EGR 277

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Lecture 22 EGR 260 Circuit Analysis
Read Chapter 9 and Appendix B in Electric
Circuits, 8th Edition by Nilsson
Using Phasors to Add Sinusoids Sinusoidal
voltages or currents could be added using various
trigonometric identities however, they are more
easily combined using phasors.
Example If v1 10cos(200t 15?), v2
15cos(200t -30?), and v3 8sin(200t), find v4.
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Lecture 22 EGR 260 Circuit Analysis
sin(wt) or cos(wt)? Since phasor analysis is
used to calculate results that are relative to
the sources, it generally doesnt matter whether
the sinusoidal source is expressed using sin(wt)
or cos(wt). If the sources are expressed using
sin(wt), then the results will also be in terms
of sin(wt) and if the sources are expressed using
cos(wt), then the results will also be in terms
of cos(wt). However, the approach for a given
circuit containing multiple sources must be
consistent either using cos(wt) or sin(wt).

• Review of DC Circuit Analysis Techniques
• Analyzing AC circuits is very similar to
  analyzing DC resistive circuits. Several
  examples are presented below which will also
  serve to review many DC analysis techniques,
  including
• Source transformations
• Mesh equations
• Node equations
• Superposition
• Thevenins and Nortons theorems
• Maximum Power Transfer theorem

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Lecture 22 EGR 260 Circuit Analysis

• Source transformations
• A phasor voltage source with a series impedance
  may be transformed into a phasor current source
  with a parallel impedance as illustrated below.
  The two sources are identical as far as the load
  is concerned.
• Notes
• Not all sources can be transformed. Discuss.
• The two sources are not equivalent internally.
  For example, the voltage across
• Zs is not equivalent to the voltage across
  Zp.
• Dependent sources can be transformed.

Converting a real current source to a real
voltage source
Converting a real voltage source to a real
current source
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Lecture 22 EGR 260 Circuit Analysis
Example Solve for the voltage V using source
transformations.
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Lecture 22 EGR 260 Circuit Analysis
Mesh equations
Example Solve for the voltage V using mesh
equations.
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Lecture 22 EGR 260 Circuit Analysis
Node equations
Example Solve for the current i(t) using node
equations.
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Lecture 22 EGR 260 Circuit Analysis

• Superposition
• Superposition can be used to analyze
  multiple-source AC circuits in a manner very
  similar to analyzing DC circuits. However, there
  are two special cases where it is highly
  recommended that superposition be used
• Circuits that include sources at two or more
  different frequencies
• Circuits that include both DC and AC sources
  (Note you could think of DC
• sources as acting like AC sources with w 0.)

Example 1 (sources with different frequencies)
Solve for the voltage V using superposition.
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Lecture 22 EGR 260 Circuit Analysis
Example 2 (AC and DC sources) Solve for the
voltage V using superposition.