.uiic.ii. /.v/TC/v/At /• IX ir.ni- iii.ii.ks so 



As ii result of t-<|ii,iti()iis (IS) ami (2(0, in ilic .il Icniiatinn r.mm', 

 the phase constant of a noii-dissipatixc s\niini-lriral lillcr section is 

 always zero or an (hUI multiple of ± ir. 



The I iit-o[f frequencies, hy which are meant the divisional fretpiencies 

 whidi si-parate the transmission hands from the attenuation hands, 

 must always occur when i^i 4/^2 = or when Zi/4Zi= — \, sin'<', 

 for the transmission bands, Zi -iZi must lie between and —1. 



The ijeneral fornudae for the image impedances of the symmetrical 

 networks shown in Figs. 2 and I are e(|uations (ti) and (7), respectively. 

 I'rom these equations, the imaRe impedances are pure resistances in 

 the transmission range of a non-dissipative structure. In the at- 

 tenuation range, howe\er, the image im])edances are pure reactances; 

 the mid-series image impedance is a reactance having the same sign 

 as Zi, while the mid-shunt image impedance is a reactance having the 

 siime sign as Zj. In these attenuation hands, the image impedances 

 (pure reactances) have positive or negative signs depending upon 

 whether they are increasing or decreasing with frequency. The order 

 of magnitude of the image impedances may he found from T.ihle I. 



TABLE I 



• When both Z, and Zj are finite and Z, = — 4Z;, the mid-series image impedance 

 is zero and the mid-shunt image impedance is infinite, 

 t This condition gives a cut-off frequency. 

 •* This condition results in infinite attenuation. 



Types of Xon-Dissipative Series-Sliiint Sections Having Not More 

 Than One Transmission Band or More Than One A lien nation Band. 

 Since the series and shunt arms of a non-dissipative filter section may 

 each he composed of any combination of pure reactances, it is possible 

 to have an infinite number of types of filter sections. However, it 

 is seldom desirable to employ filters having more than one transmission 

 band or more than one attenuation band. Under these conditions, 



