Regarding the HW1-1, the time domain differential equation:
I assumed the time domain function for i(t) is like I+A.exp(st) where A is a constant. I substituted this into the second order differential equation describing the i(t). However, the s values are imaginary and not including real part. It means that the i(t) is not damping. The inductor current should damp to I after long enough time. I cannot see the mistake I made in my approach. Should I assume any other solution for i(t) rather than the one mentioned above?
Would you please give me a hint on that.
Amin Z.
6 comments:
Hi Amin,
I think you have the correct approach. Although, I'm not sure it is expected that the oscillation will stop at some point because the problem statement mentions that all components are considered ideal. That being said, I'm not sure if I've done this problem the right way because my solutions for parts d & e seem questionable.
Keith,
Thanks for the reply.
At the steady state, the capacitance should be open and inductor should be shorted and its current is DC.
I simulated with ideal components and I got the damped oscillation...
The current source looks like R and I think it should somehow damp the oscillation ...not sure ...
Amin,
I believe that Keith is correct. There must be a DC component to the current through the inductor and the voltage across the capacitor, as you said they are a short and open DC respectively. However, if the initial conditions for the inductor and capacitor are not the values of the voltage and current sources, then an un-damped oscillation will occur.
This makes sense because you should only have a second order differential term, a non-differentiated term and a constant term in your 2nd order differential equation. This type of second order equation is an undamped forced differential equation.
In your simulations do your sources or components have default parasitic resistances built in?
well, I checked the simulation and I don't see any parasitic component , I am using LTspice and ideal components, both ideal sources are step functions at time 0....
I have the same differential equation as you said,
Anyone got a simulation with non-damped response ?
If you the current source is replaced with a resistor R you would get a damped response. With the current source, and assuming no losses, the response is not damped.
I get un-damped oscillation with my simulation now. If you don't set the parasitic resistances of the caps and inductors, LTspice would assume some default values. That was the reason I got damped responce ... good to know, never trust sim :)
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