instrumentation amplifier formula derivation

[PG1995]

Hi

It would be extremely kind you if you could help me with the queries enclosed in the attachment (please follow the given link for high-quality image). Thank you.

Link: https://img577.imageshack.us/img577/967/floydinstrumentionamp6.jpg

Regards
PG

 

[Winterstone]

Hi PG1995,

the key for understanding the formulas in the document is the fact that the differential voltage across the opamp input terminals is negligible small (assumed to be zero) for infinite open loop gain.
Then, using the superposition theorem you successively can set Vin1 and Vin2 equal to zero.

Example:
* Vin2=0 which means that RG can be assumed to be grounded.
Then Vout1,1=(1+R1/Rg)*Vin1.
* Vin1=0 with Rg grounded on its upper side.
Then Vout1,2=-R1/Rg because the input Vin2 appears also on the inv. input of opamp 2.
* Both parts together (superposition theorem): Vout1=Vout1,1+Vout1,2 .

The same can be calculated for Vout2. The common mode voltage is suppressed in the above calculation.

Both output voltages Vout,1 and Vout,2 appear as input voltages for opamp 3, which is operated as a fully symmetrical differential amplifier.
The text states that these voltages appear as inputs to opamp 3, which is not quite correct. Correct: They appear as input to the differential amplifier that is realized with opamp3.

I suppose, it is clear now - OK?

Remark1: The transfer characteristic of opamp3 (gain) can also be found using the superposition theorem. You successively calculate the output of opamp3 for Vout1 (Vout2=0) and Vout2 (Vout1=0).
Then, both parts are added. Because all 4 resistors are equal you arrive at the final result
Vout=Vout2-Vout1.

Remark2: PG1995, I have discovered this posting by accident only, because you have placed it in "mathematics and physics". When you have similar questions, I suggest to use the "general electronics" section or any suitable section.

 

[PG1995]

Thank you very much, Winterstone.

I need to go through this several times before I make any follow on queries. In the past someone suggested to me that whenever I need help with some formula derivation, I should port it in math forum.

Regards
PG

 

[ericgibbs]

Thank you very much, Winterstone.

I need to go through this several times before I make any follow on queries. In the past someone suggested to me that whenever I need help with some formula derivation, I should port it in math forum.

Regards
PG

hi PG,
When asking for maths/formula's I would recommend that you continue using the Maths & Physics Forum, the type of help/guidance you seem to asking for will be 'buried' in the General Electronics section.

If you recall this is one of the reasons we agreed some time ago to move your multiple Maths equations Threads to the Maths & Physics Forum, it seems to have worked well for the past 6 months or so.

Eric

 

[Winterstone]

hi PG,
When asking for maths/formula's I would recommend that you continue using the Maths & Physics Forum, the type of help/guidance you seem to asking for will be 'buried' in the General Electronics section.

If you recall this is one of the reasons we agreed some time ago to move your multiple Maths equations Threads to the Maths & Physics Forum, it seems to have worked well for the past 6 months or so.

Eric

Hi Eric,
the reason for my recommendation was the following:
I doubt if somebody who is an expert in mathematics or physics (only) can answer questions like this. The problem is and was not how to manipulate existing formulas but how to derive the correct formulas from a given circuit.
This is one of the most important task for an engineer in electronics. It requires (1) a good knowledge of circuit theory and (2) some experience with electronic parts and subsystems (like opamps).
And I am not sure if forum members who are interested in math and physics feel competent to help for solving problems like this.
Regards
W.

 

[ericgibbs]

hi W,

We have a number of 'helpers' who have both an excellent maths and electronics background, they have helped 'PG' extensively over the past months with his studies.

To name but a few, MrAl, Ratchitt, The Electrician and yourself etc.

We did find that when 'PG's maths questions were posted to the very busy General Electronics section they were scattered and difficult to follow by other members interested in the topics.

Sometimes PG had as many as five maths threads running at the same time in the General Forums.

As PG was using a reference book to teach himself electronics and maths it made sense to bring the work together in the Maths Forums in a more concise form, so that other members could benefit from his questions and the answers he was given.

Eric

 

[Winterstone]

We have a number of 'helpers' who have both an excellent maths and electronics background, they have helped 'PG' extensively over the past months with his studies..........

OK, Eric. As you probably know, I am rather new to this forum and I don't know much about the past month. If it works like this - fine.
Thus. I have learned that electronic problems/questions can be found also in the math/physics section. Good to know.
Thanks and regards
Winterstone

 

[PG1995]

hi W,

We have a number of 'helpers' who have both an excellent maths and electronics background, they have helped 'PG' extensively over the past months with his studies.

To name but a few, MrAl, Ratchitt, The Electrician and yourself etc.

We did find that when 'PG's maths questions were posted to the very busy General Electronics section they were scattered and difficult to follow by other members interested in the topics.

Sometimes PG had as many as five maths threads running at the same time in the General Forums.

As PG was using a reference book to teach himself electronics and maths it made sense to bring the work together in the Maths Forums in a more concise form, so that other members could benefit from his questions and the answers he was given.

Eric

Hi Eric, Winterstone

@Eric: Yes, I do remember it when you suggested me to post that stuff here in math/physics forum. And when I repiled to Winterstone I was referring to you by saying "...someone suggested to me...".

@Winterstone: Yes, Eric is correct in saying that in the past I have found it really helpful posting math oriented circuits problems in the math/physics forums. And without the help of fine persons like MrAl, Ratch, misterT and many others it would have been extremely difficult for me to sail thru my academic journey. I hope you stick around and keep helping me!

Best wishes
PG

 

[Winterstone]

OK, PG1995 - I got it. By the way, could you follow my explanations in post#2 ?

 

[PG1995]

OK, PG1995 - I got it. By the way, could you follow my explanations in post#2 ?

Yes, I understand it now. Many thanks. Actually I was also able to find another reference today which also uses superposition approach as you did to reach the end result. Please follow the link to see that reference. Thank you.

Link: https://img848.imageshack.us/img848/4194/malvinoinstrumentation7.jpg

Regards
PG