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A circuit or a group of circuit connected together as a system is said to be stable, if its o/p reaches a fixed value in a finite time.

**Circuit Stability:**

A circuit
or a group of circuit connected together as a system is said to be stable, if
its o/p reaches a fixed value in a finite time. (or) A system is said to be
unstable, if its o/p increases with time instead of achieving a fixed value. In
fact the o/p of an unstable sys keeps on increasing until the system break
down. The unstable system are impractical and need be made stable. The criteriangn
for stability is used when the system is to be tested practically. In
theoretically, always used to test system for stability , ex: Bode plots.

Bode
plots are compared of magnitude Vs Frequency and phase angle Vs frequency. Any
system whose stability is to be determined can represented by the block
diagram.

The block
between the output and input is referred to as forward block and the block
between the output signal and f/b signal is referred to as feedback block. The
content of each block is referred

―Transfer
frequency‘ From fig we represented it by AOL (f) which is given

by A_{OL}
(f) = V_{0} /V_{in} if V_{f} = 0. -----(1)

where A_{OL}
(f) = open loop volt gain. The closed loop gain A_{f} is given by

A_{F}
= V_{0} /V_{in}

A_{F}
= A_{OL} / (1+(A_{OL} ) (B) ----(2)

B = gain
of feedback circuit.

B is a
constant if the feedback circuit uses only resistive components. Once the
magnitude Vs frequency and phase angle Vs frequency plots are drawn, system
stability may be determined as follows

**1. Method:1:**

Determine
the phase angle when the magnitude of (A_{OL} ) (B) is 0dB (or) 1. If
phase angle is > .-180^{0} , the system is stable. However, the some
systems the magnitude may never be 0, in that cases method 2, must be used.

**2. Method 2:**

Determine
the phase angle when the magnitude of (A_{OL} ) (B) is 0dB (or) 1. If
phase angle is > .-180^{0} , If the magnitude is –ve decibels then
the system is stable. However, the some systems the phase angle of a system may
reach -180^{0} , under such conditions method 1 must be used to
determine the system stability.

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