Series RLC Circuit Transient Response

Discussion in 'Homework Help' started by lvjudge1, Jun 4, 2009.

1. lvjudge1 Thread Starter New Member

Jun 3, 2009
9
0
This problem has been haunting me for 2 weeks and I still can't figure it out! Please help before it drives me absolutely insane!

I have an RLC circuit and I need to calculate the voltage across each component for the overdamped case, critically damped case, and underdamped case. For each case, the resistance is changed. The circuit is powered by a square wave of peak voltage 2 V. The square wave is used to model a DC source. I have not been given any initial conditions of the circuit, so I am having trouble figuring out how to apply the current equations to this circuit, since the initial conditions are needed to find the constants A and B, which are utilized in the equations for current in a series RLC circuit.

Overdamped Case:
I(t)=Ae^(s1*t) + Be^(s2*t)
Critically damped Case:
I(t)=(A + Bt)estUnderdamped Case:
I(t)=e^(-alpha*t)*(Csin(wt)+Dcos(wt))

2. lvjudge1 Thread Starter New Member

Jun 3, 2009
9
0
*BUMP* Please help. Just some general pointers would be great.

3. mik3 Senior Member

Feb 4, 2008
4,846
70
At t=0 the current will be zero. This is one initial condition.

Also, the derivative of I at t=0 will be zero since I=0.

4. lvjudge1 Thread Starter New Member

Jun 3, 2009
9
0
Thanks! That was very helpful.
I have continued working on this for the overdamped condition and found that:
Vs(0)=-2 (Everywhere else in the transient response, Vs=2)
i(t)=Ae^(s1t)+Be^(s2t)
i(0)=0
Vr(t)=i*R
Vr(0)=0
Vl(t)=L*(di/dt)=L*(As1e^(s1t)+Bs2e^(s2t))
Vl(0)=0
Vc(0)=1/C *∫i dt =1/C *(A/s1 e^(s1t)+B/s2 e^(s2t))
Vc(0)=-2

Using these equations, I found that A=-B and B=(-2Cs1s2)/(s1-s2) and I then calculated the voltage in each component at various times.

As part of my assignment, I created a simulation of the circuit in MultiSim. For some reason that I cannot figure out, at every point in time, Vr and Vl calculated using the above equations are half the voltage that I found in the simulation! Meanwhile the calulated and simulations value for Vc are off by varying amounts at each time interval! Needless to say, I am very confused. A screen shot of the MultiSim circuit is attached for evalution. It would be very very helpful if someone could tell me whether my math is wrong or my circuit is wrong.

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