Hybrid Equivalent For CC Transistor

The figure shows the transistor connected in common emitter configuration and the figure also shows the hybrid equivalent circuit of such a transistor.

In common emitter transistor configuration, the input signal is applied between the base and emitter terminals of the transistor and output appears between the collector and base terminals. The input voltage (V_bc) and the output current (i_c) are given by the following equations:

V_bc = h_ic.i_b + h_re.V_ec

i_e = h_fe.i_b + h_oe.V_ec

Hybrid expression

Expression can be obtained from the general hybrid formulas derived in this article Hybrid Equivalent of Transistor by adding a second subscript letter ‘b’ (which stands for common Collector) with the h-parameters and are as discussed below.

Current Gain

It is given by the relation,

A_i = -(h_fc/(1 + h_oc.r_L))

Where r_L is the A.C load resistance. Its value is equal to the parallel combination of resistance R_E and R_C. Since h_fe of a transistor is a positive number, therefore A_i of a common emitter amplifier is negative.

Input Resistance

The resistance looking into the amplifier input terminals (i.e. base of a transistor) is given by the relation,

R_i = h_ie + h_re.A_i.r_L = h_ie – ((h_rc.h_fc)/(h_oc + (1/r_L)))

The input resistance of the amplifier stage (called stage input resistance R_is) depends upon the biasing arrangement. For a fixed bias circuit, the stage input resistance is,

R_is = R_s

Voltage Gain

It is given by the relation,

A_v = A_i.r₁/R_i

Since the current gain (A_i) of a common base amplifier is positive, therefore the voltage gain (A_v) is also positive. It means that there is no phase difference between the input and output signals of the common base amplifier. The voltage gain, in terms of h-parameters, is given by the relation.

A_v = h_fc.r_L/(h_ic + ∆h.r_L)

Where

∆h = h_ic.h_oc – h_rc.h_fc

Output Resistance

The resistance looking into the amplifier output terminals is given by the relation,

R_o = (R_s + h_ic)/(R_s.h_oc + ∆h)

Where

R_s = Resistance of the source, and

∆h = h_ic.h_oc – h_rc.h_fc

Overall Voltage Gain

It is given by the relation,

A_vc = (A_v.R_is)/(R_s + R_is) 

Overall Current Gain

It is given by relation,

A_is = (A_i + R_s)/(R_i + R_is)

Example

A transistor used in a common collector amplifier has the following vaules of h-parameters:

h_ic = 2 KΩ, h_fc = -.51, h_rc = 1 and h_oc = 25 X 10^-6mhos

Calculate the values of input resistance, output resistance, current gain and voltage gains of the amplifier stage.

Solution

Given Data:

h_ic = 2 KΩ = 2000 Ω
h_fc = -.51
h_rc = 1
h_oc = 25 X 10^-5mhos
r_L = R_E = 5 KΩ = 5 X 10³ Ω
R_s = 1 KΩ = 1000 Ω
R₁= R₂ = 10 KΩ

Input resistance of the amplifier stage

We know that the input resistance,

A_i = -(h_fc/(1 + h_oc.r_L))

= -51/[1 + {(25 x 10^-6) x (5 x 10³)}]
= 45.3

and input resistance

R_i = h_ie + h_re.A_i.r_L
= 2000 + (1 x 45.3 x 5 x 10³ Ω
= 228 x 10³Ω
= 228 kΩ

As input resistace of the amplifier

R_is = R₁ // (R₁ // R₂)

= 228 // (10 // 10) = 4.9 kΩ

= 4900 Ω Ans

Output Resistance of Amplifier Stage

We know that:

R_o = - (R_s + R_ic)/h_fc

= - ( 1000 + 2000)/-51

= 59 Ω

and output resistance of the amplifier stage

R_os = R_o // R_E

= 59 // ( 5 x 10^-3)

= 58.3 Ans

Current Gain

We know that the current gain of amplifier stage,

A_is = -(A_i.R_s)/(R_s.R_is) = (45.3 x 1000)/(1000 + 4900) = 7.7 Ans.

Voltage Gain Amplifier Stage

We know that voltage gain is

A_v = A_i.r_L/R_i = (45.3 X ( 5 x 10³) / 228 x 10³= 1 Ans.

and the voltage gain of the amplifier stage

A_vs = A_v.A_is/(R_s + R_is) = (1 + 4900)/ (1000 + 4900) = 0.83 Ans