Ml If. II. I\ni\ T.IXi. I l.\ ll'.M / lU.IIHS 'J? 



l)otl) M-rirs arms, it c.ui Ik- n-platvd, in symnu-lrical siructuri's, hy 

 two i'<|ual wiiulings of a sin^;Ii' coil ha\'inK iiuitual iiKliictaiiCf lH-tvvri;n 

 ttu-m ami of siuh \aliio that tlio si-rii-s aiding inductance of tiiese two 

 coils is c<iiiai to the total inductance rccjuircd in the correspond in^; 

 unhal.mccd structure. I'or example, the structures shown in Fins. 

 :?f>.\ .111(1 M are electrically e(|uivalent to each other, that is, tlu-y 

 have the same imaj;e impedance and transfer constant. 



Types of Sections Obtainable Whose Equivalent Series-Shunt Sections 

 Contain \o Xe^ative Inductances. It has previously been stated that 

 an intinite mmiber of t>pes of series-shunt filter sections may be had, 

 if no limitations arc placed on the comjilexity of their reactance arms. 

 It has also been stated, however, that for filters employing only one 

 transmission or one attenuation band, the maximum number of ele- 

 ments which can ordinarily be used economically per section is six. 

 A similar limitation exists when mutual inductance is emploNcd, in 

 that sections can seldom be economically used whose prototype 

 structures contain more than six reactance elements. 



Inasmuch as by the equi\a!ences which ha\e been discussed, many 

 varient forms of a section may exist, which forms are reducible to the 

 same series-shunt prototype, an effort only to list and discuss the 

 p:o"otype sections will be made. The prototype to which an\' given 

 section then reduces will readily be found by the application of the 

 foregoing principles. A few examples will later serve to make this clear. 



In ccmsidering the prototype sections which exist when mutual 

 inductance is present in a filter section, we shall first list the reactance 

 meshes of which mutual inductance may^ form a part. Referring to 

 Fig. o, an inspection of the equivalences so far discussed will show- 

 that the following meshes may be parth- or wholly composed of mutual 

 inductance: 



1, 3, 4, .5 (a and b),7 (a and b), and 8 (a and b). 



Consequently, a large number of the sections listed in Table II and 

 formetl from the reactance meshes of Fig. 5 may represent not only 

 actual sections containing no mutual inductance, but also equivalent 

 prototypes of sections containing mutual inductance. Sections con- 

 taining mutual inductance within only the series arm or the shunt 

 arm, respectively, are not included in this discussion since such arms 

 may lie readily reduced to e(|uivalent arms, without mutual induct- 

 ances, by the substitution of equivalent two-terminal meshes. The 

 prototypes which are under discussion are listed below: 



Ltw pass High pass 



1-3,5-3 4-1,4-5 



