Consider the circuit shown in Figure P7.23. (a) Write the transfer function
Figure P7.23
a.
The transfer function
Answer to Problem 7.23P
The expression for transfer function of the circuit is,
Explanation of Solution
Given:
The circuit is given as:
Calculation:
Refer to the given circuit:
Drawing the small signal equivalent circuit using the simplified hybrid
Now drawing the frequency domain equivalent circuit of above figure:
Applying the nodal analysis to derive the expression for
Solving the above equation:
Applying the Kirchhoff s current law at node
Applying the Kirchhoff s current law at output node:
Evaluating the expression for
Substituting
The expression for transfer function of the circuit is given as:
Solving the above equation:
So,
Therefore, the expression for transfer function of the circuit is,
b.
The expression for the time constant associating with the input portion of the circuit.
Answer to Problem 7.23P
The expression of the time constant associated with the input portion of the circuit:
Explanation of Solution
Given:
The circuit is given as:
Calculation:
Evaluating the expression for the time constant associated with the input portion of the circuit.
From the equation (3) , the time constant associated with the input portion of the circuit is,
Hence, the expression of the time constant associated with the input portion of the circuit .
c.
The expression for the time constant associating with the output portion of the circuit.
Answer to Problem 7.23P
The expression of the time constant associated with the output portion of the circuit:
Explanation of Solution
Given:
The circuit is given as:
Calculation:
Evaluating the expression for the time constant associated with the input portion of the circuit.
From equation (3), the time constant associated with the input portion of the circuit is expressed as:
Therefore, the expression for the time constant associated with the output portion of the circuit:
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Chapter 7 Solutions
Microelectronics: Circuit Analysis and Design
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