A METHOD OF IMPEDANCE CORRECTION 799 



This theorem can be appHed immediately to the problem of filter 

 impedance correction discussed in the introduction. The networks re- 

 quired for this problem were defined there as sections which within the 

 transmitting band would have image impedances matching the line at 

 one end and matching the image impedance of the main body of the 

 filter at the other. If we represent the filter proper and the line by Zi 

 and Z2 in Fig. 1, these image impedance requirements reduce to the 



a 



o 



Fig. 1 — Diagram to illustrate the reciprocal properties of impedance correcting 



networks. 



statement that the network must be so chosen that an impedance 

 match exists both at ab and at cd. Z\ and Zi for this particular circuit 

 are however, pure resistances, and therefore equal to their conjugates, 

 within the required frequency range. The theorem shows that an 

 impedance match will be obtained at cd provided an impedance match 

 exists at ab, and vice versa. ^ If we please, therefore, we can consider 

 that our problem is that of obtaining a network which, when termin- 

 ated by a filter, has an actual impedance equal to a constant resistance. 

 On the other hand we can start with the resistance and attempt to 

 build up a network whose impedance matches that of the filter. 

 Both the first or "direct" and the second or "reverse" methods of 

 constructing terminating networks for filters are considered in the 

 next section. With either procedure the resulting networks have both 

 required image impedances and can be used, when properly connected, 

 either at the line or the receiving end of the filter. The "correction" 

 of one impedance to match another and the construction of a network 

 having given image impedance characteristics are therefore inter- 

 changeable conceptions. 



Separate Correction of Real and Imaginary Components of 

 Impedance or Admittance 



The image impedance method of defining the properties of the term- 

 inating network is a convenient one when we are concerned with the 

 operation of the structure in the transmission system as a whole. The 

 methods used in designing the network can, however, be described 



* See also Feldtkeller's paper, "Uber einige Endnetzwerke von Kettenleitern " in 

 the Elektrische Nachrichten-Technik, June 1927, for a very similar use of this property 

 of reactive networks. 



