10.6.6. Design across multiple corners
We are going to find the values of design parameters for which the design requirements specified in definitions.py are satisfied across multiple operating conditions and process variation MOS models. The script is in file 03-corner-based-design.py in folder demo/design/miller/
# Sizing across corners
from definitions import *
from pyopus.design.cbd import CornerBasedDesign, generateCorners
from pyopus.evaluator.aggregate import formatParameters
# If MPI is imported an application not using MPI will behave correctly
# (i.e. only slot 0 will run the program) even when started with mpirun/mpiexec
from pyopus.parallel.mpi import MPI
from pyopus.parallel.cooperative import cOS
if __name__=='__main__':
# Prepare statistical parameters dictionary with nominal values (0)
nominalStat={ name: 0.0 for name, desc in statParams.items() }
# Prepare operating parameters dictionary with nominal values
nominalOp={ name: desc['init'] for name, desc in opParams.items() }
# Prepare initial design parameters dictionary
# Uncomment this if you want to use initial values from definitions.py
# initialDesign={ name: desc['init'] for name, desc in designParams.items() }
# Uncomment this if you want to use lower bounds for initial values of design parameters
# initialDesign={ name: desc['lo'] for name, desc in designParams.items() }
# Uncomment this if you want to use the result of nominal design as initial point
initialDesign={
'c_out': 2.0125484638530715e-12,
'diff_l': 9.0173130168525476e-07,
'diff_w': 1.3748137933373763e-05,
'load_l': 3.1959280853504449e-06,
'load_w': 8.9130317977231035e-05,
'mirr_l': 1.9427037931893832e-06,
'mirr_ld': 2.4749186739319866e-06,
'mirr_w': 7.9105009110997434e-05,
'mirr_wd': 2.0887405636991897e-05,
'mirr_wo': 3.8316438575060692e-05,
'out_l': 2.7397889227076129e-06,
'out_w': 1.3868429320545923e-05,
'r_out': 1.7894053483506941e+04,
}
# Prepare corners, cartesian product of
# MOS model: wp, ws, wo, and wz (named wp, ws, wo, and wz)
# voltages: 1.7 and 2.0 (named vl and vh)
# temperatures: 0 and 100 (named tl and th)
corners, names = generateCorners(
specs=[
(
'model', 'mos',
['wp', 'ws', 'wo', 'wz'],
['wp', 'ws', 'wo', 'wz']
),
(
'param', 'vdd',
[opParams['vdd']['lo'], opParams['vdd']['hi']],
['vl', 'vh'],
),
(
'param', 'temperature',
[opParams['temperature']['lo'], opParams['temperature']['hi']],
['tl', 'th'],
),
],
heads=[ 'opus' ],
)
# Add nominal corner (model tm, 1.8V, 25degC), defined for head opus
nominalCorner={
('nom',('opus',)): {
'modules': [ 'tm' ],
'params': {
'vdd': opParams['vdd']['init'],
'temperature': opParams['temperature']['init']
},
}
}
corners.update(nominalCorner)
# Now we have 4x2x2+1=17 corners, print their names
print("Corner names")
print(sorted(corners.keys()))
# Area should be evauated only in corner 'nom'
measures['area']['corners']=[ 'nom' ]
# Prepare parallel environment
cOS.setVM(MPI(mirrorMap={'*':'.'}, persistentStorage=False))
# Design it, nominal statistical parameters are treated as fixed parameters
cbd=CornerBasedDesign(
designParams, heads, analyses, measures, corners,
fixedParams=[nominalStat], variables=variables, norms={ 'area': 100e-12 },
# tradeoff=1e-6,
# stepTol=1e-4,
initial=initialDesign,
method='global',
incrementalCorners=True,
evaluatorOptions={'debug': 0},
debug=1
)
# Run optimization
atDesign, aggregator, analysisCount = cbd()
# Print design parameters and performance measures
print(formatParameters(atDesign))
print(aggregator.formatResults())
# Finalize cOS parallel environment
cOS.finalize()
# Result
# c_out: 6.4025057781114802e-12
# diff_l: 3.4247816773735976e-07
# diff_w: 1.6738092946223754e-05
# load_l: 2.3668072815514710e-06
# load_w: 5.3240803355989389e-05
# mirr_l: 1.0157035640188838e-06
# mirr_ld: 1.6182520447950098e-06
# mirr_w: 5.8107861163445226e-05
# mirr_wd: 6.1242813846216839e-05
# mirr_wo: 6.8277846319352392e-05
# out_l: 4.1088626829554061e-07
# out_w: 8.1812469568552345e-05
# r_out: 5.1647907484619873e+02
After preparing dictionaries with statistical parameter values, nominal
operating parameter values, and initial design parameter values the
dictionary holding the corners is built (generateCorners). A total
of 16 corners are generated (combinations of 2 supply voltages, 2 operating
temperatures, and 4 MOS models). The name of a corner reflects the
combination of parameters and MOS model). The corner name is composed as
c<corner number>_<MOS model name>_<vdd value name>_<temperature value name>
The nominal corner is constructed manually and added to the dictionary.
The evaluation of the area performance measure is limited to the
nominal corner by adding an entry named corners to the dictionary
describing it.
Next, the cooperative multitasking OS is initialized. It uses MPI as the backend and starts every task in its own local folder which contains the copies of all files from the current folder (mirrorMap argument to MPI).
A pyopus.design.cbd.CornerBasedDesign is created from
designParams, heads, analyses, measures, variables
defined in
definitions.py
and the corners variable constructed in this script. The setup is
essentially the same as for nominal design, with the exception of the
incrementalCorners argument which turns on the iterative algorithm
for finding the worst corner. Without this algorithm every candidate
circuit measure must be evaluated across all corners which can take
a lot of time.
It is recommended that you run this case with multiple CPUs. To run it in parallel on 5 local CPUs by typing
mpirun -n 5 python3 03-corner-based-design.py
During optimization messages are printed that show the progress of the optimizer. First, the initial design is evaluated across all corners. For this example we start with the result obtained with the previous example (nominal design). We can see that two design requirements (cmrr>90 and pm>50) are not satisfied in some corners. The names of corners with the worst values of individual performance measures are printed alongside with the contributions to cost function value.
calypso_7b2b_1 CBD: Pass 1, full corner evaluation
calypso_7b2b_1 CBD: Pass 1, corner summary
calypso_7b2b_1 CBD: area < 9.000e-09 | 1.448e-09 nom : 0
calypso_7b2b_1 CBD: cmrr > 9.000e+01 | o 8.059e+01 c10_wo_vl_th : 0.105
calypso_7b2b_1 CBD: gain > 6.000e+01 | 7.903e+01 c1_wp_vl_tl : 0
calypso_7b2b_1 CBD: isup < 1.000e-03 | 1.709e-04 c3_wp_vh_tl : 0
calypso_7b2b_1 CBD: overshdn < 1.000e-01 | 2.537e-03 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: overshup < 1.000e-01 | 2.219e-02 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: pm > 5.000e+01 | 6.368e+01 c3_wp_vh_tl : 0
calypso_7b2b_1 CBD: psrr_vdd > 6.000e+01 | 7.290e+01 c10_wo_vl_th : 0
calypso_7b2b_1 CBD: psrr_vss > 6.000e+01 | 8.496e+01 c5_ws_vl_tl : 0
calypso_7b2b_1 CBD: slewdn > 2.000e+06 | 2.182e+06 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: slewup > 2.000e+06 | 2.133e+06 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: swing > 1.000e+00 | 1.007e+00 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: tsetdn < 1.000e-06 | 4.731e-07 c16_wz_vh_th : 0
calypso_7b2b_1 CBD: tsetup < 1.000e-06 | 4.438e-07 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: ugbw > 1.000e+07 | o 6.222e+06 c6_ws_vl_th : 0.378
calypso_7b2b_1 CBD: vds_drv > 0.000e+00 | 6.171e-02 c5_ws_vl_tl : 0
calypso_7b2b_1 CBD: vgs_drv > 0.000e+00 | 5.395e-02 c1_wp_vl_tl : 0
The initial sets of corners where the performance measures will be evaluated are constructed
calypso_7b2b_1 CBD: Pass 1, updating corner lists
calypso_7b2b_1 CBD: area: ['nom']
calypso_7b2b_1 CBD: cmrr: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: dep gain: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: dep gain_com: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: isup: ['c3_wp_vh_tl']
calypso_7b2b_1 CBD: overshdn: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: overshup: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: pm: ['c3_wp_vh_tl']
calypso_7b2b_1 CBD: psrr_vdd: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: dep gain: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: dep gain_vdd: ['c10_wo_vl_th']
calypso_7b2b_1 CBD: psrr_vss: ['c5_ws_vl_tl']
calypso_7b2b_1 CBD: dep gain: ['c10_wo_vl_th', 'c5_ws_vl_tl']
calypso_7b2b_1 CBD: dep gain_vss: ['c5_ws_vl_tl']
calypso_7b2b_1 CBD: slewdn: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: slewup: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: swing: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: tsetdn: ['c16_wz_vh_th']
calypso_7b2b_1 CBD: tsetup: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: ugbw: ['c6_ws_vl_th']
calypso_7b2b_1 CBD: vds_drv: ['c5_ws_vl_tl']
calypso_7b2b_1 CBD: vgs_drv: ['c1_wp_vl_tl']
an the optimization is started. The optimizer stops when it finds a circuit that satisfies all design requirements across the intial corner sets. Next, this circuit is evaluated across all corners.
calypso_7b2b_1 CBD: Pass 2, full corner evaluation
calypso_7b2b_1 CBD: Pass 2, corner summary
calypso_7b2b_1 CBD: area < 9.000e-09 | 1.024e-09 nom : 0
calypso_7b2b_1 CBD: cmrr > 9.000e+01 | o 7.958e+01 c13_wz_vl_tl : 0.116
calypso_7b2b_1 CBD: gain > 6.000e+01 | 6.935e+01 c1_wp_vl_tl : 0
calypso_7b2b_1 CBD: isup < 1.000e-03 | 1.991e-04 c11_wo_vh_tl : 0
calypso_7b2b_1 CBD: overshdn < 1.000e-01 | 9.678e-03 c9_wo_vl_tl : 0
calypso_7b2b_1 CBD: overshup < 1.000e-01 | 9.448e-02 c9_wo_vl_tl : 0
calypso_7b2b_1 CBD: pm > 5.000e+01 | 6.155e+01 c9_wo_vl_tl : 0
calypso_7b2b_1 CBD: psrr_vdd > 6.000e+01 | 7.090e+01 c14_wz_vl_th : 0
calypso_7b2b_1 CBD: psrr_vss > 6.000e+01 | 8.204e+01 c16_wz_vh_th : 0
calypso_7b2b_1 CBD: slewdn > 2.000e+06 | 1.035e+07 c14_wz_vl_th : 0
calypso_7b2b_1 CBD: slewup > 2.000e+06 | 9.645e+06 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: swing > 1.000e+00 | 1.320e+00 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: tsetdn < 1.000e-06 | 1.219e-07 c16_wz_vh_th : 0
calypso_7b2b_1 CBD: tsetup < 1.000e-06 | 2.013e-07 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: ugbw > 1.000e+07 | 1.561e+07 c6_ws_vl_th : 0
calypso_7b2b_1 CBD: vds_drv > 0.000e+00 | 5.821e-02 c5_ws_vl_tl : 0
calypso_7b2b_1 CBD: vgs_drv > 0.000e+00 | 5.708e-02 c13_wz_vl_tl : 0
Corners where some design requirement is not satisfied are added to the corresponding corner sets
calypso_7b2b_1 CBD: Pass 2, updating corner lists
calypso_7b2b_1 CBD: cmrr: ['c10_wo_vl_th', 'c13_wz_vl_tl']
calypso_7b2b_1 CBD: dep gain: ['c10_wo_vl_th', 'c5_ws_vl_tl', 'c13_wz_vl_tl']
calypso_7b2b_1 CBD: dep gain_com: ['c10_wo_vl_th', 'c13_wz_vl_tl']
and a new optimization is started. This procedure is repeated until a circuit is found that satisfies all design requirements across all corners. In the end the values of the design parameters obtained by the optimizer are printed
c_out: 1.110200e-12
diff_l: 3.247602e-06
diff_w: 6.042974e-06
load_l: 1.614003e-06
load_w: 5.796995e-05
mirr_l: 7.731257e-07
mirr_ld: 3.243680e-06
mirr_w: 9.007543e-05
mirr_wd: 1.878471e-05
mirr_wo: 8.233483e-05
out_l: 4.108898e-07
out_w: 6.003844e-05
r_out: 3.574993e+04
followed by the circuit’s performance.
area < 9.000e-09 | 1.010e-09 nom : 0
cmrr > 9.000e+01 | 9.040e+01 c10_wo_vl_th : 0
gain > 6.000e+01 | 6.972e+01 c1_wp_vl_tl : 0
isup < 1.000e-03 | 2.096e-04 c11_wo_vh_tl : 0
overshdn < 1.000e-01 | 1.884e-03 c9_wo_vl_tl : 0
overshup < 1.000e-01 | 5.750e-02 c9_wo_vl_tl : 0
pm > 5.000e+01 | 5.721e+01 c9_wo_vl_tl : 0
psrr_vdd > 6.000e+01 | 7.226e+01 c1_wp_vl_tl : 0
psrr_vss > 6.000e+01 | 8.058e+01 c4_wp_vh_th : 0
slewdn > 2.000e+06 | 6.449e+06 c6_ws_vl_th : 0
slewup > 2.000e+06 | 6.259e+06 c6_ws_vl_th : 0
swing > 1.000e+00 | 1.332e+00 c6_ws_vl_th : 0
tsetdn < 1.000e-06 | 1.846e-07 c16_wz_vh_th : 0
tsetup < 1.000e-06 | 1.956e-07 c5_ws_vl_tl : 0
ugbw > 1.000e+07 | 1.435e+07 c6_ws_vl_th : 0
vds_drv > 0.000e+00 | 8.508e-02 c5_ws_vl_tl : 0
vgs_drv > 0.000e+00 | 2.965e-02 c1_wp_vl_tl : 0
For every performance measure the corner where the worst value was found is printed. Because all design requirements are satisfied all penalty contributions are 0.
Note that due to the random nature of the delays on the network parallel runs may yield different solutions for the same design problem.