Which opamp parameters are used to calculate the inaccuracy of this circuit?

Hello,

The attached is a differential op amp. It uses the LTC1006, but in the actual circuit, it will use the LM358.

Which of the parameters in the LM358 datasheet have the most effect on the accuracy of the output of this circuit?

Also, how do you use the parameter(s) to come up with a maximum error value in the output voltage?

[please note that there is a common mode voltage of 3.6V]


LM358 DATASHEET
https://www.ti.com/lit/ds/symlink/lm358.pdf

In first approximation, the loop gain A_LG is responsible for the inaccuracy = nonlinearity:

inaccuracy = 1/A_LG = |A_FB| / A_OL

In your case A_FB = -10 ≙ -20dB
A_OL(LM358,typ) = 100dB
inaccuracy = 20dB - 100dB = -80dB ≙ 0.01% = 100ppm

The (amplified) offset is another source of inaccuracy, but it's constant and can be eliminated computationally.

A further source of inaccuracy (outside of the opAmp) is the (also amplified) mismatch of your feedback resistors
(R8/R4) / (R5/R3) . Its deviation from the factor 1 also is inversely responsible for the inaccuracy (like the loop gain).

Which overall circuit errors are you asking for? There are a least:
- gain error (current scaling)
- offset error
- common mode sensitivity
- dynamic error

At first sight, resistor mismatch (altready discussed in a same topic thread, why don't you continue it) and OP offset voltage will be dominant error contributions.

Thanks, i thought the Common Mode voltage of 3.6V would be most responsible for the biggest potential inaccuracy?

...thats why i thought people use instumentation amplifiers instead of what i have shown...i.e. instrumentation amplifiers are to overcome the inaccuracy caused by common mode effects.

...so i would have thought that the CMRR was the most important parameter in the case shown?

OP CMRR won't play a big role, resistor mismatching is the problem. A dedicated high side current sense IC is the usual solution, I think it has been also mentioned in your previous thread.

Though as mentioned above, amplification of the input offset voltage is also a problem....10*0.007V = 70mV in this case.

I am seeking a general equation for the differential amplifier which can allow one to work out exactly the error......ie an equation which incorporates the input offset, CMRR etc etc.

It amazes me that the resistor mismatch is the biggest problem...it shows that the diff amp equation (Rf/Ri) * (V1-V2) is clearly wrong, and there is much more to it than this.

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treez said:

It amazes me that the resistor mismatch is the biggest problem...it shows that the diff amp equation (Rf/Ri) * (V1-V2) is clearly wrong, and there is much more to it than this.

Click to expand...

No it is not "wrong". It is based on some idealizing assumptions, which however in practice can never be met.
But this restriction applies to each formula which includes parts with tolerances.
Take a simple voltage divider of two "equal" resistors - in reality, the divider ratio will never be 2:1. Clearly wrong?

treez said:

...................................
I am seeking a general equation for the differential amplifier which can allow one to work out exactly the error......ie an equation which incorporates the input offset, CMRR etc etc.

It amazes me that the resistor mismatch is the biggest problem...it shows that the diff amp equation (Rf/Ri) * (V1-V2) is clearly wrong, and there is much more to it than this.[/COLOR]

Click to expand...

You could generate such an equation but it would tend to be somewhat big and messy. It's easier just to calculate the various error terms separately and then add the results together.

That diff amp equation is a simplified version which assumes ideal, perfectly matched component values and, in that sense, it is wrong. It should never be used for a real circuit. The original equation from which it was derived include the value of all four resistors. In the real world this must include the tolerance of those resistor values.

I am seeking a general equation for the differential amplifier which can allow one to work out exactly the error......ie an equation which incorporates the input offset, CMRR etc etc.

Click to expand...

The equation won't help you much, because most parameter deviations are randomly distributed. The usual answer to the problem is a sensitivity analysis which tells you how each parameter influences the total error. You can focus on the parameters with highest sensitivity, e.g. by using more precise resistors for it.

crutschow said:

................
That diff amp equation is a simplified version which assumes ideal, perfectly matched component values and, in that sense, it is wrong. It should never be used for a real circuit. The original equation from which it was derived include the value of all four resistors. In the real world this must include the tolerance of those resistor values.

Click to expand...

Yes, that`s certainly true.
Treez, I take this opportunity to remind you on the following general rule:

You always should know WHAT you are doing and WHY/IF you are allowed to do this.
Do you understand what I mean?
In particular, this applies to application of formulas (as in your case).
You should know that in circuit design/analysis no formula can be correct by 100% because it always contains simplifications and neglected influences.
Thus, for each application it is necessary to prove if the conditions allow the usage of the particular formula.
Simple example: The gain of an inverting opamp configuration (-R2/R1) is a good approximation only as long as the operating frequency is far below the transit frequency (gain-bandwidth product) of the opamp.