For the transistors in the circuit in Figure P 12.53, the parameters are:
The value of the closed loop current gain of the circuit.
Answer to Problem 12.53P
The value of the current gain is
Explanation of Solution
Given:
The given diagram is shown in Figure 1
Calculation:
The small signal model of the above circuit is shown below.
The required diagram is shown in Figure 2
The expression to determine the value of the Thevenin resistance of the circuit is given by,
The Thevenin voltage of the circuit is calculated as,
The expression for the base current of the first transistor is given by,
Substitute
The expression to determine the collector current of the first transistor is given by,
Substitute
The expression to determine the value of the base voltage of the second transistor is given by,
Substitute
The expression for the current
Substitute
The expression to determine the value of the collector current
Substitute
The expression for the transconductance of the first transistor is given by,
Substitute
The expression for the small signal resistance is given by,
Substitute
The expression for the transconductance of the second transistor is given by,
Substitute
The expression for the small signal resistance is given by,
Substitute
Apply KCL at source
Substitute
Apply KCL at node A.
Substitute
Apply KCL at node
Substitute
Apply KCL at
Substitute
Substitute
Substitute
Substitute
Substitute
The expression to determine the value of the output current is given by,
Substitute and
Substitute
Conclusion:
Therefore, the value of the current gain is
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Chapter 12 Solutions
Microelectronics: Circuit Analysis and Design
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