What is transmission matrix of ideal transformer with turns ratio
A. <span class="math-tex">\(\left[ {\begin{array}{*{20}{c}} n&0\\ 0&{\frac{1}{n}} \end{array}} \right]\)</span>
B. <span class="math-tex">\(\left[ {\begin{array}{*{20}{c}} {\frac{1}{n}}&0\\ 0&n \end{array}} \right]\)</span>
C. <span class="math-tex">\(\left[ {\begin{array}{*{20}{c}} n&0\\ 0&{ - \frac{1}{n}} \end{array}} \right]\)</span>
D. <span class="math-tex">\(\left[ {\begin{array}{*{20}{c}} {\frac{1}{n}}&0\\ 0&{ - n} \end{array}} \right]\)</span>
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Right Answer is: A
SOLUTION
The two-part networks of n : 1 ideal transformer is shown below.
V1 = nV2
\({I_2} = - n{I_1} \Rightarrow {I_1} = \frac{{ - 1}}{n}{I_2}\)
ABCD parameters of a two-port network can be represented as follows.
V1 = A V2 – B I2
I1 = C V2 – D I2
The equations of ideal transformer are
V1 = n V2 – 0 I2
\({I_1} = 0{V_2} - \frac{1}{n}{I_2}\)
By comparing with standard equations,
A = n, B = 0, c = 0, \(D = \frac{1}{n}\)
\(\left[ {\begin{array}{*{20}{c}} A&B\\ C&D \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} n&0\\ 0&{\frac{1}{n}} \end{array}} \right]\)
The given matrix describes the transformer in terms of ABCD parameters.
