[HN Gopher] Solving the Nerd-Sniping Problem: When Electronics M...
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Solving the Nerd-Sniping Problem: When Electronics Meets Heat
Equations
Author : pkoird
Score : 63 points
Date : 2024-03-24 02:58 UTC (20 hours ago)
(HTM) web link (praveshkoirala.com)
(TXT) w3m dump (praveshkoirala.com)
| bgnn wrote:
| Nice write-up.
|
| Latest generation circuit simulators don't solve the whole R or
| RC matrix anymore but they deduce the circuit to an equivalent
| one between the two points of interest during netlisting. If you
| have only resistors like this, it only makes sense to deduce it
| to a single equivalent resistor. This is one of the major
| simulation speed-up techniques enabling us to simulate more
| complicated circuits.
| pkoird wrote:
| It'd be cool to learn how one could reduce this resistances in
| this grid to an equivalent resistance. Perhaps you could share
| some insights?
| bsder wrote:
| Got a ref? I haven't seen anything like this in the DAC (Design
| Automation Conference) proceedings, but I could very well have
| missed it.
| bgnn wrote:
| I don't think they disclosed their algorithms but both
| Cadence Spectre-X and Mentor AFS-XT have an "improved" RC
| matrix solver as they market it. I think Spectre-X was
| launched at DAC 2019, but I've been using it since 2018. AFS-
| XT is launched couple of years ago as a response. The main
| goal of RC reduction is post-layout simulation. With these
| simulators what you would see in the results is there is a
| primitive called RC, which doesn't exist in the netlist. You
| need to define an fmax of the circuit, and it will reduce RC
| routing parasitics to approximately create same delays within
| that frequency range with a much more reduced matrix.
| Netlisting take some time but simulation is like 10x faster
| due to this reduction. I'm mainly using FinFET processes, so
| each transistor comes with tens of parasitics annotated. For
| a moderately large design it's normal to have millions of R
| and C.
|
| There are also tools doing this on the extracted netlist
| directly by the way. Cadence's tool is called Quantus
| Standalone Reduction (qreduce).
| bsder wrote:
| Thanks for the breadcrumbs. I'll follow them around.
| bdjsiqoocwk wrote:
| I once found an exact solution to this problem (exact in some
| limit) in a condensed matter physics textbook. I never managed to
| go back and find the textbook name (it was a library book). I was
| wondering if someone would recognize the textbook and tell me the
| name.
| pkoird wrote:
| The only analytical solution I could find was this:
|
| https://www.mathpages.com/home/kmath668/kmath668.htm
|
| I admit it kinda flew over my head (as I mentioned, I'm an
| empiricist through and through)
| 127 wrote:
| Physicists like to call it heat equation. I like to call it
| energy preserving Gaussian blur. I mean, it's more fundamental
| than just physics. To me, it seems a core mathematical function.
| https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/
| Sharlin wrote:
| The classic demoscene fire effect is surprisingly simple and at
| the same time surprisingly physically accurate, or at least
| physically inspired: https://lodev.org/cgtutor/fire.html
| pkoird wrote:
| I believe it's a kinda-sorta reformulation of the Gauss-Seidel
| method of solving systems of linear equations (which, obviously
| are fundamental in physics).
| lambdaone wrote:
| A version of this was set to me in a university interview.
|
| There is an easier and far more elegant way to solve this than
| the solution given. Consider the circuit as two superimposed
| elements; one with a current being injected at the first point
| and flowing outward to a sink at infinity, and the second with
| current flowing in from a source at infinity and exiting at the
| second point. (For the sake of argument, say the current is 1
| amp).
|
| The current flow patterns in each case are easy to calculate
| because of the symmetry of each problem.
|
| Now add the two superimposed elements together, and the sources
| and sinks at infinity cancel out, leaving only the point source
| and sink.
|
| You now know the current through the overall circuit and the
| currents through each resistor, and because you know the values
| of the resistors, you also know the voltages across each
| resistor. Add up the voltages along any simple path between the
| two points to get the voltage between the points, and since you
| also know the overall current, you can now calculate the
| equivalent resistance.
| pkoird wrote:
| Indeed, sounds like an interesting approach! This was just the
| first thing that came to my mind and it was cool to relate a
| concept from thermodynamics to electronics. I'll go and see if
| I can find the superposition version now.
| quibono wrote:
| I believe the following has the symmetry based solution you
| mention (and more!)
| https://www.mathpages.com/home/kmath668/kmath668.htm
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