Design rules for oamp bootstrap
Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:.
This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap). The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
Now, to make my question precise:
I have an AC sinusoidal source of known frequency w;
I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
I want the RMS input current be equal to at most I_max.
Question: how should I choose the values of the two resistors and of the capacitor in the schematic above?
Edit: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
Simulation with bootstrap:
Result (current through the sine generator):
Result of the same simulation but without cap C1:
Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case. Here is the schematic for the simulation:
And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the oamp:
So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
Without cap C1, the current through the sine generator (and hence through C2) is the same as previously