On Sat, 26 Apr 2003 22:18:02 -0000, you wrote:
I have tried your 1ps too. It's really wrong with
.tran 0.1 for example.
It is simulated correctly, if you specify a minimum step size like
.tran 0 0.1 0 1u .
Yes, I see. Thanks. So it's just a matter of "being too dumb"
about what's been specified. It's up to me to tinker a little.
Small price to pay.
------------------------------------------------------------------
By the way, I have a nice approximation formula for the PWM ripple
voltage:
Vpp = 0.25 * Vp' * Tpwm / Tau
Vp' = Voltage pulse at the output without capacitor(C=0) and with
zero bias voltage(V=0V). Vp' = Vp * R1/(R1+R2)
Tau = C * (R1*R2)/(R1+R2)
Tpwm = period of the PWM
My RC is your tau and my tcyc is your Tpwm. I'm not quite sure
what your Vp' is, though. Is it my Va or my Vb or something
else?
But here's my derivation. Let's see...
1+e^(-tcyc/(R*C))-e^(-ton/(R*C))-e^(-toff/(R*C))
dV = (Va-Vb) * ------------------------------------------------
1 - e^(-tcyc/(R*C))
Using Taylor's for a first-order estimate, it comes out to:
dV = (Va - Vb) * 0
Which definitely isn't right, so taking it out to the next order
of Taylor's yields:
tcyc^2 - ton^2 - toff^2
dV = (Va - Vb) * -----------------------
tcyc * (tcyc + 2*R*C)
Which seems pretty darned close to right.
Ah!! Now it dawns on me! Your Vp' is my (Va - Vb)! Here's
why:
Looking at the above 2nd-order Taylor's estimate, the
denominator has the factor, (tcyc + 2*R*C). But since we are
assuming that RC >> tcyc, which should be true if we are doing
our job in filtering, then (tcyc + 2*R*C) is about 2*R*C. No
point bothering to add in a disappearing tcyc, so just drop it.
That leaves us with:
tcyc^2 - ton^2 - toff^2
dV = (Va - Vb) * -----------------------
tcyc * 2*R*C
so,
| tcyc ton ton toff toff |
dV = (Va - Vb) * | ---- - ---- * --- - ---- * ---- |
| 2RC tcyc 2RC tcyc 2RC |
Still a little messy, but let's assume that ton is about 1/2 of
tcyc (and so is toff, then.) In this case, it becomes:
| tcyc 1 1/2*tcyc 1 1/2*tcyc |
dV = (Va - Vb) * | ---- - --- * -------- - --- * -------- |
| 2RC 2 2RC 2 2RC |
so,
| tcyc 1 tcyc |
dV = (Va - Vb) * | ---- - --- * ---- |
| 2RC 2 2RC |
or,
| 1 tcyc | 1 tcyc
dV = (Va - Vb) * | --- * ---- | = --- * (Va - Vb) * ----
| 2 2RC | 4 R*C
or,
dV = (Va - Vb) * tcyc / (4*R*C)
Since Tau=R*C and tcyc=Tpwm, this turns into:
dV = (1/4) * (Va - Vb) * Tpwm / Tau
Which looks a heck of a lot like your:
Vpp = 0.25 * Vp' * Tpwm / Tau
However, this makes explicit and clear that there is one more
assumption playing into this, than just Tau >> Tpwm; namely,
that it also assumes that ton=toff and thus that the PWM duty
cycle is 50%. Which is an "average assumption."
Thanks, again!
Jon
