ENB205 Lecture Electrical and Computer Engineering
Common time-dependent waveforms
Periodic Signals Sinusoidal Signal
The electric power for household and industry is in the form of sinusoidal voltages and currents. All periodic signals
can be represented by means of superposition of various sinusoidal signals of different amplitudes, phases and
1. This provides no information about the
2. It merely tells the DC offset value.
Average value over a period of time
1 Week 4 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering
Root-Mean-Square (RMS) Value
Takes into account the fluctuations of the singal about
its average value.
1. It provides amplitude information
2. It offers computational advantages, especially
when dealing with power.
A useful measure of an AC waveform.
Example find the aerage RMS values of 1 and X2.
The results only tell you the DC offset.
Amplitude information is retained
The RMS value of a sine function is equal t√
of its peak value.
‘Borrow’ ideas of complex numbers to represent phasor diagrams, make computation and circuit analysis easier.
Note: j is used instead of j in electrical engineering.
J is included in the rectangular form to distinguish between the real and imaginary axis. The terms real and imaginary
are related only to mathematical definition. J is defined mathematically as:
Represent a point in a two-dimensional place located with reference to two distinct axes.
2 Week 4 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering
Complex Exponential Form
The complex exponential as a point in the complex plane can be represented by real and imaginary components:
Just the polar form in a different representation
Simple Complex Number Arithmetic
Concept of Phasors In AC circuits
Voltages and currents in AC circuits are in the same frequency, but differ in phase. Simpler analysis is possible if we
only look at phases of voltage and current, and their relationships.
Resistance in AC circuits
No phase difference