Step response of underdamped RLC series circuit

[cupoftea]

Hi,

We wish to solve a circuit which is a step response of a series RLC circuit.
We wish to find the peak of the capacitor voltage following the step.
Its underdamped. Initial conditions are all zero apart from the supply = 27V

So We are solving the Fig 1 on page 1 of this....

https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/a929d33896839a7bf1ca2631cd87e711_16_transint_rlc2.pdf

We wish to find vc(t). As such we will find the peak of the vc.

So we have the underdamped case since VS=27, L=470nH, C=47uF, R = 0.034
So we need to find A1 and A2 in equation 1.15 of page 2.

At t=0, all voltages and currents are zero, so A1 + A2 = -27 ___[A]

Then we have to do dvc(t)/dt at t=0.

However, this ends up with 0 = -a(A1+A2) -jwd(A1-A2)
where wd = SQRT(wo^2-a^2)

..but that could only be true if A1 + A2 = 0, and we already found out as above in [A], that A1+A2 = -27

Do you know where we have veered off?

 

[D.A.(Tony)Stewart]

You also forgot to include Cap ESR and a soft start for this >1kW power surge at 10 us /div.

 

[cupoftea]

Thanks, 12:41 of this has the correct solution...

..anyway, thanks , yes , there is a huge surge into the 47uF aluminium poly cap at the switch on.....as shown.
And the datasheet doesnt say how many of these current surges can be withstood.

A wet electrolytic cap has more inrush surge withstand than a Al Poly...but of course, a wet el cap can dry out.