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What is the step response of \$I_1(t)\$ in the following circuit? (I mean if we apply step as input I what will be the I1?

I simply used Laplace transform and calculated the step response, but it was wrong according to the book I'm reading. It says in this circuit the current is not continuous at t=0 because we have a inductor loop, which I don't understand.

schematic

simulate this circuit – Schematic created using CircuitLab

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  • \$\begingroup\$ Thanks for the accept, but feel free to hold off before giving it out. You might get an actual answer about Laplace transforms if you give people around the world 24 hours to read the question. (As for myself, in 15 years of work and 5 years of grad school, I've never used Laplace transforms to solve a real problem, so I don't bother giving answers in those terms) \$\endgroup\$
    – The Photon
    Jan 21 '15 at 19:24
  • \$\begingroup\$ This answer completely addressed my problem, because now I can solve all such problems with discontinuities by adding series or shunt resistances. Anyway, I'll wait till tomorrow. Thanks again! \$\endgroup\$
    – user215721
    Jan 21 '15 at 19:30
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This circuit is not adequately modeled with ideal components. In this model, for the current source to produce a step output, its voltage must approach infinity, because it will be trying to produce an infinite \$\frac{\mathrm{d}I}{\mathrm{d}t}\$ through an inductive load.

If you include a parasitic shunt conductance or interwinding capacitance in parallel with each inductor, your model will be more realistic and the results won't have infinite voltages.

If you don't include parasitic elements, most SPICE simulators will automatically add something like 1 Gohm resistors from each node to ground, and your simulation result will depend on these "hidden" parasitic elements.

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  • \$\begingroup\$ Thanks. If I want to solve this by hand and obtain the step response, can I add a resistor parallel to the left inductor, and after solving the circuit in the s-domain, approach the resistance to infinity to obtain the current result? \$\endgroup\$
    – user215721
    Jan 21 '15 at 18:50
  • \$\begingroup\$ You can do that, but the result will be \$v(0^+)\to\infty\$. So it still won't tell you what a real circuit would do. \$\endgroup\$
    – The Photon
    Jan 21 '15 at 19:13
  • \$\begingroup\$ By the way, if you labelled the nodes in your circuit, I could say exactly which v I'm talking about. \$\endgroup\$
    – The Photon
    Jan 21 '15 at 19:14
  • \$\begingroup\$ Thanks, I got it. I used this method (parallel infinite resistance) and the result was correct. What do you mean by it does not represent the behavior of a real circuit? \$\endgroup\$
    – user215721
    Jan 21 '15 at 19:17
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    \$\begingroup\$ I mean that no real current source has zero parasitic conductance, and no real inductor has zero parasitic capacitance; and that for this circuit, those parastics determine the behavior of the v(t) response. \$\endgroup\$
    – The Photon
    Jan 21 '15 at 19:20

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