Week 10 day 1

Lecture

Finding Initial Value Problem of an RLC circuit:

Our Initial Value Problem Solution: After switch is turned on for a long time Capacitor acted as an open circuit and Inductor acted as a short circuit.

Second order RLC formula derivation  in series :

Overdamped RLC Problem:

Parallel RLC problem :

Series RLC Step Response Lab

Pre Lab: Calculating damping ratio (1/𝛼) , natural frequency (𝝎o), damped frequency (𝝎d) and overshoot (

We calculated a damping ratio of 0.002 and a damped frequency 99999 with an overshoot of 4 V.
We measured the value of capacitor and resistor :

Since the value of the resistor is relatively small, our DMM couldn't measure the proper resistance :

View of our Breadboard :

WE used a unit step response of 2 V with zero offset

scope of  Voltage across the capacitor:

Graph of voltage across the capacitor in response with the unit step function we can measure the damping period by dividing 2𝝿 with the distance across peak to peak of the sinusoidal function.

We can measure the overshoot of the graph by finding the distance between the highest peak and the equilibrium line . we obtain an overshoot of 5.75 V and damping frequency of 101341.

Summary 

 To Determine the  total step response of a second order circuit we need to calculate both a steady state response and transient response of the second order circuit. Steady state response of a second order circuit is the value of either voltage or current across a component after a long time (t approaching infinity). To calculate transient response of a second order circuit we turned off independent sources and uses KCL and KVL to calculate our characteristic root. In our lab today we tried to measure the response of voltage across capacitor in response of a unit step function with 2 V amplitude with zero offset( the input voltage is switching between 2 V and -2V). Our calculated damoing frequency is 9999, 1/s while  our measured damping frequency is 101341 1/s  We obtained a 1.34 %  difference in theoretical and our measured value of damping frequency.