POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 



317 



instead of finite sums. To the best of the author's knowledge, the first appli- 

 cation of the continuous charge concept to network synthesis was by H. W. 

 Bode, who used the so-called "condenser plate" analogue to design phase 

 equalizers for experimental coaxial cable systems for television, in the 

 late nineteen-thirties. An extension of the ''condenser plate" technique, 

 combining gain and phase equalization, is described in a patent issued 

 to Bode^ in 1944. The integration idea was used independently by W. 

 Cauer,2 [^ connection with applications of Poisson's integrals to network 

 problems. Development of the potential analogue method was interrupted 

 by the war, but in the last few years there has been considerable activity 

 in this field.^ The aim of the present paper is to systematize the development 

 of the potential analogue method, and to extend it in various directions in 

 order to obtain a more versatile design tool. Much of the material has been 

 presented orally at meetings of the Basic Science Division of the A.I.E.E. 

 In principle, at least, the method may be used to simulate or equalize, 

 over a finite range of useful frequencies, any gain or phase characteristic 



Fig. 1- 



F(p)=flr+L/3=L0G -^ 

 -A transducer used as a transmission circuit. 



which may be represented by an analytic function. Network types to which 

 the method has been successfully applied include filters, equalizers, delay 

 networks and combinations of networks required for long communication 

 systems such as coaxial cables. As experience increases, the range of appli- 

 cations is still being extended. 



2. Analytic Properties of the Transmission Function 



We shall consider the transmission function of a typical transducer, 

 Fig. 1. The absolute value of the ratio of the output voltage to the input 

 voltage represents the gain in transmission through the network, while the 

 phase of the ratio represents the phase shift. If a is the gain in nepers and 

 j8 the phase shift in radians we have 



V/E = e"e^, 



(1) 



and we define the transmission function as the logarithm of this ratio, 

 F{icc) = log (V/E) = « + t/8. (2) 



