Re: dv/dt [was: ALCON Capacitors for MMC]

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Jim Lux <jimlux-at-earthlink-dot-net> 

At 06:16 PM 3/25/2004 -0700, you wrote:
>Original poster: Matthew Smith <matt-at-kbc-dot-net.au>
>Tesla list wrote:
>>Original poster: "Luke" <Bluu-at-cox-dot-net>
>>May I ask what is meant by dv/dt?
>
>Ooh, ooh, I think I know this one!  Just starting to study calculus after 
>having managed to away with it for twenty years or so...
>
>Someone correct me if I'm wrong, but I think that this is:
>
>"instantaneous value of voltage divided by instantaneous value of time".
>
>As opposed to DELTAv/DELTAt (where DELTA should be a triangle symbol) 
>which is, once again correct me if I'm wrong:
>
>"change in voltage divided by change in time".
>
>Cheers
>
>M
>(Back at School)


Almost Matt...

dv/dt would be instantaneous rate of change of voltage

deltaV/delta T would be the average rate of change of voltage over some 
time interval (delta T)

given some voltage V(t)
deltaV/deltaT = (V(t2) - V(t1)) / (t2-t1)

if you make the time interval very, very small (as in infinitely small) 
then you get to dV/dt. (for what it's worth, it cannot actually be 
measured...since you cannot make a measurement in zero time... all you can 
get is arbitrarily close).

For certain straightforward cases, (i.e. an ideal resistor, capacitor and 
inductor), you can calculate what dv/dt is (at any given instant) because 
you can write an equation for what v(t) is, and determine dv/dt by 
"analytic" means (that is, using calculus and symbolically translating one 
equation into another... if v(t) = sin(t) then you KNOW that dv/dt = cos(t) ).

For non-ideal cases (particularly where the circuit is complex, or there 
are nonlinear or random components involved), one approximates it by 
"numerical" means (that means simulating the behavior at ever finer time 
steps using some form of approximation).  SPICE is a fine example of a 
numerical calculation, as opposed to an analytical.


Interestingly, of course, you can also take dv/dt (which potentially varies 
as function of time) and integrate it to determine deltaV/deltaT for any 
arbitrary time and deltaT.