Circuits and Systems Design Automation of Analog VLSI

Design Optimization § Analog circuit design automation § For a design § Determine the

Z. Yan, P. Mak, M. Law, R. P. Martins, "A 0. 016 -mm^2 144µW

§ Performance Concerned: minimize current consumption § Parameter Space: device dimensions § Constraints: design

Features of multi-start-point method § Two features make it outperform other methods The probability

Comparison of Optimization Methods on Test Functions Eason’s function Rastrigin’s function Six-hump camel back’s

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Circuits and Systems Design Automation of Analog VLSI Prof. D. Zhou UT Dallas Analog Circuits Design Automation 1

Design Optimization § Analog circuit design automation § For a design § Determine the specs § Choose the intended manufacture process § Choose the circuit topology § Determine the variables and their “ranges” § Transistor size, input and supply voltage, noise and etc. § Choose the simulation tool § SPICE, mixed signal and etc. § Construct the objective functions and constraints § Choose an efficient optimization method Analog Circuits Design Automation 2

Z. Yan, P. Mak, M. Law, R. P. Martins, "A 0. 016 -mm^2 144µW Three-Stage Amplifier Capable of Driving 1 -to-15 n. F Capacitive Load With> 0. 95 -MHz GBW, "IEEE Journal of Solid-State Circuits, vol. 48, no. 2, pp. 527, 540, Feb. 2013.

§ Performance Concerned: minimize current consumption § Parameter Space: device dimensions § Constraints: design specifications Manual Design TT, 27°C FF, -40°C SS, 125°C σ / Mean GBW (MHz) ≥ 0. 92 1. 17 0. 7 ≤ 25. 8% PM (Degree) ≥ 52. 5 51. 8 55. 5 ≤ 3. 7% GM (d. B) ≥ 19. 5 21. 2 18. 5 ≤ 6. 95% SR+(V/μs) ≥ 0. 18 0. 26 0. 14 ≤ 31. 6% SR- (V/μs) ≥ 0. 20 0. 26 0. 11 ≤ 39. 7% 1% Ts+(μs) ≤ 5. 17 4. 07 6. 78 ≤ 25. 5% 1% Ts- (μs) ≤ 5. 71 3. 80 9. 02 ≤ 42. 7% Min IQ (µA) ≤ 69. 2 72. 1 71. 7 ≤ 2. 2%

Features of multi-start-point method § Two features make it outperform other methods The probability for hitting a • “Region hit” issue vs. “Point hit” issue region is much larger than • Guided search vs. random and independent search hitting a point! Sample points local optimum global optimum local optimum Region of attraction global optimum Start point MC method used to find the global optimum None of 200 Monte Carlo sample points exactly hits the global optimum. MGO method used to find the global optimum Once a start point hits the region containing the global optimum, the global optimum can be found easily by a local optimization search. 5

Comparison of Optimization Methods on Test Functions Eason’s function Rastrigin’s function Six-hump camel back’s function Genetic, simulated annealing and particle swarm methods are using MATLAB build-in functions. The result s are based on an average of 10 trials for each method. *Data source: Marcin Molga and Czeslaw Smutnicki, “Test functions for optimization needs, ” in 2005. 6