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I'm currently trying to use the MCP6142 op amp in an ultra-low power project (sub-uA ideally). This op-amp has been chosen because it has the highest GBW in the set of the sub-uA op-amp we've reviewed. However in the range of the frequencies we'd like to amplify (3800-4000 Hz) the gain of this op-amp is far from "ideal". See this figure from the datasheet:

enter image description here

So we've come up with this circuit to amplify the signal:

schematic

simulate this circuit – Schematic created using CircuitLab

Considering the following equations:

Vout = G(w)*exp(j * phi(w))*(V+ - V-)
V- = R1 / ( R1 + R2 + 1/(jwC1) ) * Vout

We've derived the transfer function H(w):

H(w) = G(w) * (1+j*w*(R1+R2)*C1) / (G(w) + j*w.*G(w)*R2*C + exp(-j*phi(w)) + exp(j*(pi/2-phi))*w*(R1+R2)*C);

We've used G(w) and phi(w) plots from the datasheet to compute H(w) and plot its curve:

enter image description here

So we expected a peak gain around 4000 Hz... that we never observed when pluging a waveform generator at the input of the op-amp. Of course, we tried to find the peak by tuning the waveform generator frequency, but we never found it. What could we have done wrong? Have me made a good use of the Gain-Phase plots from the datasheet?

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    \$\begingroup\$ Sanity check : your expected peak gain is 40dB, at a frequency where the open loop gain is under 30dB according to Fig 2-14. Which raises the question why you expected 40dB. \$\endgroup\$ – Brian Drummond Oct 17 '16 at 14:32
  • \$\begingroup\$ Closed-loop gain cannot be higher than open loop gain? \$\endgroup\$ – Vincz777 Oct 17 '16 at 14:41
  • \$\begingroup\$ It can, but that requires positive feedback. \$\endgroup\$ – Brian Drummond Oct 17 '16 at 14:43
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    \$\begingroup\$ No, forget the positive feedback as that will not make a reliable circuit. If you're short on gain then better use two opamps, each giving 20 dB of gain. \$\endgroup\$ – Bimpelrekkie Oct 17 '16 at 15:07
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    \$\begingroup\$ No. And attempting it would bring stability problems (oscillation) you really don't want to deal with. \$\endgroup\$ – Brian Drummond Oct 17 '16 at 15:30
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"What could we have done wrong? Have me made a good use of the Gain-Phase plots from the datasheet?"

The wrong is that you didn't use the normal engineering practice to model the behavior of your circuit in any SPICE simulator. Linear Technology offers a good LTspice tool free of charge, Texas Instruments does the same (TIna). Microchip has some tools as well. Download the free LTspice tool that will do all "calculations" for you, but with a fairly realistic model of your OPA.

If you can't get the particular Microchip model, get something similar from Linear offering, and see all effects right away. The models usually include input parasitic and output limitations. It is advisable to include extra components that would represent parasitics of your PCB and to use more realistic SPICE models for passive components as well.

The LTspice has plenty of ready to go examples, from which it is easy to learn, and modify circuits for your needs.

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Reality check - the data sheet shows an open loop gain of about 30 dB at 4 kHz - in numbers, that's a gain of about 31.6. In your derived graph (also at 4 kHz) you are expecting a gain of 100.

Now somewhere you have either your expectations or your math badly wrong.

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    \$\begingroup\$ And in the circuit diagram you seem to be trying for ~60dB at high frequency if the amp had GBP sufficiently high. Using the GBP limit to provide a lowpass function is not a good idea, if you want a bandpass, design a bandpass, not a HPF with a slow opamp. Further tip, negative feedback is good, you want lots of excess gain it makes all the surrounding stuff more ideal. \$\endgroup\$ – Dan Mills Oct 17 '16 at 16:53

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