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We all know how operational amplifiers behave in real world. I am trying to figure out the transfer function of an operational amplifier, part number UA741CN, from the data sheet. The data sheet from ST for this part does not have any performance graphs, but they do have GBWP and other parameters listed.

My goal is to derive a very accurate transfer function given this information to me. The unity gain occurs at 1MHz (the GBWP) but the phase margin is around 50 at the point. This would mean that they are introducing a zero in the part somewhere to compensate for the dominant pole. I would like find where that zero is in addition to other things that I may need to know to figure out the transfer function in Laplace domain.

The question refers to the open loop configuration of this operational amplifier.

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  • \$\begingroup\$ Is real op-amp linear time invariant system? \$\endgroup\$ – venny Aug 25 '14 at 20:33
  • \$\begingroup\$ What makes you think they are putting a zero in to compensate for the pole (around 10 Hz)? Also I wish we did all "know how operational amplifiers behave in real world"! \$\endgroup\$ – Andy aka Aug 25 '14 at 20:51
  • \$\begingroup\$ @venny, there is no physical system that is LTI. \$\endgroup\$ – Alfred Centauri Aug 25 '14 at 22:57
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You are trying to create a detailed model of a sloppy process. For one thing, the gain-bandwidth product is a minimum spec, or sometimes even just "typical". The actual gain-bandwidth can be quite different for any one part, and I wouldn't count on the phase margin either. The raw DC gain can also vary a great deal, as can other parameters.

Getting this detailed is useless for circuit design because the point is to have the circuit work with the minimum guaranteed parameters, but keep working for higher ones. If you are looking at this level of detail around what a 741 can do, then you are using the wrong opamp.

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In general it is impossible to determine the transfer function for an op amp from the datasheet -- you need to know the topology of the op amp design and the compensation scheme for it. Even so, you will not get a "very accurate" transfer function from part to part due to manufacturing variances.

In the specific case of the 741, the design is well known and you can actually derive a decent transfer function. Kent Lundberg from MIT has written a paper on compensation for the Fairchild 741 which includes the full schematic and information on how it can be compensated. He even includes a full transfer function for a two-stage op amp that uses a compensation capacitor (Appendix III). Plugging the component values in Appendix II into the full transfer function will give you a decent transfer function for a 741. But even so I would not call it "very accurate" due to component tolerances.

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