AIM OF THIS ASSIGNMENT
You will undertake a number of problem solving techniques designed to develop your understanding of complex waves.
Task 1 - Calculate the properties of complex periodic waves
Task 2 - Analyse complex periodic waves
TASK INTRODUCTION
You are an engineer working for an electronics company. You have been asked to analyse and create complex periodic waveforms.
TASK 1: Calculate the properties of complex periodic waves
Part A: A complex voltage waveform is given by:
v = 90sinωt +30sin(3ωt + Π/2)+10sin(5ωt + Π/2) + 3sin(7ωt - Π/2) + lsin(9ωt - Π/6) Volts
Note: ω = 1500 rads-1
This voltage is applied to a series circuit consisting of the following components:
Determine:
(i) An expression for the current flowing in the circuit.
(ii) The % value of each harmonic
(iii) The total power dissipated by the circuit.
(iv) The overall power factor of the circuit.
TASK 2: Analyse complex periodic waves
This question refers to the waveform shown in Figure 1.
(i) State if the waveform is odd or even.
(ii) By inspection what is the average d.c. level.
(iii) Using Fourier Analysis techniques, determine the Fourier coefficients of the waveform and write an equation for f(t) up to the ninth harmonic term.
Task 3: Verify the spectral analysis in task 2c by re-creating the waveform (by any means), based upon the function f(t) you derived.