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# Output Resistance

Author: Leonard Krugman

Fig. 3-13. Analysis of output resistance ro: (A) equivalent circuit

The output resistance can be found in a similar manner. Consider Fig. 3-13 (A), which illustrates the equivalent circuit for analyzing the output resistance. The equations for the two loops on the basis of Kirchoff's law are:

 Loop 1: O = i1 (Rg + re + rb) + i2rb Eq. (3-14) Loop 2: E2 - rmie = i1rb + i2 (rc + rb + RL) Eq. (3-15) Since ie = i1, then E2 = i1 (rb + rm) + i2 (rc + rb + RL) Eq. (3-15A)

Solving the two independent equations 3-14 and 3-15A for the unknown load current,

 - Eq. (3-16)

Looking back into the transistor, the generator E2 with its internal resistance RL sees the output resistance r0. Again the circuit may be simplified as shown in Fig. 3-13 (B).

Fig. 3-13 (B) simplified circuit.

Then

 E2 = (RL+ro)i2 or Eq. (3-17)

Substituting equation 3-16 in 3-17,

 Eq. (3-18) Eq. (3-19)

Then

 Eq. (3-20)*

In terms of the open-circuit parameters

 Eq. (3-21)*

Fig. 3-14. Output resistance vs generator resistance for typical point-contact transistor (grounded base).

The latter equation indicates that the output resistance depends to some extent on the value of the signal generator input resistance. The variation of r0 vs Rg is illustrated in Figs. 3-14 and 3-15 (for the same point-contact and junction transistors considered in the preceding section) . In the case of the typical point-contact transistor, the transistor output resistance varies from 2,400 to 12,000 ohms as the signal generator internal resistance increases from zero to infinity. The junction transistor output resistance varies from 270,000 to 2,000,000 ohms as the signal generator internal resistance increases from zero to infinity.

Fig. 3-15. Output resistance vs generator resistance for typical junction transistor (grounded base).

Last Update: 2010-11-17