Step by Step WCCA

INTRODUCTION TO THE

WORST CASE ANALYSIS

PROCEDURES

1

2

A STEP BY STEP PROCEDURE TO PERFORM

A WORST CASE CIRCUIT ANALYSIS

1. MEET WITH THE CIRCUIT DESIGNER:A. REVIEW THE SCHEMATICB. DETERMINE EXACTLY WHICH CIRCUITS (AND THEIR ATTRIBUTES) ARE TO BE ANALYZEDC. DETERMINE THE PASS/FAIL CRITERIA

2. LIST THE PART TYPES THAT WILL REQUIRE PART PARAMETER VARIATION DATA

3. DOCUMENT THE PART PARAMETER VARIATIONS DUE TO:A. INITIAL TOLERANCEB. TEMPERATURE EFFECTSC. RADIATION EFFECTSD. END OF LIFE (AGING) EFFECTS

4. FOR EACH CIRCUIT IDENTIFIED IN (1) ABOVE, PERFORM A WORST CASE CIRCUIT ANALYSIS USING THE PART PARAMETER VARIATIONS FROM (3) ABOVE. COMPARE THE RESULTS TO THE PASS/FAIL FROM (1) ABOVE.

5. WRITE THE FORMAL REPORT.

3

STEP 1

What circuits are to be analyzed ?

The designer, and the analyst together, identify those circuits to be evaluated. These would typically bethe ones that are critical to the mission, sensitive to part variation, have written numerical performancerequirements, etc. Then for each circuit selected the specific performance criteria of importance is statedand the pass/fail requirement is determined.

Basically, working together the designer and the analysts make up a Statement of Work for the WCCA tobe done. For example:

On the SEVC INTERFACE SCHEMATIC (24899) the following circuit functions are to be analyzed for worstcase performance:

SCHEMATIC DESIGNATOR ATTRIBUTES LIMITSU8A & U8B Current Integrator Reset timing

LinearityOffsets

10VDC to 0VDC in 1.2msec0.23% best straight line 0 - 10 VDC<45mV

U21, 32,33,34 Local Memory Bus Set timeHold time

Per WC Part Parameter DatabasePer WC Part Parameter Database

The table above must be approved by the component design lead engineer before the analysis begins.

4

STEP 2&3

Part Parameter variations

Since the purpose of the WCCA is to evaluate the circuit performance due to part parameter variations,these variations need to be determined and documented. As a minimum a given part parameter will changefrom its nominal value due to:

A. INITIAL TOLERANCEB. TEMPERATURE EFFECTSC. RADIATION EFFECTSD. END OF LIFE (AGING) EFFECTS

For some parts, factors such as humidity, vacuum and applied voltage must also be considered. The datasheet for the part usually provides this information. The initial tolerance and temperature effects arelikewise given in the data sheet. The parameter variations from all of the effects are added together withthe proper sign to obtain the numerical value for the maximum and minimum value to be used in theWCCA.

Radiation effects are dependant upon the spacecraft shielding and the test condition used. The parametervariations due to radiation are to be obtained from the program’s part engineer. To request this informationuse the following form:

PARTDESCRIPTION

PROGRAM WHERE USED PARAMETER VARIATION DUE TORADIATION

LM139 ISS SHUNT CNTRL Vos 2.3 mV " " " Ios 35nAREF01 KEPLER CEU DONWLINK Vout 12 mV

Leave this column blank,the part engineer will complete it.

The end-of-life data (EOL) data is shown in Appendix A. While these parameter variations have beendetermined based on a 10 year mission they are to be used on all programs. Special notice should be takenof the "EOL" factor for microcircuits: instead of adding the variations due to initial tolerance, temperatureand aging (EOL), simply use the parameter value given on the data sheet at the two temperature extremesallowed for the device (typically -55oC and +125oC). The variation due to radiation (the right most columnin the table above) is then added giving, the Worst Case maximum and minimum numerical values to usein the WCCA calculations.

5

Step 2&3 (continued)

To document the part parameter variations, the data collection forms shown in Figure 1 are to becompleted for each part type used in the WCCA. Additional rows may be added as necessary to addressvariations due to factors other then the ones listed (e.g., humidity, applied voltage, etc.). The top section ofthe form simply collects general information while the "Parameter" section is used for a specific partparameter (Vos, hfe, etc.). Since additional parameters for the same part do not need the generalinformation repeated, only the "Parameter" sections are required. The parameter variation due to eacheffect (temp, EOL, etc.) is entered in the appropriate line in the "Deterministic variation" columns. (The"Random variation" columns are not used unless the circuit fails the WCCA ). The column labeled "NEG"would contain the variations that reduce the nominal value, while the "POS" is for those variations thatincrease the nominal value. The boxes labeled "Worst Case Minimum" and "Worst Case Maximum"contain the combined totals of the "NEG" and "POS" columns respectively. Figure 2 shows a examplecompleted for an RNC resistor. A more involved example for a 2N2907A transistor is given in Figure 3.An example of a Microcircuit is shown in Figure 4 for an AD713.

If the specific part exhibits parameter variation due to factor others than Initial, Temperature, Radiationand EOL, then additional rows may be added as needed. Since WCCA is a quality audit of the circuitrythe sources of data used is of great importance. The column "Data Sources" must be completed for eachrow.

6

Program namePart Number(s)

Generic part typeDescriptionCase style

Conditions of use: Min Temp (oC): Max Temp (oC):Radiation Dose (kRAD): Service Life (months):

Parameter: Symbol: Nominal Value: Units:

NEG POS (+/-) NotesInitial

Low temp. High temp. Radiation End-of-life

Worst Case Minimum: 0.00 Worst Case Maximum: 0.00









Part Variation Worksheet for Worst Case Analysis

Data SourceDeterministic variation Random variation

Deterministic variation Random variationData Source

Deterministic variation Random variation Data Source

Figure 1 Part Parameter Variation Sheet

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Program nameI ISS NORTH BUS RIUPart Number(s) RNC55HXXXXFP

Generic part type RNC55HDescription RESISTOR, +1%Case style

Conditions of use: Min Temp (oC): -10 Max Temp (oC): 68Radiation Dose (kRAD): 50 Service Life (months): 120

Parameter: Symbol: Nominal Value: any Units:

NEG POS (+/-) NotesInitial -1.00 1.00 Percent change

Low temp. -0.18 -0.005%/CHigh temp. 0.22 +0.005%/CRadiation 0.00 0.00End-of-life -1.00 1.00 Web Site, +1% change

Worst Case Minimum: -2.18 % Worst Case Maximum: 2.22 %








Worst Case Minimum: 0.00 db Worst Case Maximum: 0.00 db



EOL DATA

MIL-PRF-55182GN/A


Data SourceMIL-PRF-55182GMIL-PRF-55182G

Deterministic variation Random variation

Resistance

Figure 2 Part Parameter Variation Sheet for an RNC 1% resistor

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Program nameI ISS NORTH BUS RIUPart Number(s) JANS2N2907A (19500/219H)

Generic part type 2N2907ADescription Transistor, switching, PNPCase style


Parameter: Symbol: HFE

Nominal Value: 225 Units: na

NEG POS (+/-) NotesInitial 100.00 450.00

Low temp. -27.00 27% reductionHigh temp. 157.50 35% increaseRadiation -10.00 45.00 +10% changeEnd-of-life -25.00 112.50 Web site, +25% change



Nominal Value: 150 Units: na

NEG POS (+/-) NotesInitial 100.00 300.00 Assumed max = 3 * min

Low temp. -40.00 40 % reductionHigh temp. 240.00 80% increaseRadiation -10.00 30.00 +10% changeEnd-of-life -25.00 75.00 Web site, +25% change



Nominal Value: 150.00 Units: na

NEG POS (+/-) NotesInitial 100.00 300.00

Low temp. -38.00 38% reductionHigh temp. 180.00 60% increaseRadiation -10.00 30.00End-of-life -25.00 75.00 Web site, +25% change



Data Source19500/219H

Motorola data sheet


Gain at VCE = 10V, IC = 1mA


EOL DATA

Motorola data sheetRadiation Engr


Motorola data sheet

Radiation Engr

Data Source19500/219H

Motorola data sheet

Radiation EngrEOL DATA

EOL DATA

Deterministic variation Random variation Data Source19500/219H

Motorola data sheetMotorola data sheet


Figure 3 Part Parameter Variation Sheet for a 2N2907A

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Program name ISS NORTH BUS RIUPart Number(s) 5962-9063301MCX

Generic part type AD713Description Quad BiFET Op-AmpCase style 14 pin DIP


Parameter: Symbol: VosNominal Value: +0.5 Units: mV

NEG POS (+/-) NotesInitial -2.00 2.00 Over full temp

Low temp. 0.00 0.00 Included in initialHigh temp. 0.00 0.00 Included in initialRadiation -0.80 0.80 Radiation DatabaseEnd-of-life 0.00 0.00 Included in initial

Worst Case Minimum: -2.80 mV Worst Case Maximum: 2.80 mV

Parameter: Symbol: IbNominal Value: +40 Units: pA


Low temp. 0.00 0.00 Included in initialHigh temp. 0.00 0.00 Included in initialRadiation -82.00 82.00 Radiation DatabaseEnd-of-life 0.00 0.00 Included in initial

Worst Case Minimum: -236.00 pA Worst Case Maximum: 236.00 pA

Parameter: Symbol: CMRRNominal Value: -80.00 Units: db


Low temp. 0.00 0.00 Included in initialHigh temp. 0.00 0.00 Included in initialRadiation 3.00 0.00 Radiation DatabaseEnd-of-life 0.00 0.00 Included in initial

Worst Case Minimum: -69.00 db Worst Case Maximum: 0.00 db

RADIATION ENGRSMD

SMD


SMDSMDSMD

Common Mode Rejection Ratio

SMD

RADIATION ENGR

Data SourceSMD

SMD


SMD

SMDRADIATION ENGR

Input Bias Current


Data SourceSMDSMD


Input Offset Voltage

Figure 4 Part Parameter Variation Sheet for a AD713

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STEP 4

Worst Case Circuit Mathematical Methodology

The Extreme Value Analysis (EVA) methodology is to be used in calculating circuit performance. In thisapproach the circuitry is examined to determine the part parameters that results in the worst possibleperformance of the circuitry. The circuit performance is then calculated assuming that these parametersvalues occur simultaneously.

If the circuit fails to meet its performance criteria the analyst should investigate the acceptability ofstatistically combining the contributors to the part parameter variation. Part parameter variations can begrouped into correlated and random variations. Correlated is taken to mean the relationship between theparameter value and the independent variable (temperature, radiation, etc.) can be expressed as a singlevalued function. Random is taken to mean the relationship between the parameter value change and theoriginating cause (temperature, radiation) cannot be expressed as a single valued function. All thecorrelated variations should be added (or subtracted if the sign is negative) while the random variationsshould be combined using the root sum of the squares method. The column labeled "Random variations"on the Part Variation sheets are used in applying this method of recalculating the part parameter used in thecircuit analysis. (See Figure 5 for an example). The use of statistically combining parameter variationsmust be quantitatively justified in the final report.

If the circuit still fails then the Root Sum of Squares (RSS) or the Monte Carlos (MC) methodology may beconsidered at the circuit level. The both RSS and MC are statistical approaches that make use of thepotential random variations of the part parameters, and as such the mathematical justification must beprovided in the report. Appendix B provides more detailed information on all three approaches.

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Program name NSTAR NORTH BUS RIUPart Number(s) RNC55HXXXXFP

Generic part type RNC55HDescription RESISTOR, +1%Case style


Parameter: Symbol: Nominal Value: any Units:

NEG POS (+/-) NotesInitial 0.00 0.00 1.00 Percent change

Low temp. -0.18 -0.005%/CHigh temp. 0.22 +0.005%/CRadiation 0.00 0.00End-of-life 0.00 0.00 1.00

Worst Case Minimum: 1.24 % Worst Case Maximum: 1.63 %

(1) From NSTAR Design Note DN 089-143 (study of resistors in NSTAR storage)








Worst Case Minimum: 0.00 db Worst Case Maximum: 0.00 db



See (1) below

MIL-PRF-55182GN/A


Data SourceSee (1) below

MIL-PRF-55182G


Resistance

Figure 5 Example of using RSS at the part level

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STEP 5

REPORT FORMATThe results of the WCCA analysis are to be documented using the following report format:

WORST CASE CIRCUIT ANALYSISREPORT

TABLE OF CONTENTS

1.0 Introduction .....................................................................................................................

2.0 Summary .....................................................................................................................

3.0 Applicable Documents ....................................................................................................

4.0 Assumptions and Groundrules ........................................................................................

5.0 Detailed Analysis .............................................................................................................

5.1 Circuit Description ..........................................................................................................

5.2 Worst Case Circuit Analysis ...........................................................................................

6.0 Conclusions and Recommendations ...............................................................................

Appendix ....................................................................................................................................

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STEP 6 (Continued)

1.0 Introduction

This section states what was analyzed. It includes a list of the specific circuits that were examined and the pass/fail criteria for each.

2.0 Summary

This section provides a brief listing of the results, specifically the circuits thatFAILED.

3.0 Applicable Documents

This section lists those documents that were used in the analysis. (Schematics, P/Ls, performance specs, etc.)

4.0 Assumptions and Groundrules

This very important section lists and explains all assumptions and groundrules used in theanalyses. The difference between an assumption and a groundrule is: an assumption is what youmade, a groundrule is what you were told to use.

5.0 Detailed Results

This section contains the technical details.

5.1 Circuit Description

Provide a description of each circuit analyzed.

5.2 Worst Case Circuit Analysis

Contains the actual circuit analysis calculations.

6.0 Conclusions and Recommendations

This is where you wrap up the report. Tell the audience what you did, what you found and whatthey should do about it (redesign, additional testing , more analyses, etc.)

APPENDIX

Put the part parameter variation sheets here. May also include documents,(e-mail, spice/saber netlists, etc.) that are referenced elsewhere in the report.

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Appendix A(Example only)

End of life (EOL) factors to use in performing Worst Case Circuit Analyses

The EOL design limits for parts are the expected variation in the electrical parametersof parts for which allowance made be made in circuit design. The parameter variationsare expressed as a percentage change from the specified initial minimum or maximumvalues. The EOL design limits to be used as guidelines are extracted from MIL-STD-1547.

EOL DESIGN LIMITS

Part TypeApplicable MIL-Spec Parameter

End-of-LifeDesign Limits

CapacitorsCeramic, CKS(General Purpose BX)

MIL-C-123 C ± 21%

IR -50 %Ceramic, CKSTemperature CompensatedBP)

MIL-C-123 C(3) ± 0.5% OR 0.45 pF,whichever is greater

IR -50%Metallized Film, CRH MIL-PRF-83421 C ± 2%

IR -30%Metallized Film, CHS MIL-C-87217 C ± 2%

IR -30%Glass, CYR MIL-C-23269 C ± 0.5% OR 0.5 pF,

whichever is greaterIR 500,000 Megohms @

25oC.50,000 Megoohms @125oC

Mica, CMS MIL-C-87164 C ± 0.5%IR -30%

Tantalum, Foil, CLR MIL-C-39006 C ± 15%DCL +130%

Tantalum, Slug, CLR MIL-C-39006 C ± 10%DCL +130%

Tantalum, Solid,CSS and CWR

MIL-PRF-39003MIL-C-55365

C ± 10 %

Variable Piston MIL-C-14409 C ±5%IR -30%

Variable Ceramic MIL-C-81 C(1) ±0.5pF1) EOL Design Limits were derived from MIL-STD-1547, except those annotated.2) Use maximum specification limit for wide temperature range (-55oC to +125 oC) for total worst-case

tolerance (EOL and temperature).3) Derived from NASA Parts Application Handbook, MIL-HDBK-978.

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EOL DESIGN LIMITS (Continued)

Part TypeApplicableMIL-Spec Parameter

End-of-LifeDesign Limits

ResistorsFilm, RLR MIL-PRF-39017 R ±2%Film, RNC MIL-PRF-55182 R ±1%Film, RNC90Y (Vishay) MIL-PRF-55182 R(1) ±0.1%Wire Wound, RBR (Accurate) MIL-R-39005 R ±0.5%Wire Wound, RWR (Power) MIL-PRF-39007 R ±1%Wire Wound, RER (ChassisMount)

MIL-PRF-39009 R ±1%

Network, RZO MIL-PRF-83401 R ±1%Chip, Thick Film MIL-PRF-55342 R(1) ±2%Chip, Thin Film, TantalumNitiride, (IRC only)

MIL-PRF-55342 R(1) ±0.5%

Thermistors, Glass Bead, NegTC

MIL-T-23648 R ±1.3%

Bead Encapsulated, Pos TC R ±1.8%Disc, Pos or Neg TC R ±5%EMI Filters MIL-PRF-28861 C ±20%

IR -50%Coils, RF Molded MIL-C-39010 L(1) ±3%

Q(1) ±6%Transistors MIL-PRF-19500 HFE(1) ±25%

ICBO(1) +100%ICES(1) +100%ICEX(1) +100%

VBE ±0.01VVCE(sat) ±15%

VTH(MOSFETS) (1) +0.1, -0.0vDiodes MIL-PRF-19500 VF ±1%

IR +100%VZ(1) ±1%

Microcircuits* MIL-M-38510 (2)1) EOL Design Limits were derived from MIL-STD-1547, except those annotated.2) Use maximum specification limit for wide temperature range (-55oC to +125 oC) for total worst-case tolerance (EOL and temperature).3) Derived from NASA Parts Application Handbook, MIL-HDBK-978.

If a part type is not shown contact Parts Engineering

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Appendix B

Calculation Methodology

Three calculation methodologies are recognized as suitable for the performance of a WCCA: 1) ExtremeValue Analysis (EVA), 2) Root Sum of Squares (RSS) and 3) Monte Carlo analysis (MC). The EVAmethod is always used as the primary approach. If the circuit fails the performance criteria, either theRSS or MC method may be used with mathematical justification provided in the report.

Extreme Value Analysis (EVA)

This approach assumes that all part parameters are at their respective extreme values such that the circuitperformance deviates the most from its nominal value. As an example consider a simple two resistorvoltage divider circuit feed by a battery. The nominal output voltage is given by

⎥⎦⎤

⎢⎣⎡

+⋅=

212RR

RVV BATOUT

By inspection it is seen the VOUT has a maximum value of

⎥⎦

⎤⎢⎣

⎡+

⋅=MAXMIN

MAXBATOUT RR

RVVMAXMAX 21

2

and a minimum value of

⎥⎦

⎤⎢⎣

⎡+

⋅=MINMAX

MINBATOUT RR

RVVMINMIN 21

2

The min/max values to use for VBAT, R1 and R2 are obtained from their part parameter variation sheets.

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Root Sum of Squares

The probability of all part parameters simultaneously aligning in the various combinations that produceworst case circuit performance is very small. In reality some variations will cancel out other variationsleading to less departure from the nominal circuit performance then is given by an EVA. This fact may beaddressed through the use of statistical circuit calculations commonly known as the Root Sum of Squares(RSS) technique. Basically the objective is to calculate the standard deviation of the circuit attribute (e.g.,Vout) due to random variations in part parameters (e.g., hfe, VOS, etc.). Assuming that the standarddeviation (σ) for each part parameter is known, then the standard deviation of the circuit attribute is:(using the voltage divider example from above)

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

∂∂

=2

2

2

1

2

21 ROUT

ROUT

VBAT

OUTV R

VR

VVV

BAToutσσσσ

Accordingly the worst case values of VOUT are:

( )OUTNOMMAX VOUTOUT VV σ⋅+= 3

and

( )OUTNOMMIN VOUTOUT VV σ⋅−= 3

It is important to note that the RSS technique is appropriate only for linear transfer functions and even thenthe following three conditions must be met:

1. The part parameter variations are normally distributed.2. The part parameter variations are independent of each other.3. The actual average value of the part parameter must equal the statistical mean.

The requirement of a linear transfer function may be relaxed somewhat by taking a Taylor series expansionabout the operating point and discarding second and higher terms (provided that the resultant error isacceptable). Of the conditions given above, (3) is probably the most difficult to prove in the spacecraftindustry. It states, for instance, that if the circuit uses 1K +5% resistors then average value of the actualresistors from the storeroom must be 1K. This simply implies that, indeed, some parts will be on the highside while others will be on the low side resulting in the desired cancellation effects. For mass productionwhere parts are bought in large quantities this most likely is true. However, parts are typically purchasedin small lots. Intuitively it would seem that in this case part parameters might very well be all on the highside or all on the low side and thus would not cancel out. Additionally some parameters are correlated tothe operating environment (e.g., hfe vs temperature) in which case a modified RSS analysis must be usedby combining the results of an EVA approach on the correlated parameters and RSSing the truly randomparameters. All of these difficulties require that mathematical justification be provided when using theRSS methodology.

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Monte Carlo analysis

The Monte Carlo technique is also a statistical analysis that circumvents some of the short comings of theRSS analysis. Basically, MC is a analytical description of a pilot production run from which theprobability of obtaining a working circuit may be found (even if only one spacecraft in being built). Forthe electronic circuitry normally used in spacecraft, computer tools such as Spice and Saber make the MCapproach viable. It still is imperative to obtain the actual distributions for the parameters of interest, butonce obtained the power of the computer may be brought to bear on the analysis problem. The output of aMC analysis is then the probability that the circuit will work correctly. This probability is to be reported atthe 95% confidence level in the final report along with the quantitative justification of the distributionsused.

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