A' METHOD OF IMPEDANCE CORRECTION 



801 



extensive discussion. The problem of designing a four- terminal re- 

 active network which will transform one arbitrary resistance or con- 

 ductance characteristic into another arbitrary characteristic must, 

 however, be treated with more respect. The configuration which has 

 been adopted for this purpose is shown in Fig. 2. The quantities of 



REACTANCE 



CONTROLLING 



NETWORK 



r 1 r- 



RESISTANCE CONTROLLING NETWORK 



CORRECTED 

 IMPEDANCE 



2 -TERMINAL 



REACTANCE 



NETWORK 



ian-|X •— id3X 



I 



idnx 



IA4X 



IdiX 



IdgX 



IMPEDANCE 



TO BE 

 CORRECTED 



.J L. 



Fig. 2 — Generalized schematic of impedance correcting network. 



the general form iajX are analytic representations of the impedances 

 of the series branches and admittances of the shunt branches. The 

 a's are constants whose choice determines the particular resistance 

 or conductance controlling properties of the structure, and :x: is a 

 function of frequency. Since the series impedances and shunt ad- 

 mittances are all proportional to x all of the series branches will 

 have a given physical configuration and all of the shunt branches will 

 have the inverse configuration. For example if the series branches 

 are inductances the shunt branches will be capacities, while x, of course, 

 will be proportional to frequency. By using other series arm configura- 

 tions we can obtain a considerable variety of networks. Each such 

 network, it will be noticed, is similar to a "constant-^" filter in 

 physical configuration. The appropriate network in any particular 

 situation is that one which resembles a constant-^ filter transmitting 

 the frequency range of interest. 



The property of this network configuration which makes it partic- 

 ularly suitable as a resistance or conductance controlling device is the 

 fact that in most instances the modification it produces in the resistance 

 or conductance of the load can be expressed as a single polynomial. 

 To be more explicit, when the load impedance is of a certain mathemat- 

 ical type, which includes the impedances in which we are most inter- 

 ested, the resistance or conductance of the corrected structure is given 

 by a formula of the following sort. 



F(x) 



Rior G) = 



Ao -j- Aix -\- AiX'^ +•••-!- AnX'' 



