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# Vacuum-Tube Analysis on a Four-Terminal Basis

Author: Leonard Krugman

Fig. 3-2. Equivalent circuit of a triode: (A) with negative grid bias, (B) with positive grid bias.

Figure 3-2 (A) illustrates the familiar case of a conventional grounded-cathode triode operated at low frequencies with its control grid biased sufficiently negative so that no grid current flows. (It should be noted at this point that the current arrows in this diagram and those that follow indicate the direction of electron flow). The applied grid signal causes a voltage μeg to appear in series with the plate resistance rp. Since the grid current ig is zero, the network is completely described by a single equation:

μeg = iprp + ep

The four-pole equivalent network for this same circuit when the grid draws current is illustrated by Fig. 2 (B). In this case, the grid voltage acts across a series circuit consisting of the voltage μpep and the grid resistance rg. The term μp equals the reverse voltage amplification factor: μp = eg/ep. As in the previous case, the grid signal voltage causes a voltage μeg to appear in series with the plate resistance. Since there are two voltage loops in the case when the grid is driven positive, two equations are required to describe the network completely; these are

μee = iprp + ep

eg = igrg + μpep

This analysis of triode vacuum tubes on a four-pole basis is not limited to the grounded-cathode operation of these tubes. The choice of this type of operation is dictated on the basis of reader familiarity with the circuit. The grounded-grid and grounded-plate connections (which have useful counterparts in transistor circuitry) may be analyzed in similar fashion. The basic four-terminal current-voltage relationships for all three cases are illustrated in Fig. 3-3.

Fig. 3-3. Four-terminal network ground connection: (A) cathode, (B) grid, (C) plate.

Last Update: 2010-11-17