RC's and thermal modeling

So from a previous thread,

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it was suggested by John L. that I try some RC modeling. I did that today and the results were not what I expected. I sent a step voltage into a single RC (R=1 C=1) and then into a string of 10 R/C's. (R=0.1 and C=0.1). With the long string the voltage was a bit slower at the beginning, but it reached a 1/e value quicker than the single RC. My colleague says I have reproduced the error function (erf). And this looks about right.

Very interesting,

Thanks John

George H.

Reply to
George Herold
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On Jan 20, 4:36=A0pm, George Herold wrote:

=3D0.1

Here's the LTspice file if you are interested... (might be easier to make it yourself?)

Version 4 SHEET 1 1012 680 WIRE 144 -496 80 -496 WIRE 224 -400 224 -432 WIRE 304 -400 304 -432 WIRE 384 -400 384 -432 WIRE 80 -272 80 -496 WIRE 144 -272 80 -272 WIRE 224 -176 224 -208 WIRE 304 -176 304 -208 WIRE 80 -64 80 -272 WIRE 144 -64 80 -64 WIRE 224 32 224 0 WIRE 80 128 80 -64 WIRE 80 128 -32 128 WIRE 112 128 80 128 WIRE 272 192 192 192 WIRE 352 192 272 192 WIRE 432 192 352 192 WIRE 512 192 432 192 WIRE 592 192 512 192 WIRE 672 192 592 192 WIRE 752 192 672 192 WIRE 832 192 752 192 WIRE 912 192 832 192 WIRE -32 224 -32 208 WIRE 192 224 192 192 WIRE 192 224 -32 224 WIRE -32 256 -32 224 WIRE 0 0 0 0 FLAG -32 256 0 FLAG 224 32 0 FLAG 224 -176 0 FLAG 304 -176 0 FLAG 224 -400 0 FLAG 304 -400 0 FLAG 384 -400 0 SYMBOL res 208 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R1 SYMATTR Value 0.1 SYMBOL res 288 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R2 SYMATTR Value 0.1 SYMBOL res 368 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R3 SYMATTR Value 0.1 SYMBOL res 448 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R4 SYMATTR Value 0.1 SYMBOL res 528 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R5 SYMATTR Value 0.1 SYMBOL res 608 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R6 SYMATTR Value 0.1 SYMBOL res 688 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R7 SYMATTR Value 0.1 SYMBOL res 768 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R8 SYMATTR Value 0.1 SYMBOL res 848 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R9 SYMATTR Value 0.1 SYMBOL res 928 112 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R10 SYMATTR Value 0.1 SYMBOL cap 176 128 R0 SYMATTR InstName C1 SYMATTR Value .1 SYMBOL cap 256 128 R0 SYMATTR InstName C2 SYMATTR Value .1 SYMBOL cap 336 128 R0 SYMATTR InstName C3 SYMATTR Value .1 SYMBOL cap 416 128 R0 SYMATTR InstName C4 SYMATTR Value .1 SYMBOL cap 496 128 R0 SYMATTR InstName C5 SYMATTR Value .1 SYMBOL cap 576 128 R0 SYMATTR InstName C6 SYMATTR Value .1 SYMBOL cap 656 128 R0 SYMATTR InstName C7 SYMATTR Value .1 SYMBOL cap 736 128 R0 SYMATTR InstName C8 SYMATTR Value .1 SYMBOL cap 816 128 R0 SYMATTR InstName C9 SYMATTR Value .1 SYMBOL cap 896 128 R0 SYMATTR InstName C10 SYMATTR Value .1 SYMBOL voltage -32 112 R0 WINDOW 0 -74 28 Left 0 WINDOW 3 -235 -36 Left 0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value PULSE(0 10 0 1m 1m 100 200 1) SYMBOL res 240 -80 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R11 SYMATTR Value 1 SYMBOL cap 208 -64 R0 SYMATTR InstName C11 SYMATTR Value 1 SYMBOL res 240 -288 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R12 SYMATTR Value .5 SYMBOL cap 208 -272 R0 SYMATTR InstName C12 SYMATTR Value .5 SYMBOL res 320 -288 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R13 SYMATTR Value .5 SYMBOL cap 288 -272 R0 SYMATTR InstName C13 SYMATTR Value .5 SYMBOL res 240 -512 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R14 SYMATTR Value .333 SYMBOL cap 208 -496 R0 SYMATTR InstName C14 SYMATTR Value .333 SYMBOL res 320 -512 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R15 SYMATTR Value .333 SYMBOL cap 288 -496 R0 SYMATTR InstName C15 SYMATTR Value .333 SYMBOL res 400 -512 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R16 SYMATTR Value .333 SYMBOL cap 368 -496 R0 SYMATTR InstName C16 SYMATTR Value .333 TEXT -272 280 Left 0 !.tran 0 10 0 1m

George H.

Reply to
George Herold

George Herold a écrit :

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Heat flux (power) is more seen as a current which is integrated by the thermal mass (cap). Then you have two thermal resistances: the one from your heated structure between each blob of capacitance node as you've drawn, and the convection one, which is tied from each cap node and a voltage source representing ambient temperature.

--
Thanks,
Fred.
Reply to
Fred Bartoli

e

R=3D0.1

he

Yeah, That's right Fred. I was just simulating a step change in the temperature. Simulating the other losses is an interesting question. It looks to me that other resistive losses, will just be a loss of voltage and not a change in the time response. No that's not right. I'll loss more near the hot end than at the far end...

I can simulate that too. Say is there a way to get numbers out of an LTspice simulation?

George H.

Reply to
George Herold

You could use the "ltline" lossy transmission line model with L==0, or there's a couple of pure RC line models, urc and urc2. The metalization lines in ICs are so lossy that L is essentially zero, so they behave like thermal conductors.

There are no thermal inductors, which is why temperatures don't overshoot in purely thermal-conductive systems. There *is* a tricky RC circuit that has above-unity gain at some frequencies... I wonder if the thermal version would be interesting.

John

Reply to
John Larkin

Yes it would--as in, breaking the second law of thermodynamics by making heat flow from cold to hot.

Unfortunately there's no way to wire the two thermal masses in series--a thermal mass is always a _grounded_ capacitor.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
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Reply to
Phil Hobbs

...

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R=3D0.1

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There are special cases (I think) with ballistic phonons, that travel as some 'coherent thing'. There must be something like inductance (..momentum), but it's rare. I don't really understand (never measured) second sound in helium

George H.

Reply to
George Herold

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Yeah, the charge Q is the thermal energy stored in the thing. It seems like it would make sense to use the absolute temperature scale (K). Then it's easy to see that discharging a thermal capacitor involves tieing one end to absoulte zero.

George H.

Reply to
George Herold

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