Electric Circuits Test 9

Result

Electric Circuits Test 9

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Weekly Quiz Competition

Question 1
1 / -0

A reciprocal two-port network has following z parameters
z₁₁ = 6 + j3, z₁₂ = 5 – j2, z₂₂ = 8 – j
The parameter y₂₂ is

A
-0.03 + j0.11

B
-0.125 + j0.06

C
0.03 – j0.11

D
0.125 – j0.06

Solution

For reciprocal network, z₂₁ = z₁₂
⇒ z₂₁ = z₁₂ = 5 – j2
\(\left[ z \right] = \left[ {\begin{array}{*{20}{c}}{6 + j3}&{5 - j2}\\{5 - j2}&{8 - j}\end{array}} \right]\)
[y] = [z]^-1
|z| = (6 + j3) (8 - j) – (5 – j2) (5 – j2)
= 48 – 6j + 24j + 3 – 25 + j10 + j10 + 4
= 30 + 38j
\(\left[ y \right] = \frac{1}{{30 + 38j}}\;\left[ {\begin{array}{*{20}{c}}{8 - j}&{ - 5 + j2}\\{ - 5 + 12}&{6 + j3}\end{array}} \right]\)
\({y_{22}} = \frac{{6 + j3}}{{30 + 38j}} = 0.125 - j0.06\)