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 mm^2 144µW Three-Stage Amplifier Capable of Driving 1-to-15 nF Capacitive Load With> 0.95-MHz GBW,"IEEE Journal of Solid-State Circuits, vol.48, no.2, pp.527,540, Feb

Manual Design TT,27°CFF,-40°CSS,125°Cσ / Mean GBW (MHz)≥ ≤ 25.8% PM (Degree)≥ ≤ 3.7% GM (dB)≥ ≤ 6.95% SR+(V/μs)≥ ≤ 31.6% SR- (V/μs)≥ ≤ 39.7% 1% Ts+(μs)≤ ≤ 25.5% 1% Ts- (μs)≤ ≤ 42.7% Min I Q (µA)≤ ≤ 2.2%  Performance Concerned: minimize current consumption  Parameter Space: device dimensions  Constraints: design specifications

 Two features make it outperform other methods “Region hit” issue vs. “Point hit” issue Guided search vs. random and independent search MC method used to find the global optimum MGO method used to find the global optimum None of 200 Monte Carlo sample points exactly hits 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. global optimum local optimum Sample points 5 global optimum local optimum Start point Region of attraction The probability for hitting a region is much larger than hitting a point!

6 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 results 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.