72 HIJ.L SiSriiM TECIIXIC.IL JOL KX.II. 



Krimi lormulae ((5), (29), (30), and (33) the niiil-st-ries imago impedance 

 at aiiN' frc-<|iK'nc\' is 



^ V/„ J J 



An inspiTtion of fonnul.i {'A4) indicates that the mid-series image 

 impedance is symmetrical with respect to the niid-freciuency, /«. 



In a similar way, the mid-shunt image impedance (Zo') at the mid- 

 fretjuency is 



z'= iZjnn- ! ^' - (35) 



" Vc,(g+4) Vr,(^+4) 



and the mitl-shunt impedance, (Zi'), at any fre(|uency is 



^,..z.._kl UlAiI^ (36) 



-m'^HB' 



It will lie noli'd, ihat if llif values of I he iiiiliukiiucs and resistances of 

 a filler are multiplied by any factor and if all the values of the capacities 

 are divided by the same factor, the transmission loss-frequency character- 

 istic is not changed'- (neither are the cut-off frequencies, nor the frequencies 

 of infinite attenuation) but the intake impedances are multiplied by this 

 factor. 



From the preceding; formulae, exjilicit e.\|)ressi()ns may he derived 

 for the values of Li, i'l, Lj, and t\.. These expressions, which are 

 given by Zolx?!,' in a slightly diflferent form, are as follows: 



"SiiKi- the y.iliic iif ihi- tr.insrer factor, «-«, is dependent simply u(K)n the ratio 

 X,/iX,, it is I'videni from ctiualiiin (111,) ihiit lite Iransmissum toss caused bv the inser- 

 tion of any nrtuork in a dnuit is drprndenl simt>ly upon impedance ratios. Con- 

 iH-<|iicntly, the alxjve thcori-ni is unite Kener.il and applies not only to filters hut to 

 any pauivr network. 



