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CSE 245: Computer Aided Circuit Simulation and Verification

CSE 245: Computer Aided Circuit Simulation and Verification. Winter 2003 Lecture 1: Formulation. Instructor: Prof. Chung-Kuan Cheng. Agenda. RCL Network Sparse Tableau Analysis Modified Nodal Analysis. History of SPICE. SPICE -- Simulation Program with Integrated Circuit Emphasis

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CSE 245: Computer Aided Circuit Simulation and Verification

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  1. CSE 245: Computer Aided Circuit Simulation and Verification Winter 2003 Lecture 1: Formulation Instructor: Prof. Chung-Kuan Cheng

  2. Agenda • RCL Network • Sparse Tableau Analysis • Modified Nodal Analysis Cheng & Zhu, UCSD @ 2003

  3. History of SPICE • SPICE -- Simulation Program with Integrated Circuit Emphasis • 1969, CANCER developed by Laurence Nagel on Prof. Ron Roher’s class • 1970~1972, CANCER program • May 1972, SPICE-I release • July ’75, SPICE 2A, …, 2G • Aug 1982, SPICE 3 (in C language) • No new progress on software package since then Cheng & Zhu, UCSD @ 2003

  4. RCL circuit Cheng & Zhu, UCSD @ 2003

  5. RCL circuit (II) • General Circuit Equation • Consider homogeneous form first and Q: How to Compute Ak ? Cheng & Zhu, UCSD @ 2003

  6. Solving RCL Equation • Assume A has non-degenerate eigenvalues and corresponding linearly independent eigenvectors , then A can be decomposed as where and Cheng & Zhu, UCSD @ 2003

  7. real eigenvalue Conjugative Complex eigenvalue Solving RCL Equation (II) • What’s the implication then? • To compute the eigenvalues: where Cheng & Zhu, UCSD @ 2003

  8. Solving RCL Equation (III) In the previous example Let c=r=l=1, we have where hence Cheng & Zhu, UCSD @ 2003

  9. Solving RCL Equation (IV) • What if matrix A has degenerated eigenvalues? Jordan decomposition ! J is in the Jordan Canonical form And still Cheng & Zhu, UCSD @ 2003

  10. Jordan Decomposition similarly Cheng & Zhu, UCSD @ 2003

  11. Agenda • RCL Network • Sparse Tableau Analysis • Modified Nodal Analysis Cheng & Zhu, UCSD @ 2003

  12. Equation Formulation • KCL • Converge of node current • KVL • Closure of loop voltage • Brach equations • I, R relations Cheng & Zhu, UCSD @ 2003

  13. Types of elements • Resistor • Capacitor • Inductor • L is even dependent on frequency due to skin effect, etc… • Controlled Sources • VCVS, VCCS, CCVS, CCCS Cheng & Zhu, UCSD @ 2003

  14. Cut-set analysis 1. Construct a spanning tree 2. Take as much capacitor branches as tree branches as possible 3. Derive the fundamental cut-set, in which each cut truncates exactly one tree branch 4. Write KCL equations for each cut 5. Write KVL equations for each tree link 6. Write the constitution equation for each branch Cheng & Zhu, UCSD @ 2003

  15. KCL Formulation #nodes-1 lines #braches columns Cheng & Zhu, UCSD @ 2003

  16. KCL Formulation (II) • Permute the columns to achieve a systematic form Cheng & Zhu, UCSD @ 2003

  17. KVL Formulation Remove the equations for tree braches and systemize Cheng & Zhu, UCSD @ 2003

  18. Cut & Loop relation In the previous example Cheng & Zhu, UCSD @ 2003

  19. Sparse Tableau Analysis (STA) • n=#nodes, b=#branches b b n-1 (n-1) KCL b b KVL b b branch relations n-1 Due to independent sources Totally 2b+n-1 variables, 2b+n-1 equations Cheng & Zhu, UCSD @ 2003

  20. STA (II) • Advantages • Covers any circuit • Easy to assemble • Very sparse • Ki, Kv, I each has exactly b non-zeros. A and ATeach has at most 2b non-zeros. • Disadvantages • Sophisticated data structures & programming techniques Cheng & Zhu, UCSD @ 2003

  21. Agenda • RCL Network • Sparse Tableau Analysis • Modified Nodal Analysis Cheng & Zhu, UCSD @ 2003

  22. Nodal Analysis • Derivation (1) From STA: (2) (3) (3) x Ki-1  (4) (4) x A  (5) Using (a) (6) Tree trunk voltages Substitute with node voltages (to a given reference), we get the nodal analysis equations. Cheng & Zhu, UCSD @ 2003

  23. Nodal Analysis (II) Cheng & Zhu, UCSD @ 2003

  24. Modified Nodal Analysis • General Form Independent current source Node Conductance matrix KCL Due to non-conductive elements Independent voltage source • Yn can be easily derived • Add extra rows/columns for each non-conductive elements using templates Cheng & Zhu, UCSD @ 2003

  25. MNA (II) • Fill Yn matrix according to incidence matrix Choose n6 as reference node Cheng & Zhu, UCSD @ 2003

  26. MNA Templates Add to the right-hand side of the equation Independent current source Independent voltage source Cheng & Zhu, UCSD @ 2003

  27. MNA Templates (II) CCVS CCCS Cheng & Zhu, UCSD @ 2003

  28. MNA Templates (III) VCVS + - VCCS + - Cheng & Zhu, UCSD @ 2003

  29. MNA Templates (IV) Mutual inductance M Operational Amplifier Cheng & Zhu, UCSD @ 2003

  30. MNA Example Circuit Topology MNA Equations Cheng & Zhu, UCSD @ 2003

  31. MNA Summary • Advantages • Covers any circuits • Can be assembled directly from input data. Matrix form is close to Yn • Disadvantages • We may have zeros on the main diagonal. • Principle minors could be singular Cheng & Zhu, UCSD @ 2003

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