Chapter 5 - 11/29/2010 1 Electrical Engineering Principles...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 11/29/2010 1 Electrical Engineering Principles & Applications 5- Steady State Steady State Sinusoidal Sinusoidal Analysis Analysis Slide 1 Outline 1. Identify the frequency, angular frequency, peak value RMS value and phase of a peak value, RMS value, and phase of a sinusoidal signal 2. Solve steady-state AC circuits using phasors and complex impedances Slide 2 11/29/2010 2 Importance of Sinusoidal Sources • Appear in many practical applications – Electric power is distributed by sinusoidal currents and voltages – Sinusoidal signals are used widely in radio communications • Any signal can be represented by a sum of sinusoidal components (Fourier Analysis) • Sinusoids have good mathematical properties – Derivative is a sinusoid – Integral is a sinusoid Slide 3 Sinusoidal steady-state • Whenever the forced input to the circuit is sinusoidal the response will be sinusoidal • If the input persists, the response will persist and we call it steady-state response Sinusoidal Currents or Voltages Slide 4 11/29/2010 3 Sinusoidal Currents and Voltages V m is the peak value ) cos( ) ( t V t v m ω is the angular frequency in radians per second θ is the phase angle T is the period , where is the frequency T f 1 Slide 5 T 2 f 2 90 cos sin z z T is the angular frequency , where: Root-Mean-Square (RMS) Values of a Sinusoid ) ( 2 2 i R V R I P eff eff For DC circuit the power is For AC circuit the power is T T T T ii dt v RT dt i T R Rdt i T P 2 2 2 1 ) ( 1 1 Slide 6 T rms eff rms eff dt v T V V I dt i T I 2 2 1 & 1 Equate (i) and (ii) 11/29/2010 4 Root-Mean-Square (RMS) Values of a Sinusoid T dt t v T V 2 rms 1 T dt t i T I 2 rms 1 R V P 2 rms avg R I P 2 rms avg The RMS value for a sinusoid is the peak value divided by the square root of 2. Slide 7 2 rms m V V This is NOT true This is NOT true for other periodic waveforms such as square waves or triangular waves Voltage applied to a 50- Ω resistance 2 V Voltage Applied to Resistors Voltage Voltage W 100 50 ) 2 / 100 ( 2 R V P rms avg 2 Power Power Slide 8 W ) 100 ( cos 200 ) ( ) ( 2 2 t R t v t p Power Power 11/29/2010 5 Phasor Definition Phasors Phasors are complex numbers that can be used to represent sinusoidal signals The magnitude magnitude of the phasor = Peak Peak value 2 1 1 sin t I t i and 1 1 1 cos t V t v Consider The magnitude magnitude of the phasor = Peak Peak value Angle Angle of the phasor = phase phase of the sinusoid (written as a cosine ) 90 is phaso The Slide 9 1 1 1 V V is phasor The 90 2 1 1 I I is phasor The The steady state analysis of sinusoidal signals can be carried out easily if signals are represented as phasors (vectors) Real and Complex Signals jy x Z Real part...
View Full Document

Page1 / 30

Chapter 5 - 11/29/2010 1 Electrical Engineering Principles...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online