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A new circle diagram is presented for systems having an isolated single resonant mode, in addition to frequency-insensitive structures of arbitrary complexities, and ending in an outgoing wave guide or other transmission line. The diagram is obtained from standing-wave measurements in the outgoing line performed at three or more frequencies near resonance. The diagram permits the mapping, in the complex plane of load impedances or reflection coefficients, of such contour lines as loaded-resonator Q, frequency pulling, and the circuit efficiency when the resonator is electronically excited. The proof of these relations, as given in Part II (to be published in a subsequent issue), rests on field theory and establishes in effect the use of general circuit methods in the realm of microwave applications.