. The Bell System technical journal . e by an a mount6(df/f) and Bl will change by an amount dB:^ = {dBJdd){2T,N){df/f). () We now define a parameter Mm expressing the effect of the mismatch asfollows TidB^/dd) = Mm. () Then dBj^ = INMuidf/f). () If the characteristic admittance of the resonator is Mr , then the characteris-tic admittance of the resonator plus the line is M = Mji-\- NMm. () If, instead of a coaxial line, a wave guide is used, and Xo and X are the cutoffand operating wavelengths, we have dB^ = 2NMM{df/f)(l - (X/Xo)2)-^ () and ikr = M« + NMm(1 - (X/Xo)2)-^ (9
. The Bell System technical journal . e by an a mount6(df/f) and Bl will change by an amount dB:^ = {dBJdd){2T,N){df/f). () We now define a parameter Mm expressing the effect of the mismatch asfollows TidB^/dd) = Mm. () Then dBj^ = INMuidf/f). () If the characteristic admittance of the resonator is Mr , then the characteris-tic admittance of the resonator plus the line is M = Mji-\- NMm. () If, instead of a coaxial line, a wave guide is used, and Xo and X are the cutoffand operating wavelengths, we have dB^ = 2NMM{df/f)(l - (X/Xo)2)-^ () and ikr = M« + NMm(1 - (X/Xo)2)-^ () In Fig. 49 contour lines for Mm constant are plotted on a Smith Chart(reflection coefficient plane). Over most of the plane Mm has a moderate REFLEX OSCILLATORS 535 positive value tending to increase characteristic admittance and hencedecrease electronic tuning. Over a very restricted range in the high admit-tance region Mm has large negative values and over a restricted rangeoutside of this region Mm has large positive Fig. 49.—Lines of constant value of a parameter. Mm shown on a chart giving the con-ductance and susceptance of the terminating admittance of a short line. The parameterplotted multiplied by the number of wave lengths in the line gives the additional charac-teristic admittance due to the resonant effects of the line. The parameter Mm is of course0 for terminated lines (center of chart). This is an appropriate point at which to settle the issue: what do we meanby a short line as opposed to a long line. For our present purposes,a short line is one short enough so that Mm does not change substantiallyover the frequency range involved. Thus whether a line is short or notdepends on the phase of the standing wave at the resonator (the position 536 BELL SYSTEM TECHNICAL JOURNAL on the Smith Chart) as well as on the length of the line. Mm changes mostrapidly with frequency in the very high admittance region. As a simple example of the effect of a short
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