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#22
October 15th 04, 06:33 AM
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"John Larkin" wrote in message ... On 11 Oct 2004 16:11:16 -0700, (Alan Horowitz) wrote: when a current just starts flowing into a RL or RC circuit, how does the voltage "know" that it should be increasing exactly 63% during each time-constant period? And whence the number 63%? How about this: Charge a 1 farad capacitor to 1 volt and slap a 1 ohm resistor across it. The resistor current is 1 amp, so the cap discharges, and the voltage is at first declining at a rate of 1 volt per second. But 1/100 of a second later, the voltage is 0.99 volts, so the current is only 0.99 amps, so the rate of discharge is only 0.99 volts per second. So we write a Basic program: v = 1 ' charge the cap for t = 1 to 100 ' then, for 1 second at 0.01 sec steps, v = v - 0.01 * v ' discharge the cap by 1% next print v ' voltage is this, 1 second later which simulates what I was doing above, but for a full second. The value of v at the end is 0.36603 volts. That's close to 1/e, not exact because I took 100 discrete steps, as an approximation to continuous-time math. With 1000 steps, simulating 1 second of discharge in 1 millisecond steps, you get 0.367700, even closer. 'e' is just nature's answer to a natural discharge curve. John Egads!. You've just given away the secret of Spice Transient Analysis. The programmers will be calling for you with torches ablaze. Why is it that if anyone wants to *clearly* explain an algorithm or sequential idea, they'll use "Basic" or a very Basic looking 'Pseudo-code', yet most programmes seem written in "C". It just isn't logical. regards john |
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