Concept explainers
Using the y parameters, derive formulas for Zin, Zout, Ai, and Av for the common-emitter transistor circuit.
Derive the formulae for input impedance, output impedance, current gain, and voltage gain for the common-emitter transistor circuit using y parameters.
Explanation of Solution
Formula used:
Write the expressions for admittance parameters of a two-port network as follows:
Refer to Figure 19.56 (a) for schematic circuit of common-emitter amplifier (transistor) and write the formulae for input impedance, output impedance, current gain, and voltage gain for the common-emitter transistor circuit as follows:
Write the expression for voltage gain of a common-emitter transistor as follows:
Here,
Write the expression for current gain of a common-emitter transistor as follows:
Here,
Write the expression for input impedance of a common-emitter transistor follows:
Write the expression for output impedance of a common-emitter transistor as follows:
Calculation:
Draw a two-port circuit to obtain input impedance, current gain, and voltage gain for the common-emitter transistor circuit as shown in Figure 1.
From Figure 1, write the expression for current
Substitute
Substitute
Consider
As the
Rearrange the expression as follows:
Substitute
As the current
Modify the expression in Equation (7) for common-emitter transistor circuit as follows:
Substitute
Substitute
From Equation (8), substitute
Substitute
Draw a two-port circuit to obtain output impedance for the common-emitter transistor circuit as shown in Figure 2.
From Figure 2, write the expression for output impedance as follows:
From Equation (2), substitute
From Figure 2, write the expression for
Substitute
Substitute
From the calculations, the formulae for input impedance, output impedance, current gain, and voltage gain for the common-emitter transistor circuit are derived as follows:
Conclusion:
Thus, the formulae for input impedance, output impedance, current gain, and voltage gain for the common-emitter transistor circuit are derived.
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Chapter 19 Solutions
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