How did he get the last answer ? I need STEPS please !! Thanks a loooot. Write t

Question

How did he get the last answer ? I need STEPS please !! Thanks a loooot.

Write the dynamic equations and find the transfer functions for the circuits shown in Fig. 2.48. passive lead circuit active lead circuit active lag circuit. passive notch circuit Passive lead circuit With the node at y+, summing currents into that node, we get Vu - Vy/R1 + C d/dt (Vu - Vy) - Vy/R2 = 0 rearranging a bit, C y + (1/R1 + 1/R2) Vy = C + 1/R1 Vu and, taking the Laplace Transform, we get Vy(s)/Vu(s) = Cs + 1/R1/Cs + (1/R1 + 1/R2)

Explanation / Answer

CVy+(1/R1 +1/R2)Vy=CVu+Vu/R1

taking Vy as common in L.H.S and Vu in R.H.S

Vy(C+(1/R1+1/R2)=Vu(C+1/R1)

Vy/Vu=(C+1/R1)/(C+(1/R1+1/R2)

asthe function in the laplace transform is s we get

Vy(s)/Vu(s)=(Cs+1/R1)/(Cs+(1/R1+1/R2)

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