. The Bell System technical journal . one actuated by a sinusoidal acoustic wave can be represented by the resistance r = Rq -\- R cos qt. This is exactly the form of the variable resistance already discussed,with Tq = Ro, 2ri — R, and rn — 0 for n > I. If one were interested in the modulation products with otherfrequency components impressed electrically, the systems would be ofthe same type as those of the previous section. In the case of themicrophone the d-c. voltage impressed leads to current componentswhich are d-c. and harmonics of the signal q. In this case, the equa-tions are = Rol
. The Bell System technical journal . one actuated by a sinusoidal acoustic wave can be represented by the resistance r = Rq -\- R cos qt. This is exactly the form of the variable resistance already discussed,with Tq = Ro, 2ri — R, and rn — 0 for n > I. If one were interested in the modulation products with otherfrequency components impressed electrically, the systems would be ofthe same type as those of the previous section. In the case of themicrophone the d-c. voltage impressed leads to current componentswhich are d-c. and harmonics of the signal q. In this case, the equa-tions are = Rolo + RIil2, = Roll + Rio + RI2/2, = Roh + R{Ii + h)/2, Vo = Eo — Rblol\ = - R,h Viq = — Riql2 Vnq = — Rnqln = RqI n + R{I n-\ + In+l)l2, (16) 46 BELL SYSTEM TECHNICAL JOURNAL in which Rb represents the external d-c. resistance, and Rnq representsthe external resistance to the nth. harmonic. Figure 10 shows the equivalent circuit for this system in the formof an infinite ladder structure. From this circuit relative magnitudes. Fig. 10—Equivalent circuit of idealized variable resistance microphone. Heremesh currents represent amplitudes of the various frequency components. Rorepresents the fixed and R the variable internal microphone resistance, while Rnqrepresents the external circuit resistance to the nth harmonic of the signal. of the various frequency components are readily perceived; evidentlythe successive harmonic current components decrease progressivelyin magnitude. A large value of Rnq makes the nth harmonic and allsuccessive harmonics small. A case in which quantitative informationis obtainable in simple form is that in which the resistances to allharmonics are equal {Rnq = Rt, n > I). In this case the equivalentnetwork beyond terminals (1) and (2) is a simple recurrent structureand the resistance is obtainable by the customary methods of handlinginfinite recurrent networks. The admittance looking in at theterminals (1, 2) is the iterative admittance of t
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