LPV531 datasheet(16/17 Pages) NSC

16 / 17 page

Typical Application (Continued)

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

with a unity gain frequency of A

0 . Hence, its transfer function

(or gain) in the frequency domain is A

0/s. Solving the circuit

equations in the frequency domain, ignoring C

F for the mo-

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

1 and R2 are

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

the bandwidth of the amplifier is decreased. Furthermore, R

and R

2 are related by the gain of the amplifier.

V =−R2/R1, or alternatively

2 =−AVR1

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

1 and R2, the optimum value for R1 can be

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

1 is chosen to be

larger than this optimum value, gain peaking will occur.

(3)

In Figure 9,C

F is added to compensate for input capacitance

and to increase stability. In addition, C

F reduce or eliminates

the gain peaking that can be caused by having a larger

feedback resistor.

LPV531 Datasheet(PDF) 16 Page - National Semiconductor (TI)