RESISTANCES AND CAPACITANCES 



from the simple low-pass filter by the addition of an extra resistance. By 

 inspection 



R2 + 



'out 



>c 



an 



R1 + R2 + 



1 



j(oC 



We can simphfy the calculation if we make an assumption which is usually 

 permissible, that R^ <^ Ri- Then, multiplying through by ycoC, 



^out 1 +JC0CR2 

 Kin ~1 +jcoCR^ 



Now take R', the geometric mean of R^ and R2, and define a such that 

 R,=aR' and R. = R' la. Then 



r/ 1 Y 1^^'^ 



Kout \+j(oCR'ja ^ ,_ iFoutl \\oyCRJ'^a^ 



ir~ = 1 I • ^ p/ froin which -r^ = ^ 



Fin 1 + JOiCaR I Kin I 



Rationalizing, 



(-^h^\ 



Voxxx (1 +>CJ?7a)(l -jojCaR') 

 Fm ~ 1 + oj^C^a^R'^ 



(1 + co2c2iJ'2) ^j(ajCR'la - coCaR') 



:. (f> = tan-i — 



+Qn— 1 



tan-1 — 



1 + (o^C^a^R'^ 

 oiCR'a — (oCR'la 

 1 + co^C^R'^ 



1 



a — - 

 a 



1 



7 + oiCR' 



oiCR 



High-pass type — This is shown in Figure 3.43. Again, it differs from the 



/?2 



Figure 2.43 



simple high-pass filter only in the addition of an extra resistance. By inspec- 

 tion, 



Fout Ri 



in 



R. 



^1 + 



1 



' joiC 



R2 + 1 



jcoC 



44 



