Concept explainers
(a) Using the small-signal equivalent circuit in Figure 12.25 for the circuit in Figure
(a)
To derive: The expression for the small signal current gain of the circuit.
Answer to Problem 12.50P
The value of the small signal current gain is
Explanation of Solution
Given:
The given circuit is shown in Figure 1.
Figure 1
Calculation:
Mark the nodes and redraw the circuit.
The given diagram is shown in Figure 2
Figure 2
By KCL the expression for the current
The expression for the node voltage is given by,
Apply KCL at node
Substitute
The expression for the output current is given by,
Apply KCL at node
Substitute
Substitute
Consider
Thus, the expression for the small signal current gain is,
Conclusion:
Therefore, the value of the small signal current gain is
(b)
The value of the gain
To compare: The obtained value with the given value of gain. and compare it to the value of 9.58.
Answer to Problem 12.50P
The value of the current gain is
Explanation of Solution
Given:
The given circuit is shown below.
The given value of gain is 9.58.
Also, the values are:
Calculation:
The expression to determine the value of the resistance
The expression for the value of the voltage
The expression to determine the value of the current
Substitute
The value of the current
Substitute
The expression to determine the value of the resistance
The value of the Thevenin voltage is given by,
The expression to determine the value of the current
Substitute
The value of the current
Substitute
The expression to determine the transconductance of first transistor is calculated as,
The expression to determine the transconductance of second transistor is calculated as,
The value of the small signal input resistance is calculated as,
The value of the small signal input resistance is calculated as,
The value of A is calculated as,
The value of B is calculated as,
The value of C is calculated as,
The value of D is calculated as,
Substitute
Substitute
The value of the current gain is
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Chapter 12 Solutions
Microelectronics Circuit Analysis and Design
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