RESISTANCE AND CAPACITANCE IN SERIES 



which simplifies to 



jcoCR^R^ + Ri 



jcoCR^R^ + i?i + i?2 

 Now assume, as is usually possible, that R2 ^ Ri 



Fout jcoCR^R^ + Ri 



Now let Re, 



Kin jcoCR^R^ + i?2 

 aR' and i?i = i^'/a 



1 



Fout 



Kin 



ycoCi?'2 + aR' jcoCR' + a 

 Kin 



UcoCT?')' + a' 



Rationalizing, we find the phase shift is 



a 



(f> = tan" 



1 



a 



1 



coCR 



7 + coCi?' 



The performance of these 'limited phase shift' filters is plotted in Graphs 12 

 and 13 for various values of a. Evidently the price one has to pay for limited 

 phase shift is limited attenuation. 



R-C circuits which phase shift but do not filter 



Phase-shifting networks are occasionally useful; they may be employed 

 in conjunction with other circuitry to produce time delays, and are also 



Figure 3.44 



valuable in circuits for producing a 50 cycle signal of variable amplitude and 

 phase for cancelling interference from mains pickup in amplifiers. 

 One such is shown in Figure 3.44 ; we have 



C-D 



Kin 



B-D 



in 



K 



B-C 

 Kin 



jcoCR 

 1 + jcoCR 

 1 

 2 

 1 jcoCR 



1 + JcoCR 



45 



