RESISTANCE AND CAPACITANCE IN SERIES 



Thus, in the present case, when oo is very high the reactance of C^ will 

 become small compared with R^ and may be neglected in comparison with 

 it. Moreover, the reactance of Q will be small compared with R^, but as 

 these elements are in parallel the one with the lower impedance is the more 

 important. Hence, R^ may be neglected in comparison with the effect of Q. 



c 



? 



a> 



Figure 3.46 



Figure 3.47 



At CO large, then, the circuit simplifies to R^ and Q, a simple low-pass 

 filter, and Kout will fall with increasing frequency. By a similar process, we 

 can deduce that when m is low, the important elements are C^ and R^, 

 forming a simple high-pass filter, with Fout falhng as the frequency is reduced. 

 If the output is falling at both ends of the frequency spectrum, it presumably 

 has a maximum at intermediate frequencies and the transmission charac- 

 teristic has probably some such shape as Figure 3.47. 



This, in fact, proves to be the case. Re-drawing the network in terms of 



-"^i K>ut 



Figure 3.48 



reactances instead of capacitances gives Figure 3.48. To prevent the investiga- 

 tion taking too long we shall set X-^— X^ — X, and see what happens as 

 we vary R^ and R^. 



By inspection we can write down 



which simplifies to 



-jR^X 



out 



R.-jX 



Fin 



Rr-JX- 



R,-jX 



out 



-jR,X 



Fin (i?ii?2 - ^') - m2R2 + Ri) 

 47 



