Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

THE TRANSMISSION OF A FREQUENCY-MODULATED WAVE THROUGHA NETWORKSByWalter J. FrantzResearch Department, RCA Laboratories Division,Princeton, N. J.Summary— A practical method for calculating the effect of a fourterminalnetwork upon a frequency-modulated wave being transmittedthrough it is developed and demonstrated. The form of the solution is simpleenough to be applied by anyone familiar with electric circuits. No knowledgeof calculus or higher mathematics is required; nor is the solution restrictedin any way, being equally accurate and practical for large and small valuesof modulation index, and for any physical network.In order to determine whether or not a particlular network probleminvolving a frequency-modulated input wave may be analyzed from the"instantaneous frequency" viewpoint, a test, or validity condition, has beendeveloped. This test quickly classifies the problem either as one for whichonly a complete, straightforward analysis determines the response, or as onefor which a quasi-steady state exists. The quasi-steady state is a conditionunder which the amplitude— instantaneous-input-frequency envelope andthe phase-shift— instantaneous-input-frequency envelope of the output wai>eapproach closely enough to the steady-state-amplification— frequency andphase-shift— frequency characteristics of the network.WITHIntroductionTHE increasing use of a frequency-modulated wave forcircuit alignment and test, spectrum analysis, altitude ortime-delay measurement, and the transmission of intelligence,there arises the need for a practical and dependable method ofcalculating the response of a network to a frequency-modulated inputwave.Suppose that it is desired to picture accurately the steady-stateamplification—frequency characteristic of a tuned one-megacycle amplifierwith an effective Q of tOO. The layout of Figure 1 is often usedfor visual circuit test and alignment in the communications industry.Since the modulating voltage is applied also to the horizontal plates ofthe oscilloscope, the horizontal axis is linear in instantaneous frequencyof the input frequency-modulated wave. In Figure 2, (a) is the oscillogramobtained when the frequency-modulated signal generator is oper-* Decimal classification : R630.f Reprinted from Proc. I.R.E., March, 1946.419