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In control theory, an accurate transfer function of the components of your system, and some sort of guarantee that they are independent (low output impedance and high input impedances) are important for understanding your system, if you want to model it accurately.

Sometimes, this can be simplified -- when the frequencies of interest are far below the GBP of the components used for example, the component can be approximated as a component with a single pole and a large DC gain, both of which can be pulled pretty easily from the datasheet.

However, when you are trying to eek out all the performance you can out of a component -- ie using an op amp with a GBP of 3MHz and you want to use all 3MHz -- then an accurate transfer function might be helpful.

How do you find such a transfer function? Can I just find all the points of the open loop Bode plot for an op amp and digitize it? It is easier if I understand where the poles and zeros are, are there any tools to take something like this and turn it into a transfer function? Is this done in "real life", or do people just work with approximations (or spice)?

As an aside, if this is something that is typically done, why don't manufacturers give the transfer function in the datasheet?

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  • \$\begingroup\$ If you can't find or derive a specific information from the datasheet, you should not rely on your empirical tests, as no one will guarantee they will persist across different instances of the same PN. \$\endgroup\$ – Eugene Sh. Aug 8 '16 at 16:25
  • \$\begingroup\$ @EugeneSh.: that is important for consumer products, but not for one-offs. There are a number of areas that might do this kind of analysis where the part in front of you is more important than the general PN -- though typically life will be easier if you can rely on the general PN instead of just the part in front of you. \$\endgroup\$ – Andrew Spott Aug 8 '16 at 16:38
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using an op amp with a GBP of 3MHz and you want to use all 3MHz

Generally this isn't done. To do it might require manually tuning the feedback circuit to optimize the overall circuit performance in some kind of test jig. But usually it's cheaper to just choose a 30-MHz GBW op-amp, than to pay a technician to tune circuits in production.

How do you find such a transfer function?

Many vendors will provide a SPICE model, which will encompass as much as they are willing to share about the transfer function of the amplifier. It may also account for variations of the transfer function due to changing the power supply voltages, input common mode voltage, output load impedance, etc.

Typically it won't include variations due to temperature changes.

And of course it will only be a "typical" response. As far as I know there's no vendor that provides statistical models of how the performance varies from part to part.

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  • \$\begingroup\$ How do I go from a SPICE model to a transfer function? \$\endgroup\$ – Andrew Spott Aug 8 '16 at 17:02
  • \$\begingroup\$ Most EE's would just simulate and tune the whole circuit in SPICE without worrying about exactly what is the transfer function of the op-amp. But if you want to use some other tool for the higher-level design, you could simulate the circuit in SPICE and get a tabular output. Then use curve fitting to extract a pole-zero representation of the response. \$\endgroup\$ – The Photon Aug 8 '16 at 17:05
  • \$\begingroup\$ "Generally this isn't done." Why is manual tuning on a per part basis required in order to use the full GBP of 3MHz? \$\endgroup\$ – Andrew Spott Aug 8 '16 at 17:08
  • \$\begingroup\$ Because some devices might actually be 2.7 MHz and others 3.5 MHz. If you're trying to use every Hz of bandwidth, you'd need a slightly different feedback network for each one. And then you'd need to make sure your users always use the device at the same temperature you tested it at. \$\endgroup\$ – The Photon Aug 8 '16 at 17:11
  • \$\begingroup\$ Is the swing that large between parts? Is a factor of 10 really required? \$\endgroup\$ – Andrew Spott Aug 8 '16 at 17:12

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