ESE 271 / Spring 2013 / Lecture 12
Last time: Phasors.
Harmonic Signal in time domain
Corresponding Phasor
Amplitude of sine wave or Signal Magnitude
Initial phase of sine wave or Signal Phase
Phasor contains information about both Signal Magnitude and Signal Phase
Frequency of the signal remains unchanged in linear circuits.
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ESE 271 / Spring 2013 / Lecture 12
Complex Impedance – generalized resistance.
Ohm’s law for Phasors:
Complex impedance:
Series
Parallel
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Complex Impedance of R, C and L.
Resistor:
Capacitor:
Inductor:
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Phasor circuits.
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Phasor diagrams.
Magnitude and phase of complex impedance are functions of frequency:
Hence, the phasor diagram changes with frequency!
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ESE 271 / Spring 2013 / Lecture 12
Phasor diagram of series RLC circuit.
Voltage and current phasors can be treated as vectors on complex plane.
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Series RLC circuit at different frequencies.
Resonance !
At resonant frequency and they can be but
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Series RLC resonance.
resonant frequency 8
ESE 271 / Spring 2013 / Lecture 12
How to use phasor diagrams?
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Thevenin and Norton equivalents for phasors.
Can be represented by equivalent circuit
Active circuit
Thevenin form
Norton form
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ESE 271 / Spring 2013 / Lecture 12
Example 1.
Find current using phasor analysis and by replacing circuit to the left of AB by its Norton equivalent Phasor circuit
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Example 1 ‐ cont.
Phasor circuit
Norton equivalent Phasor circuit
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Example 1 ‐ cont.
Phasor circuit
Norton equivalent Phasor circuit
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Example 1 ‐ cont.
Norton equivalent Phasor circuit
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Example 2.
Find Norton and Thevenin equivalents
Norton
Thevenin
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Example 2 – cont.
Equivalent impedance is inductive
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Nodal analysis of Phasor circuits.
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Example 1.
Phasor circuit
Let’s simplify the circuit a bit
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Example 1 ‐ cont.
Simplified Phasor circuit contains 4 nodes.
Node 2:
Node 3:
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Example 1 ‐ cont.
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Example 1 ‐ cont.
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Example 2.
Phasor circuit
Phasor circuit contains 4 nodes:
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Example 2 ‐ cont.
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Example 2 ‐ cont.
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Example 2 ‐ cont.
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