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EE 6161
EE 616 Computer Aided Analysis of Electronic Networks
Lecture 2
Instructor: Dr. J. A. Starzyk, ProfessorSchool of EECSOhio UniversityAthens, OH, 45701
EE 6162
Review and Outline
Review of the previous lecture
-- Class organization
-- CAD overview Outline of this lecture
* Review of network scaling
* Review of Thevenin/Norton Analysis
* Formulation of Circuit Equations
-- KCL, KVL, branch equations
-- Sparse Tableau Analysis (STA)
-- Nodal analysis
-- Modified nodal analysis
EE 6166
Voc
Thevenin equivalent circuit
ZTh
+–
Norton equivalent circuit
ZThIsc
Note: attention to the voltage and current direction
Review of the Thevenin/Norton Analysis
EE 6167
1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable).
2.Replace the load by either an open circuit and calculate the voltage E across the terminals A-A’, or a short circuit A-A’ and calculate the current J flowing into the short circuit. E will be the value of the source of the Thevenin equivalent and J that of the Norton equivalent.
3. To obtain the equivalent source resistance, short-circuit all independent voltage sources and open-circuit all independent current sources. Transducers in the network are left unchanged. Apply a unit voltage source (or a unit current source) at the terminals A-A’ and calculate the current I supplied by the voltage source (voltage V
across the current source). The Rs = 1/I (Rs = V).
Review of the Thevenin/Norton Analysis
EE 61612
Determined by the topology of the circuit
Kirchhoff’s Current Law (KCL): The algebraic sum of all the currents leaving any circuit node is zero.
Kirchhoff’s Voltage Law (KVL): Every circuit node has a unique voltage with respect to the reference node. The voltage across a branch eb is equal to the difference between the positive and negative referenced voltages of the nodes on which it is incident
KVL and KCL
EE 61613
Unknowns– B branch currents (i)– N node voltages (e)– B branch voltages (v)
Equations– KCL: N equations– KVL: B equations– Branch equations: B equations
Formulation of circuit equations (cont’d)
EE 61614
Determined by the mathematical model of the electrical behavior of a component– Example: V=R·I
In most of circuit simulators this mathematical model is expressed in terms of ideal elements
Branch equations
EE 61616
55
4
3
2
1
5
4
3
2
1
4
3
2
1
0
0
0
0
00000
01
000
001
00
0000
00001
sii
i
i
i
i
v
v
v
v
v
R
R
GR
Kvv + i = is B equations
Branch equation
EE 61617
1 2 3 j B
12
i
N
branches
nodes (+1, -1, 0)
{Aij = +1 if node i is terminal + of branch j-1 if node i is terminal - of branch j0 if node i is not connected to branch j
PROPERTIES•A is unimodular•2 nonzero entries in each column
Node branch incidence matrix
EE 61618
– Sparse Table Analysis (STA) Brayton, Gustavson, Hachtel
– Modified Nodal Analysis (MNA) McCalla, Nagel, Roher, Ruehli, Ho
Equation Assembly for Linear Circuits
EE 61621
1. Write KCLA·i=0 (N equations, B unknowns)
2. Use branch equations to relate branch currents to branch voltagesi=Yv (B equations, B unknowns)
3. Use KVL to relate branch voltages to node voltagesv=ATe (B equations, N unknowns)
Yne=insN equationsN unknowns
N = # nodesNodal Matrix
Nodal analysis
EE 61623
Spice input format: Rk N+ N- Rkvalue
kk
kk
RR
RR11
11N+ N-
N+
N-
N+
N-
iRk
sNNk
others
sNNk
others
ieeR
i
ieeR
i
1
1KCL at node N+
KCL at node N-
Nodal analysis – Resistor “Stamp”
EE 61624
Spice input format: Gk N+ N- NC+ NC- Gkvalue
kk
kk
GG
GGNC+ NC-
N+
N-
N+
N-
Gkvc
NC+
NC-
+
vc
-
sNCNCkothers
sNCNCkothers
ieeGi
ieeGi KCL at node N+
KCL at node N-
Nodal analysis – VCCS “Stamp”
EE 61626
Rules (page 36):
1. The diagonal entries of Y are positive and
admittances connected to node j
2. The off-diagonal entries of Y are negative and are given by
admittances connected between nodes j and k
3. The jth entry of the right-hand-side vector J is
currents from independent sources entering node j
Nodal analysis- by inspection
jky
jjy
jJ
EE 61633
Modified Nodal Analysis (2)
0
6
0
0
0
001077
000110
1011
00
0111
00
0100111
0000111
5
7
6
4
3
2
1
88
88
433
32
32
1
ES
i
i
i
e
e
e
e
EE
RR
RR
RRR
RG
RG
R
s
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