LOAOl.n USES ASn COMri-.SSATISC ST.TWORKS 4/0 



( haracteristir reactance can l)e exactly siiniilaied (for am tivcil 

 value of a lietween and 12) In tin- luiwork in V'\^. Hi. 



The Admiltinuf-Siruiilalor in /•Vt;. \'.i 



This network takes advantage of the fact, depicted in Fig. 0, that 

 the graph of the (x'-load characteristic conductance of a loaded line, 

 for values of a' in the neighborhood of 0.2, is nearly flat over most 

 of the transmitting band and hence can be approximately simulated 

 by a mere constant conductance chosen approximately equal to the 

 nominal admittance v C L'. This is the basis for the d'-portion 

 of the network in Fig. 1.3. The basis for the L'ld-portion is the fact 

 (proved in Appendix C) that, in the transmitting band, the w'-load 

 characteristic susceptance can be exactly simulated (for any fixed 

 value of a' between and 1 2) by the network in Fig. 17. 



APPENDIX C 



Dhriv.ations of the Design'-Formul.xs for the Compensating 

 Networks in Figs. 16 and 17 



The Reaclance-Com pensalor in Fig. 16 

 For any values of d and L,s the reactance 7" of this network is 



T = 



1-w^LiCi 



By equation (4) the characteristic reactance A' of the loaded line 

 within its transmitting band is 



XT k{l—2(T)w/ci)c 



i V = ; 



1-4(t{1-<tW/o>c'' 



Comparison of these two equations shows that 7' and .V are of the 

 same functional form in to; and that the cf)nditions for T to be iden- 

 tically equal to ± A' are 



L,= ±kil- 2a) 'oic, Lid, = 4(7( 1 - (t) W, 



whence Ci= ±-l<T{l-(T),'{l-2a)ko)^, 



the upper and the lower sign of ± corresponding to the use of the 

 compensator as a reactance-simulator and a reactance-neutralizer. 

 respectively. These values of Ls and d are equivalent t o tho se 

 appearing in F"ig. 16, because k = 'VL'/C and oic = 2rfc = 2 "V L'C. 



