RL circuit and differentiation

[niarn]

Since analog modelling seems to be an important topic for this forum maybe someone has encountered a similiar problem.

How to numerically compute the voltage across both the resistor and inductor given the current in a RL circuit?

I'm unsure if there is a 'best way' of doing the differentiation? and with best way I mean something that takes place in a process loop (realtime) and at the same time also accurate (I know this is vague).

[Z1202]

Personally I would (almost) never do differentiation in analog emulation. Differential equations are just a mathematical notation (probably historically evolved) for an integration process. Remember that one term for solving differential equations is integrating them. Integration also describes what is "actually" happening in nature. E.g. even though speed is a derivative of the position, one cannot say that the position is the mechanical system's "input" and speed is its "output". Rather mechanical system somehow controls its speed and the position is emerging as an integral of the speed.
For that reason I'd kindly ask, how do you manage to have the current in an RL circuit as the circuit's "input" signal? I would rather expect, that when looked in a larger context, the "input" would be the voltage rather than the current.

That's not to say you can't do that formally, and you can e.g. develop a bilinear differentiator which is an "inverse" of the bilinear integrator, but as I said, unless there is a good reason to, that'd feel rather weird for me. The desire to differentiate also might imply some flaw in the system's analysis. E.g. if you try to drive an RL circuit with a current source, I'd expect that the current source being an idealized thing would not reflect what is actually happening in such system. Pretty much the same as trying to connect a capacitor to a voltage source. People with a proper electrical engineering background might correct me.

[niarn]

Thanks z1202, I actually looked into your book for inspiration

I would also avoid the differentiation if I could! but not sure it can be avoided when input is current.

I agree that it may seem unnormal to have current as input, but the reason I have current as input is that I'm inverting a circuit. So I'm going backwards from output to input.

You probably mean bilinear differentiator?

[Z1202]

I agree that it may seem unnormal to have current as input, but the reason I have current as input is that I'm inverting a circuit. So I'm going backwards from output to input.

In that case I'd consider using a bilinear differentiator, since it corresponds to doing bilinear integration in the "normal" direction.

You probably mean bilinear differentiator?

Yes, that was a typo.

Edit: I think inverting a circuit can result in a system which cannot be implemented, if the zeros of the original transfer function are in the right semiplane. Or, actually, I'm not sure what "inverting a circuit" means. Is that finding the input signal from the output?

[niarn]

Thanks z1202, I will take a look at the bilinear differentiator.

[niarn]

Yes, with inverting I mean given a sample output waveform compute the corresponding input (voltage) that generated the output.

[AnalogGuy1]

...Integration also describes what is "actually" happening in nature. E.g. even though speed is a derivative of the position, one cannot say that the position is the mechanical system's "input" and speed is its "output". Rather mechanical system somehow controls its speed and the position is emerging as an integral of the speed....The desire to differentiate also might imply some flaw in the system's analysis. E.g. if you try to drive an RL circuit with a current source, I'd expect that the current source being an idealized thing would not reflect what is actually happening in such system.

If you're modeling a circuit, why not explicitly solve the DE and do what SPICE does - solve for the output given the input using Newton-Raphson? Sorry if this is a "dumb" question that's obvious to all but me.