For simplicity, the op amp is modelled as an ideal integrator

with a unity gain frequency of A

(or gain) in the frequency domain is A

equations in the frequency domain, ignoring C

ment, results in the following equation for the gain:

(1)

It can be inferred from the denominator of the transfer func-

tion that it has two poles, whose expressions can be ob-

tained by solving for the roots of the denominator:

(2)

Equation (2) shows that as the values of R

increased, the magnitude of the poles is reduced, and hence

the bandwidth of the amplifier is decreased. Furthermore, R

1

and R

A

R

It is the presence of pairs of poles in Equation (2) that causes

gain peaking. In order to eliminate this effect, the poles

should be placed in Butterworth position, since poles in

Butterworth position do not cause gain peaking. To achieve a

Butterworth pair, the quantity under the square root in Equa-

tion 2 should be set to equal −1. Using this fact and the

relation between R

found. This is shown in Equation (3).IfR

larger than this optimum value, gain peaking will occur.

(3)

In Figure 9,C

and to increase stability. In addition, C

the gain peaking that can be caused by having a larger

feedback resistor.

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