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In many radio-engineering applications it is desired to provide a network having a narrow pass-band and very high rejection near by. In lumpedconstant work it has been found that a useful solution to this problem is the familiar coupled circuit. Two resonant circuits are generally used, and occasionally three. Similar problems arise at very-high frequencies, where transmission-line or even wave-guide networks must be used. This paper provides a general analysis of this type of circuit. It is shown that, to a first approximation, the optimum response obtainable has a universal form which depends solely on the number of resonant circuits, and not on the type of circuits or of coupling. The problem of construction of such circuits is thus greatly simplified. The engineer can immediately select from the curves given here the minimum number of tuned circuits which he can use in view of the specifications given him. He can then be sure that other factors are perfectly arbitrary. Hence, he may select the type of resonators and coupling to be used entirely from considerations of ease of manufacture, ease of calculation or of empirical adjustment, stability, cost, procurements, etc.