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Circuit Parameters

Author: Leonard Krugman

The general open-circuit characteristics derived for the grounded base connection apply equally well to the grounded emitter and grounded base connections, since the characteristics were determined on the basis of a sealed box. However, since the internal parameters of the transistor have been rearranged, the values of the general characteristics are different. It is necessary then, to evaluate the open-circuit characteristics r11 r12, r21, and r22 in terms of the transistor internal parameters re, rb, rc, and rm. The same basic measuring circuits, illustrated in Figs. 3-8, may be used to determine the four-terminal parameter for the grounded emitter connection:

 A r11 = e1/i1 when i2 = 0, r11 = re + rb Eq. (4-1) B r21 = e2/i1 when i2 = 0, r21 = re - rm Eq. (4-2) C r12 = e1/i2 when i1 = 0, r12 = re Eq. (4-3) D r22 = e2/i2 when i1 = 0, r22 = re + rc - rm Eq. (4-4)

These grounded-emitter relationships are derived as follows:

A.

Using Fig. 4-1 (B), the input loop equation on the basis of Kirchoff's law is:

e1 = i1 (re + rb) + i2re

when

i2 = 0, e1 = i1(re + rb)

then

B.

For the same input loop equation, when i1 = 0

e1 = i2re;

then

C.

The output loop equation for Fig. 4-1 (B) on the basis of Kirchoff's law is:

e2 - rmic = i1re + i2 (re + rc)

Also

ie = -(i1 + i2)

Substituting for ie,

e2 + im (i1 + i2) = i1re + i2 (re + rc) e2 = i1 (re - rm) + i2 (re + rc - rm)

when

i2 = 0, e2 = i1(re-rm)

then

D.

Using the same equations as in C above, when

i1 = 0, e2 = i2 (re + rc - rm)

then

The open-circuit characteristics can now be numerically evaluated for the typical point-contact and junction transistors previously considered in Chapter 3. For the point-contact transistor in the grounded emitter connection:

r11 = re + rb = 150 + 100 = 250 ohms

r12 = re = 150 ohms

r21 = re- rm = 150 - 23,900 = -23,750 ohms

r22 = re + rc - rm = 150 + 11,900 - 23,900 = -11,850 ohms

For the junction transistor in the grounded emitter connection:

r11 = re + rb = 50 + 500 = 550 ohms

r12 = re = 50 ohms

r21 = re- rm = 50 - 1,899,500 = -1,899,450 ohms

r22 = re + rc - rm = 50 + 1,999,500 - 1,899,500 = 100,050

Because of the large values of rm and rc with respect to re, r21 in the practical case can be approximated by -rm, and r22 by (rc - rm). The emitter resistance, re = r12, is the feedback resistance and is equivalent to rb = r12 in the grounded base connection. Notice, however, that since there is phase inversion in the grounded emitter connection, re produces degenerative (negative) feedback, rather than regenerative (positive) feedback. The degenerative effect of the output current through re is similar to the degenerative action of an unbypassed cathode resistor in a grounded cathode vacuum tube.

Last Update: 2010-11-17