Characteristics of Resistance-Coupled Amplifiers

Figure 20. Either incorrect grid bias or a signal of too great magnitude causes nonlinear distortion as indicated.

The equivalent circuit of one stage of a resistance-coupled amplifier is shown in Fig. 21. The condenser C_g' is the sum of the wiring capacitance C_w and the equivalent grid input capacitance C_g of the second tube, given by the equation¹²

In this expression C_gk is the grid-to-cathode capacitance and C_gp is the grid-to-plate capacitance of the tube, and A_v is the voltage gain per stage. This equation applies to triodes only. For tetrodes and pentodes C_g' is the sum of the wiring capacitance and the grid input capacitance which is given in vacuum-tube manuals.

Gain at Intermediate Audio Frequencies. From the values given in Fig. 19 and assuming that C_g' is about 50 micromicrofarads, at an intermediate frequency of 1000 cycles, the effects of C_c and C_g' are negligible. Then, from equation 9, A_v = (20 x 41,700)7(10,000 + 41,700) = 16.1. The value of R_L used in this equation is the equivalent resistance of R_L and R_g of Fig. 21 in parallel, or (50,000 x 250,000)/(50,000 + 250,000) = 41,700 ohms. At this frequency the circuit is resistance only, and there is no phase shift except as discussed in connection with Fig. 18.

Figure 21. Equivalent circuit for one stage of Fig. 19.

Gain at Low Audio Frequencies. At low frequencies, such as 50 cycles, the effect of C_g' of Fig. 21 becomes negligible, but C_c must be considered. The frequency at which the gain is 3 decibels below the intermediate audio frequency and the phase shift caused by the circuit is 45° is

where f is in cycles, C_c is in farads, and the resistances are in ohms.

Gain at High Audio Frequencies. At high frequencies, such as 20,000 cycles, the effect of C_c of Fig. 21 becomes negligible but C_g' must be considered. The frequency at which the gain is 3 decibels below the intermediate audio frequency and the phase shift caused by the circuit is 45° is

where f is in cycles, C_g' is in farads, and the resistances are in ohms.

Theory alone predicts that R_L and R_g of Figs. 19 and 21 should be very high so that the alternating current will be low, the internal voltage drop caused by the plate resistance will be low, and most of the available voltage μE_g will appear across the output terminals. Because the direct-current component must flow through R_L, it is impractical to make R_L more than three to five times r_p this rule applying only to triodes. For triodes, R_s is from about 250,000 to 1,000,000 ohms. For tetrodes and pentodes, the plate resistances are so high that this rule cannot be followed, and typical values of R_L are from 250,000 to 500,000 ohms, with values of R_g about the same as for triodes.

The equations that have been used were derived¹² using Thévenin's theorem (page 148). Because of the very high internal plate resistance of a pentode (usually over 1,000,000 ohms) and the relatively low load resistance used, equations can be derived using Norton's theorem (page 149). Thus the gain at intermediate frequency is

where R_e is the equivalent parallel resistance of r_p, R_L, and R_ff. Often the effect of r_p is neglected because it is so high, and R_e is assumed to equal the parallel resistance of R_L and R_g. This assumption should not be made with triodes and equation 14 should not be used with triodes.