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In the measurement of impedance at ultra-high frequencies by means of detecting standing waves on transmission lines, it is necessary to know the response law of the detector. This usually involves either a calibration of the detector or an assumption as to its characteristics. By means of the basic transmission line equations and the general law of detection, expressions are derived which give the voltage standing-wave ratio as a function of measurable electrical angles, the expressions being independent of the response law of the detector. Special cases of the general equations are discussed covering applications where high or low VSWR's are to be determined, with or without the use of the voltage maxima or minima. The extension of the methods to the case of attenuating transmission lines is given.