Miir.ii. iMwcr.-wcE i\ ir.iri: iii.rr.Rs 



105 



As .1 tuiiiu-rii-.il fx.iiiipic I'l' ilu- solution of ilu- |>|-otoi\|H- disrusM-d 

 .issiinif, .IS ill ilu- i-x.implr following ('(|it.iti<)n (.H ), ili.it ilu- lowiT cut-ofT 

 lrt<|iu'iu y /i is 2(),(HM) cNik's .iml tli.it tlu- upper lUl-otT frf(iiii-iu y /j 

 is J.'j.tMHt r\rlis. Assume/,, a convenient par.iineter for the families 

 of .ittenu.ition .iiul phase constant curves which this sectioti may 

 h.i\e, for .iiu- j;i\en cut-otT fretiiiency, to Ix' UO.OOO cycles. Assume 

 lh.it the \aiiie of the mici-series image impedance Z.. at the niid-fre- 

 (|iuncy isliOOtihms; then from formula (!>!•) m' = l.OS.l: hence /., =.(1412 

 henries. T, =.00153 X lO"' farads, L; = .00152 henries and C",; = .01SlX 

 10 * farads. The structure with the numerical \alues of induclance 

 .iiid capiirity for this specific example is shown in I'ijj. 47. \. 



2C = 

 .00306 mf 



2C = 

 .00306Tnf 



^Cr.L!03O6w-. 

 L,=.C0l52h. 



L=.0336h.i°g*|fl L=.0336h 



: C,=.OI64nif 



(!C,=.00306:nf.,, L.=.0412k ,, 2Cr.00306n,f 

 U=.0i3lh.|g ;M=T=.0206h. 



Fig. 47 — N'umeric.il Example of Equivalent Filter Sections Containing Negative 

 Inductance 



If, for the y mesh inductances in Fig. 47.A, we subslilute a trans- 

 former mesh having the \alucs shown in P"ig. 47 B, the mesh of the latter 

 figure is electrically equi\alent to the prototype structure and is an 

 example of the method of employing the structure. Similarly, F"ig. 47C 

 illustrates the substitution of another type of three element mesh 

 for the coil mesh of the prototype structure of Fig. 47A and is another 

 example of the inanner in which the prototype may be physically 

 expressed. 



The structure of Fig. 47B represents a similar case to that of 48A. 

 However, as the mutual inductance is here series opposing, the proto- 



