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 h_{oe}. R_{L} < 0.1, then we may neglected , being in parallel with R_{L}.
- 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 is 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} (= R_{0} || R_{L}) 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)
Input resistance
Voltage gain ……(3)
Output resistance R_{0} : From this approximate equivalent circuit of figure 1(b) with V_{s} = 0 and with external voltage source connected across the output, we get I_{b} = 0 and therefore I_{C} = 0. Hence output resistance . However, in actual practice, R_{0} 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
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 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 collector grounded, input signal applied between the base and the ground and the load impedance R_{L} connected between 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 approximate h-model.
Table 1 Expressions for A_{I}, R_{i}, A_{V}, R_{0} and R_{ot} using Approximate h-model | |||
Quantity | CE | CB | CC |
A_{I} | -h_{fe} | 1 + h_{fe} | |
R_{i} | h_{ie} | h_{ie} + (1 + h_{fe})R_{L} | |
A_{V} | |||
R_{0} | |||
R_{ot} | R_{L} | R_{L} | R_{0} || R_{L} |