Grounded Collector Connection

Author: Leonard Krugman

The grounded collector connection is illustrated in Fig. 4-8 (A). In this connection, the input signal is connected between the base and collector electrodes, and the output is taken between the emitter and the common collector. The equivalent active "T" is illustrated in Fig. 4-8 (B).

Fig. 4-8. (A) The grounded collector connection. (B) Equivalent active "T" for groundedcollector connection.

The general four-terminal parameters can be measured in terms of the internal transistor parameters using the basic measuring circuits of Fig. 3-8. The four-terminal parameter equations for the grounded collector connection are:

A.	when i2 = 0, r11 = rb + rc	Eq. (4-10)
B.	when i2 = 0, r21 = rc	Eq. (4-41)
C.	when i1 = 0, r12 = rc - rm	Eq. (4-12)
D.	when i1 = 0, r22 = re + rc— rm	Eq. (4-13)

These equalities are derived as follows:

A. 

Using Fig. 4-8 (B), the input loop equation on the basis of Kirchoffs law is:

e₁ + r_mi_e = i₁ (r_b + r_c) + i₂r_c

For this connection

i₂ = i_e

and 

e₁ = i₁ (r_b + r_c) + i₂ (r_c - r_m)

when

i₂ = 0, e₁ = i₁ (r_b + r_c),

and

B. 

Using the same input loop equation, when

i₁ = 0, e₁ = i₂(r_c - r_m),

and

C. 

The output voltage loop equation is:

e₂ +r_mi_e = i₁r_c + i₂ (r_e + r_c)

Since 

i₂ = i_e, e₂ = i₁r_c + i₂ (r_e + r_c - r_m)

when

i₂ = 0, e₂ = i₁r_c

D.

Using the same outputloop equation,

when

i₁ = 0, e₂ = i₂ (r_e + r_c - r_m)

The numerical values of the four-terminal parameters can now be determined for the typical point-contact transistor. The values are:

r₁₁ = r_b + r_c = 100 + 11,900 = 12,000 ohms

r₁₂ = r_c - r_m = 11,900 - 23,900 = -12,000 ohms

r₂₁ = r_c = 11,900 ohms

r₂₂ = r_e + r_c - r_m = 150 + 11,900 - 23,900 = -11,850 ohms

The numerical values for the junction transistor are:

r₁₁ = r_b + r_c = 500 + 1,999,500 = 2,000,000 ohms

r₁₂ = r_c - r_m = 1,999,500 - 1,899,500 = 100,000 ohms

r₂₁ = r_c = 1,999,500 ohms

r₂₂ = r_e + r_c-r_ra = 50 + 1,999,500 - 1,899,500 = 100,050 ohms

Because of the very low values of r_b and r_e compared to the quantities r_c and (r_c — r_m), r_n is approximately equal to r₂₁, and r₂₂ is approximately equal to r₁₂.

Fig. 4-9. Operating circuit, grounded collector connection

Figure 4-9 illustrates the operating circuit for the grounded collector connection. As in the analysis of the grounded emitter circuit, the performance characteristics for this connection can now be determined by straightforward substitution in the general four-terminal circuit equations.