Chapter 13 – Overview
Chapter 13 – Overview ............................................................................... 1
13.1 Introduction.................................................................................... 2
2
Durham
Electric Circuits Concepts
13.1 Overview
The table is an overview of techniques to resolve network problems.
Name
Form 1
Form 2
Laplace
s = σ + jω
−j=
1
j
ψ
= j
Durham
ratio
frequency
ψ=
s
ω
Durham
pq
electromagnetic energy W =
t
Law
σ =0
W=
pq bYS dT sY
t sS sT sY
3 Measures
V , I, t
Voltage, Current, Time
Apparent power
S = VI *
Product
Ohm’s Law
Z=
Time delay
V
I
Ratio
θ = ∠V − ∠I = ∠Z = ∠S
td = tV − t I
= cos −1 pf = 2π ft
1
sC
Z ( jω ) = R + jω L +
1
jωC
3 Elements
Z ( s ) = R + sL +
Complex impedance
Z ( s) = R +ψ ( X L − X C )
Z ( jω ) = R + j ( X L − X C )
Complex power
S ( s ) = P +ψ (QL − QC )
S ( jω ) = P + j (QL − QC )
Reactance
X L = ωL
XC =
Kirchhoff Laws
KVL
1
ωC
KCL
One-Port
ΣV = 0 around mesh or ΣI = 0 at node or point
loop
Substitute Ohm V = IZ for Substitute Ohm I = V Z for
V
I
Solve for unknown I
Solve for unknown V
Series
Parallel
Single-phase
Same I, V divides across Z
Independent sources
ZTotal = ΣZ
Mesh / nodal analysis
VZ = VSource
Z Adjacent
ΣZ
Same V, I divides through Z
1
1
=Σ
Z Total
Z
Z
I Z = I In Opposite
ΣZ
Chapter 13
Overview
3-phase
is
V
ZP = P
IP
an
VLine − Line = VPhase
Dependent sources
Find ZEQ at terminals
Replace source by
internal Z
Combine Z into
equivalent
1
VLine − Line = 3VPhase
S3 Ph = 3VL I L = 3VP I P
S3 Ph = 3VL I L = 3VP I P
Delta-Wye
Zb Z c
Z a + Zb + Z c
Thevenin
Find VTH at terminals
Open circuit terminals.
Zc
a
Z1
b
Z2
Z3
Zb
2
Za
4
c
Wye-Delta
Za =
3
n
I Line = I Phase
Z1 =
Equivalent source
V
ZP = P
IP
I Line = 3I Phase
Delta-Wye
conversion
Z EQ =
Wye or Tee (Y – T)
Delta or Pi (Δ – Π)
Two-Port
A phase
impedance
3
Z1Z 2 + Z 2 Z 3 + Z 3 Z1
Z1
Norton
Z
VTH
Vs
Find ISC at terminals
Short circuit terminals.
Calculate V across Z at Calculate I that bypasses Z at
terminals
terminals
VTH
I SC
Dr. Marcus O. Durham, PhD, PE
www.DrMod.com
March 13, 2007
$
universal
engineering
symbol
$, t, quality
engineering trade-offs
PAGE 3