3 ms·
My dad designed Frequency Response Analyzers in the 60's and 70's that used OpAmps to compute Fourier Integrals and then "solve the right triangle". That is, r
by drfuchs 10y ago
My dad designed Frequency Response Analyzers in the 60's and 70's that used OpAmps to compute Fourier Integrals and then "solve the right triangle". That is, relative to a sine wave it generated, it would take a return analog signal, multiply by sine and cosine waves, integrate both, and then take the square-root of the sum of the squares and also the arctangent of their ratio, to finally output amplitude and phase-shift of the return signal. All as analog voltages; all with OpAmps (and a tiny bit of TTL to turn the integrators on and off). It simply wasn't feasible to do this digitally; it's not just that doing a real-time FFT in the digital sphere was cost-prohibitive at the time, but also the A-to-D converters weren't fast enough to keep up (at the required accuracy).
Typical users went from aerospace and automotive ("will our wing or chassis oscillate badly when we hit a thermal or pothole"?) to audio (that's how they would make those Frequency Response charts for speakers) to hard disk drive head servos ("if we send the head from track X to track Y, will it get there directly, or "ring" -- slightly overshoot and then overcorrect for a while?").
One fun detail: eventually they had to encase their OpAmps in special little heaters that would keep them at a constant temperature, to avoid drift as the ambient temperature changed.
You can still occasionally buy one surplus on eBay for a few hundred dollars; they were about $10k new (in 70's dollars).
- CapacitorSet 10y agoThat sounds _extremely_ interesting for people who are into control theory! Do you happen to have schematics?
- drfuchs 10y agoI think so; I'll have to look through storage. Drop me a line at {myid} at yahoo.com. Let me point out that the description here is as understood by a pure-digital person: I didn't seem to inherit the analog gene, and as a teen couldn't grok his deeper explanations ("What do you mean 'the imaginary part of the signal'? We're in the real world; the electrons don't have any imaginary components!").
- dragontamer 10y agoImaginary numbers are pretty easy to understand, once you realize they're just a 2x1 matrix, and that all "imaginary numbres" math are equivalent to 2x1 Matrix linear algebra. Roughly speaking, you need 2-degrees of freedom to represent a circuit: the voltage and the current. Instead of throwing "two numbers" around all the time, we create a complex number. We call the two parts of the number "real" and "imaginary", but really... they're roughly lining up with "voltage" and "current". We just call them "real" and "imaginary" because that's what all the math guys call it. A "purely imaginary" number in phasor world is when the current is +/- 90-degrees out of phase with the voltage. (180-degrees out of phase means the current is simply negative, going backwards). A "purely real" number happens at 0-degrees (positive current) or 180-degrees (negative current). "Purely Real" numbers line up exactly to all of the DC-voltage experiments from beginner-level electronics. As it turns out, all circuits are made up of resistors, capacitors, and inductors can be calculated using "simple" addition, subtraction, multiplication and division with complex numbers. ------------- The above is a gross simplification of whats going on. More details can be found here: https://en.wikipedia.org/wiki/Phasor https://en.wikipedia.org/wiki/Phasor