EE 616 Computer Aided Analysis of Electronic Networks Lecture 2

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EE 616 Computer Aided Analysis of Electronic
NetworksLecture 2

• Instructor Dr. J. A. Starzyk, Professor
• School of EECS
• Ohio University
• Athens, OH, 45701

09/09/2005
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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

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Network scaling
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Network scaling (contd)
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Network scaling (contd)
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Review of the Thevenin/Norton Analysis
ZTh

Voc
ZTh
Isc
Thevenin equivalent circuit
Norton equivalent circuit
Note attention to the voltage and current
direction
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Review of the Thevenin/Norton Analysis

• 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).

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Modeling
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Formulation of circuit equations (contd)
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Ideal two-terminal elements
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Ideal two-terminal elements
Topological equations
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KVL and KCL

• Determined by the topology of the circuit
• Kirchhoffs Current Law (KCL) The algebraic sum
  of all the currents leaving any circuit node is
  zero.
• Kirchhoffs 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

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Formulation of circuit equations (contd)

• Unknowns
• B branch currents (i)
• N node voltages (e)
• B branch voltages (v)
• Equations
• KCL N equations
• KVL B equations
• Branch equations B equations

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Branch equations

• Determined by the mathematical model of the
  electrical behavior of a component
• Example VRI
• In most of circuit simulators this mathematical
  model is expressed in terms of ideal elements

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Matrix form of KVL and KCL
B equations
N equations
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Branch equation
Kvv i is
B equations
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Node branch incidence matrix

• PROPERTIES
• A is unimodular
• 2 nonzero entries in each column

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Equation Assembly for Linear Circuits

• Sparse Table Analysis (STA)
• Brayton, Gustavson, Hachtel
• Modified Nodal Analysis (MNA)
• McCalla, Nagel, Roher, Ruehli, Ho

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Sparse Tableau Analysis (STA)
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Advantages and problems of STA
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Nodal analysis

• 1. Write KCL
• Ai0 (N equations, B unknowns)
• 2. Use branch equations to relate branch currents
  to branch voltages
• if(v) (B unknowns ? B unknowns)
• Use KVL to relate branch voltages to node
  voltages
• vh(e) (B unknowns ? N unknowns)

Yneins
N equations N unknowns
N nodes
Nodal Matrix
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Nodal analysis
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Nodal analysis Resistor Stamp
Spice input format Rk N N- Rkvalue
KCL at node N KCL at node N-
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Nodal analysis VCCS Stamp
Spice input format Gk N N- NC NC-
Gkvalue
vc -
KCL at node N KCL at node N-
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Nodal analysis- independent current sources
stamp
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Nodal analysis- by inspection

• Rules (page 36)
• 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

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Example of nodal analysis by inspection (handout)
Example 1 Page 35 36.
Example 2 inspection for networks with VCTs Page
40 41.
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Nodal analysis (contd)
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Modified Nodal Analysis (MNA)
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Modified Nodal Analysis (2)
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Modified Nodal Analysis (3)
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General rules for MNA
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Example 4.4.1(p.143)
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Advantages and problems of MNA
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Analysis of networks with VVTs Op Amps
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Example 4.5.2 (p.145)
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Example 4.5.5 (p. 148)
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Example 4.5.5 (contd)