46 BELL SYSTEM TECHNICAL JOURNAL 



in which Rb represents the external d-c. resistance, and Rnq represents 

 the external resistance to the nth. harmonic. 



Figure 10 shows the equivalent circuit for this system in the form 

 of an infinite ladder structure. From this circuit relative magnitudes 



Fig. 10 — Equivalent circuit of idealized variable resistance microphone. Here 

 mesh currents represent amplitudes of the various frequency components. Ro 

 represents the fixed and R the variable internal microphone resistance, while Rnq 

 represents the external circuit resistance to the nth harmonic of the signal. 



of the various frequency components are readily perceived ; evidently 

 the successive harmonic current components decrease progressively 

 in magnitude. A large value of Rnq makes the nth harmonic and all 

 successive harmonics small. A case in which quantitative information 

 is obtainable in simple form is that in which the resistances to all 

 harmonics are equal {Rnq = Rt, n > I) . In this case the equivalent 

 network beyond terminals (1) and (2) is a simple recurrent structure 

 and the resistance is obtainable by the customary methods of handling 

 infinite recurrent networks. The admittance looking in at the 

 terminals (1, 2) is the iterative admittance of the latter and is given by "^ 



L = l + ^ (17) 



Ri R^ Ro - R -^ Rt -\- Ri ^ ^ 



Solving for Ri gives 



Ri = 



R 



1+A 1 4 



2R 



Ro- R-\- Rt 



As far as d-c. and fundamental current components are concerned, 

 the network beyond (1), (2) may be replaced by Ri and the system 

 reduces to a two-mesh circuit from which Q, Iq and power relations 

 are obtainable very simply. If harmonic current amplitudes are 



^ In an infinite recurrent structure, the resistance Ri must be the same looking 

 in at successive point pairs (1, 2) (3, 4) etc. This is stated in (17). 



