Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

:TRANSMISSION THROUGH A NETWORK 421ating at a center frequency of one megacycle, a total sweep width of 50kilocycles, and a modulating frequency of 100 cycles per second; theamplification— -frequency characteristic of the amplifier has been fairlywell pictured. If the modulating frequency is increased to 1000 cyclesper second, the pattern (b) departs considerably from the steady-stateamplification—frequency characteristic of the network. The two tracesare the frequency upsweep and the downsweep. The upsweep traceleans to the right and the downsweep trace leans to the left.In Figure2, (c) is the oscillogram obtained for a total sweep width of 150 kilocyclesand a modulating frequency of 333 cycles per second, whileis the oscillogram obtained for a total sweep width of 150 kilocyclesand a modulating frequency of 1000 cycles per second.These oscillograms will be referred to quantitatively later in thearticle. They are presented here only to persuade those unfamiliarwith the problem that it is real, important, and frequently encountered.The problem is probably given the most attention by the designers ofhigh-quality frequency-modulated transmitters and receivers.It is the purpose of this paper to devise a simple test by which onemay determine whether or not the effects of a network upon a frequency-modulatedwave being transmitted through it differ appreciablyfrom the steady-state amplification—frequency and phase-shift—frequencycharacteristics of the network, and, if so, to offer a general andpractical method of calculating these effects as a function of eithertime or instantaneous input frequency.(d)The Response-Envelope EquationThe following procedure is a rigorous and general method of obtainingthe output-voltage envelope for a network driven by a frequencymodulatedwave1. Measure or calculate the steady-state amplification—frequencyand phase-shift—frequency characteristics of the network in question.2. Express the frequency-modulated input wave in terms of itssteady-state spectrum of sinusoidal side frequencies.3. Pass the individual side frequencies through the network, alteringthe amplitude and phase of each according to the steady-stateamplification and phase characteristics of the network at the particularfrequency of the side frequency.4. Plot the sum of the altered side frequencies point by point toobtain the output wave as a function of time.5. Draw a smooth curve through the carrier-voltage peaks to obtainthe response envelope of the output voltage.Such a procedure, however, is not a solution to the frequency-