RC circuit current, large signal

It's only a sine burst if you include the case where the voltage source is turned on, ie it's not steady state, continuous. Usually when dealing with a sine wave source it's the steady state that we assume we're talking about.

That's the dilemma of a differential equation solution: the sine has to be turned on.

You see the same thing in Spice.

Basically the problem is that the DEQs as-written don't describe anything physical.

Either the system is steady state and you have to _assume_ a form of the solution that describes a steady-state system. The solution as given isn't that.

Or the system isn't steady-state and there must also be a step function at 0 to "switch on" the sine, in addition to the driving sine that runs for all time. The equations as written don't describe that situation, either.

Basically the problem is that the DEQs as-written don't describe anything physical.

Either the system is steady state and you have to _assume_ a form of the solution that describes a steady-state system. The solution as given isn't that.

Or the system isn't steady-state and there must also be a step function at 0 to "switch on" the sine, in addition to the driving sine that runs for all time. The equations as written don't describe that situation, either.

Am 05.09.2019 um 22:18 schrieb bitrex:

Hello,

Here is the solution from a script found in the Internet.

T = R*C w = 2*pi*f A = 1/(1+(w*T)**2) B = w*T/(1+(w*T)**2)

ue(t) = sin(w*t)

uc(t) = B*exp(-t/T) +A*sin(w*t) -B*cos(w*t)

-------------------------------------------

Because B/T is the same as A*w,

ic(t) = w*C*(-A*exp(-t/T) +A*cos(w*t) +B*sin(w*t))

--------------------------------------------------

I have checked the result with LTspice.

Helmut

The issue is that I got my EE degree before Spice existed. I had to write my own simulation code. Sometimes I still do.