ELECTRIC CIRCUITS ECSE2010 Spring 2003 Review for Final Exam

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ELECTRIC CIRCUITSECSE-2010Spring 2003Review
for Final Exam

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REVIEW FOR FINAL EXAM

• 25 Unit IV 75 Comprehensive
• 8-10 Problems
• 3 Hours for Final
• 2 Crib Sheets for Final
• Laplace Tables will be Provided

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• Unit I Circuit Analysis Techniques
• Class 11 Review for Exam I
• Variables, Sources and Conventions
• Ohms Law
• Kirchhoffs Current Law Kirchhoffs Voltage Law
• Series/Parallel Resistors Voltage/Current
  Dividers
• Controlled Sources
• Equivalent Resistance
• Node Equations Mesh Equations
• Source Conversions
• Superposition
• Thevenin and Norton Equivalent Circuits
• Maximum Power Transfer

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• Node Equations
• Technique to Solve Any Linear Circuit
• Label Unknown Node Voltages, v1, v2, v3, etc.
• Unknown Nodes Nodes - Voltage Sources 1
  (Reference)
• Write a KCL at Each Unknown Node
• Sum of Currents OUT of Node 0
• Relate Currents to Node Voltages
• Will Always Get the Same Number of Equations as
  Unknowns
• Solve Linear Equations using any Technique that
  Works for You

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• Mesh Equations
• Another Technique to Solve Any Linear Circuit
• Define All Mesh Currents
• Unknown Mesh Currents (i1, i2, i3, etc.) and
  Current Sources (Independent and Controlled)
• Write KVL around Each Unknown Mesh
• Sum of Voltages around Unknown Mesh 0
• Relate Voltages to Mesh Currents using Ohms Law
• Always get same number of equations as unknowns
• Solve linear equations for i1, i2, i3, etc.

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• Add Controlled Sources
• Things get harder!
• Must find a Constraint Equation
• Relate Controlling Voltage or Current to Unknown
  Node Voltages or Unknown Mesh Currents
• Must Do By Inspection THINK!
• Find Constraint Equation directly from circuit
• Try Ohms Law, KCL, KVL, etc.
• Its there you just have to find it!

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• Define v, i using Active Convention

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• Superposition
• Total Output Sum of all Outputs due to each
  independent source with all others dead
• Simply Add them
• Works only for Linear Ckts
• Leave Controlled Sources Alone!!
• Find Outputs due to Independent Sources only
• Do NOT set Controlled Sources 0

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• Define v, i using Active Convention

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• Define v, i using Active Convention

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• Unit II Op Amps, Circuits with C L, and
  Laplace Transforms
• Class 19 Review for Exam II
• Op Amps
• Energy Storage Elements (C L)
• 1st Order Circuits with Switched DC Inputs
• Laplace Transforms finding F(s) from f(t)
• Partial Fraction Expansion finding f(t) from
  F(s)
• s-domain Circuit Analysis and H(s)
• Zero State Response

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Output
Input
Circuit
y(t) yN yF
x(t) Switched DC
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• 1st Order Circuits

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• 1ST Order Switched DC Circuit
• yo y(t to)
• yss y(t )
• to Switching Time
• Time Constant Req C for Ckt with 1 C
• L / Req for Ckt with 1 L
• Req Equivalent Resistance Seen at Terminals of
  C or L

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• Simply Write Down Output
• y(t) yss (yo - yss) e - (t - to)/
• Find yss, yo , directly from circuit
• Follow 4 Step Procedure
• Draw Ckt at t t0- Find vC(t0-) vC(t0)
  iL(t0-) iL(t0)
• Draw Ckt at t t0 Find yo
• Draw Ckt at t Find yss
• DC Steady State, C gt Open Ckt L gt Short Ckt
• Draw Dead Network Find Req gt Calculate

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• Laplace Transforms

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• Partial Fraction Expansion

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• Simple, Real Poles

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• Initial and Final Value Theorems

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• Zero State Response y(t) when the
  Circuit/System has No Initial Stored Energy (Ckt
  starts from a Zero State)
• gt x(t) 0 for all t lt 0
• gt All Initial Conditions 0
• y(t) yN(t) yF(t) Complete Response
• Y(s) H(s)X(s)
• H(s)Network Function

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• Zero-State Response

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• Unit III AC Steady State and s-Domain Circuit
  Analysis
• Class 33 Review for Exam III
• Second Order Natural Modes
• Sinusoids and Phasors Complex Math
• AC Impedance AC Circuit Analysis
• AC Power Power Systems pf Correction
• Ideal Transformers Mutual Inductance
• 3 Phase AC Circuits
• Network Functions, H(s)
• Poles and Zeros
• Stability

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• AC Steady State
• Input x(t)
• Steady State Output yF(t) yss(t)
• yss(t)
• Phasors Express x(t) as Phasor X

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A
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• Complex Math
• Addition/Subtraction Rectangular Form
• Multiplication/Division Polar Form
• Rationalization No Complex s in Denominator
• Complex Conjugates
• Ks Laws for Phasors
• Express all v(t)s and i(t)s as Phasors
• KCL, KVL Hold for Phasors
• I1 I2 I, V1 V2 V etc
• Complex Addition

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• AC Impedance
• In General, V Z I in AC Steady State
• Z AC Steady State Impedance
• Ohms Law for AC Steady State

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• Define v, i using Active Convention

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• AC Node Equations
• Label Unknown Phasor Node Voltages, V1, V2, etc.
• Unknown Nodes Nodes - Voltage Sources 1
  (Reference)
• Write a KCL at Each Unknown Node
• Sum of Phasor Currents OUT of Node 0
• Relate Phasor Currents to Phasor Node Voltages
  using Ohms Law for AC Steady State
• Solve Complex Linear Equations for V1, V2, etc.

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• AC Mesh Equations
• Define All Phasor Mesh Currents
• Unknown Mesh Currents (I1, I2, I3, etc.) and
  Current Sources (Independent and Controlled)
• Write KVL around Each Unknown Mesh
• Sum of Phasor Voltages around Unknown Mesh 0
• Relate Phasor Voltages to Phasor Mesh Currents
  using Ohms Law for AC Steady State
• Solve Complex Linear Equations for I1, I2, I3,
  etc.

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• Phasor Diagrams
• Plot of Phasors in Complex Space
• Can Use to Solve/Analyze AC Ckts
• Solve Graphically
• Often Easier than Complex Math

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Imaginary
V
Real
I
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Imaginary
S
Q
Real
P
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• Power Systems
• STotal S1 S2 S3 .
• STotal (P1P2..)j(Q1Q2..) Add Ps Qs
• Use Power Triangle
• Difficult definitions Easy calculations
• Power Factor Correction
• Add C or L to make pftotal 1 Qtotal 0
• Makes circuit most efficient
• Note that Xtotal 0 if Qtotal 0

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• Impedance Matching
• For PMAX to ZL gt Want ZL Zs
• If ZL is Fixed Use Transformer
• Make ZL/ N2 Zs
• Transformer provides another knob

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i1
i2
v1 -
v2 -
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i1
i2
v1 -
v2 -
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Vc
Vca
Vbc
Va
Vab
Vb
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• Phase Voltages in Phasor Form
• Scale amplitudes to RMS values
• Line Voltages in Phasor Form

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• Can Convert any Delta Load to an Equivalent Wye
  Load
• ZYeq ZDelta / 3
• Easier to analyze circuit using Wye loads
• Equivalent 1 Phase Model for Wye
• Phase Voltage across ZY
• Line Current through ZY
• Ia Va / ZY
• Write down all other Is, Vs by Inspection

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• 3 Phase Power
• Phase Voltage and Line Current at Load

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• s-Domain Circuit Analysis
• Transform Circuit from Time Domain to s-Domain
• Replace i(t), v(t) gt I(s), V(s)
• Replace R, L, C gt s-domain Models
• Use V (s) Z (s) I (s)
• Use All Techniques from Unit I

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• Factor H(s)

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• Unit IV Frequency Response, Resonant Circuits,
  Complete Response, Filters
• Classes 32-40
• s-plane Vectors
• 1st Order Filters
• Bode Plots
• Lissajous Figures
• Series and Parallel Resonance
• Complete Response with Laplace
• Higher Order Filters

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• Frequency Response

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• Method of s-plane Vectors

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• Choose Convenient Values

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• Filters

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• Bode Plots

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• Procedure

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• Known Functions

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• 1st Order Corrections
• Multiply by N for Nth Order

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• Notes

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I
V
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• Series/Parallel Resonance

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• When There Are Initial Conditions

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• Bandpass and Notch Filters require the order of
  the circuit n gt 2
• Higher n gt Better Performance
• Looked briefly look at 2nd Order Bandpass and
  Notch Filters