Op Amp Studies: Virtual Ground

published 2025-09-07

by Christopher Howard

I've continued slowing working through Roberge's 2nd ed op amp book, taking another pass through the first chapter. The biggest take away so far has been the value of the "virtual ground" technique. It is possible to work out mathematically, e.g., the output of any inverting configuration using the amplification value of the amplifier, and a voltage divider equation, but the math gets rather tedious and complicated. With the "virtual ground" approach you are allowed — for inverting configurations — to assume that the non-grounded input terminal is kept at ground, and that there is zero current into the input terminal. This, in turn, allows you to separate the input circuit from the feedback circuit, and to assume (1) that the current of the input circuit is the same magnitude as the current of the feedback circuit and (2) that the voltage across the feedback circuit is the same as that of the op amp output. This greatly simplifies calculating the output for any given input circuit and feedback circuit, because all you have to do is (1) calculate the current of the input circuit, and then (2) plug that current into the voltage/current equation of the feedback circuit.

Usually your input circuit is just the input source (V_s) and a resistor (R1), so current is I = V_s/R1. A simple feedback circuit is just another resistor (R2). E=IR, or V_o = I R2, where V_o is the output of the op amp. Mind you, the current I is reversed, and so your V_o will be inverted.

Replacing R2 with a capacitor is a similar calculation, except that the impedance in the feedback loop is also dependent on the frequency of the signal, and you can do this with complex numbers, meaning you'll have a phase output as well, if you are interested in it.

If you replace R2 instead with a diode, the current-voltage relationship used in the feedback circuit becomes

i_D = I_s (e^(q v_D / k T) - 1)

where "I_s is a constant dependent on diode construction, q is the charge of an electron, k is Boltzmann’s constant, and T is the absolute temperature". Fundamentally — setting the constants to 1 — that is simply

i_D = e^v_D - 1

For i_D, you use the current from the input circuit, and v_D will be the output of the op amp. Of course, you probably want to solve for v_D, which turns this into a logarithm, and thus we have a log amp.

A few days ago, I set up a simple log amp with a diode across one of the open amplifiers on my home-made analog computer. This worked, though I was getting a lot noise as well, which prompted some further studies and experiments with passive RC low-pass filters.

Copyright

This work © 2025 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.