AN2653 datasheet(3/22 Pages) STMICROELECTRONICS

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AN2653

Stability basics

3/22

Stability basics

1.1

Introduction

Consider a linear system modeled as shown in Figure 1.

Figure 1.

Linear system with feedback model

The model in Figure 1 gives the following equation:

is named closed loop gain.

From this equation, it is evident that for A

β = -1, the circuit is unstable (Vout is independent of

Vin).

β is the loop gain.

To evaluate it, the loop is opened and -Vr/Vs is calculated as shown in Figure 2.

Figure 2.

Loop gain calculation

Opening the loop leads to the following equation:

If a small signal Vs is sourced into the system, and if Vr comes back in phase with it with an

amplitude above that of Vs (which means that Aβ is a real number greater than or equal to 1)

then the system oscillates and is unstable.

This leads to the definition of the gain margin, which is the opposite of the loop gain (in dB)

at the frequency for which its phase equals -180°. The bigger the gain margin, the more

stable the system. In addition, the phase margin is defined as the phase of the loop gain

plus 180° at the frequency for which its gain equals 0 dB. Therefore, from the value of A

β it

is possible to determine the stability of the system.

Vin

Vout

out

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

⋅

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

Vout

------

–

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