# Frequency Response of an Opamp - Operational Amplifiers Types Tutorials Series

http://www.ingenuitydias.com/2015/05/frequency-response-of-opamp-operational.html

*Frequency
Response of an Op-amp

* Op-amp Output Current Limit:

•An
open-loop op-amp has a constant gain Ao
only at low frequencies, and a continuously reducing gain at higher frequencies
due to internal device and circuit inherent limits.

–For
a single dominant pole at freq
fp,
the frequency-dependent gain A(jw)
can be written as

A(jw) = Ao/[1 + jw/wp] = Ao/[1 + jf/ fp]
where wp
= 2pfp

–the
gain rolls off at 20dB/decade for frequencies above fp,
as shown below

•An
op-amp may have additional higher frequency poles, as well, but is often
described over a large frequency range by the dominant pole (as assumed in the
figure Above)

•The
unity gain frequency fo
is defined as the frequency where the gain = 1

–For
the single dominant pole situation assumed in the figure below, fo
can be found by extrapolating the 20 dB/decade roll-off to the point where the
gain is unity.

*Frequency-Dependent
Closed-Loop Gain in Operational Amplifiers

•The
effect of the frequency-dependent open-loop gain on the closed-loop gain can
easily be found by deriving vOUT(jw)
as a function of the open-loop gain A(jw)
in the op-amp configuration shown at the left

vOUT
= A(jw)
(v+ - v-)

=
A(jw)
[vIN
– vOUT(R1/(R1
+ R2))], or

vOUT = A(jw)/[1 + A(jw)b] where

b
= R1 / (R1 + R2) is the closed-loop feedback function

–Substituting
A(jw)
into the above equation gives us the complete frequency dependent result for
the closed loop gain

vOUT/vIN = Ao/[1 + Aob + jw/wp]

=
[Ao/(1 + Aob)]/[1 + jw/wp(1 + Aob)]

•The
dc gain is given by

–Ao/(1
+ Aob)
= ~ 1/b
= (R1 + R2)/R1

•The
closed-loop response is seen to contain a single pole at wfb
= wp(1
+ Aob)
>> wp

–Closed-loop BW = ~ Aob x open-loop BW

*Gain-Bandwidth
Product:

•Multiplication
of the closed-loop BW by the closed-loop gain gives us

[Ao/(1+Aob)]wfb =
[Ao/(1+Aob)]wp(1+Aob)

= Aowp

–which
is the open-loop gain-BW product

•For
the assumption of a single dominant pole and very high Ao,
the gain-bandwidth product is a constant

•Unity-gain
frequency wo
(= 2pfo)
is the freq
where the op-amp response extrapolates to a gain of 1

–we
can show that wo
= Aowp
(for a system with a single dominant pole)

* Op-amp Output Current Limit:

A typical op-amp contains circuitry to limit the output current to a specified maximum in order to protect the output stage from damage.If a low value load impedance is utilized, the output current limit may be reached before the output saturates at the rail voltage, forcing the op-amp to lower gain