The two-port of Fig. 16.65 can be viewed as three separate cascaded two-ports A, B, and C. (a) Compute t for each network. (b) Obtain t for the cascaded network. (c) Verify your answer by naming the two middle nodes Vx and Vy, respectively, writing nodal equations, obtaining the admittance parameters from your nodal equations, and converting to t parameters using Table 16.1.
(a)
The
Answer to Problem 54E
The
Explanation of Solution
Calculation:
The required diagram is shown in Figure 1.
Here,
The mesh equation from the input side is given by,
The mesh equations at the output side is given by,
Substitute
The
Here,
Write equations (6) and (7) in matrix form.
Compare equation (3) with equation (4).
Compare equation (2) with equation (6).
The
The required diagram is shown in Figure 2.
The mesh equation from the input side is given by,
The mesh equations at the output side is given by,
Substitute
Compare equation (8) with equation (4).
Compare equation (7) with equation (5).
The
The required diagram is shown in Figure 3.
The mesh equation from the input side is given by,
The mesh equations at the output side is given by,
Substitute
Compare equation (11) with equation (4).
Compare equation (10) with equation (5).
The
Conclusion:
Therefore, the
(b)
The
Answer to Problem 54E
The
Explanation of Solution
Calculation:
The
Substitute
Conclusion:
Therefore, the
(c)
To verify: The above answers by obtaining the admittance parameter and converting them to
Answer to Problem 54E
The values have been verified.
Explanation of Solution
Calculation:
The required diagram is shown in Figure 4.
The nodal equation at node
The nodal equations at node
Substitute
Substitute
The current
Substitute
The current
Substitute
The
Here,
Compare equation (16) with equation (18).
Compare equation (17) with equation (19).
The determinant of the matrix
Substitute
The relation between
Substitute
Within the limits of error, the values have been verified.
Conclusion:
Therefore, the values have been verified.
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