Systems Modeling Question (First order thermal circuit)

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KingDaniel
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Homework Statement


I have a problem with understanding the thermal circuit I attached to this thread. Please help. It's a Thermal circuit of a computer CPU that needs to be simplified to have just 2 lumped capacitances and resitances. How would one go about doing that? along with the equations?

Handwritten notes, rotated on the page, titled Auslor Thermal Circuit: Computer CPU board, showing a Si to ceramic to paste to heat-sink to air temperature profile diagram and an approximate equivalent thermal circuit with resistances and capacitances.
 

Discussion

This is what they simplified it to but I don't understand it:

Handwritten notes, rotated sideways, showing a two-capacitance thermal system diagram with Q_in(t), C_t1, C_t2, R1, R2 and theta_amb, the equations d(theta_1)/dt and d(theta_2)/dt, and a list of analogies between thermal and electrical quantities.
 
I tried to picture it like this but I'm not sure if it's right:

Hand-drawn thermal circuit diagram on lined paper, rotated sideways: input temperature θin(t) feeds series resistor R1 with capacitor Cth1 in parallel, then node θ2, then resistor R2 with capacitor Cth2 in parallel to θamb, with θ1 and θ3 labeled between elements.
 
KingDaniel said:

Homework Statement


I have a problem with understanding the thermal circuit I attached to this thread. Please help. It's a Thermal circuit of a computer CPU that needs to be simplified to have just 2 lumped capacitances and resitances. How would one go about doing that? along with the equations?

View attachment 86866
that is as simple as you are going to get it without losing data. Why are you trying to simplify it?

If you only need the thermal profile at one location you can use equivalent circuits to simplify i guess.
 
@donpacino , okay, but is my circuit the same as their version of the circuit? Cause I'm trying to comprehend it in terms of an electrical circuit analogy but their drawing just looks weird...
 
your circuit is not equivalent. If you look, the capacitances go to ground, not across the resistances.