Stability basics

AN2653

4/22

1.2

Operational amplifier modeling for stability study

Figure 3 illustrates the definition of phase and gain margins in a gain configuration.

To apply this stability approach to operational amplifier based applications, it is necessary to

know the gain of the operational amplifier when no feedback and no loads are used. It is the

open loop gain (A(

ω )) of the amplifier (shown in Figure 4 for the TS507). From this

parameter, it is possible to model the amplifier and to study the stability of any gain

configuration.

Figure 5.

Equivalence between schematics and block diagram

The loop gain is:

loop gain of the system increases and the loop gain decreases. Because the phase remains

the same, the gain margin increases and stability is improved.

In addition, if you consider the case of a second order system such as the one shown in

Figure 6, a decrease of the loop gain allows to pass the 0 dB axis before the second pole

occurs. It minimizes the effect of the phase drop due to this pole, and as a result, the phase

margin is higher. Therefore, a voltage follower configuration is the worst case for stability.

Figure 3.

Illustration of phase and gain

margins

Figure 4.

TS507 open loop gain

Loop Gain

-200

-160

-120

-80

-40

0

40

Frequency (Hz)

-270

-225

-180

-135

-90

-45

0

Gain

Phase

Phase Margin

Gain Margin

TS507 Open Loop Gain

-20

10

40

70

100

130

160

Frequency (Hz)

-180

-150

-120

-90

-60

-30

0

Gain

Phase

TS507 :

Vcc = 5 V

Vicm = 2.5 V

T = 25 °C

V

r

V

s

------

–

A

ω

()

R

g

R

f

R

g

+

-------------------

⋅

=