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Phasor Diagrams and Impedance
Lecture 21
Set Phasors on Stun1.Sinusoids-amplitude, frequency and phase (Section 8.1)2.Phasors-amplitude and phase (Section 8.3 [sort of])2a. Complex numbers (Appendix B).
Lecture 21
Set Phasors on Kill3.Complex exponentials-amplitude and phase 4.Relationship between phasors, complex exponentials, and sinusoids5.Phasor relationships for circuit elements (Section 8.4)5a. Arithmetic with complex numbers (Appendix B).
Lecture 21
Set Phasors on Vaporize6.Fundamentals of impedance and admittance (some of Section 8.5)7.Phasor diagrams (some of Section 8.6)
Lecture 21
Phasor DiagramsA 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.
Lecture 21
An Example-1mFVC+-2mA 401kWVR++-V
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An Example (cont.)I = 2mA 40VR = 2V 40 VC = 5.31V -50V = 5.67V -29.37
Lecture 21
Phasor DiagramReal AxisImaginary AxisVRVCV
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ImpedanceAC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohms law:V = I ZZ is called impedance.
Lecture 21
ImpedanceResistor:
The impedance is R
Inductor:
The impedance is jwL
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ImpedanceCapacitor:
The impedance is 1/jwL
Lecture 21
Some Thoughts on ImpedanceImpedance depends on the frequency w.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.
Lecture 21
Impedance Example:Single Loop Circuitw = 377Find VC20kW+-1mF10V 0VC+-
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Impedance ExampleHow do we find VC?First compute impedances for resistor and capacitor:ZR = 20kW= 20kW 0 ZC = 1/j (377 1mF) = 2.65kW -90
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Impedance Example20kW 0+-2.65kW -9010V 0VC+-
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Impedance ExampleNow use the voltage divider to find VC:
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What happens when w changes?w = 10Find VC20kW+-1mF10V 0VC+-
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Low Pass Filter:A Single Node-pair CircuitFind v(t) for w=2p 3000
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Find Impedances1kW-j530kW5mA 0+-V
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Find the Equivalent Impedance
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Parallel Impedances
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Computing V
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Change the FrequencyFind v(t) for w=2p 455000
Lecture 21
Find Impedances
Lecture 21
Find an Equivalent Impedance
Lecture 21
Parallel Impedances
Lecture 21
Computing V
Lecture 21