Help needed to analyse the circuit

LvW said:

Zohra,
start with the classical feedback model (for a fixed opamp gain A) and - as a second step - insert A=-Ao/(1+s/wo) .
The, rearrange the resulting expression with the aim to get a polynominal in "s" in the denominator.

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albbg said:

You can start from the classical feedback from the system control theory:



α is the input divider coefficient, that is α=Z2/(Rin+Z1+Z2)
β is the feedback coefficient, that is β=(Rin+Z1)/(Rin+Z1+Z2)

if "x" is the input node of the amplifier, then:

x=α•Vin-β•Vout
Vout=-F(s)•x

from which:

Vout/Vin=-α•F(s)/[1+β•F(s)]

Using now the expressions for α and β:

Vout/Vin=-Z2•F(s)/[Rin+Z1+Z2+(Rin+Z1)•F(s)]

Now if you model the op amp as a first order system, having DC gain Ao and pole ωp, then:

F(s)=Ao/(1+s/ωp), then:

Vout/Vin=[-Z2*Ao/(1+s/ωp)]/[Rin+Z1+Z2+Z1•Ao/(1+s/ωp)]

Dividing now, both numerator and denominator, by Z1•Ao/(1+s/ωp) and rearranging you will obtain the equation you post.

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