A lot of years ago (38 to be exact) a wise old "rule of thumb" engineer taught me a slick way of getting maximum gain out of an opamp without resorting to very high or very low values of resistors.
As we all know, for an inverting opamp, the gain is given simply by Rf/Ri, where Rf is the feedback resistor from output to inverting input and Ri is the resistor between signal and inverting input. The DC level of the output may be set anywhere you choose by an appropriate bias level on the noninverting input. For AC amplifiers from a single supply, this is generally Vcc/2 with capacitive coupling between Ri and the signal.
However, for very large AC gains, either Rf must be rather large or Ri rather small. Rf being rather large makes the input voltage/current errors become significant as regards quiescent DC output point and Ri being rather small requires large capacitors for coupling and loading errors from the signal source.
So, sez old wily rule-of-thumb, just break Rf into two reasonable sized equal value resistors equal to Rf/2 and run them in series from output back to (-) input. And, from the midpoint tap on these two resistors run a series RC circuit to ground. Bingo, the AC gain improves greatly.
And guess what, it works. How do I calculate the R in the series RC circuit I asks old wily. The answer comes back "Tweak it until you get the gain you want." (Assume that C can be made appropriately large to get the low-frequency gain you want.)
I haven't used that trick in an awfully long time, but I've got an application that needs it. And, if I want to use Diddle's constant in a simulation program I can fool around (ahem, heuristically experiment) to get the gain I need.
However, I can't convince myself that I can mathematically come up with the resistor value. I have googled the problem and come up short. Anybody got a pointer to a URL that goes through the math of how this configuration works? And what I'm doing to my phase margin?
Jim