EEE445_hw06sln

EEE445_hw06sln - EEE 591 Homework #6 Solutions 4.4 Show...

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EEE 591 Homework #6 Solutions 4.4 Show that the input impedance, Z , of a parallel RLC circuit satisfies the condition that  * Z Z . Solution: For a parallel RLC circuit, we have   2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 L LC R LC LR j R L L j LC R LR j C j L j R Z   * 2 2 2 2 2 2 2 2 2 1 1 Z L LC R LC LR j R L Z 4.7 Derive the [ Z ] and [ Y ] matrices for the two-port networks shown below. Solution: For circuit (a): Let’s use circuit analysis: connect a 1 A test source directly to port 1 such that I 1 = 1A, leave port 2 open-circuited, and evaluate V 1 and V 2 . B A B A A Z Z Z Z Z V 2 1 B A A Z Z Z V 2 2 2 Therefore, 11 2 12 2 2 AA B AB A Z ZZ Z Z Z From symmetry,
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 B A A B A B A A Z Z Z Z Z Z Z Z Z Z Z Z 2 2 2 21 12 11 22 Hence,    B A A A A B A A B A Z Z Z Z Z Z Z Z Z Z Z 2 2 2 1 and  
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EEE445_hw06sln - EEE 591 Homework #6 Solutions 4.4 Show...

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