Approximate h-model: In the analysis of 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 error < 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 CE amplifier using exact h-model for CE transistor.
The following steps are used to driving the approximate h-model:
- If . If hoe. RL < 0.1, then we may neglected , being in parallel with RL.
- Having neglected hoe, the collected current IC equals hfe. Ib and the magnitude of the dependent voltage generator in the emitter circuit is then given by,
But . Hence the voltage hre |VC | in the emitter circuit may be neglected in comparison with the voltage drop hie.Ib provided that RL 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 AI, Ri, AV or output terminal resistance Rot (= R0 || RL) caused by use of approximate model does not exceed 10% if .
Analysis of CE Amplifier using Approximate h-model
Figure 2 gives the equivalent circuit of CE amplifier using approximate h-model for the transistor. For this equivalent circuit we get,
Current gain …..(2)
Voltage gain ……(3)
Output resistance R0 : From this approximate equivalent circuit of figure 1(b) with Vs = 0 and with external voltage source connected across the output, we get Ib = 0 and therefore IC = 0. Hence output resistance . However, in actual practice, R0 lies between depending on the value of RS.
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 RL less than .
Analysis of CB Amplifier using the Approximate Model
From figure 4 gives the equivalent circuit of a CB amplifier using the approximate model for the transistor as given in figure 2 with base grounded, the input applied between emitter and base and output obtained across load resistor RL between the collector and the base.
Current gain …..(4)
Input resistance Ri : from figure 4,
Voltage Gain AV : From figure 4,
Output resistance In the equivalent circuit of figure 3, with Vs = 0, we get Ie = 0. Hence, Ib = 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 collector grounded, input signal applied between the base and the ground and the load impedance RL connected between emitter and ground.
Current gain AI : from the circuit of figure 5,
Load current …..(10)
Hence Current gain …..(11)
Input resistance Ri : from figure 5,
Voltage Gain AV: From figure 5,
Output Resistance From figure 5, Open circuit output voltage = VS
Short circuit output current
Hence output impedance
Output terminal Impedance
Table 1 gives expressions for current gain etc. for the three configurations using approximate h-model.
|Table 1 Expressions for AI, Ri, AV, R0 and Rot using Approximate h-model|
|AI||-hfe||1 + hfe|
|Ri||hie||hie + (1 + hfe)RL|
|Rot||RL||RL||R0 || RL|