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E E 2415 Lecture 8 - Introduction to Phasors
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The Sinusoidal Function
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Euler Functions
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Sinusoid to Phasor Exponential form: Separate exponents: Phasor transform: Also:
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Simple Harmonic Motion - 0 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 0 degrees
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Simple Harmonic Motion - 30 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 30 degrees
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Simple Harmonic Motion - 60 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 60 degrees
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Simple Harmonic Motion - 90 Phasor rotates CCW about origin of complex plane Blue dot shows projection on real axis plotted vs time Phasor shown at 90 degrees
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Simple Harmonic Motion - 120 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 120 degrees
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Simple Harmonic Motion - 150 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 150 degrees
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Simple Harmonic Motion - 180 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 180 degrees
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Simple Harmonic Motion - 210 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 210 degrees
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Simple Harmonic Motion - 240 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 240 degrees
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Simple Harmonic Motion - 270 Phasor rotates CCW about origin of complex plane Blue dot shows projection on real axis plotted vs time Phasor shown at 270 degrees
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Simple Harmonic Motion - 300 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 300 degrees
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Simple Harmonic Motion - 330 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 330 degrees
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Simple Harmonic Motion - 360 Phasor rotates CCW about origin of complex plane Blue line shows projection on real axis plotted vs time Phasor shown at 360 degrees
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Impedance of an Inductor
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Phasor Diagram of Inductor V-I Relationship Voltage leads current by 90°
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Impedance of a Capacitor
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Phasor Diagram of Capacitor V-I Relationship Current leads Voltage by 90°
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Phasor R-L Example (1/3)
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Phasor R-L Example (2/3)
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KVL now in complex plane. Phasor R-L Example (3/3)
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Numerical Phasor R-L Example (1/2)
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