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Lecture 211 Phasor Diagrams and Impedance

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Lecture 212 Set Phasors on Stun 1.Sinusoids-amplitude, frequency and phase (Section 8.1) 2.Phasors-amplitude and phase (Section 8.3 [sort of]) 2a. Complex numbers (Appendix B).

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Lecture 213 Set Phasors on Kill 3.Complex exponentials-amplitude and phase 4.Relationship between phasors, complex exponentials, and sinusoids 5.Phasor relationships for circuit elements (Section 8.4) 5a. Arithmetic with complex numbers (Appendix B).

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Lecture 214 Set Phasors on Vaporize 6.Fundamentals of impedance and admittance (some of Section 8.5) 7.Phasor diagrams (some of Section 8.6)

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Lecture 215 Phasor Diagrams A phasor diagram is just a graph of several phasors on the complex plane (using real and imaginary axes). A phasor diagram helps to visualize the relationships between currents and voltages.

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Lecture 216 An Example - 1F1F VCVC + - 2mA 40 1k VRVR V

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Lecture 217 An Example (cont.) I = 2mA 40 V R = 2V 40 V C = 5.31V -50 V = 5.67V

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Lecture 218 Phasor Diagram Real Axis Imaginary Axis VRVR VCVC V

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Lecture 219 Impedance AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V = I Z Z is called impedance.

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Lecture 2110 Impedance Resistor: –The impedance is R Inductor: –The impedance is j L

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Lecture 2111 Impedance Capacitor: –The impedance is 1/j L

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Lecture 2112 Some Thoughts on Impedance Impedance depends on the frequency . Impedance is (often) a complex number. Impedance is not a phasor (why?). Impedance allows us to use the same solution techniques for AC steady state as we use for DC steady state.

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Lecture 2113 Impedance Example: Single Loop Circuit 20k + - 1F1F10V 0 VCVC + - = 377 Find V C

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Lecture 2114 Impedance Example How do we find V C ? First compute impedances for resistor and capacitor: Z R = 20k = 20k 0 Z C = 1/j (377 1 F) = 2.65k -90

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Lecture 2115 Impedance Example 20k 0 k -90 10V 0 VCVC + -

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Lecture 2116 Impedance Example Now use the voltage divider to find V C :

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Lecture 2117 What happens when changes? 20k + - 1F1F10V 0 VCVC + - = 10 Find V C

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Lecture 2118 Low Pass Filter: A Single Node-pair Circuit Find v(t) for =2 k 0.1 F 5mA 0 + - V

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Lecture 2119 Find Impedances 1k -j530k 5mA 0 + - V

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Lecture 2120 Find the Equivalent Impedance 5mA 0 + - VZ eq

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Lecture 2121 Parallel Impedances

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Lecture 2122 Computing V

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Lecture 2123 Change the Frequency Find v(t) for =2 k 0.1 F 5mA 0 + - V

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Lecture 2124 Find Impedances 1k -j3.5 5mA 0 + - V

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Lecture 2125 Find an Equivalent Impedance 5mA 0 + - VZ eq

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Lecture 2126 Parallel Impedances

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Lecture 2127 Computing V

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