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EEE445_hw07sln

# EEE445_hw07sln - EEE 445 Homework#7 Solutions 4.16 A...

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EEE 445 Homework #7 Solutions 4.16 A four-port network has the scattering matrix shown below. (a) Is this network lossless? (b) Is this network reciprocal? (c) What is the return loss into port 1 when all other ports are terminated with matched loads? (d) What is the insertion loss and phase delay between ports 2 and 4, when all other ports are terminated with matched loads? (e) What is the reflection coefficient seen at port 1 if a short circuit is placed at the terminal plane of port 3, and all other ports are terminated with matched loads?         0 45 6 . 0 45 4 . 0 0 45 6 . 0 0 0 45 3 . 0 45 4 . 0 0 0 45 8 . 0 0 45 3 . 0 45 8 . 0 90 1 . 0 S Solution: (a)   * 2 2 2 2 11 12 13 14 e.g., S S S S 1 S S U Therefore, the network is not lossless. (b)     0 S S t Therefore, the network is reciprocal. (c) The return loss into port 1 with all other ports terminated in matched loads. By definition (4.41) and the text beneath: 1 1 2 3 4 1 10 11 0.1 90 0.8 45 0.3 45 0 0.8 45 0 0 0.4 45 0 0.3 45 0 0 0.6 45 0 0 0.4 45 0.6 45 0 0 using the input as unity 20log 20 dB V V V V V V RL S                     (d) The insertion loss between ports 2 and 4 with all other ports terminated in matched loads: dB 96 . 7 log 20 42 10 S IL The insertion phase (not a delay) is 45 42 S .

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EEE445_hw07sln - EEE 445 Homework#7 Solutions 4.16 A...

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