Approximate h-model of CE, CB, CC amplifier

Approximate h-model:

In the analysis of the transistor amplifier, we have as far used the exact h-model for the transistor. In practice, we may conveniently use an approximately h-model for the transistor which introduces an error of < 10% in most cases.

This much error may be conveniently tolerated since the h-parameters themselves are not steady but vary considerably for the same type of transistor. We first derive this approximate CE h-model.

Figure 1 gives the equivalent circuit of the CE amplifier using the exact h-model for the CE transistor.

The following steps are used to drive the approximate h-model:

1. If . If h_oe. R_L < 0.1, then we may neglected , being in parallel with R_L.
2. Having neglected h_oe, the collected current I_C equals h_fe. I_b and the magnitude of the dependent voltage generator in the emitter circuit are then given by,

        …..(1)

But . Hence the voltage h_re |V_C | in the emitter circuit may be neglected in comparison with the voltage drop h_ie. I_b provided that R_L is not very large. Then the approximate CE h-model reduces to the form shown in Figure 2.

Approximate h-model Valid for all the three Configuration

The approximate CE h-model of Figure 2 is redrawn in figure 3. This model may be used for any of the three configurations by grounding the appropriate node and analysis done accordingly. It may be proved that the error in values of A_I, R_i, A_V, or output terminal resistance R_ot (= R₀ || R_L) caused by the use of an approximate model does not exceed 10% if .

Analysis of CE Amplifier using Approximate h-model

Figure 2 gives the equivalent circuit of a CE amplifier using an approximate h-model for the transistor. For this equivalent circuit, we get,

Current gain       …..(2)

Input resistance

Voltage gain       ……(3)

Output resistance R₀: From this approximate equivalent circuit of figure 1(b) with V_s = 0 and with an external voltage source connected across the output, we get I_b = 0 and therefore I_C = 0. Hence output resistance . However, in actual practice, R₀ lies between depending on the value of R_S.

With load resistance (the maximum practical value), the output terminal resistance

Condition For a typical transistor S. Hence to meet the condition that , we must use R_L less than .

Analysis of CB Amplifier using the Approximate Model

Figure 4 gives the equivalent circuit of a CB amplifier using the approximate model for the transistor as given in figure 2 with the base grounded, the input applied between the emitter and base, and output obtained across load resistor R_L between the collector and the base.

Current gain      …..(4)

Input resistance R_i: from figure 4,

        ……(5)

        …….(6)

Hence,          …..(7)

Voltage Gain A_V: From figure 4,

Hence,        …..(8)

Output resistance In the equivalent circuit of figure 3, with V_s = 0, we get I_­e = 0. Hence, I_b = 0. Hence the output resistance .

Output Terminal Resistance       …..(9)

Analysis of CC Amplifier (Emitter Follower) using Approximate h-model

Figure 5 gives the equivalent circuit of an emitter follower using the approximate model as given in figure 3, with the collector grounded, the input signal applied between the base and the ground, and the load impedance R_L connected between the emitter and ground.

Current gain A_I: from the circuit of figure 5,

Load current      …..(10)

Hence Current gain      …..(11)

Input resistance R_i: from figure 5,

       …..(12)

Hence,         ……(13)

Voltage Gain A_V: From figure 5,

       ……(14)

Hence,

Output Resistance From figure 5, Open circuit output voltage = V_S

Short circuit output current

Hence output impedance

Output terminal Impedance

Table 1 gives expressions for current gain etc. for the three configurations using an approximate h-model.

Table 1 Expressions for AI, Ri, AV, R0, and Rot using Approximate h-model
Quantity	CE	CB	CC
AI	-hfe		1 + hfe
Ri	hie		hie + (1 + hfe)RL
AV
R0
Rot	RL	RL	R0 || RL