EE-211
ELECTRICAL NETWORK
ANALYSIS
INSTRUCTOR: DR. RABEEA BASIR
DEPT. OF ELECTRICAL ENGINEERING
COLLEGE OF ELECTRICAL AND MECHANICAL ENGINEERING
NUST
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AC RESPONSE
• Goal is to gain the knowledge about the AC response of basic circuit elements and their
combinations.
• Time domain analysis becomes prohibitive as complexity increases.
• Frequency domain analysis changes the differential equations into simpler algebraic
equations.
• In frequency domain analysis a sinusoid is represented by a vector like quantity known as
a phasor
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SINUSOIDS
𝝎 has the units of rad/sec
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EE-211 ELECTRICAL NETWORK ANALYSIS
GENERAL EXPRESSION FOR AC SIGNALS
• An AC signal has the general expression
• Where
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EE-211 ELECTRICAL NETWORK ANALYSIS
EFFECT OF THE PHASE ANGLE
•
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EE-211 ELECTRICAL NETWORK ANALYSIS
TIME SHIFT IN TERMS OF PHASE ANGLE
• Given a shift 𝜽 along the 𝝎𝒕 axis, the corresponding shift along the t axis will be
•
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASE DIFFERENCE
• Given
• The phase difference between the two signals is defined as
• It’s the phase difference of y(t) relative to x(t).
• Phase is a relative concept like the voltage. One signal in the circuit is assigned an
arbitrary phase of zero and all other signals are assigned phases relative to the phase
of the relative signal.
• Phase is constrained to the range
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EE-211 ELECTRICAL NETWORK ANALYSIS
IMPORTANT CASES OF PHASE
• Some important cases are
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EE-211 ELECTRICAL NETWORK ANALYSIS
EXERCISES
• Calculate the phase angle between v1 = −10 cos(ωt + 50◦) and v2 =12 sin(ωt − 10◦).
State which sinusoid is leading.
• Find the phase angle between i1 = −4 sin(377t + 25◦) and i2 = 5 cos(377t − 40◦). Does i1
lead or lag i2?
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Sinusoids are easily expressed in terms of phasors,
which are more convenient
• A phasor is a complex number that represents the
amplitude and phase of a sinusoid.
• Phasors provide a simple means of analyzing linear
circuits excited by sinusoidal sources
• A complex number z can be written in rectangular
form as z = x + jy
• The complex number z can also be written in polar or
exponential form as
• where r is the magnitude of z, and 𝚽 is the phase of
z
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Z can be represented in three ways
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Addition and subtraction of complex numbers are better performed in rectangular
form; multiplication and division are better done in polar form.
• Given the complex numbers
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Complex Conjugate
• The idea of phasor representation is based on Euler’s identity
• A given sinusoid v(t) can be expressed as
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Time domain to the phasor domain transformation
• Sinusoid phasor representation
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EE-211 ELECTRICAL NETWORK ANALYSIS
PHASORS
• Differentiating a sinusoid is equivalent to multiplying its corresponding phasor by jω.
• Integrating a sinusoid is equivalent to dividing its corresponding phasor by jω.
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EE-211 ELECTRICAL NETWORK ANALYSIS
PRACTICE
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