RESISTANCES AND CAPACITANCES 



In Figure 3.34, if 7?^ = i? = R^ and Q = Cg = C, applying Thevenin's 

 theorem at the points A-B and looking to the left, we see 



an open-circuit voltage 



in series with an impedance 



— r^VW^ 



R-jXc 

 R ■ -jXc 

 R -jXc 



A «' 



Fi 



in 



'1 



-•AAAA- 



c,-r 



t 



i^ouf 



B 

 Figure 3.34 



The equivalent circuit is therefore Figure 3.35 — an elaboration of a potentio- 

 meter circuit. Fout is therefore 



-jXc 





R -jXc + 



R ■ -J^c 



-Fi 



Y 2 



m 



R^ + Xc^ -jOXcR) 



R-jXc 



Fput 



Fin 

 Fput 

 Fin 



A-^^ 



{(i?2 + Xo^f + 9A'c2i?2p/2 



1 



{(1 + ay'Cm^f + 9a>2C2i?2}i/2 



Substituting — -^ for Xq 



This function is also plotted in Graph 11. Clearly the degradation of the 

 performance due to cascading the sections takes the form of a lack of 'square- 

 ness' in the characteristic in the region of the turn-over frequency. 



A ^ 



10 R 



W\Ar-9 



I'out 



I'oat 



Figure 3.36 



Tapered sections — ^The effect can be mitigated by 'tapering' the sections, that 

 is, by making the resistance greater, and the capacitance lower, in the second 

 section than in the first. Thus if R^ -= 10 R^, and Cg =- 1/lOth of Cg {Figure 

 3.36), the turn-over frequency of both sections is still the same, but the 

 loading effect of the second on the first is much less severe ; the performance 

 will much more nearly approach the ideal for two sections, as in Graph 11. 



Resistance and capacitance in parallel, connected to constant direct current 

 generator 



This is another circuit showing an exponential response (Figure 3.37). At 



40 



