ENB205 Electrical and Computer Engineering Week 4.dotx.docx

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Negareh Ghasemi

ENB205 Lecture Electrical and Computer Engineering AC Sources Common time-dependent waveforms Periodic Signals Sinusoidal Signal Why Sinusoidal? 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 frequencies. Average Value 1. This provides no information about the amplitude. 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. Phasors ‘Borrow’ ideas of complex numbers to represent phasor diagrams, make computation and circuit analysis easier. Complex Numbers 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
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