Current Through an Inductor at time t

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Homework Statement

Homework Equations

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V = 1/L di/dt

I = I_o x (1 - e^(-t/L/R)

Tau = L/R

The Attempt at a Solution

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I_i = 0mA ; I_f = 1mA

V_i = 1V ; V_f = 0V

Tau = 15uH / 1k Ohms = 10ns

If my above is correct, then voltage and current equations through inductor should be as follows:

V = 15uH di/dt

I = 1mA (1-e^(-t/10ns)


The problem is when I test current I don't get the graphical answer.
For instance, I tested at 30ns:

I = 1mA (1-e^(-30ns/10ns)
I= .001A (1-e^-3)
i= .00095A or 950uA

...but on the graph the answer is just under 0.855uA

One hypothesis I had is that since the voltage doesn't pulse till 1ns, somehow t time or Tau is affected. But I have tried playing with the equation by adjusting t time and/or Tau by 1ns and still don't seem to be able to come to the right answer.

 

[gneill]

One hypothesis I had is that since the voltage doesn't pulse till 1ns, somehow t time or Tau is affected. But I have tried playing with the equation by adjusting t time and/or Tau by 1ns and still don't seem to be able to come to the right answer.

That's certainly a good hypotheses. Clearly time needs to be shifted in some manner (not Tau, it is not affected by changing clocks). You should be able to subtract a nanosecond from time to get your equation to line up with the simulation, but there's another way, too. You can adjust LTspice to start saving data only after 1 ns. Go to the Simulate menu and choose Edit Simulation Command. Note the entry "Time to Start Saving Data". Try it out.

 

[Lapse]

That's certainly a good hypotheses. Clearly time needs to be shifted in some manner (not Tau, it is not affected by changing clocks). You should be able to subtract a nanosecond from time to get your equation to line up with the simulation, but there's another way, too. You can adjust LTspice to start saving data only after 1 ns. Go to the Simulate menu and choose Edit Simulation Command. Note the entry "Time to Start Saving Data". Try it out.

Thanks for that tip on LTspice. After applying that new simulation command:
I = 860mV - 865mV @ t = 30ns.

As you may notice, this answer is still different from what I am getting.

When I do the calculation at t = 30ns - 1ns = 29ns, my answer comes out to 945mV.

So I am still going wrong somewhere...

 

[gneill]

I think we'll need to see some more details of your calculations. Here's what I get using Mathcad:

 

[Lapse]

I think we'll need to see some more details of your calculations. Here's what I get using Mathcad:

Oh... my... goodness. I said Tau = 15uH / 1k = 10ns ? It is 15ns!

Another lesson in simple mistakes can lead to greater consequences.

Thanks for your help gneill.

 

[gneill]

Happy to help!