Frequency Response of an Opamp - Operational Amplifiers Types Tutorials Series

*Frequency Response of an Op-amp

•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