CLASSICAL FILTER 



Clearly the arrangement is by no means perfect, for to preserve matching 

 the generator and load impedances evidently have to alter in a special way 

 with frequency, which is hardly practicable. When co is small Zq = (Z,/C)^'^, 

 a resistance; when a> equals 2/(LC)^'", Zq = 0; and when co > 2/(LC)^'" the 

 bracketed term becomes imaginary, which means Zq has turned into a 

 reactance ! 



In practice the best we can do is to arrange for matching to be correct 

 within the pass-band, which we shall show lies over frequencies below 

 oj = 2/(LCy^. We let the load and generator impedances be constant resis- 

 tances, equal to {LjCY'~ {Figure 5.15). 



L/1 L/2 



-f 00 WOO ^-^-nps^mw--o- 



R--U/CJV2 



R=(L/C)^ 



Figure 5.15 



At CO = 2l(LCy'", Zq becomes zero because a series resonance occurs in the 

 filter between C, and the two inductances L/2 in parallel (the net inductance 

 is L/4, so the resonant frequency should be at co = IKLC/Ay^^ = 2j{LCy^ 

 which is right). This frequency is co^, the cut-oflF frequency for the filter; we 

 dignify it with the name cut-off rather than turn-over because the transmission 

 characteristic of L-C filters is much squarer than that of R-C filters, as we 

 shall see. 



Combining the equations (Oq = 2l{LCy'^ and R = {L/Cy^^ gives us 



2R , 2 



L = — and C = — - 



(Oq c^c^ 



as expressions for the values of our filter elements. Let us see how they will 

 behave. / / 



Figure 5.16 



Transmission characteristic — In Figure 5.16, by inspection we have 



J 



(oC 



Kout 



R 



"■^i'^i-ic 



in 



R 



L 



R+jco 



(oC 



L 



R+jcoj 



coC 



L 



2 



+ Ja>--\-R 



85 



