Worst Case Analysis Using Analog Workbench by Andrew

Worst Case Analysis Using Analog Workbench by Andrew G. Bell ITT Industries

Worst Case Analysis Using Analog Workbench has two powerful capabilities, which makes it very useful in WCA. First, it has parameterized models that can be toleranced. Second, it allows the user to establish marker functions of the user choosing. A. G. Bell ITT Industries 2

Worst Case Analysis Using Analog Workbench Input Tools Output Tools Multi-Simulation Tools A. G. Bell ITT Industries 3

Worst Case Analysis Using Analog Workbench small signal analysis (frequency domain) Input Tools large signal analysis (time domain) A. G. Bell ITT Industries 4

Output Tool small signal analysis (frequency domain) Worst Case Analysis Using Analog Workbench Marker Function M 1 allows for the measurement of the magnitude and phase at 390 Hz to be made A. G. Bell ITT Industries 5

Output Tool large signal analysis (time domain) Worst Case Analysis Using Analog Workbench Use of these Marker Functions can show that the large signal results match the small signal results A. G. Bell ITT Industries DC tool not shown 6

WCA Example Worst Case Analysis Using Analog Workbench Consider the following example: A requirement is established and a circuit must be designed to meet the requirements worst case. Analog Workbench will be used to develop statistical device models and perform the worst case analysis using Monte Carlo and Sensitivity analyzes. For the parts: All parameters will be assigned a Flat distribution All parameters will vary independently Passive tolerances will be set to their extremes For the analysis: A Sensitivity/Worst Case analysis will be performed A 400 sample Monte Carlo will be run If needed additional analysis will be done to show the expected worst case performance A. G. Bell ITT Industries 7

Worst Case Analysis Using Analog Workbench First it is necessary to develop device models A. G. Bell ITT Industries 8

Worst Case Analysis Using Analog Workbench Extracting device parameters may require assumption to be made about max or min values not defined. A. G. Bell ITT Industries 9

Extracted parameters used to create a device model using Analog Workbench’s Parameter Entry Tool Worst Case Analysis Using Analog Workbench When in doubt it’s a good idea to assign a small symmetrical tolerance. A. G. Bell ITT Industries 1 0

Now the design. . . Worst Case Analysis Using Analog Workbench The requirement is that when implemented the above transfer function should be within ± 0. 1 d. B at four frequencies with a ± 2 confidence interval A. G. Bell ITT Industries 11

Worst Case Analysis Using Analog Workbench Simulation of the transfer function show a close but not exact match with the requirements Requirements 2 A. G. Bell ITT Industries 1 2

A circuit implementation is proposed and simulated against the requirements Worst Case Analysis Using Analog Workbench Parameterized model for the op amp was created Passive part values and tolerances were also determined A. G. Bell ITT Industries 1 3

Worst Case Analysis Using Analog Workbench Requirements 2 Simulated circuit matches closely with requirements A. G. Bell ITT Industries 1 4

A Sensitivity Analysis is performed next to determine how changes in each parameter will change the frequency response at all four frequencies. Worst Case Analysis Using Analog Workbench Most sensitive to passive part variations Keyed to Network Analyzer marker functions Relatively insensitive to OP AMP changes In spec Out of spec A. G. Bell ITT Industries 1 5

Worst Case Analysis Using Analog Workbench Still most sensitive to passive part variations but order of sensitivity has changed for the 1. 57 k. Hz gain A. G. Bell ITT Industries 1 6

Worst Case Analysis Using Analog Workbench Next perform a 400 sample Monte Carlo M 1 and M 2 set at 390 Hz upper and lower limits M 3 and M 4 set at 780 Hz upper and lower limits A. G. Bell ITT Industries Curve appears gaussian 100% of the 390 Hz Gain performance is met but only 82. 5% of the 780 Hz is achieved 1 7

Worst Case Analysis Using Analog Workbench M 1 and M 2 moved to 1. 17 k. Hz upper and lower limits M 3 and M 4 moved to 1. 57 k. Hz upper and lower limits A. G. Bell ITT Industries Only 47. 9% of the 1. 17 k. Hz requirement and 30. 3% of the 1. 57 k. Hz requirement is met 1 8

Parametric Plots are performed to determine how variation in some of the more sensitive components change the performance at 1. 57 k. Hz Need to tighten tolerances on C 1 -C 4, R 1 & R 3 A. G. Bell ITT Industries Worst Case Analysis Using Analog Workbench R 2 and R 4 not that important 1 9

Worst Case Analysis Using Analog Workbench Purchase tolerance = ± 1% Original Worksheet Aging (10 years) = ± 1. 5% Temperature (+75°C to -55°C) = ± 0. 5% Purchase tolerance = 0% Modified Tolerance Aging (5 years) = ± 0. 75% Temperature (+40°C to 0°C) = ± 0. 25% A. G. Bell ITT Industries Can the passive part tolerances be relaxed or will other parts be needed? We can reduce the resistor tolerance because we know something about how it is being used, i. e. 5 years, tailored and over smaller temperature range This reduces the resistor variation to ± 0. 8% and likewise we will reduce the capacitor tolerance by the same proportion to ± 2% We will also change the distribution of each passive parameter to gaussian and link the passive part variations together 2 0

Worst Case Analysis Using Analog Workbench To reduce the Severity of the WCA use: 1. Linked parameters 2. Gaussian distributions 3. Reduced tolerances A. G. Bell ITT Industries 2 1

Worst Case Analysis Using Analog Workbench The results look good but just how good? ± 1 = 68. 26% ± 2 = 95. 44% ± 3 = 99. 74% Ten 400 sample Monte Carlo were run. Note six of the seeds failed to meet the requirements but the other four did. When you are close to the requirement limit you may need to take more samples to prove that you meet the requirement. We fail to meet the requirements for the 1. 57 k. Hz gain so either the requirements need to be changed or we will need to use some tighter tolerance parts. If you used 4000 samples it would take longer but you have more confidence in the answer. A. G. Bell ITT Industries 2 2

Worst Case Analysis Using Analog Workbench Conclusions: ü AWB is a powerful tool that can be used for WCA ü Marker Functions provide a unique ability to check performance ü Both the Sensitivity and Monte Carlo tools are needed for WCA ü Much more work is still needed to develop statistical device models ü It still may be necessary to apply some realism to part variations A. G. Bell ITT Industries 2 3