Reply-To: "fred bartoli"
From: "fred bartoli"
Newsgroups: sci.electronics.design
References: <2a4ddbec.0212101600.5a2d432c@posting.google.com> <3df6fe93$0$2155$626a54ce@news.free.fr> <4ba3370d78tonyw@ledelec.demon.co.uk>
Subject: Re: Power converter, 12v DC to 16v RMS
Date: Wed, 11 Dec 2002 18:01:58 +0100
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Tony Williams a écrit dans le message :
4ba3370d78tonyw@ledelec.demon.co.uk...
> In article <3df6fe93$0$2155$626a54ce@news.free.fr>,
> fred bartoli wrote:
>
> > For a resistive load, that also *don't* have to see symetrical voltages
> > (only 16V RMS / 10A), the simplest one could do is the following :
>
> > +--------------------+--------.
> > | | |
> > | | |
> > | | |
> > | ( | |
> > | ( | | Load = 1.6R
> > 12V ( | |
> > DC ( | |
> > | | |
> > | +--------'
> > | |
> > | |--
> > | -----|--
> > | |
> > +--------------------+
>
> > The load being driven part time directly from the 12V source, this also
> > relax the constrains on the inductor.
>
> I keep looking at this and still can't develop
> a set of sums that defines the effective output
> voltage.... F, Ton, Toff, L, R, L/R and so on.
>
> --
> Tony Williams.
Tony,
say we are in continuous conduction mode (in fact, strictly speaking we are
always in CC mode here), and low ripple for the immediate simplicity.
With E = DC source, L the inductor, R the load, U the load voltage when the
switch is open, Urms the 16V target and winding resistance negligible,
we have :
ILmax-ILmin = E Ton/L
ILmax-ILmin = U Toff/L
so, U = E Ton/Toff
Urms = F sqrt(Ton E^2 + Toff U^2)
so Urms = sqrt(F(Ton E^2 + Toff E^2 Ton^2 / Toff^2))
or Urms = sqrt(F(Ton E^2 + E^2 Ton^2 / Toff))
Note that R doesn't appear at all, which means that as long as the
conditions are satisfied (low ripple, CC) the output is a voltage source.
Solving the last eq for the duty cycle and the given conditions we have :
Ton = Urms^2 /(F(Urms^2+E^2))
Toff = E^2 /(F(Urms^2+E^2))
or duty cycle = F Ton = Urms^2 /(Urms^2+E^2) = 64%
How stringent is the low ripple condition for the Urms accuracy ?
So, with say F = 10kHz, R = 1.6 ohm we have (from simulations)
Inductance F L/R Urms ILpk Delta IL L ILpk^2
500u 3.125 16.307 14.67 1.547 0.107
100u 0.625 16.45 18.1 7.73 0.033
50u 0.312 16.88 22.9 15.46 0.026
20u 0.125 19.31 41.0 38.71 0.033
10u 0.0625 24.31 77.4 77.17 0.060
So the optimum inductor size seems to be around 50uH (for the core size).
Fred.