# Slew Rate Limitation in an OpAmp - Operational Amplifiers Types Tutorials Series

http://www.ingenuitydias.com/2015/05/slew-rate-limitation-in-opamp.html

Slew
Rate Limitation in an Operational Amplifiers

1. A
real op-amp is limited in its ability to respond instantaneously to an input
signal with a high rate of change of its input voltage. This limitation is called the slew rate,
referring to the maximum rate at which the output can be “slewed”.

–Typical
slew rates may be between 1–10 V/ms
= 1E6 – 1E7 V/s

–Max
slew rate is a function of the device performance of the op-amp components
& design

–If
the input is driven above the slew rate limit, the output will exhibit
non-linear distortion

2. Slew
rate limitation behavior:

–Assume
an inverting op-amp with a gain of –10 has a max slew rate of 1 V/ms
and is driven by a sinusoidal input with a peak of 1V. At what input frequency will the output start
to show slew rate limitation?

•Output
has a peak of 10 volts since gain is –10 and input peak is 1 volt

•If
the input is given by vIN
= Vo sin wt,
the max slope will occur at t=0 and will be given by

d (Vo sin wt)/dt
|(t=0) = wVo
= 2pf
Vo

–The
max frequency is therefore given by

fmax = slew rate/2pVo
= 1E6 V/s / 2p
10V = ~ 16 kHz

–Note: This surprisingly low max frequency is
directly proportional to the slew rate limit spec and inversely proportional to
the peak output voltage!

Exceeding
the slew rate limitation:

•If
the inverting op-amp (with gain = –10 and slew rate = 1 V/ms)
is driven by a 16 kHz sinusoidal input with a peak of 1.5V, what is the effect
on the output waveform?

–Since
we are now exceeding the slew rate limit, the output will be distorted

–Let
vOUT
= - Vo cos
wt
(for visual simplicity) where Vo = 10 x 1.5V = 15V

–Then
dvOUT/dt
= wVo
sin wt

–Above
some t = t1
the slew rate will limit the output response

t1
= (1/w)
sin-1
(slew rate/wVo)
= (1/2p
16 kHz) sin–1
(1E6 /2p
16 kHz x 15V) = 7.2 ms

–The
resulting waveform is shown below. At t1
the slew-limited output can’t keep up with the input until it catches up at t2,
when the cycle starts all over again.