Reply-To: "fred bartoli"
From: "fred bartoli"
References: <email@example.com> <firstname.lastname@example.org> <email@example.com> <firstname.lastname@example.org>
Subject: Re: Power converter, 12v DC to 16v RMS
Date: Wed, 11 Dec 2002 18:44:43 +0100
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Organization: Guest of ProXad - France
NNTP-Posting-Date: 11 Dec 2002 18:45:52 MET
Oops, sorry. Some typo...
> say we are in continuous conduction mode (in fact, strictly speaking we
> 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
> 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)
Forgot to correct this one.
Should have wrote :
Urms = sqrt(F(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).