1. Automatic Synthesis Using Genetic Programming of Both the Topology and Sizing for Five Post-2000 Patented Analog and Mixed Analog-Digital Circuits Matthew J. Streeter Genetic Programming, Inc. Mountain View, California mjs@tmolp.com Martin A. Keane Econometrics, Inc. Chicago, Illinois martinkeane@ameritech.net John R. Koza Stanford University Stanford, California koza@stanford.edu SSMSD 2003, Las Vegas, February 23-25

2. Overview Basics of Genetic Programming (GP) Circuit Synthesis using GP Five post-2000 circuits

3. Basics of Genetic Programming (GP)

4. Main Ideas of GP Breed computer programs to solve problems Programs represented as trees in style of LISP language Programs can create anything (e.g., circuit, equation, circuit+equations)

5. Pseudo-code for GP 1) Create initial random population 2) Evaluate fitness 3) Select fitter individuals to reproduce 4) Apply reproduction operations (crossover, mutation) to create new population 5) Return to 2 and repeat until solution found

6. Random Initial Population Function set: {+, *, /, -} Terminal set: {A, B, C} (1) Choose “+”(2) Choose “*”(3-5) Choose “A”, “B”, “C”

7. Fitness Evaluation 4 random equations shown Fitness is shaded area Target curve ( x 2 +x+1 ) Fitness: 0.67 1.0 1.67 2.67

8. Crossover Subtrees are swapped to create offspring Picked subtree Parents Offspring Picked subtree

9. Some Applications of GP Classic AI problems (simple planning & control strategies, classification, equation discovery) Algorithms (sorting networks, search heuristics, quantum algorithms) Art (evolved melodies, images) Synthesis (circuits, controllers, antennas, metabolic pathways)

10. Circuit Synthesis Using GP Computer programs represent circuits via developmental process Programs grow a circuit from an initial embryo Fitness measured (primarily) by circuit’s frequency or transient response

11. Initial Circuit Consists of test fixture (VSOURCE, RSOURCE, RLOAD) and embryo (Z0, Z1)

12. Developmental Process Component-inserting functions Topology-modifying functions Connection functions

13. Developmental Process: An Example

16. Fitness Measure Curve-matching (like earlier example) based on circuit’s response in frequency or time domain Sometimes have additional constraints (e.g., distortion, low component count)

17. Previously Evolved Circuits Filters (lowpass, highpass, bandpass) Amplifiers (60 and 96 dB amplifiers, negative feedback amplifier) Computational circuits (squaring, cubing, square root, cube root, logarithm) Voltage reference circuit Digital circuits (DAC, NAND)

18. Five Post-2000 Patented Circuits

19. PatentInventorInstitution Low-voltage balun circuit Sang Gug LeeInformation and Communications University Mixed analog- digital variable capacitor Turgut Sefket AyturLucent Technologies Inc. Voltage-current converter Akira Ikeuchi and Naoshi Tokuda Mitsumi Electric Co., Ltd. High-current load circuit Timothy Daun- Lindberg and Michael Miller IBM Corporation Low-Voltage cubic function generator Stefano Cipriani and Anthony A. Takeshian Conexant Systems, Inc.

20. Setup All circuit simulations in SPICE Circuits evolved on 1,000 processor supercomputer Population between 2 and 5 million, 100-200 generations

21. Setup: Low-voltage Balun Circuit Produces two half-amplitude signals with 180 degree phase difference Patented circuit operates with 1 V power supply Patented circuit

22. Setup: Low-voltage Balun Circuit Frequency sweep fitness cases for magnitude & phase angle Penalty for total harmonic distortion (THD) Embryo & Test fixture

23. Setup: Voltage-current Converter Produces stable output current proportional to difference between two inputs voltages Advantage over prior art: inputs not limited by power supply Patented circuit

24. Setup: Voltage-current Converter Four time-domain fitness cases using various input signals Time-varying voltage source VS forces stable output current at IOUT0 Embryo & Test fixture

25. Setup: Low-voltage Cubic Function Generator Cubing computational circuit using 2 V power supply Patented circuit

26. Setup: Low-voltage Cubic Function Generator Four time-domain fitness cases using various input signals Embryo & Test fixture

27. Results: Low-voltage Balun Circuit Evolved solution is better in terms of frequency response & THD C302 is in the patent claims Evolved circuit reads on some, but not all, claims of patent Evolved circuit

28. Results: Voltage-current Converter Evolved solution has 62% of absolute error of patent circuit on our fitness cases Evolved circuit solves problem in explainable way Evolved circuit

29. Results: Low-voltage Cubic Function Generator Evolved solution has 59% of absolute error of patent circuit on our fitness cases Evolved circuit

30. Future Work Verify SPICE results Consider manufacturability (e.g., variation in component values, parasitic effects) We are looking for good problems

32. Results: Low-Voltage Balun Circuit

33. Results: Voltage-current converter

34. Results: Low-voltage cubic function generator