# How to electronically generate exponential and logarithmic functions

i mean, it is possible to generate with Op amps, or diodes, etc, to generate complex exponential and logarithmic functions, like one can create sinusoidal signals using a Wien bridge oscillator.

Thank you very much, if it does what devices can help me on that?

• How would the voltage level decrease? Maybe a combination of a sine wave and sawtooth wave? – Dean Apr 17 '13 at 20:56
• You mean a time-varying signal with v(t) proportional to exp(a*t)? You can do that with an RC filter, at least for a < 0. Logarithm is not so easy, though. – The Photon Apr 17 '13 at 20:59
• Capacitor charge/discharge is exponential. – pjc50 Apr 17 '13 at 22:14

Well I have seen this circuit for Exponential output and this one forLog output but I have never used it or build it. So I do not know if they actually work.

• Please consider adding a summary of the content of those links: Link-only answers are not ideal for this site, both because the links themselves could become invalid over time, leaving the answer meaningless, and also because it helps to get at least an overview of the "answer" without having to visit external links. – Anindo Ghosh May 1 '13 at 6:46

The current thru a diode is close to a exponential function of the applied voltage, at least for a part of the operating range. Therefore the reverse is also true, which is that voltage is a logarithmic function of the current thru a diode.

Making a rough analog log function therefore is mostly putting a controlled current thru a diode and returning the voltage accross it. You could use a diode directly to make a exponential by driving it with voltage and measuring the current, but little errors can cause problems that way. Often the log function is used in a feedback loop instead, which has the effect of inverting it.

In days long past there were analog multipliers built on this principle. Take the log of the two input signals, add them, then unlog by doing a exponential. With a lot of careful tweaking and calibration and temperature control (or compensation), you can get meaningful results like this.

Nowadays the first reaction should be to convert the input signals to digital values as soon as possible, then do all the fancy mathematical manipulations digitally.

The standard approach for this kind of thing uses precision-matched transistor pairs. National Semiconductor has AN-30 "Log Amps", a classic app note on log amps. Texas Instruments has a couple of very good app notes on it. I have them, but they're on the work machine and I'm at home right now.