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Analog Circuits for Calculus

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CycloWizard

Lifer
I have heard that derivatives are easy to do using analog circuits if I'm willing to sacrifice accuracy. For my current application, it would be great if I could get a rough estimate (within 1-5%) of the result of a very complicated differential equation on the fly for feedback purposes. It looks like any sort of digital sampling and calculation I try takes at least 200 microseconds to complete, which is a very long time for this process (feedback control of a voice coil motor).

I was wondering if anyone knows if this is actually possible and how it could be done. Specifically, I need to compute time derivatives of voltage and/or current.
 
The convenient things about derivatives/integrals is that they're very, very simple in the s-domain. Integration is just division by s, and taking a derivative is just multiplication by s.

Thus, an integrator is just a system with a single DC pole, while a differentiator requires a DC zero. This is generally very easy to implement in analog circuitry. Anyway, if you don't care about the theory and just want to build one, there are schematics on Wikipedia here:

http://en.wikipedia.org/wiki/O...pplications#Integrator
 
Integrators and differentiators are easy to build: one op-amp, one cap, and a ~3 resistors.

The tricky parts are providing an appropriate input signal and keeping the output within the supply rails.

There is an upper and lower limit to both your inputs and outputs; the lower limit is the noise floor and op-amp imperfections and the upper limit is the supply rails.

I don't really see how beneficial it would be to build. Matlab would be more appropriate in my opinion.

EDIT: Oh, time is a factor. 🙂 Analog control loops are very common and simple to build and use integrators, gain, and differentiators. They're also very fast!
 
Originally posted by: bobsmith1492
Integrators and differentiators are easy to build: one op-amp, one cap, and a ~3 resistors.

The tricky parts are providing an appropriate input signal and keeping the output within the supply rails.

There is an upper and lower limit to both your inputs and outputs; the lower limit is the noise floor and op-amp imperfections and the upper limit is the supply rails.

I don't really see how beneficial it would be to build. Matlab would be more appropriate in my opinion.
Click to expand...
I have a very high-speed controller that needs an analog input to use for feedback, so it has to be higher speed than I could get Matlab to do. The equation is very complex such that even as a simple finite difference equation, it took Matlab ~250 us to compute it, whereas the feedback loop time step is only about 190 us.
 
Yeah, sorry I missed the speed part the first time through.

If you're doing an analog feedback circuit, you won't want to use ideal integrators and differentiators; particularly on the integrator you'll want a large R across the feedback C to compensate for DC offset at the op-amp inputs. Otherwise your output sum will drift away when it shouldn't.
 
Differentiators are known for being noise amplifiers. My advice would be to talk to someone in your EE dept and have them take a decent look at your equpiment/requirements. Bring a beer with ya!
 
Originally posted by: futuristicmonkey
Differentiators are known for being noise amplifiers. My advice would be to talk to someone in your EE dept and have them take a decent look at your equpiment/requirements. Bring a beer with ya!
Click to expand...
Yeah, like bobsmith said, I need to incorporate a filter into it, which I've already figured out how to do. I remember the very basics of circuit design, but I never realized until recently that I could use it to do my math for me. 😛
 
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