A vector method for amplitude-modulated signals

The paper describes a vector notation for amplitude-modulated alternating quantities. This notation enables vector expressions to be derived for the impedances, admittances and transfer ratios of electrical circuits, and these expressions in turn operate directly on the vector for the amplitude-modulated voltages and currents to give the vectors for the dependent variables in the circuit. The results obtained by this vector analysis are in a convenient form for the direct calculation of the output of a demodulator, for any general input to the circuit. Examples are given to show that when the modulation frequency is comparable with the carrier frequency the modulation (or signal) may be appreciably modified by impedances in the carrier channel. The paper includes a description of a complementary operational method, which enables the response of circuits to non-sinusoidal amplitude-modulated signals to be determined.