For a DA converter, the LRC circuit chosen has inductance L= 10 H , resistance R= 10 ohms and inductance C= 0.2 F . The input digital signal is a power surge (impulse) of magnitude 100 V lasting an instant at t = a . Use your notes to model the second order differential equation in terms of the charge q suited to this application. Simplify the equation with the coefficient of q'' as 1. Use the Laplace transform and calculate the (general) output voltage vo if vo = 1/C q . Your solution will be in terms of a . Use the initial conditions q(0)=0 and q'(0)=0 . Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution: 1. The simplified differential equation in terms of the charge q you will be solving 2. The simplified Laplace transform of this equation where you have made L{q} subject of the equation 3. The partial fractions process if required 4. The completing the square process if required 5. Express the solution q as a piecewise function
For a DA converter, the LRC circuit chosen has inductance L= 10 H , resistance R= 10 ohms and inductance C= 0.2 F . The input digital signal is a power surge (impulse) of magnitude 100 V lasting an instant at t = a . Use your notes to model the second order differential equation in terms of the charge q suited to this application. Simplify the equation with the coefficient of q'' as 1. Use the Laplace transform and calculate the (general) output voltage vo if vo = 1/C q . Your solution will be in terms of a . Use the initial conditions q(0)=0 and q'(0)=0 . Do not use Matlab as its solution will not be identifiable in the solution entry.
You must indicate in your solution:
1. The simplified differential equation in terms of the charge q you will be solving
2. The simplified Laplace transform of this equation where you have made L{q} subject of the equation
3. The partial fractions process if required
4. The completing the square process if required
5. Express the solution q as a piecewise function
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