Computer-Aided Circuit - Circuit Simulation - Lecture Slides, Slides of Computer Science

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CSE245: Computer-Aided Circuit

Simulation and Verification

Lecture 1: Introduction and Formulation

Motivation: Analysis

• Energy: Fission, Fusion, Fossil Energy,

Efficiency Optimization

• Astrophysics: Dark energy, Nucleosynthesis
• Climate: Pollution, Weather Prediction
• Biology: Microbial life
• Socioeconomic Modeling: Global scale

modeling

Nonlinear Systems, ODE, PDE, Heterogeneous

Systems, Multiscale Analysis.

Motivation: Analysis

• Modeling: Inputs, outputs, system models.
• Simulation: Time domain, frequency domain,

wavelet simulation.

• Sensitivity Calculation: Optimization
• Uncertainty Quantification: Derivation with

partial information or variations

• User Interface: Data mining, visualization,

Motivation: Circuit Analysis

• 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

Program Structure (a closer look)

Numerical Techniques:

• Formulation of circuit equations
• Solution of ordinary differential equations
• Solution of nonlinear equations
• Solution of linear equations

Input and setup Models

Output

Lecture 1: Formulation

• Derive from KCL/KVL
• Sparse Tableau Analysis (IBM)
• Nodal Analysis, Modified Nodal Analysis

(SPICE)

*some slides borrowed from Berkeley EE219 Course

Branch Constitutive Equations (BCE)

Ideal elements

Element Branch Eqn Variable parameter Resistor v = R·i - Capacitor i = C·dv/dt - Inductor v = L·di/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 =?

Formulation of Circuit Equations

• Unknowns
  • B branch currents (i)
  • N node voltages (e)
  • B branch voltages (v)
• Equations
  • N+B Conservation Laws
  • B Constitutive Equations
• 2B+N equations, 2B+N unknowns => unique solution

Equation Formulation - KVL

0

1 2

R 1

G 2 v 3

R 3

R 4 Is

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0

0

0

0

0

0 1

0 1

1 1

1 0

1 0

2

1

5

4

3

2

1

e

e

v

v

v

v

v v - AT^ e = 0

Kirchhoff’s Voltage Law (KVL)

B equations

Law: State Equation:

vi = voltage across branch i ei = voltage at node i

Equation Formulation - BCE

0

1 2

R 1

G 2 v 3

R 3

R 4 Is

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5 5

4

3

2

1

5

4

3

2

1

4

3

2

1

0

0

0

0

0 0 0 0 0

0 0 0 1 0

0 0 1 0 0

0 0 0 0

(^10000)

i i s

i

i

i

i

v

v

v

v

v

R

R

G

R

Kvv + Kii = is

B equations

Law: State Equation:

Equation Assembly (Stamping Procedures)

• Different ways of combining Conservation

Laws and Branch Constitutive Equations

• Sparse Table Analysis (STA)
• Nodal Analysis (NA)
• Modified Nodal Analysis (MNA)

Sparse Tableau Analysis (STA)

1. Write KCL: Ai=0 (N eqns)
2. Write KVL: v - ATe=0 (B eqns)
3. Write BCE: Kii + Kvv=S (B eqns)

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e S

v

i

K K

I A

A

i v

T 0

0

0

0

(^00) N+2B eqns N+2B unknowns

N = # nodes B = # branches

Sparse Tableau Docsity.com

Nodal Analysis (NA)

1. Write KCL

Ai=0 (N equations, B unknowns)

2. Use BCE to relate branch currents to branch

voltages

i=f(v) (B equations  B unknowns)

3. Use KVL to relate branch voltages to node voltages

v=h(e) (B equations  N unknowns)

Yne=ins

N eqns N unknowns N = # nodes Nodal Matrix Docsity.com

Nodal Analysis - Example

R 3

0

1 2

R 1

G 2 v 3

R 4 Is

1. KCL: Ai=
2. BCE: Kvv + i = is  i = is - Kvv  A Kvv = A is
3. KVL: v = ATe  A KvATe = A is

Yne = ins

2 5

1

3 3 4

3

2 3

2 1 0 1 1 1

e i s

e

R R R

R

G

R

G

Yn = AKvAT R Ins = Ais