CSE245: Computer-Aided Circuit Simulation and Verification - PowerPoint PPT Presentation

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CSE245: Computer-Aided Circuit Simulation and Verification

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Electronic Circuit and System Simulation Methods ... by the topology of the circuit. Kirchhoff's Voltage Law (KVL): Every circuit node has a unique voltage with ... – PowerPoint PPT presentation

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Title: CSE245: Computer-Aided Circuit Simulation and Verification


1
CSE245 Computer-Aided Circuit Simulation and
Verification
  • Spring 2006
  • Chung-Kuan Cheng

2
Administration
  • CK Cheng, CSE 2130, tel. 534-6184,
    ckcheng_at_ucsd.edu
  • Lectures 930am 1050am TTH U413A 2
  • Office Hours 1100am 1150am TTH CSE2130
  • Textbooks
  • Electronic Circuit and System Simulation Methods
  • T.L. Pillage, R.A. Rohrer, C. Visweswariah,
    McGraw-Hill
  • Interconnect Analysis and Synthesis
  • CK Cheng, J. Lillis, S. Lin, N. Chang, John
    Wiley Sons
  • TA Vincent Peng (hepeng_at_cs.ucsd.edu), Rui Shi
    (rshi_at_cs.ucsd.edu)

3
  • Outlines
  • Formulation (2-3 lectures)
  • Linear System (3-4 lectures)
  • Matrix Solver (3-4 lectures)
  • Integration (3-4 lectures)
  • Non-linear System (2-3 lectures)
  • Transmission Lines, S Parameters (2-3 lectures)
  • Sensitivity
  • Mechanical, Thermal, Bio Analysis

4
Grading
  • Homeworks and Projects 60
  • Project Presentation 20
  • Final Report 20

5
Motivation
  • Why
  • Whole Circuit Analysis, Interconnect Dominance
  • What
  • Power, Clock, Interconnect Coupling
  • Where
  • Matrix Solvers, Integration Methods
  • RLC Reduction, Transmission Lines, S Parameters
  • Parallel Processing
  • Thermal, Mechanical, Biological Analysis

6
Circuit Simulation
CdX(t)/dtGX(t)BU(t) YDX(t)FU(t)
  • Types of analysis
  • DC Analysis
  • DC Transfer curves
  • Transient Analysis
  • AC Analysis, Noise, Distortions, Sensitivity

7
Program Structure (a closer look)
Input and setup
Models
  • Numerical Techniques
  • Formulation of circuit equations
  • Solution of ordinary differential equations
  • Solution of nonlinear equations
  • Solution of linear equations

Output
8
CSE245 Course Outline
  • Formulation
  • RLC Linear, Nonlinear Components,Transistors,
    Diodes
  • Incident Matrix
  • Nodal Analysis, Modified Nodal Analysis
  • K Matrix
  • Linear System
  • S domain analysis, Impulse Response
  • Taylors expansion
  • Moments, Passivity, Stability, Realizability
  • Symbolic analysis, Y-Delta, BDD analysis
  • Matrix Solver
  • LU, KLU, reordering
  • Mutigrid, PCG, GMRES

9
CSE245 Course Outline (Cont)
  • Integration
  • Forward Euler, Backward Euler, Trapezoidal Rule
  • Explicit and Implicit Method, Prediction and
    Correction
  • Equivalent Circuit
  • Errors Local error, Local Truncation Error,
    Global Error
  • A-Stable
  • Alternating Direction Implicit Method
  • Nonlinear System
  • Newton Raphson, Line Search
  • Transmission Line, S-Parameter
  • FDTD equivalent circuit, convolution
  • Frequency dependent components
  • Sensitivity
  • Mechanical, Thermal, Bio Analysis

10
Lecture 1 Formulation
  • KCL/KVL
  • Sparse Tableau Analysis
  • Nodal Analysis, Modified Nodal Analysis

some slides borrowed from Berkeley EE219 Course
11
Formulation of Circuit Equations
  • Unknowns
  • B branch currents (i)
  • N node voltages (e)
  • B branch voltages (v)
  • Equations
  • NB Conservation Laws
  • B Constitutive Equations

12
Branch Constitutive Equations (BCE)
  • Ideal elements

Element Branch Eqn
Resistor v Ri
Capacitor i Cdv/dt
Inductor v Ldi/dt
Voltage Source v vs, i ?
Current Source i is, v ?
VCVS vs AV vc, i ?
VCCS is GT vc, v ?
CCVS vs RT ic, i ?
CCCS is AI ic, v ?
13
Conservation Laws
  • Determined by the topology of the circuit
  • 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
  • No voltage source loop
  • Kirchhoffs Current Law (KCL) The algebraic sum
    of all the currents flowing out of (or into) any
    circuit node is zero.
  • No Current Source Cut

14
Equation Formulation - KCL
A i 0
N equations
Kirchhoffs Current Law (KCL)
15
Equation Formulation - KVL
R3
1
2
Is5
R1
R4
G2v3
0
v - AT e 0
B equations
Kirchhoffs Voltage Law (KVL)
16
Equation Formulation - BCE
Kvv i is
B equations
17
Equation FormulationNode-Branch Incidence Matrix
branches
n o d e s
(1, -1, 0)
18
Equation Assembly (Stamping Procedures)
  • Different ways of combining Conservation Laws and
    Constitutive Equations
  • Sparse Table Analysis (STA)
  • Modified Nodal Analysis (MNA)

19
Sparse Tableau Analysis (STA)
  1. Write KCL Ai0 (N eqns)
  2. Write KVL v -ATe0 (B eqns)
  3. Write BCE Kii KvvS (B eqns)

N2B eqns N2B unknowns
N nodes B branches
Sparse Tableau
20
Sparse Tableau Analysis (STA)
  • Advantages
  • It can be applied to any circuit
  • Eqns can be assembled directly from input data
  • Coefficient Matrix is very sparse
  • Problem
  • Sophisticated programming techniques and data
  • structures are required for time and memory
  • efficiency

21
Nodal Analysis (NA)
  • 1. Write KCL
  • Ai0 (N eqns, B unknowns)
  • 2. Use BCE 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)

N eqns N unknowns
Yneins
N nodes
Nodal Matrix
22
Nodal Analysis - Example
R3
  1. KCL Ai0
  2. BCE Kvv i is ? i is - Kvv ? A Kvv A
    is
  3. KVL v ATe ? A KvATe A is

Yne ins
23
Nodal Analysis
  • Example shows NA may be derived from STA
  • Better Yn may be obtained by direct inspection
    (stamping procedure)
  • Each element has an associated stamp
  • Yn is the composition of all the elements stamps

24
Nodal Analysis Resistor Stamp
Spice input format Rk N N- Rkvalue
What if a resistor is connected to
ground? . Only contributes to the diagonal
KCL at node N KCL at node N-
25
Nodal Analysis VCCS Stamp
Spice input format Gk N N- NC NC-
Gkvalue
KCL at node N KCL at node N-
26
Nodal Analysis Current source Stamp
Spice input format Ik N N- Ikvalue
N N-
N N-
Ik
27
Nodal Analysis (NA)
  • Advantages
  • Yn is often diagonally dominant and symmetric
  • Eqns can be assembled directly from input data
  • Yn has non-zero diagonal entries
  • Yn is sparse (not as sparse as STA) and smaller
    than STA NxN compared to (N2B)x(N2B)
  • Limitations
  • Conserved quantity must be a function of node
    variable
  • Cannot handle floating voltage sources, VCVS,
    CCCS, CCVS

28
Modified Nodal Analysis (MNA)
How do we deal with independent voltage sources?
Ekl
k l

-
l
k
ikl
  • ikl cannot be explicitly expressed in terms of
    node voltages ? it has to be added as unknown
    (new column)
  • ek and el are not independent variables anymore ?
    a constraint has to be added (new row)

29
MNA Voltage Source Stamp
Spice input format Vk N N- Ekvalue
0 0 1
0 0 -1
1 -1 0
N
30
Modified Nodal Analysis (MNA)
  • How do we deal with independent voltage sources?
  • Augmented nodal matrix

In general
Some branch currents
31
MNA General rules
  • A branch current is always introduced as and
    additional variable for a voltage source or an
    inductor
  • For current sources, resistors, conductors and
    capacitors, the branch current is introduced only
    if
  • Any circuit element depends on that branch
    current
  • That branch current is requested as output

32
MNA CCCS and CCVS Stamp
33
MNA An example
Step 1 Write KCL i1 i2 i3 0 (1) -i3
i4 - i5 - i6 0 (2) i6 i8
0 (3) i7 i8 0 (4)
34
MNA An example
Step 2 Use branch equations to eliminate as many
branch currents as possible 1/R1v1 G2 v3
1/R3v3 0 (1) - 1/R3v3 1/R4v4 - i6
is5 (2) i6 1/R8v8 0 (3) i7
1/R8v8 0 (4) Step 3 Write down unused
branch equations v6 ES6 (b6) v7 E7v3
0 (b7)
35
MNA An example
Step 4 Use KVL to eliminate branch voltages from
previous equations 1/R1e1 G2(e1-e2)
1/R3(e1-e2) 0 (1) - 1/R3(e1-e2) 1/R4e2 -
i6 is5 (2) i6 1/R8(e3-e4) 0 (3) i7
1/R8(e3-e4) 0 (4) (e3-e2)
ES6 (b6) e4 E7(e1-e2) 0 (b7)
36
MNA An example
37
Modified Nodal Analysis (MNA)
  • Advantages
  • MNA can be applied to any circuit
  • Eqns can be assembled directly from input data
  • MNA matrix is close to Yn
  • Limitations
  • Sometimes we have zeros on the main diagonal
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