Consider the operational amplifier circuit below, where the impedances Z_i(s)and

Question

Consider the operational amplifier circuit below, where the impedances Z_i(s)and Z_f(s) are to be designed Design the circuit to be a ''low-frequency boost" amplifier, with the (asymptotic) Bode magnitude frequency response shown below: Specify suitable circuits for Z_i(s) and Z_f(s), and determine the circuit parameters, (e.g., R_1, R_2, C_1, C_2) so that the filter frequency response satisfies the Bode (asymptotic) magnitude response shown. Design the circuit using capacitors and resistors of reasonable values. Determine the transfer function, H(s), for your design and indicate all finite poles and zeros.

Explanation / Answer

From the diagram, it is clear that

step 1: 20log(X)=-10---the constant line on y-axis in bode diagram

if we calculate X using log X=-10/20

X=.3162, so the numerator is 0.3162 and there is no zero

step 2: to find pole, the point on x-axis on bode diagram, where the constant ends and starts increasing, is 10000 or 10exp(3).

thereby pole is at s=+10000

step 3: numerator=0.3162

denominator=s-p=s-10000

we have pole at s=10000

the value of H(s)=0.3162/{s-10000}

This s answer for part b

part a:

(v0/vi)=gain=-10

because it is an inverting amplifier

w.k.t, gain=-Zf/Zin

10Zin=Zf....equation 1

For the TF H(S), thus obtained,if we assume R1=10K AND C1=1MICRO FARAD

Zin=R1-jXc1

Zf=R2-jXc2

FROM equation 1, substituting and equating real and imaginary parts,

we get R2=1k ohm and c2=10micro farad

as xc1=1/2*pi*f*c1 similarly, xc2=1/2*pi*f*c2

this is answer for part a

verify part a comparing with part b and any doubts feel free to write on the blog..

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