TASK INTRODUCTION
You are an electronics engineer working as a consultant for a company. You have been asked to analyse a circuit mathematically to determine the voltages and frequencies using Laplace transforms.
TASK 1: (Use Laplace transforms for the transient analysis of networks, and calculate circuit responses to a step input in practical situations)
Complete the following tasks associated with the above circuit.
Using Laplace transforms, derive expressions in the time domain for the following:
(a) The current in the circuit
(b) The voltage across the resistor
(c) The voltage across the inductor.
(d) The voltage across the capacitor.
From the above circuit calculate the following:
(e) The undamped natural frequency (f0)
(f) The Q factor
(9) The damped natural frequency (In)
Opportunity for Merit
(i) Using simulation software, produce graphical data of the transient response of the circuit. From the graph as estimate the value of Q and fn.
(ii) Explain the meaning of the terms over-damped, under-damped, and critically damped.
(iii) Determine the value of R that will result in the above circuit being critically damped. Use the simulation software to prove that the result is as expected.
Opportunity for Distinction
Verify the spectral analysis in task 2c by re-creating the waveform (by any means), based upon the function f(t) you derived.