* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download ppt - Weber State University
War of the currents wikipedia , lookup
Three-phase electric power wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Opto-isolator wikipedia , lookup
Electric machine wikipedia , lookup
Mains electricity wikipedia , lookup
Electronic engineering wikipedia , lookup
History of electric power transmission wikipedia , lookup
Music technology wikipedia , lookup
Electrification wikipedia , lookup
Plug-in electric vehicles in Germany wikipedia , lookup
Alternating current wikipedia , lookup
Semiconductor device wikipedia , lookup
History of the electric vehicle wikipedia , lookup
Electric vehicle wikipedia , lookup
Transmission tower wikipedia , lookup
Integrated circuit wikipedia , lookup
0 EE 1270: Introduction to Electric Circuits Lecture 18: Phasors Chapter 9: Sinusoidal SteadyState Analysis Section 9.3, 9.4 EE 1270 Introduction to Electric Circuits Suketu Naik Representation of Complex Numbers 1 Rectangular Form (real and imaginary) a jb; j 1 Imaginary Polar Form (magnitude and phase) c Real Exponential Form ce j c cos j sin c a b a c cos ; b c sin 1 b tan a EE 1270 Introduction to Electric Circuits 2 2 Suketu Naik 2 Phasors v Vm cost Re{Vm e j (t ) j jt } Re{Vm e e } V Vm e j Vm Phasor Transform or Phasor Representation 1) A phasor is a complex number that represents the amplitude and phase of a sinusoid 2) Phasors provide a simple means of analyzing linear circuits excited by sinusoidal sources EE 1270 Introduction to Electric Circuits Suketu Naik Phasors: Addition, Subtraction, Multiplication, and Division 3 Amplitude and Phase Complex Conjugate Addition Subtraction Multiplication Division EE 1270 Introduction to Electric Circuits Suketu Naik Phasors 4 v Re{Vm e j e jt } EE 1270 Introduction to Electric Circuits Suketu Naik Example 9.5: Hard Way 5 Problem Solution EE 1270 Introduction to Electric Circuits Suketu Naik Example 9.5: Easy Way 6 Problem Solution Use Phasors EE 1270 Introduction to Electric Circuits Suketu Naik AP 9.1, AP 9.2 7 1090 V 518 (e)(5545)(0.1 45)mA (d ) EE 1270 Introduction to Electric Circuits Suketu Naik Phasor Notation for Resistor EE 1270 Introduction to Electric Circuits 8 Suketu Naik Phasor Notation for Inductor 9 Verify in SPICE 1) Transient 2) AC Sweep Voltage leads Current by 90° in an Inductor EE 1270 Introduction to Electric Circuits Suketu Naik Phasor Notation for Capacitor 10 i CVm sin( t V ) I CVm e j (V 90) CVm e jV e j 90 jCVm e jV jCV Verify in SPICE 1) Transient 2) AC Sweep Current leads Voltage by 90° in a Capacitor EE 1270 Introduction to Electric Circuits Suketu Naik Impedance and Reactance EE 1270 Introduction to Electric Circuits 11 Suketu Naik AP 9.3, AP 9.4 EE 1270 Introduction to Electric Circuits 12 Suketu Naik