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I'm trying to simulate this long 14AWG cable with DC power to multiple loads. These loads expect about 12W of power and can therefore not really be modeled with a resistor easily. As the voltage drops over the length of the cable, the resistive load would have to change as well to equal 12W of power.

So I managed to put together a solution that uses a behavioral current source, but only seems to work for up to 6 branches. When I add a 7th branch as seen below, the simulation throws an error. Any idea what might be causing this?
enter image description here enter image description here

Works with just 6 branches enter image description here

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  • \$\begingroup\$ Hmm. Have you tried to remove all of R2..R7 and B2..B7 and just solve it for R1 and B1? Should be simple, right? Please tell me what answer you get for V(BRANCH1). \$\endgroup\$
    – periblepsis
    Commented Apr 29 at 7:49
  • \$\begingroup\$ I mentioned in the post, I can remove R7 and B7, and the circuit solves correctly. In fact, any it seems to work find up to 6 "branches" and breaks on the 7th one. I have added a screenshot of just 6 branches. \$\endgroup\$
    – adamski93
    Commented Apr 29 at 8:22
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    \$\begingroup\$ Let's say there is just R1 and B1. (Perhaps I am failing to understand your circuit -- it happens.) Then the KCL I get is \$\frac{V_{{\text{BRANCH}_1}}}{R_1=127\:\text{m}\Omega}+\frac{12\:\text{W}}{V_{{\text{BRANCH}_1}}}=\frac{12\:\text{V}}{R_1=127\:\text{m}\Omega}\$. This has two positive, real-valued solutions. Not one. That test alone makes me not surprised when simulation problems may arise. There may be more than one stable solution. Not sure why you are finding good results for just one branch. But I don't like the math I see. \$\endgroup\$
    – periblepsis
    Commented Apr 29 at 8:31
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    \$\begingroup\$ Try reading this article. You should probably use the LTspice built-in constant power load since it has a built-in mechanism that handles the problem you are seeing (via vprxover parameter). \$\endgroup\$
    – Ste Kulov
    Commented Apr 29 at 8:36

3 Answers 3

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I'll treat this as a homework problem, because it's a compact but useful learning experience:

  • Try putting a capacitor (with initial condition equal to V1) on each node, to GND. What is the transient behavior? What can we conclude from this about the DC situation in the two cases?
  • Or, vary V1 up and down a few volts in the 6-branch case, what do you observe at each node? Does the same failure happen if V1 drops enough?
  • What is the Thevenin resistance at the end of the chain? (This can be tested with a IPULSE for example.) What is the incremental resistance of each branch at the operating voltage? Is there any coincidence in parameters at the point where the error occurs?
  • What is the nodal analysis of the basic system:

schematic

simulate this circuit – Schematic created using CircuitLab

you should be able to solve this easily by hand, including the Thevenin resistance at V2. What happens as V1 decreases from some initial/nominal value?

Mathematically, what this should lead you to is the nature of a singularity, as applied to nodal analysis equations, and also the behavior of negative resistance elements. Notice that you are dividing by the voltage, so response is reciprocal, current is divergent towards zero, and undefined at zero (a singularity).

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Tried with some branches ...
Errors (number of iterations exceeded ...) appeared as well when serial resistors grew...
and the last voltage is ~ 45% of the initial 100 V.
Seems to appear at some particular values of the rr parameter.

Made with microcap v12.
Seems to be "SPICE error" ...

enter image description here

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I tried .options itl1=5000000 with the 7 branches version.

The simulation runs a very long time and the fan in my laptop goes bezerk after a few minutes. I did not run it until it finished.

From Help .options: enter image description here

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