ELECTRIC WAVE-FILTERS 319 



transducer which cxjiitains three impedances. In this case the series 

 z-21: impedance of this branch would l)e arbitrariK' divided and one part 

 transformed by another well-known transformation w^ith the parallel 

 branch in series with it. The final result would be a Zoa in series with a 

 parallel combination of a z-^u and series Su and So/.-; that is, four imped- 

 ances but no additional mesh. Here again the magnitudes would 

 have a continuous range but at the limits with three impedances they 

 are fixed. Other methods of transformations can be used on the 

 network as a whole and most of the equivalents have more elements. 



As a matter of interest a number of equivalents of the networks of 

 Fig. 11 will be pointed out, all of which have the same minimum 

 number of impedances. Starting with the transformations mentioned 

 above, the latter series transducer has a star of su impedances which 

 may be transformed into a delta, thereby adding another mesh. 

 Similarly the latter shunt transducer has a delta of z-^k impedances 

 which may be given the form of a star which eliminates a mesh. Two 

 other forms are given as Vi and V^ in Appendix II, being respectively 

 equivalent to the series and shunt transducers. They are inverse 

 networks just as are the originals in Fig. 11, In Vi a still further 

 transformation can be made from a star to a delta of Su- impedances; 

 in Vo, from a delta to a star of z-zk impedances. The possibility of 

 obtaining the particular forms Vi and V^ was pointed out by H. W. 

 Bode. I have derived them directly from the networks of Fig. 11 

 by a transformation of the major part of each network, using the 

 simple formulas for the equivalent transducer transformations, re- 

 spectively 1 and 2, of Appendix III. 



The transformation formulas for these latter equivalent transducers 

 in Appendix III are readily verified by the ordinary transformations 

 from 2" to TT networks, and vice versa. 



In the higher class wave-filters which contain more than one element 

 in Zik and Soa-, transformations of only parts of Zik and Zik are also possible. 

 For various other kinds of transformations see footnote 16 to Appendix 

 III. 



2.6 Terminal Losses at MM' -Type Terminations 



When the terminal image impedance of a wave-filter is PFu-(/«, m') or 

 Wok{m, m') and the wave-filter is terminated by a resistance R, there 

 is a reflection loss at the junction due to the impedance irregularity 

 which will be called the terminal loss L,n,m'- It is defined by the 

 relations 



T , \R+ Wik{m, m') 



2iRWxk{m, m') 



R + Wu{m, m') 



2^RW2k{m, m') 



(37) 



