Chapter 10 Sinusoidal Steady State Analysis

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Chapter 10Sinusoidal Steady State Analysis

• Chapter Objectives
• Apply previously learn circuit techniques to
  sinusoidal steady-state analysis.
• Learn how to apply nodal and mesh analysis in the
  frequency domain.
• Learn how to apply superposition, Thevenins and
  Nortons theorems in the frequency domain.
• Learn how to analyze AC Op Amp circuits.
• Be able to use PSpice to analyze AC circuits.
• Apply what is learnt to capacitance multiplier
  and oscillators.

Huseyin Bilgekul Eeng224 Circuit Theory
II Department of Electrical and Electronic
Engineering Eastern Mediterranean University
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Steps to Analyze AC Circuits

• Transform the circuit to the Phasor Domain.
• Solve the problem using circuit techniques listed
  below
• Nodal Analysis
• Mesh Analysis
• Superposition
• Source transformation
• Thevenin or Norton Equivalents
• Transform the resulting circuit back to time
  domain.

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Steps to Analyze AC Circuits

• Transform the circuit to the phasor or frequency
  domain.
• Solve the problem using circuit techniques (nodal
  analysis, mesh analysis, superposition, etc.).
• Transform the resulting phasor to the time domain.

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Nodal Analysis

• Since KCL is valid for phasors, we can analyze
  AC circuits by NODAL analysis.
• Determine the number of nodes within the network.
• Pick a reference node and label each remaining
  node with a subscripted value of voltage V1, V2
  and so on.
• Apply Kirchhoffs current law at each node
  except the reference. Assume that all unknown
  currents leave the node for each application of
  Kirhhoffs current law.
• Solve the resulting equations for the nodal
  voltages.
• For dependent current sources Treat each
  dependent current source like an independent
  source when Kirchhoffs current law is applied to
  each defined node. However, once the equations
  are established, substitute the equation for the
  controlling quantity to ensure that the unknowns
  are limited solely to the chosen nodal voltages.

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Nodal Analysis

• Since KCL is valid for phasors, we can analyze
  AC circuits by NODAL analysis.

• Practice Problem 10.1 Find v1 and v2 using
  nodal analysis

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Nodal Analysis

• Practice Problem 10.1

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Nodal Analysis

• Practice Problem 10.1

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Mesh Analysis

• Since KVL is valid for phasors, we can analyze
  AC circuits by MESH analysis.

• Practice Problem 10.4 Calculate the current Io

Meshes 2 and 3 form a supermesh as shown in the
circuit below.
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Mesh Analysis

• Practice Problem 10.4 Calculate the current Io

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Mesh Analysis

• Practice Problem 10.4 Calculate the current Io

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Superposition Theorem

• The superposition theorem eliminates the need for
  solving simultaneous linear equations by
  considering the effect on each source
  independently.
• To consider the effects of each source we remove
  the remaining sources by setting the voltage
  sources to zero (short-circuit representation)
  and current sources to zero (open-circuit
  representation).
• The current through, or voltage across, a
  portion of the network produced by each source is
  then added algebraically to find the total
  solution for current or voltage.
• The only variation in applying the superposition
  theorem to AC networks with independent sources
  is that we will be working with impedances and
  phasors instead of just resistors and real
  numbers.
• The superposition theorem is not applicable to
  power effects in AC networks since we are still
  dealing with a nonlinear relationship.
• It can be applied to networks with sources of
  different frequencies only if the total response
  for each frequency is found independently and the
  results are expanded in a nonsinusoidal
  expression .
• One of the most frequent applications of the
  superposition theorem is to electronic systems in
  which the DC and AC analyses are treated
  separately and the total solution is the sum of
  the two.

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Superposition Theorem

• When a circuit has sources operating at
  different frequencies,
• The separate phasor circuit for each frequency
  must be solved independently, and
• The total response is the sum of time-domain
  responses of all the individual phasor circuits.

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a) All sources except DC 5-V set to zero
Superposition Theorem

• Superposition Theorem applies to AC circuits as
  well.
• For sources having different frequencies, the
  total response must be obtained by adding
  individual responses in time domain.

Exp. 10.6 Superposition Technique for sources
having different frequencies
b) All sources except 10cos(10t) set to zero
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c) All sources except 2 sin 5t set to zero
Superposition Theorem
Exp. 10.6 Superposition Technique for sources
having different frequencies
vo v1 v2 v3
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Superposition Theorem
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Superposition Theorem
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Superposition Theorem
P.P.10.6 Superposition Technique for sources
having different Frequencies
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Superposition Theorem
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Superposition Theorem