Change in strategy. Make a collection of branches and for each branch have the entries for A, E and B matrices. So this will give an indication of the L, R and V values in every branch.

What is a stiff branch?

- It is not a branch with negligible or zero inductance. If the resistance is small enough, it could be a load resistance or even a branch resistance.
- It is a branch with a large resistance and negligible or zero inductance.

After this, I need to calculate the L/R ratio just in case though a very large inductance accompanying a large resistance is not very practical. A large resistance simply means an open circuit or a non-conducting medium but a large inductance means a huge core and a large number of turns in the winding. The worst I can think of in a huge transformer that has a large magnetising inductance but this will have a low winding resistance and a large core loss resistor across it. So it won't be a stiff system. On the contrary it will be a system with a large time constant which is actually the case because when you energize one of these monsters, the magnetizing current can take a long time to decay.

The smallest resistance and inductance would really be the measure of a circuit because they would be the parasitics. So suppose I take these as a base and try to calculate ratios of other elements with respect to it. So a parasitic resistance of 0.005 ohm for a 120 V circuit would be acceptable wire resistance. And a 10 ohm load resistor would result in a ratio of 10/0.005=2000 which is quite OK. But a 1 megaohm resistor would result in a ratio 2.0e+8 which should raise an alarm.

Taking such a ratio is itself a form of per unit, just that the per unit is arbitrary and if a user puts ridiculous values and an equally impractical simulation time step, a circuit will classified as stiff.

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