INDUCTANCES, CAPACITANCES AND RESISTANCES 



Combining the equations R = {LfCf^ and coq == \j{l{LCf'~] we get for 

 the values of the filter elements 



L = 



R 



2a) 



and 



1 



c 



IcOnR 



We find the transmission characteristic, phase shift and terminal impedance 

 in a manner similar to that for the low-pass section. The transmission factor 

 comes to 



Kout 



V 



m 



and the phase shift to 



(f) = tan" 





and the impedance seen by generator and load is 



R 



(CO \" . /Mq 



2coq/ L\ <^ 



2a> 



(S 



~ + 



' CO 



.2co/ 



These are also plotted in Graphs 26, 27 and 28, and reveal the symmetrical 

 properties of the two filters. 



'Pr section filter 



Suppose we take a string of similar T sections (Figure 5.19), then this may 

 be redrawn as in Figure 5.20, and redrawn again as in Figure 5.21. Then, 

 between each pair of dotted fines, we have a pi section. 



Low-pass — Clearly the low-pass Tin Figure 5.22 transforms to the pi version 

 as in Figure 5.23. The two networks are equivalent up to a point; they have 

 the same transmission characteristic and phase shift ; but the impedance seen 

 looking into the end of the pi section is 



Z= Ri 



\2co) •^LWc/ \2we/_ 



' CO 



' CO ' 



+ 



,2co 



High-pass — By a similar argument the high-pass T section in Figure 5.24 

 is, in the pi form, given by Figure 5.25. Once again the two have similar 



88 



