1. Prof. D. Zhou UT Dallas Analog Circuits Design Automation 1

2. Design Optimization  Analog circuit design automation  It has been an active research area for several decades  Automation of creating new topology is still “impossible”.  For a chosen topology, we can search the parameter space to find the optimal design.  For a specific application, there are usually a few topologic options. Therefore we can test them all. Analog Circuits Design Automation 2

3. 3

4. Optimization Engine Circuit Simulator Circuit performance Design Decisions Unsized fixed topology PDK Design parameters and ranges PVT variations analysis Post layout parasitics Design specs Design Constraints Behavioral Models using verilog-AMS, systemC, etc. Transistor level using SPICE … Start point 2 + local search 2 Start point 1 + local search 1 Start point n + local search n Mixed-Signal Co-simulation Parallel Evaluation

5. Design Optimization  Formulation and an example Analog Circuits Design Automation 5

6. Z.Yan, P.Mak, M.Law, R.P.Martins, "A 0.016-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. 2013.

7. Manual Design TT,27°CFF,-40°CSS,125°Cσ / Mean GBW (MHz)≥ 0.921.170.7≤ 25.8% PM (Degree)≥ 52.551.855.5≤ 3.7% GM (dB)≥ 19.521.218.5≤ 6.95% SR+(V/μs)≥ 0.180.260.14≤ 31.6% SR- (V/μs)≥ 0.200.260.11≤ 39.7% 1% Ts+(μs)≤ 5.174.076.78≤ 25.5% 1% Ts- (μs)≤ 5.713.809.02≤ 42.7% Min I Q (µA)≤ 69.272.171.7≤ 2.2%  Performance Concerned: minimize current consumption  Parameter Space: device dimensions  Constraints: design specifications

8. Manual design / Automatic design (Bolded are better performance) Improvement @TT, 27°C TT @27°CFF @-40°CSS @125°C GBW (MHz)0.92 / 1.071.17 / 1.150.7 / 1.02 16.3% PM (Degree)52.5 / 61.751.8 / 64.455.5 / 59.1 17.5% GM (dB)19.5 / 22.821.2 / 23.918.5 / 21.3 16.9% SR+(V/μs)0.18 / 0.240.26 / 0.310.14 / 0.18 50% SR- (V/μs)0.20 / 0.460.26 / 0.680.11 / 0.29 84% 1% Ts+(μs)5.17 / 3.654.07 / 2.846.78 / 4.43 29.4% 1% Ts- (μs)5.71 / 2.333.80 / 1.419.02 / 2.70 59.2% I Q (µA)69.2 / 60.772.1 / 58.371.7 / 64.4 12.3%  Performance improvements at nominal condition

9. Design Optimization  Computation efficiency  A local optimal is easy to find, but a global optimal one is very difficult.  We need to check multiple start point to increase the probability of finding the global optimal.  Or use SA or GA and etc. methods to get of local optimal. Analog Circuits Design Automation 9

10.  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 10 global optimum local optimum Start point Region of attraction The probability for hitting a region is much larger than hitting a point!

11. 11 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.