Impossibility of a completely matched three-port network

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Impossibility of a completely matched three-port network. When a wave is sent into any one of the ports of the four-port beam splitter shown in this section, there is no reflected wave directly back out the same port, so that ry = 0 for all i. In transmission line jargon this system is said to be matched looking into each of the four ports. Show that it is impossible in principle to devise any kind of lossless three-port network in which all three ports are similarly matched.