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Design >> Analog Design >> Gain of two opamp instrumentation amplifier
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Message started by Horror Vacui on Nov 15^th, 2017, 5:35am

Title: Gain of two opamp instrumentation amplifier
Post by Horror Vacui on Nov 15^th, 2017, 5:35am

Hi Everyone,

I started to go over Bob Pease*'s Analog Circuits book, and there is the gain formula for a two opamp instrumentation amplifier. I do not remember this circuit from my studies, so I tried to derive it myself, but I got a bit different result than in the book: I do not have a factor of 2. Could you help me to point out if I made a mistake, or confirm that my calculation seems right?
I assumed that the opamp's output resistance is 0Ohm, and also that the virtual ground point is an ideal low ohmic node. I think I did not used any other assumptions, just separated the circuit to the two well-known opamp amplifier circuit.
My hand calculation is also on the picture. I hope it is readable enough. :)
Thanks in advance.

* He was the editor. Many authors has written one or more chapters.

Title: Re: Gain of two opamp instrumentation amplifier
Post by Frank_Heart on Nov 17^th, 2017, 12:00am

Hi, Horror,

My answer matches testbook:

Current (from right to left) through left R, I_left = (V1-V2)/RG + (Vx-V2)/R2
Current (from right to left) through right R, I_right = (V1-V2)/RG + (V1-Vx)/R2

Vout = Vref + R1*Ileft + (V1-V2) + R1*Iright
= Vref + (V1-V2)(1+2*R1/RG+R1/R2)

-Frank

Title: Re: Gain of two opamp instrumentation amplifier
Post by Horror Vacui on Nov 19^th, 2017, 10:12am

I got the cause for the deviation. I wrongly assumed that the inverting terminal of the right hand side amplifier is grounded (it's still correct), and therefore I can replace Rg cross-connection with two grounded Rg (which is wrong). In that case a feedforward path was missing from the final equation.
So I guess we can not cut the amplifier in half and assume that we have two voltage-input, voltage-output stages (which has seemed so elegant to me :( ). One has to write down the current equations.

Title: Re: Gain of two opamp instrumentation amplifier
Post by Frank_Heart on Nov 19^th, 2017, 10:18pm

Hi, Horror,

Glad you find out the loop hole.

Any insights why CMRR is limited by R1/R2 matching? Is it also ture for the conventional 3-amp instrumentation amplifier?

What's the advantage of this topology, other than saving one opamp?

Thanks
Frank

Title: Re: Gain of two opamp instrumentation amplifier
Post by Horror Vacui on Nov 21^st, 2017, 2:19pm

Frank_Heart wrote on Nov 19^th, 2017, 10:18pm:

Any insights why CMRR is limited by R1/R2 matching?

The ideally same value (except from sign) of the gain from V1 and V2 is achieved with nominally same valued, but still different resistors. If these resistors differs (R1_1 from R1_2) than the gain from V1 and V2 will differ, thus there will be a common mode component at the output.

Frank_Heart wrote on Nov 19^th, 2017, 10:18pm:

Is it also ture for the conventional 3-amp instrumentation amplifier?

Yes. The same principle.

Frank_Heart wrote on Nov 19^th, 2017, 10:18pm:

What's the advantage of this topology, other than saving one opamp?

Saving the opamp. I just read a book chapter just for fun, so this is my first encounter with this circuit and I did no detailed comparison. This circuit is asymmetrical. Enough reason to be skeptical about it if high performance is required. The path from the two input voltages will see different amount of offset, noise, PSR, coupling noise, and who know what else. I would go for this topology only if power and area is important while the other specifications are relaxed.