The conditions of infinite directivity for transmissionline directional couplers are derived in a general and rigorous way. Exact expressions valid for any degree of coupling are found. The case of small coupling and the case of a matched primary line are considered as particular cases of this general analysis. In the case of small coupling, the condition Z11Z44 = 1 and Z22Z33 = 1 given by W. L. Firestone in a recent paper are found to be correct; it is shown also that these simple conditions do not apply anymore when the coupling becomes large.
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R. C. Knechtli (1955) studied this question.