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March 08, 2011

Comments

Birocchi

Without integration, it can be seen also in the following way:

Initial energy in the C: Es=1/2CVs^2
Final energy in the C: Ef=1/2CVf^2
Energy supplied by the C: E=Es-Ef=1/2C(Vs^2-Vf^2)
Energy to the load: E=PdeltaT

so:

PdeltaT=1/2C(Vs^2-Vf^2)

George Storm

Constant power loads can cause other, even more "interesting" behaviours. These are mostly a result of their negative slope conductance (Gslope = - P/V^2).
One example is the potential (pun originally accidental) of regulated power supplies to oscillate when their principal loading is by a constant-power load.

BTW, for this case I find the analytic approach more revealing...

John Dunn

Hi, George.

Indeed so! Please see:

http://licn.typepad.com/my_weblog/2010/11/switchmode-dynamic-input-impedance-john-dunn-consultant-ambertec-pe-pc.html#more

Carl Schwab

Your notes are also useful when studying the use of supercaps for electrostatic storage in place of electrochemical storage for powering vehicles. Of course the time scales are quite different. But what comes out of this is that the supercap pack only has to discharge to 1/3 peak voltage to deliver all but 1/9 of the stored energy.

The advantage is that the supercap pack can be recharged much more quickly than a rechargeable battery. Also the supercap is more efficient than a battery. Nano-engineering is providing the path to both better rechargeable batteries an MUCH better supercaps. Thanks for the blog.

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