Transcript Lecture Notes - Nodal and Mesh Analysis of Phasor Ciruits

Chapter 10
Sinusoidal 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, Thevenin’s and Norton’s 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
Eeng 224
‹#›
Steps to Analyze AC Circuits

Transform the circuit to the Phasor Domain.

Solve the problem using circuit techniques listed below
1)
2)
3)
4)
5)

Nodal Analysis
Mesh Analysis
Superposition
Source transformation
Thevenin or Norton Equivalents
Transform the resulting circuit back to time domain.
Eeng 224
‹#›
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.
Time to Freq
Solve
Variables in Freq
Freq to Time
Eeng 224
‹#›
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 Kirchhoff’s current law at each node except the reference.
Assume that all unknown currents leave the node for each
application of Kirhhoff’s current law.
Solve the resulting equations for the nodal voltages.
For dependent current sources: Treat each dependent current
source like an independent source when Kirchhoff’s 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.
Eeng 224
‹#›
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
Eeng 224
‹#›
Nodal Analysis
 Practice Problem 10.1
Eeng 224
‹#›
Nodal Analysis
 Practice Problem 10.1
Eeng 224
‹#›
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.
Eeng 224
‹#›
Mesh Analysis
 Practice Problem 10.4: Calculate the current Io
Eeng 224
‹#›
Mesh Analysis
 Practice Problem 10.4: Calculate the current Io
Eeng 224
‹#›
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.
Eeng 224
‹#›
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.
Eeng 224
‹#›
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
a) All sources except DC 5-V set to zero
b) All sources except 10cos(10t) set to zero
Eeng 224
‹#›
Superposition Theorem
Exp. 10.6 Superposition Technique for sources having different frequencies
c) All sources except 2 sin 5t set to zero
vo= v1+ v2+ v3
Eeng 224
‹#›
Superposition Theorem
Eeng 224
‹#›
Superposition Theorem
Eeng 224
‹#›
Superposition Theorem
P.P.10.6 Superposition Technique for sources having different Frequencies
Eeng 224
‹#›
Superposition Theorem
Eeng 224
‹#›
Superposition Theorem
Eeng 224
‹#›