Circuit Optimization
Virtuoso ADE Assembler
Product Version: IC6.1.8, ICADVM18.1
August 2019
Copyright Statement
© 2019 Cadence Design Systems, Inc. All rights reserved worldwide. Cadence and the Cadence logo are
registered trademarks of Cadence Design Systems, Inc. All others are the property of their respective
holders.
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Circuit Optimization
Contents
Introduction .............................................................................................................. 4
Intended Audience................................................................................................ 4
Overview .............................................................................................................. 4
Circuit Optimization Overview .................................................................................. 5
Circuit Optimization Definitions ............................................................................. 5
Pros and Cons of Circuit Optimization .................................................................. 8
Circuit Optimization Flow ......................................................................................... 9
Data Preparation .................................................................................................... 11
Setup Common to Global and Local Optimization.................................................. 12
Running Circuit Optimization with Global Optimization .......................................... 21
Running Circuit Optimization with Local Optimization ............................................ 26
Running Circuit Optimization Considering Process Variation ................................. 33
Overall Flow........................................................................................................ 33
Steps to Run Optimization Considering Process Variation ................................. 34
Circuit Optimization Results ................................................................................... 41
Results ............................................................................................................... 41
Comparison between Manual Design and Circuit Optimization Design .............. 42
Support .................................................................................................................. 42
Feedback ............................................................................................................... 42
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Circuit Optimization
Introduction
This document describes the application of circuit optimization using Virtuoso ADE.
Intended Audience
The audience includes circuit designers who are interested in reducing the time and
effort spent in sizing the circuit device parameters to meet the specifications over
corners.
Overview
This document focuses on the steps to apply circuit optimization.
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Circuit Optimization
Circuit Optimization Overview
This chapter describes circuit optimization and algorithm types.
Circuit Optimization Definitions
Circuit optimization is an iterative mathematical process to search the circuit design
space to find the most optimal solution without simulating all possible combinations as
in a brute force sweep. The optimization algorithm does not have circuit knowledge
itself. The algorithm attempts to solve a mathematical optimization problem.
•
•
Device
parameters with
sweep ranges
Output
measurements
including
specification
targets
Circuit
Optimization
Optimal
Solution
Figure 1 Optimization Flow Overview
Inputs to optimization include the circuit device parameters, output measurements, and
target specifications. The device parameter ranges define the design space.
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Circuit Optimization
The optimizer varies device parameter values (within the allowed ranges defined by the
user), simulates the circuit, and determines the cost of each simulated design point. The
goal is to minimize the cost. A design point (candidate circuit for simulation) that meets
all specifications has lower cost than a design point which fails to meet one or more
specifications.
Circuit
Performance
Cost
Starting Point
Local Optimum
Global
Optimum
Input
Parameter
Figure 2 One-Dimension Example of Global and Local Optimum
Global Optimization
Global optimization searches multiple areas of the circuit design space to find the global
minimum cost and optimal design point. The Virtuoso ADE global optimizer is based on
the proven NeoCircuit technology, now in use for more than 15 years (Neolinear
developed NeoCircuit and was acquired by Cadence). The global optimizer applies
machine learning techniques to circuit optimization.
Local Optimization
Local optimization begins with a starting point and searches locally for the optimal
solution.
Given the one-dimensional example of Figure 2, local optimization searches the curve
around the starting point and applies sensitivity analysis to determine the search
direction.
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Circuit Optimization
The Virtuoso ADE local optimization algorithms are based on publicly documented
methods. BFGS is the default and recommended local optimization algorithm in
Virtuoso ADE.
Algorithm
Description
BFGS
Broyden-Fletcher-Goldfarb-Shanno
algorithm. This is the default and
recommended algorithm for local
optimization. BFGS is a gradient-based
method. Gradient methods do well when
the performance gradient can be
calculated (output measurements return
more than two or three states and do not
result in evaluation errors) and design
variables are naturally continuous.
Conjugate Gradient
A gradient-based algorithm. Not typically
as efficient as BFGS.
Brent-Powell
Does not require a gradient. The
algorithm searches in a fine grid around
the starting point. Use Brent-Powell if
your starting point is already close (for
example, only a few specifications not
met). The optimization should find the
local minimum around the selected point,
but it may also quit once that local
minimum is found and then miss a more
optimal solution in the local design space.
Brent-Powell is not parallelized and runs
only one point at a time, although it runs
the least number of points on average
compared to the other methods.
Hooke-Jeeves
Does not require a gradient. This method
is also known as a pattern search
algorithm. The algorithm searches in
larger steps, but it can miss a local
minimum.
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Circuit Optimization
Pros and Cons of Circuit Optimization
Circuit optimization does not replace the designer. It does not replace the need for
understanding of the circuit operation.
Circuit optimization saves time and effort by eliminating repetitive manual tweaks of the
design. Optimization handles multiple design variables and output specifications, and
automates the process of balancing the trade-offs to meet the specifications over all
corners.
The existing ADE setup is reused for optimization including ADE tests, variables,
parameters, measurements, and specifications.
It is important to define a set of circuit performance measurements (for example, ADE
calculator expressions). If the designer views output waveforms to determine circuit
performance, more effort must be spent in defining additional measurement expressions
in order to use optimization.
Additional setup is required to parameterize the design for optimization.
Parameterization includes defining the matching relationships between circuit devices
and defining the parameter ranges.
Depending on the circuit under test, optimization may require hundreds or thousands of
simulations. Optimization cannot be applied to large blocks that require very long
simulation time. It is best applied to each sub-block individually to manage simulation
time.
For best performance, additional machine resources must be made available for
optimization to search the design space more quickly. For example, you will experience
reduced run time when you submit the optimization job to say 20 machines rather than
running on 1 local machine.
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Circuit Optimization
Circuit Optimization Flow
This chapter describes the steps to follow to run circuit optimization in Virtuoso ADE.
•
Begin with the test and analysis setup in ADE Assembler.
•
Define output measurement expressions and set specification targets to measure
the performance of the circuit.
•
Define a set of worst-case corners to enable for optimization.
•
Define the matching relationships between circuit devices (diff pairs, current
mirrors, etc.).
•
Define parameter ranges for all devices that are part of the optimization.
•
Run global or local optimization.
•
If all specifications are not met, review the device parameter setup and design
constraints, make changes as necessary, and rerun the optimization. When
optimization is complete and all specifications are met, the next step is final
verification over corners or Monte Carlo analysis.
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Circuit Optimization
Circuit
Testbench
Device
Parameterization
• ADE Tests and Analyses
• Output Measurements
• Worst-Case VT Corners
• Statistical Corners
• Matching Relationships
• Parameter Ranges
• Global Optimization
• Local Optimization
Run Optimization • Size Over Corners
Final Verification
• Corners
• Monte Carlo
Figure 3 Optimization Flow
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Circuit Optimization
Data Preparation
In this example, a sub-block of a larger PLL is optimized. The op amp of the PLL lowpass filter is optimized. It is important to break up a larger system into more
manageable sub-blocks for optimization in order to reduce the simulation time.
Prepare the following data prior to running optimization.:
•
Schematic of the sub-block to be optimized
•
Create the testbench and the ADE view
•
Model setup (statistical models required for Monte Carlo analysis)
•
Circuit analyses
•
Define output measurement expressions and specification targets
•
Define a set of worst-case corners
•
Device parameterization including matching relationships and optimization
ranges
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Circuit Optimization
Setup Common to Global and Local Optimization
This chapter describes the steps to prepare the circuit for optimization.
1. Open the design in Virtuoso ADE Assembler.
Figure 4 Virtuoso ADE Assembler
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Circuit Optimization
2. Create one or more ADE tests and define the analyses for each test.
Figure 5 Define the ADE Tests and Analyses
3. Save only the selected signals that are required for measuring circuit
performance. Do not save any other data that is not required for optimization.
Saving only the necessary simulation data will reduce disk space requirements
and improve run time.
Figure 6 Save the Minimum Amount of Data Required for Optimization
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Circuit Optimization
4. Define the output measurement expressions and specification target values.
Specification types include minimize, maximize, less than (<), greater than (>),
range, and tolerance.
The “minimize” and “maximize” specifications are 'open-ended'. An open-ended
specification is when you choose either minimize (min) or maximize (max), and
then specify an ideal value. For an open-ended specification, ADE tries to
continually improve upon the ideal value. So, if the ideal value for the UGF
specification is “maximize to 1e+8”, 3e+8 is better than 2e+8.
“Less than” or “greater than” specifications are 'close-ended'. A close-ended
specification is when you specify a target value, and then specify that the
resulting specification must be greater than (>) or less than (<) that target value.
For a close-ended specification, ADE attempts to meet the target value, and
exceeding the target is no better than meeting the target. So, if the target value
for UGF is “>1e+8”, 3e+8 is no better than 2e+8.
5. Specify the 'info' type when you want to see the value of a measurement in the
Optimization view, but do not want that specification to affect sizing.
Figure 7 Output Expressions and Specification Targets
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Circuit Optimization
6. Define a set of worst-case corners.
Figure 8 Corners Setup
Device parameterization constrains the circuit in terms of the allowed device parameter
values (size of w, l, m, etc.). The matching relationships between instances are defined.
If M0 and M1 are part of a current mirror, these two instances must be matched (or
matched in ratio) rather than be sized independently.
7. Select 'Click to add' under Parameters in the Data View pane to dock the
Variables and Parameters assistant on the schematic.
Figure 9 Add Parameters
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Circuit Optimization
The schematic opens with the Variables and Parameters assistant docked on the right
side.
Figure 10 Variables and Parameters Assistant Docked to the Schematic
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Circuit Optimization
8. Select two or more instances to match. In the Variables and Parameters
assistant, select the parameters to match. Here, the two instances PM4 and PM5
of a diff pair are selected. The parameter width (total), length, and multiplier will
be matched and parameterized.
Figure 11 Matching the Parameters of a Differential Pair
9. Select the Match Parameters button in the Variables and Parameters assistant
to create the parameters.
Figure 12 Create the matched parameters
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Circuit Optimization
The newly created parameters are displayed in the lower half of the Variables and
Parameters assistant. You did not create matched parameters for fingers and finger
width parameters because they are already matched on the schematic and will not be
modified during optimization. By default, the PM5 parameters appear as collapsed
under PM4. PM4 defines the independent parameters, and PM5 is matched to PM4.
The syntax of a matched parameter is <instance name>/<parameter name>@<lib
name>/<cell name>/<view name>. If the instances are located at the same level of
hierarchy, the lib/cell/view part of the parameter syntax can be omitted.
Figure 13 PM5 Is Matched to PM4
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Circuit Optimization
10. Define ranges for the independent parameters. Enter the allowed range using the
min:step:max syntax or specify a list of comma- or space-separated values.
Figure 14 Edit the Value Column to Define the Allowed Range
11. If you do not see the parameters of interest for the selected instances, modify the
Whitelist filter or change the list to view to 'Editable' or 'All'.
Figure 15 Modify the Whitelist Filter Setup if Needed
Figure 16 Change the View to Editable or All to Show Additional Parameters
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Circuit Optimization
12. Create parameters for all other devices that will be optimized.
Figure 17 Completed Set of Parameters
The Run Summary form displays the total design space size.
Figure 18 Size of Design Space Defined by the Parameters
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Circuit Optimization
Running Circuit Optimization with Global Optimization
In this section, global optimization is performed without a starting point. First, you will
run optimization over Nominal conditions, and then include corners. Finally, you will run
optimization with the goal of minimizing power consumption of the op amp.
1. Select Global Optimization from the list of run modes.
Figure 19 Select Global Optimization
2. Open the run mode options form by selecting the Options button.
Figure 20 Select the Run Mode Options Button
3. Specify the global optimization options.
Figure 21 Global Optimization Options
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Circuit Optimization
In this example, you are not providing a starting point for the optimization. The
optimization will stop after all specifications are met (or the optimizer cannot find a
solution).
Conditional evaluation avoids unnecessary simulation by skipping points which are not
an improvement on the current best point.
4. Select the Run Simulation button to start the optimization.
Figure 22 Run Optimization
It is typically recommended to perform a quick optimization over Nominal (with Corners
disabled) to confirm that the specifications can be met. The best point of the
optimization is displayed at the top of the table.
Figure 23 All specs met at Nominal
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Circuit Optimization
Specifications are easily met at Nominal; so, corners are enabled for the next
optimization run.
Figure 24 All Specs Met over Corners
5. Open the Variable Display assistant to view the optimized values. Select the
gray Parameters row in the Results tab for any point to view the variable values.
The bar graph display is especially useful to identify if any variable is limited by
its upper or lower bound.
Figure 25 Variable Display Assistant
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Circuit Optimization
Optimizing with open-ended specifications
Next, you will run an optimization to reduce power consumption.
6. Change the specification type from less than (<) to the open-ended 'minimize'
type.
Figure 26 Minimize the Power Spec
7. Next, change the optimization-stopping criteria. Choose to stop when there has
been no improvement after 400 further points.
Figure 27 Stop When No Improvement after 400 Points
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Circuit Optimization
8. Run a global optimization to minimize power.
Figure 28 Best-Point Result and Run Log
The power was reduced from 317.7uW to 285.6uW at the worst corner
AVDD_1.26_T_1.
9. Save the variable and parameter values of the best-point optimization result to a
setup state. The result may also be back-annotated to the schematic. By saving
the values to a setup state, you can recall the point later for simulation or you can
use this result as a starting point for local optimization.
Figure 29 Save the Best Point
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Circuit Optimization
Running Circuit Optimization with Local Optimization
In this section, a local optimization is performed. Choose local optimization when you
have a starting point to improve upon.
You have already defined optimization ranges as follows. Before defining the starting
point, save these parameter ranges to recall them later.
1. Specify a name in the Variables and Parameters assistant and then select
Save to save the set of vars and parameters to the named Setup State.
Figure 30 Save (Back-Up) the Optimization Parameter Ranges
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Circuit Optimization
2. Next, define the starting point for the optimization. In ADE, the starting point is
defined as a Setup State and defines a scalar value for each optimization
variable or parameter.
To create a starting point based on the current schematic design, select each
parameter and then select 'Set to Design Value' from the context menu.
Figure 31 Create a Starting Point Based on the Current Schematic Design
The parameter values are set to the schematic values.
Figure 32 Parameters Set to the Schematic Values
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Circuit Optimization
3. Save this set of parameter values to a Setup State. Specify a name for the state
and select Save.
Figure 33 Save Schematic Design to Setup State to Use as Starting Point
4. Open the Local Optimization run options form. Select a Setup State to use as
the starting point for optimization. You can choose to use the schematic starting
point or the best point that was saved from the previous Global Optimization run.
The result of GlobalOpt.2 is selected as the starting point.
Figure 34 Set the Local Optimization Options
5. Define the parameter ranges for the local optimization. Reload the parameter
ranges that were previously defined.
Figure 35 Load the Parameter Ranges for Optimization
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Circuit Optimization
Comparing the starting point with the parameter ranges, you can see that several
parameters are at their limits. For example, the Variable Display assistant shows that
PM1.l = 3u, which is the upper limit of the range.
Figure 36 Starting Point Compared to Ranges (Best Point GlobalOpt.2)
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Circuit Optimization
Another comparison of the starting point and the parameter ranges is available through
the Variables and Parameters assistant.
Figure 37 Select the Starting Point and Open the Compare Window
Figure 38 Compare the Starting Point and Current Parameters
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Circuit Optimization
6. Modify the parameter ranges to give more freedom to the local optimization. The
new set of parameters were saved as 'ranges2'.
Figure 39 Updated Parameter Ranges to Use for Local Optimization
7. Run local optimization.
Figure 40 Run Local Optimization
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Circuit Optimization
When local optimization completes, the best point is displayed at the top of the Results
table.
All specifications are met, and power was reduced from 285.6uW (best point from the
previous run) to 269.3uW at the worst corner AVDD_1.26_T_1.
Figure 41 Local Optimization Results
8. Open the Variable Display assistant to view the parameter values. Select the
gray-colored Parameters row in the Results table to view the values of the
selected point.
Figure 42 Local Optimization Result Parameter Values
The result values may be back-annotated to the schematic or saved to a Setup State for
further verification simulation.
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Circuit Optimization
Running Circuit Optimization Considering Process
Variation
After optimization over supply voltage and temperature corners, a Monte Carlo analysis
is performed for final verification. The number of Monte Carlo samples to run depends
on the target yield requirement and probability (or confidence level). Given a 3-sigma
target yield requirement (99.87% yield), ~2000 samples must be simulated to verify the
estimate.
Simulating 2000 or more samples may be very time consuming depending on the
circuit. Virtuoso Variation Option provides efficient Monte Carlo methods to reduce the
number of simulations for yield verification and statistical corner creation. In this section,
since your op amp can be simulated quickly, you apply brute force standard Monte
Carlo.
Overall Flow
Begin with Monte Carlo analysis and then create a statistical corner for each
specification. After creating the corners, optimize the design over the statistical corners.
When specifications are met over the statistical corners, you expect the yield to
improve. Run a Monte Carlo analysis on the optimization result to verify that the yield
has improved.
Monte Carlo
Create Statistical
Corners
Optimize Over
Statistical Corners
Final Monte Carlo
Figure 43 Improve Yield by Optimizing over Statistical Corners
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Circuit Optimization
Steps to Run Optimization Considering Process Variation
1. Select the Monte Carlo Sampling run mode and specify the number of Monte
Carlo sample points to simulate.
Figure 44 Monte Carlo Options
2. Run Monte Carlo.
Figure 45 Run Monte Carlo
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Circuit Optimization
The yield estimate is 37%.
Figure 46 Monte Carlo Results
Since the yield target is not met, statistical corners will be created. Then, the design
must be modified either manually or by using optimization to meet the specifications
over the statistical corners. Once the specifications are met over the statistical corners,
another iteration of Monte Carlo is performed to verify the yield estimate.
3. Sort the transposed Results table to view the worst result for each specification.
For each specification, sort the specification column and then select 'Create
Statistical Corner' from the context menu to create the corners.
Figure 47 Create Statistical Corner from Selected Result
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Circuit Optimization
Another method to create the corners is to select the specification from the Yield view
and then select 'Create Statistical Corner from Worst Sample'.
Figure 48 Create Statistical Corner from Worst Sample
Notice that the statistical corners also include the supply voltage and temperature
variation. You can decide if any of the original supply voltage and temperature corners
are extraneous and disable them to reduce simulation time.
Figure 49 Voltage, Temperature, and Statistical Corners
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Circuit Optimization
4. Define the parameter ranges to prepare for optimization. Here, you load the
ranges from the Setup State.
Figure 50 Load the Parameter Ranges for Optimization
5. Specify the global or local optimization options. Here, local optimization is
selected. The starting point is the result of the previous optimization. No stopping
criteria is specified. After meeting all specifications, the optimizer will continue to
run with the goal of improving on the open-ended specifications.
Figure 51 Specify Local Optimization Options
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Circuit Optimization
6. Run the optimization over statistical corners.
The local optimization completes after a few hundred simulations. All specifications are
met including those over the statistical corners. The best result point is displayed at the
top of the table.
Figure 52 Optimization over Statistical Corners
7. Save the best point to a Setup State.
Figure 53 Save the Best Point
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Circuit Optimization
8. The next step is to run Monte Carlo analysis to verify that the yield estimate has
improved. In preparation for Monte Carlo, load the parameter values of the
optimization result.
Figure 54 Load the Result of the Optimization
9. In preparation for Monte Carlo, disable the statistical corners.
Figure 55 Disable Statistical Corners
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Circuit Optimization
10. Select the Monte Carlo Sampling run mode and again specify the number of
Monte Carlo sample points to simulate.
Figure 56 Monte Carlo Options
11. Run Monte Carlo.
Figure 57 Final Monte Carlo Results
All 2000 Monte Carlo samples now pass the specifications. The yield was improved by
optimizing the design over statistical corners.
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Circuit Optimization
Circuit Optimization Results
Results
The optimization result was verified over 2000 Monte Carlo samples.
Figure 58 Final Monte Carlo Verification
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Circuit Optimization
Comparison between Manual Design and Circuit Optimization Design
With manual design, the op amp block was verified to meet specifications over Nominal
conditions.
To save time and effort, optimization was applied to size the design over corners and to
verify that the Monte Carlo yield target was met.
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