Relevance of gain error in OpAmp

[oscarcot]

Hello,

I'm designing an amplifier for a fixed gain of 60dB and 10kHz bandwidth. (Just for reference, it is a Fully Differential Difference Amplifier, using XH035 CMOS-technology). The DC open-loop gain is 85dB. I read from some references that the open-loop gain needs to be at least 20dB above the closed-loop gain, which I think is more or less satisfied by my specs.

1. Now the question: do I need a gain of 80dB at 10kHz?

'cos there's an issue: if I do so, I'll end-up with a bandwidth of 100kHz when I use the 60dB closed-loop gain. That will bring more noise into the system which sooner or later would have to be filtered out.

This is a medical research application, so we're in fact more concerned about the noise performance, signal shapes and relative amplitudes rather than the absolute voltages.

2. If I implement a 10kHz low-pass using such amplifier, won't I still have some kind of gain-error?, I mean, precisely 3.01dB gain-error?

3. What is the relevance of the gain error besides knowing "I know that my gain is not accurate from 6 to 10kHz"? I would rather overcompensate the amplifier and restrict the bandwidth to 10kHz.

Can somebody help?
Cheers,
Oscar

 

[leo_o2]

Gain requirement is related to the accuracy required.
If open loop gain is A, the accuracy it can achieve is about 1/(1+A).

 

[oscarcot]

Thank you,

ok, three remaining questions please:

1. The innacuracy is frequency dependant, right? So that means I can have 95% accuracy up to 3kHz, and around 80% up to 10kHz. Is that right?
2. Will the innacuracy be random or systematically predictable? Can it be software-compensated?
3. What is the difference between this innacuracy and the 3.01dB "innacuracy" produced by a low-pass filter.

Cheers,
Oscar

 

[leo_o2]

1. Yes.
2. Inaccuracy caused by limited gain is random. And besides inaccuracy caused by gain, mismatch in real system also leads to inaccuracy.
3. I don't understand the third question.

 

[oscarcot]

Ok. Thanks. It's ok with what you told me.

Cheers,
Oscar

 

[dgnani]

Thank you,

ok, three remaining questions please:

1. The innacuracy is frequency dependant, right? So that means I can have 95% accuracy up to 3kHz, and around 80% up to 10kHz. Is that right?
2. Will the innacuracy be random or systematically predictable? Can it be software-compensated?
3. What is the difference between this innacuracy and the 3.01dB "innacuracy" produced by a low-pass filter.

Cheers,
Oscar

1. In a basic feedback system the closed-loop gain is
\[G=\frac{A}{1+\beta A}[\TEX]
for large values of A (open-loop gain) this tends to
\[G_{\infty}=\frac{1}{\beta}[\TEX]
For finite values of A, a gain error can be defined as the relative difference of the actual gain to the above ideal gain
\[G/G_{\infty}-1= \frac{\beta A}{1+\frac{1}{\beta A}} [\TEX]
this shows that
- the gain error is frequency dependent (as A and usually β are)
- it explains the rule of thumb you mentioned to keep A at least ten times larger than the G: the ratio of G/A determines the loop gain βA, which in turn determines the gain error; even more
\[G/G_{\infty}-1=-\frac{G}{A}} [\TEX]
2. the gain error is systematic and can be calibrated out but if the random component due to mismatch is not small the calibration would have to be by the die rather than by the batch; mismatch contribution strongly depends on the design and process used

So much for TEX... how does it work on this forum?