LMV792 datasheet(15/21 Pages) NSC

15 / 21 page

Application Notes (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 an expression for the gain shown in Equation

(1).

(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 and are

shown in Equation (2).

(2)

Equation (2) shows that as the values of R

1 and R2 are

increased, the magnitude of the poles, and hence the band-

width of the amplifier, is reduced. This theory is verified by

using different values of R

1 and R2 in the circuit shown in

Figure 1 and by comparing their frequency responses. In

Figure 3 the frequency responses for three different values

of R

1 and R2 are shown. When both R1 and R2 are1k

Ω, the

response is flattest and widest; whereas, it narrows and

peaks significantly when both their values are changed to

10 k

Ω or 30 kΩ. So it is advisable to use lower values of R

and R

2 to obtain a wider and flatter response. Lower resis-

tances also help in high sensitivity circuits since they add

less noise.

A way of reducing the gain peaking is by adding a feedback

capacitance C

F in parallel with R2. This introduces another

pole in the system and prevents the formation of pairs of

complex conjugate poles which cause the gain to peak.

Figure 4 shows the effect of C

F on the frequency response of

the circuit. Adding a capacitance of 2 pF removes the peak,

while a capacitance of 5 pF creates a much lower pole and

reduces the bandwidth excessively.

20116864

FIGURE 2. Inverting Amplifier

20116859

FIGURE 3. Gain Peaking Caused by Large R

1,R2

20116860

FIGURE 4. Gain Peaking Eliminated by C

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