{GQ} = -4 \text{V}.