CMRR in open loop and closed loop configuration of opamp

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anubhavsingh
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Equation: CMRR = A_d / A_cm, where A_d is the differential-mode gain and A_cm is the common-mode gain.

For an opamp in open look configuration,
Equivalent circuit of the ideal op amp: a triangle with inverting input (terminal 1, i1 = 0) fed by v1, noninverting input (terminal 2, i2 = 0) fed by v2, a dependent source A(v2 - v1) driving output terminal 3, and the power-supply common terminal at the bottom.

Equation: Vo = Ad Vd + Ac Vc, where Vo is the output voltage, Ad and Vd are the differential gain and differential input voltage, and Ac and Vc are the common-mode gain and common-mode input voltage.


Here Ad should be equal to open loop gain of opamp and

Two equations: Vd = (V+ - V-), and below it, Vd = (V2 - V1) preceded by an implication arrow.


Now consider the closed loop config of opamp (negative feedback used):

Circuit schematic of a difference amplifier: an op-amp with feedback resistor R2 from output to inverting input, input resistor R1 from v_I1 to the inverting input, input resistor R3 from v_I2 to the non-inverting input, and R4 from the non-inverting input to ground; output labelled v_O. Figure 2.16.

Equation: Vo = Ad Vd + Ac Vc, where Vo is the output voltage, Ad and Ac are the differential and common-mode gains, and Vd and Vc are the differential and common-mode input voltages.

However, Ad is closed loop gain here (according to Sedra Smith) and
Equation: Vd = (Vi2 - Vi1), defining the differential input voltage as the difference between the two input voltages.

In terms of open loop gain,
Equation Vo = A(V+ - V-), where Vo is the output voltage, A is the gain, and V+ and V- are the non-inverting and inverting input voltages.

A is open loop gain here.

So Adm is open loop gain in the first case and Adm is closed loop gain in the second case. How to know which gain to use in CMRR?

Reference: Microelectronic Circuits (Seventh Edition) by Sedra Smith
 
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  • Equation: Vo = A (V+ - V-), where Vo is the output voltage, A is the amplifier gain, and V+ and V- are the non-inverting and inverting input voltages.
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  • Equation in bold serif type: Vo = Ad Vd + Ac Vc, where Vo is the output voltage, Vd the differential input, Vc the common-mode input, Ad the differential gain and Ac the common-mode gain.
    1636817162806.png
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anubhavsingh said:
How to know which gain to use in CMRR?
An op-amp is operated with negative feedback to maintain a low differential input voltage. An op-amp is NOT designed to be used as an open loop voltage comparator.
 
anubhavsingh said:
So Adm is open loop gain in the first case and Adm is closed loop gain in the second case. How to know which gain to use in CMRR?

Sorry, I am a little confused and incomprehensible about your question.

You have proposed two different circuits, one is an open-loop amplifier and the other is a closed-loop amplifier, and you mentioned their respective voltage gains. If I understand correctly, your question is whether you should use open-loop voltage gain or closed-loop voltage gain to calculate their respective CMRR.

If you think in accordance with the general logic, isn't this thing relatively simple?

So my understanding is of course that the CMRR of the open-loop amplifier should be calculated with the corresponding open-loop gains, and the CMRR of the closed-loop amplifier should be calculated with the corresponding closed-loop gains. :smile:🐻
 
alan123hk said:
Sorry, I am a little confused and incomprehensible about your question.

You have proposed two different circuits, one is an open-loop amplifier and the other is a closed-loop amplifier, and you mentioned their respective voltage gains. If I understand correctly, your question is whether you should use open-loop voltage gain or closed-loop voltage gain to calculate their respective CMRR.

If you think in accordance with the general logic, isn't this thing relatively simple?

So my understanding is of course that the CMRR of the open-loop amplifier should be calculated with the corresponding open-loop gains, and the CMRR of the closed-loop amplifier should be calculated with the corresponding closed-loop gains. :smile:🐻
Yes, but why is that? Why can's the meaning of differential gain remains consistent whether the opamp is open loop or closed loop. Why should in closed loop configuration, the differential gain should not refer to the open loop gain of opamp as in open loop configuration? Just looks ambiguous to me.
 
anubhavsingh said:
Yes, but why is that? Why can's the meaning of differential gain remains consistent whether the opamp is open loop or closed loop. Why should in closed loop configuration, the differential gain should not refer to the open loop gain of opamp as in open loop configuration? Just looks ambiguous to me.
Try this site, it describes/explains some of the details you are asking about.
https://www.electronics-notes.com/a...erational-amplifier-op-amp/gain-equations.php

Cheers,
Tom
 
anubhavsingh said:
Yes, but why is that? Why can's the meaning of differential gain remains consistent whether the opamp is open loop or closed loop. Why should in closed loop configuration, the differential gain should not refer to the open loop gain of opamp as in open loop configuration? Just looks ambiguous to me.

To be honest, so far I don’t seem to be sure what the crux of the problem you want to discuss is.
But based on the CMRR-related content described in your first post, I believe the following article may be helpful to you. If you can fully understand the content of this article, including the equations mentioned, then your doubts may be solved.

https://www.analog.com/media/en/training-seminars/tutorials/MT-042.pdf