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Comments on Design rules for opamp bootstrapping

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Design rules for opamp bootstrapping

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Here is the bootstrapping technique for opamps, as exposed in the Art of Electronics:bootstrap.

This technique is supposed to increase considerably the input impedance of the opamp 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 The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current opamps.

I disagree with him: I see no reason to buy a somewhat expensive femtoamp opamp 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:

Assume

  1. I have an AC sinusoidal source of known frequency w;

  2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);

  3. 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: bootstrap2

Result (current through the sine generator):bootstrap3

Result of the same simulation but without cap C1:

bootstrap4

Edit 2:

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:

bootstrap5

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 opamp: bootstrap6

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

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General comments
coquelicot‭ wrote over 3 years ago · edited over 3 years ago

Following the answer of Olin, I think that the usefulness of the bootstrapping is more to provide a return path to ground without loading the AC input, than to reduce the AC input current. But I don't know how to formulate and use that quantitatively.