- #1

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## Homework Statement

Shown in attachment

## Homework Equations

## The Attempt at a Solution

I'm trying to analyze the circuit in the attached picture. This is a step response with a 3V input or 3u(t).

What I've done so far is:

1. convert all of the components to the s-domain.

R = R, L = sL, C = 1/sC

2. Combine the L and C into one impedence

[sL*(1/sC)]/[sL + (1/sC)] = Z

\[\frac{7.4999999999999985\,{10}^{7}}{0.15\,s+\frac{4.9999999999999994\,{10}^{8}}{s}}\]

3. Using voltage divider formula, solve for the voltage across R

Vout = (R*Vin)/(R+Z)

Vout = [R*(3/s)]/(R+Z)

4. Simplified all calculations

Vout = (3R/s)/R+Z

\[\frac{9000.0}{\left( \frac{7.4999999999999985\,{10}^{7}}{0.15\,s+\frac{4.9999999999999994\,{10}^{8}}{s}}+3000.0\right) \,s}\]

5. Evaluated inverse laplace transform of Vout using Maxima

\[3-\frac{30\,{e}^{-\frac{250000\,t}{3}}\,\mathrm{sinh}\left( \frac{50000\,\sqrt{13}\,t}{3}\right) }{\sqrt{13}}\]

After plugging in certain times and comparing them to actual measured values this circuit provides at the same times, I get step responses with percent differences ranging from 4-30%.

I feel like this is wrong since most formulas I've derived for earlier types of circuits resemble the real life results quite closely.