Mutual Inductance in Wave Filters with 

 an Introduction on Filter Design 



By K. S. JOHNSON and T. E. SHEA 



I'Akr I 



General I'him iii.is ui W.wi-: Fii.riiR Dksign 



Principles of Generalized Dissynitiielrical Xehcorks. W'c shall con- 

 sider first llu- inipcdanco ami propajjation cliaractcrisiics of certain gen- 

 eralized networks. It can be slunvn that any passive network haviir^ 

 one pair of input and one pair of output terminals may, at any frequency, 

 he completely and adequately represented by an equivalent T or v net- 



-? — WWV 1 WWV 9- 



I.- J I,' 



Z.,| V. Z.. |Zc Z..V, 



Fitc. 1 — C.cntTaliztil Dishyiiiinelriral T Network Connectc<l to Itiipfdanccs Kqu.il 

 to Its Image Im|K^anccs 



work} The impedance and propagation ciiaracteristios of an\- such 

 network may lie exjiressed in terms of its e(|ui\alent 7' or w network. 

 These characteristics are defined by (I) the image impedances, and 

 (2) the transfer constant, the latier including the attenuation constant" 

 and the phase constant.- In the case of a symmetrical network, 

 the image im|)e<lances and the transfer constant are, respecti\el\-, 

 the iterative impedances («)r characteristic impedances) and the propaga- 

 tion constant employi-<l by Campbell. Zobel, and iithers. The terms 

 inxolviHJ will be siibse»|iiently defined. 



Consider the dissymmetrical T network of Fig. 1. If the 3 — 4 

 terminals of the T network are connected to an impedance Z/„ the 



' Camplicll. G. .\., 'Tisoiclal Osiillalions," Traiisarlions A. I. E E (191 1) 

 Vol. XXX. Part II. pp. 873-909. ' ^ ' 



The 7" and » networks referred to aliovc are sometimes called star ( 1') and delta (A) 

 networks, rr»|:e< lively. 



> The real and iniat[inary |i,irt!. o( the transfer constant have U-en called by Zobel 

 the dimiHUlioH ,,mil<int ,ind the ijiie»/iir (omlunl, res|:e<tivel\ . (See Hililict;ra|ihy 13.1 



52 



