PowerPoint PresentationChapter 5 Steady-State Sinusoidal AnalysisSlide 3Slide 4SINUSOIDAL CURRENTS AND VOLTAGESSlide 6Root-Mean-Square ValuesRMS Value of a SinusoidSlide 9Phasor DefinitionAdding Sinusoids Using PhasorsUsing Phasors to Add SinusoidsSlide 13Slide 14Slide 15Phase RelationshipsSlide 17Slide 18Slide 19Slide 20COMPLEX IMPEDANCESSlide 22Slide 23Slide 24Slide 25Kirchhoff’s Laws in Phasor FormCircuit Analysis Using Phasors and ImpedancesSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39AC Power CalculationsSlide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 49THÉVENIN EQUIVALENT CIRCUITSSlide 51Slide 52Slide 53Slide 54Slide 55Slide 56Maximum Average Power TransferSlide 58Slide 59BALANCED THREE-PHASE CIRCUITSSlide 61Phase SequenceSlide 63Wye–Wye ConnectionSlide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Chapter 5 Steady-State Sinusoidal AnalysisELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Chapter 5 Steady-State Sinusoidal Analysis 1. Identify the frequency, angular frequency, peak value, rms value, and phase of a sinusoidal signal.2. Solve steady-state ac circuits using phasors and complex impedances.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.4. Find Thévenin and Norton equivalent circuits. 5. Determine load impedances for maximum power transfer.6. Solve balanced three-phase circuits.3. Compute power for steady-state ac circuits.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.SINUSOIDAL CURRENTS AND VOLTAGESVm is the peak valueω is the angular frequency in radians per secondθ is the phase angleT is the periodELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.T2f2  90cossin  zzFrequency Tf1Angular frequencyELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Root-Mean-Square Values dttvTVT20rms1RVP2rmsavg dttiTIT20rms1RIP2rmsavgELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.RMS Value of a Sinusoid2rmsmVV The rms value for a sinusoid is the peak value divided by the square root of two. This is not true for other periodic waveforms such as square waves or triangular waves.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Phasor Definition   111cos :function Time θtωVtv 111 :Phasor θV VELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Adding Sinusoids Using PhasorsStep 1: Determine the phasor for each term.Step 2: Add the phasors using complex arithmetic.Step 3: Convert the sum to polar form.Step 4: Write the result as a time function.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Using Phasors to Add Sinusoids  45cos201 ttv  60cos102 ttv45201V30102VELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.7.3997.2914.1906.235660.814.1414.143010452021sjjjVVV  7.39cos97.29  ttvsELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Sinusoids can be visualized as the real-axis projection of vectors rotating in the complex plane. The phasor for a sinusoid is a snapshot of the corresponding rotating vector at t = 0.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.Phase RelationshipsTo determine phase relationships from a phasor diagram, consider the phasors to rotate counterclockwise. Then when standing at afixed point, if V1 arrives first followed by V2 after a rotation of θ , we say that V1 leads V2 by θ . Alternatively, we could say that V2 lags V1 by θ . (Usually, we take θ as the smaller angle between the two phasors.)ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.To determine phase relationships between sinusoids from their plots versus time, find the shortest time interval tp between positive peaks of the two waveforms. Then, the phase angle isθ = (tp/T ) × 360°. If the peak of v1(t) occurs first, we say that v1(t) leads v2(t) or that v2(t) lags v1(t).ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.COMPLEX IMPEDANCES LLLj IV 90 LLjZLLLLZ IV ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.CCCZ IV 90111CCjCjZCRRRIV ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, ©2005 Pearson Education, Inc.ELECTRICAL ENGINEERING: