Medical Electronics Manufacturing Fall 1999



Medical Electronics Manufacturing Fall 1999

CIRCUIT ANALYSIS



Worst-Case Circuit Analysis for Electronic Parts

Evaluating electronic circuits for tolerance to simultaneous worst-case variations of the individual piece-parts helps ensure that the final circuits will function reliably over the life of the device.

Walter M. Smith

Worst-case circuit analysis (WCCA) examines the effects on electronic circuits caused by potentially large magnitudes of variations of electronic piece-parts beyond their initial tolerance. The variations can be the result of aging or environmental influences, which can cause circuit outputs to drift out of specification. WCCA also determines the mathematical sensitivity of circuit performance to these variations and provides both statistical and nonstatistical methods for handling the variables that affect circuit performance. The methods described for developing a worst-case parts variation database and sensitivity analysis, as well as extreme value analysis (EVA), root-sum-square (RSS), and Monte Carlo analysis for solving circuit equations and combining variables, have become accepted industry standards over the last eight years. The components of WCCA are shown in Figure 1. There are three primary reasons for conducting such an analysis:

• WCCA helps to design reliability into hardware for long-term, trouble-free field operation. Electronic piece-parts fail in two distinct modes: catastrophic, which is dramatic and abrupt, and by the piece-part's parameters varying beyond both its nominal and initial (purchase) tolerance limits whereby the circuit continues to function but with degraded performance, ultimately exceeding the circuit's required operating limits. To eliminate piece-part catastrophic failures, the worst-case electrical stress and derating analysis ensures that all parts are properly derated. The analysis of variables allows designers to predict whether the circuit will stay within its specified performance limits under all of the combinations.

• WCCA has been formally accepted by FDA as a design verification tool.

• Using a worst-case part variations database, WCCA is economical and is relatively easy to perform.

WCCA yields value in the return on investment that a manufacturer will get both in the short term by reducing design iterations, design change notices, and test time; and in the long term by achieving an increase in production efficiency and long-life, trouble-free field operation.

Figure 1. The three components that make up worst-case circuit analysis.

WCCA Overview

Performing WCCA on an electronic board schematic involves breaking down the circuit into simple functional blocks and performing WCCA on each block. Analysts should first document a detailed description of each block and then develop the worst-case variations of critical parameters for all parts in the circuit to arrive at a worst-case maximum and minimum for each part parameter. Determining maximum and minimum variations is addressed later in this article. The performance requirements must be established for the critical circuit attributes for each block. Using the worst-case maximum and minimum values, analysts can show whether the circuit attribute's actual performance values meet or fail to meet the circuit's requirements. Finally, analysts should show how all of the functional blocks work together to meet the overall unit (board) requirements in the worst case.

Figure 2. Worst-case analysis of a band-pass filter.

Classical Evaluation of a Band-Pass Filter. The following example, which was performed on the band-pass filter shown in Figure 2, illustrates the performance and results of WCCA. The amplifier gain at the center frequency (Af0) will be the circuit attribute selected for analysis. Given that U6 is an ideal op-amp (RIN = [pic], ROUT = 0, AVOL = [pic]), it does not enter into the equation for gain, which is

[pic]

The specified requirement for the minimum Af0 is 7 V/V. The nominal and initial tolerance values for the resistors (R) and capacitors (C) are as follows:

C1, C2 = CYR20 (1500 pF, ±1%),

R1, R2, R3 = RNR50 (15 k[pic] ±1%),

R4 = RNR50H (40.2 k[pic] ±1%),

R5 = RNR50H (10 k[pic] ±1%),

R6 = RNR50H (1.21 k[pic] ±1%).

Substituting the nominal part values into Equation 1 yields Af0 = 11.08 V/V, which shows the result to be in spec. A more pessimistic answer is achieved using the piece-part initial tolerance values (±1%), which would yield Af0 = 7.84 V/V, again in spec. It should be noted that the initial tolerance values for the Rs and Cs are the most pessimistic values available, and this is how circuits are typically designed and analyzed. These values do not, however, indicate whether the circuit will survive real environments.

Figure 3. The maximum and minimum worst-case performance is compared to the specified upper and lower tolerance limits.

Creating a Worst-Case Scenario. This methodology enables analysts to determine whether there is any margin left in the circuit after calculating its worst-case maximum and minimum performance. It also allows these values to be compared to the circuit's specified upper and lower tolerance limits, which cannot be exceeded per its design specifications (Figure 3).

Normally, the worst-case calculations must be performed twice to assess worst-case performance against the upper and lower spec limits. The band-pass filter, however, must only stay above the required minimum gain of 7 V/V.

Figure 4. Part parameter variations for worst-case drift (superimposed). The example shows a capacitor (CLR) with a nominal value of 1200 µf.

Figure 5. Statistics of part variations.

The Worst-Case Part Variations Database. When a part vendor specifies an initial tolerance (procurement tolerance), this merely guarantees that when the part is purchased that all parts in each lot will fall within the initial tolerance specified (±1% for the Rs and Cs of the band-pass filter). It is not a guarantee that the part will remain within this tolerance band. After it is selected from stock, powered up, and exposed to its working environment, the part will drift beyond its original value. In many cases, especially those involving long-term use, the part will drift beyond the initial tolerance used in designing the circuit. Each possible maximum drift value is added algebraically to the initial tolerance (Figure 4).

For WCCA, it is assumed that when a part is selected from stock, it is at its initial tolerance value already. It is also assumed that all parts in a circuit are simultaneously at their maximum drift values. Although this scenario seems unlikely, it is possible in the worst case. A more likely scenario is that some combinations of parts will be at drift values beyond their initial tolerance; however, they will not all be at their maximum possible drift. In a worst-case scenario, survival of all parts simultaneously at their maximum drift values ensures survival to any degree of part variation in any combination. Calculating circuit performance under the worst-case scenario with a margin in the circuit, i.e. not exceeding the specified upper and lower performance tolerance limits, ensures a solid design against part variation.

Designing Reliability into Electronic Circuits

Developing the worst-case parts database is a significant portion of the work and cost involved in performing WCCA. The goal of this task is to develop a document consisting of worst-case database worksheets that show the worst-case maximum and minimum variations for each critical part parameter. The worksheets provide numerical contributing factors as well as environments such as initial tolerance, temperature life, and radiation. The worksheets also note whether these factors are biased or random variables. Data sources (MIL-SPECS, vendor data sheets, etc.) should also be included on the worksheets for traceability. These worksheets serve as a quantitative assessment of each part's dominant variability sources for each environment and for the life of the device.

The worst-case database provides a uniform reference source to ensure that any WCCAs performed on the program (large programs have many) use identical source data. It is impractical to have several design engineers developing separate databases. Once developed, such a database can be maintained, expanded, and tailored for other programs.

The manner in which a part's variations are combined makes a difference. Figure 5 illustrates bias and random variations. A bias variation simply means that the parameter changes (increases or decreases) in the same direction that the environment changes. For example, if temperature increases, the part parameter value increases (positive temperature coefficient) and vice versa. This variation is predictable. A random variation's direction is unpredictable regardless of which direction the part value and the environment changes. These bias and random variations can differ for different part types. For example, a particular environment change can cause a bias change of one part parameter type but a random change for another. Some drift effects can even be a combination of bias and random variations (e.g. temperature coefficient = 100 ± 10 ppm/°C).

The question is how are bias and random variations combined to arrive at the worst-case maximum and worst-case minimum part parameter values? One acceptable method is shown in Equations 2 and 3, which add biases algebraically and root-sum-square the random variations. RSS is a statistically correct method to combine random variables.

(2) Worst-case minimum = nominal value – [pic]negative biases – square root ([pic] randoms2)

(3) Worst-case maximum = nominal value + [pic]positive biases + square root ([pic] randoms2)

Some agencies and prime contractors require that the random terms be treated as biases, and therefore the biases are added algebraically as shown in Equations 4 and 5.

(4) Worst-case minimum = nominal value – [pic]negative biases – [pic]randoms

(5) Worst-case maximum = nominal value + [pic]positive biases + [pic]randoms

This method creates a worst worst-case scenario and is known as the extreme value analysis (EVA) method for combining part variations. EVA and RSS analyses of circuits for WCCA will be discussed later.

Other Contributing Factors to a Worst-Case Scenario. Additional factors that must be considered are the interface connections—the box-circuit input power, input signals, and loads—all of which have specified tolerance limits around the nominal values. In performing WCCA, these values must be set at their limits and in the direction (positive or negative) that causes the most problem for the circuit attribute under analysis.

Figure 6. Gain versus part value (all others at nominal). Sensitivity is equal to the slope at any point on the curve. The sensitivity of Afo over worst-case part value is equal to y/x.

Sensitivity Analysis. Equation 1 for the gain of the band-pass filter showed that substituting the nominal part values for the Rs and Cs would yield a gain of 11.08 V/V and that substituting the initial tolerance values would yield a gain of 7.84 V/V. Using nominal values, it was a straightforward substitution of the part values. However, to drive the gain to a minimum using initial tolerance values, which have an algebraic sign (+/–) with each part value, means either a positive or negative value must be chosen for each part. The combination of the parts' maximum and minimum values that will yield the circuit parameter maximum and minimum values must then be determined. Designers must determine the circuit sensitivity response direction (i.e., circuit value increase or decrease) for the directional change (positive or negative) for each part. WCCA requires performing this circuit sensitivity analysis with maximum and minimum values. This analysis is required because one wrong sign for any part will void the worst-case solution. The classical solution for determining each part's sign (+/–) of its sensitivity when solving for either worst-case maximum or minimum is to take the partial derivative of the circuit equation individually with respect to each part. That will yield the sign of the part that must be used. For the band-pass filter, the equation is

[pic]

Fortunately, many circuit simulators enable engineers to perform this sensitivity analysis. However, there are other means for determining sensitivity, such as substituting small incremental changes in each part (holding all other part values constant) and solving the circuit equation to see whether it increases or decreases. It is also possible to sweep the gain over a fairly wide range or over each part value to display graphically as shown in Figure 6. Notice in Figure 6 that as C1 increases, the circuit gain (Af0) increases (positive sensitivity for C1). If the gain (Af0) decreases as the part value increases, then that part would have negative sensitivity.

Figure 7. Worst-case maximum and minimum for Rs and Cs.

Worst-Case Evaluation of the Band-Pass Filter. To evaluate the worst-case minimum gain at the center frequency (Af0) for the band-pass filter in Figure 2 and Equation 1, worst-case maximum and minimum must be determined for the Rs and Cs (Figure 7). All variations were treated as biases. Note that Vi and Vo of Figure 2 do not enter into Equation 1, which would require setting them at their maximum or minimum tolerance also. The directional (positive or negative) sensitivity of each part can also be determined using a simulator to perform sensitivity analysis (Table I).

|Piece-part |Sensitivity |Part value |Part value |

| |([pic]Afi) |for Af0 |for Af0 |

| |[pic]Pi |(max.) (pF/[pic]) |(min.) (pF/[pic]) |

|C1, 1500 pF |+ |1532 |1470 |

|C2, 1500 pF |– |1470 |1532 |

|R1, 15 k[pic] |+ |15,345 |14,655 |

|R2, 15 k[pic] |+ |15,345 |14,655 |

|R3, 15 k[pic] |– |14,655 |15,345 |

|R4, 40.2 k[pic] |+ |41,125 |39,275 |

|R5, 10 k[pic] |– |9770 |10,230 |

|R6, 1210 [pic] |– |1182 |1238 |

Table I. A simulator was used to perform a sensitivity analysis for each part.

Substituting the worst-case maximum and minimum values into Equation 1 for Af0 and in the direction dictated by the sensitivity analysis yields Af0 = 5.76 V/V, which fails the minimum gain requirement of 7 V/V by a large margin. Using all nominal or all initial tolerance values, the Af0 passes the requirement of 7 V/V (Figure 8). It is important to note the significant difference between the nominal solution (11.08 V/V) and the initial tolerance (7.84 V/V) and worst-case (5.76 V/V) solutions.

Figure 8. Minimum gain for initial tolerance, nominal values, and worst-case values.

Not all Rs and Cs must be at their worst-case limits to cause Af0 to fall below 7 V/V (worst case Af0 = 5.76 V/V). Many combinations of only several parts exceeding their initial tolerances would cause the gain to fall below 7 V/V. This substitution of piece-part worst-case maximum and minimum values into the circuit equation is called the EVA.

Alternative Techniques. Two alternative approaches for performing WCCA are the RSS analysis and the Monte Carlo analysis. Both techniques yield results that are more optimistic than the EVA solution. The example in this article uses a simple voltage divider circuit with four resistors (R1[pic] R4) and two internal voltage sources (V1 and V2). Equation 7 gives the output voltage.

[pic]

RSS is the statistical technique for combining standard deviations ([pic]). RSS is based on the law of large numbers (central limit theorem), which states that if many variables are statistically combined, the resulting distribution is normal and independent of the form of the distributions of the combined variables. It is therefore statistically valid to determine the standard deviation ([pic]) of a normal distribution for any circuit attribute by mathematically combining the standard deviations of each piece-part based on the magnitude of the circuit attribute's sensitivity to the value of the piece-part.

Figure 9. Monte Carlo analysis process.

The normal distribution of the output curve for Vo has a standard distribution related to the standard deviations of the part parameters as shown in Equation 8. The standard deviation of the output variable Vo will be identified as sT. Multiplying the solution of Equation 8 by three will yield the 3s (99.7%) value for Vo, which is defined as the worst-case value.

[pic]

Monte Carlo analysis is defined as the empirical determination of the statistical distribution of any circuit attribute by the repeated evaluation of the attribute under various circuit conditions in which the values of each piece-part are randomly selected (Figure 9).

With Monte Carlo analysis, the circuit mean and standard deviation ([pic]) can be calculated. The 3[pic] (99.7%) value is again defined as the worst-case value. Fortunately, many simulators that perform Monte Carlo analysis are available.

| |EVA |RSS |Monte Carlo |

|Vo Max |11.65 |10.544 (3[pic]) |10.562 (3[pic]) |

|Vo Min |7.69 |8.456 (3[pic]) |8.438 (3[pic]) |

|Vo Nom |9.50 |9.50 |9.50 |

Table II. Comparison of three worst-case circuit analysis techniques.

Comparing the Three WCCA Techniques. Using the voltage divider circuit for comparison, the three techniques provide the results shown in Table II for Vo Nom = +9.5V, upper tolerance limit = +10.30 V, and lower tolerance limit = +8.7 V (Table II).

EVA is the easiest technique to use and yields the most readily obtainable estimate of worst-case circuit performance, but it also yields the most pessimistic results. EVA requires development of a worst-case part parameter variation database for all the circuit piece-parts.

• The format of the required inputs for EVA is the worst-case part variation (minimum and maximum) limits (3[pic]) for all parts, plus circuit directional sensitivities.

• The format of the circuit output results is the worst-case maximum and minimum values.

The results for RSS are more realistic, but errors are inherent because of the assumptions of linearity of sensitivity and normal distributions.

• The format of the required inputs for RSS is the standard deviation of part parameters probability distribution (usually not available) and the magnitude of circuit sensitivities to part variations.

• The format of the circuit output results is the mean and standard deviation of the circuit attribute probability distribution.

Monte Carlo analysis typically yields accurate results given knowledge of the parts distribution (usually not available), and it requires a computer program.

• The format of required inputs for Monte Carlo is the probability distribution of piece-parts (no sensitivity analysis is required).

• The format of the circuit output results is a histogram of the circuit attributes probability distribution.

It is important to note that the statistical approaches of RSS and Monte Carlo enable prediction of the probability of the circuit attributes falling within any specified limits of interest. This is not available using EVA.

Conclusion

Electronic production hardware requiring reliable operation over a period of time should never be built nor fielded based on circuits designed using only the nominal or initial tolerance values of the piece-parts. Part values will drift after being assembled onto circuit boards. WCCA is not a major deviation from the classical circuit design and analysis that electronic engineers perform daily, given that the worst-case part variations are developed by or made available to the designers. In general, the required information to develop a worst-case parts database (analytically) is available or can be extrapolated or estimated with rationale.

WCCA on electronic circuits and systems has been performed for many years, and the approach and analysis methods described have been acceptable to government agencies and prime contractors for some time.

Acknowledgment

The author wishes to acknowledge the efforts of Harry Peacock, who, while serving as technical leader for reliability analysis for NASA's Jet Propulsion Laboratories (JPL), managed and contributed significantly to the modification of Design and Evaluation Inc.'s (D&E) WCCA training course. This article has been prepared using material from D&E's training course and engineering handbooks on WCCA. The course was developed and upgraded under contract to JPL to standardize an approach to performing WCCA.

Bibliography

Worst Case Circuit Analysis Handbooks (Volumes 1–5), (Laurel Springs, NJ: Design and Evaluation Inc., 1989).

Worst Case Circuit Analysis Training Course. (Laurel Springs NJ: Design and Evaluation Inc., 1989).

Walter M. Smith is president and general manager of Design and Evaluation Inc. (Laurel Springs, NJ), a reliability, maintainability, and worst-case analysis consulting company. His experience includes more than 30 years in reliability engineering and the analysis of electrical and electronic systems. He can be contacted at dande@.

Back to the Fall 99 Table of Contents

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Copyright ©1999 Medical Electronics Manufacturing

Worst-case circuit design includes component tolerances

Ignore the effects of tolerance buildup, and you'll have problems after you sign off on your prototypes.

By Ron Mancini, Texas Instruments -- [pic]EDN, 4/15/2004

Building reliable hardware requires that you account for all tolerances during the design stage. Many references discuss active component errors resulting from parameter deviations—showing how to calculate the effects of op-amp offset voltage, input current, and similar parameters—but few of them consider passive-component tolerances. References that do consider component tolerances do it from the scientist's, rather than circuit designer's, point of view.

However, you can understand worst-case design by using basic circuit equations and the component's limit values to calculate the range of worst-case values that a circuit parameter, such as output voltage, can assume over the life of the equipment. Worst-case design lets the components assume a wide range of values, which leads to a wide range of solutions; some of these solutions may be undesirable.

Passive-component-tolerances count

Resistors are fundamental in all electronic circuits, so you should consider them in detail. Resistors are specified with purchase tolerances, P, which you measure in percent; popular examples include 0.5, 1, 2, 5, and 10%. The purchase tolerance guarantees that the resistor is within its nominal value when you receive it. A resistor's value often is close to its limit when you purchase it, because many manufacturers select and remove the center of the distribution when grading resistors to sell as their tighter tolerance grades.

External stresses, such as soldering, cause resistor values to change during the assembly process. Hence, resistor values may change beyond the purchase tolerance before the completed assembly leaves the factory. Component values keep changing during their lifetime, because external stresses, such as temperature, aging, pressure, humidity, mounting, sunlight, and dust, change the component's composition, size, and surface characteristics. Component-value changes experienced during operation are called drift tolerances, D, and you measure them in percent.

| |

Table 1 shows estimated resistor tolerances. Notice that the purchase tolerance is separate from the drift tolerance, because you can trim to reduce or eliminate the purchase tolerance, but the drift tolerance occurs during normal operation and causes errors unless the system performs calibration before measurement. The drift tolerance for some resistors is greater than the purchase tolerance.

The resistor-manufacturing process and its operating environment determine the drift tolerance. Vendors manufacture tighter tolerance resistors with stable, controlled methods and materials that resist drift, because excessive drift results in manufacturing rejects. Tight process- and material-control techniques that minimize drift in the factory may not minimize drift in the field. The drift tolerances in Table 1 are worst case for an ambient temperature of –25 to +85°C and reasonable external stress. Unless the manufacturer states otherwise, temperature drift is unpredictable, and resistor values can increase or decrease due to an increase in temperature. Designers should consult the resistor manufacturer before using lower drift tolerances.

Resistors are usually represented as R1 or R2. Keeping this nomenclature, you can calculate the final resistor value as (1±T)R1 to obtain the worst-case resistor value, where T is the total tolerance expressed as a decimal. You use the plus/minus sign, because the tolerance's polarity depends on external conditions, manufacturing methods, materials, and internal stresses. You should assume the worst-case tolerance polarity during your calculations. You must represent individual resistor tolerances as positive or negative, using whichever yields the worst-case calculation, unless the data sheet states that all resistors drift in a prescribed direction. When calculating the absolute worst-case maximum value for R1=10 kΩ, 5%, you should use (1+0.01(5)+0.01(5))R1=1.1R1=11 kΩ. The absolute worst-case minimum value for this resistor is (1–0.01P–0.01D)R1=(1–0.05–0.05)R1=9 kΩ.

You handle capacitor tolerances, which these calculations do not discuss in detail, in the same manner. They vary much more between capacitor types than do resistors because of the radically different methods vendors use to manufacture them. Electrolytic capacitors often have purchase tolerances of 80, –20%, but some glass and NPO ceramic capacitors come with purchase tolerances of 1%. In general, it is best to triple all capacitor tolerances unless the manufacturer's data sheets suggest differently. This practice errs on the conservative side but is good judgment when you haven't done your homework.

Nonratiometric circuits

For nonratiometric circuits, you must assume the full resistor tolerance, because the tolerances do not divide out. You calculate the output voltage as VOUT=IR, where I is a perfect 1-mA current source, and R is a 5% resistor (Figure 1a). VOUT=1 mA (1±0.05±0.05)1 kΩ=(1±0.05±0.05)V. The range of VOUT is 0.9V≤VOUT≤1.1V, but you can narrow it by adjusting the initial tolerance with another resistor (Figure 1b).

You can calculate the adjustable resistor value, RP, as follows:

1. Select the closest decade value for R that is less than the minimum calculated value of R=0.9 kΩ; this value is R=0.82 kΩ.

2. Calculate the minimum value of the selected resistor as follows: RMIN=(1–P–D)R=0.9(0.82)=0.738 kΩ.

3. The variable resistor, RP, must make up the difference between RMIN and 1 kΩ, so RPMIN=1–0.738=0.262 kΩ.

4. The tolerance on potentiometers can be quite high, so RP=RPMIN/(1–T)=0.262 kΩ/(1–D–P)=0.262/0.8=0.328 kΩ.

5. Select RP=500Ω.

The final values are R=820Ω and RP=500Ω. Some engineers argue that the worst-case design procedures are too stringent and force a large potentiometer value, lower resolution, and higher potentiometer drift error. One possible solution to this problem is to decrease the potentiometer value and take a risk, but a better solution is to use higher precision parts. Nonratio circuits have to account for the full tolerance swing; thus, a 5% purchase tolerance results in a 20% (±10%) overall tolerance.

Ratiometric circuits

The voltage divider of Figure 2 and Equation 1 is the classic ratiometric circuit. Referring to the tolerance equation, you can see that some portion of the tolerance divides out of the equation.

[pic]EQUATION 1

To obtain the maximum gain value, you set the tolerance for R2 high and for R1 low. Because the tolerance for R2 is high, it appears as (1+T)R2 in all parts of the equation. Table 2 tabulates the ideal gain, maximum gain, and percent error in four resistor ratios. Notice that the minimum gain error occurs when R1=R2, and this gain error is equal to the tolerance. The nonratio circuit has to accept twice the tolerance or 2T, but the ratio circuit can have a tolerance of just T.

When both the resistor tolerances in a voltage divider are simultaneously high or low, the tolerances divide out. When the resistor manufacturer guarantees that all resistors drift proportionally and in the same direction during ambient-temperature changes, the temperature tolerance divides out.

Difference amplifier: on its own

Many references say that you can't build a precision differential amplifier that has good CMR (common-mode rejection) using discrete parts. This tolerance analysis of the differential amplifier explains why this statement is true. Consider the differential amplifier circuit in Figure 3 and Equation 2 (Reference 1), and assume that the amplifier is perfect.

[pic]EQUATION 2

The circuit CMR is measured in the absence of signal, so V1=V2=0.0, and Equation 2 becomes Equation 3:

[pic]EQUATION 3

When R1=R3 and R2=R4, the gain goes to zero, and the CMR is infinite. In reality, resistor tolerances and op-amp errors always limit the CMR to about 100 dB or less. Rewriting Equation 3 as Equation 4 puts your focus on the differential gain and resistor tolerances. Equation 4 contains four resistor tolerances, so there are 16 possible error factors. If you investigate all the possibilities, you'll see that the error ranges from zero when all resistor tolerances go in the same direction, to 2T/(1–T).

[pic]EQUATION 4

The resistor tolerances can cause the CMR to range from as high as the limits of the op amp to as low as

–34.89 dB, when the total tolerance is 1% (P+D for 0.5% resistors). Considering purchase and drift tolerances for 1% resistors, your resultant CMR can be as low as –24.17 dB. You calculate this error as a CMR error, but, in the absence of a common-mode voltage and with a differential input signal, it becomes a gain error.

Discrete differential amplifiers are difficult to build and trim, so most designers have gone to IC differential amplifiers with built-in trimmed resistors. Low-cost IC differential amplifiers offer as much as –86-dB CMR.

When you are analyzing your circuit to ensure both long-term performance and manufacturability, keep in mind that passive components have purchase and drift tolerances, and the drift tolerance may be larger than the purchase tolerance. You can adjust the purchase tolerance at the end of your manufacturing process, but you or your system can adjust the drift tolerance only just before making a measurement. Nonratio circuits assume twice the resistor tolerance, and ratio circuits can reduce the error to the tolerance value. Accurate differential amplifiers are hard to build with discrete devices, but ICs with their resistor trimming and matching capability often obtain –90 dB of CMR.

[pic]

|Author Information |

|Ron Mancini is staff scientist at Texas Instruments. You can reach him at 1-352-569-9401, rmancini@. |

[pic]

|Reference |

|Mancini, Ron, Op Amps for Everyone, Newnes division of Elsevier Science, May 2003. |

ECSS-Q-30-01A: Worst case circuit performance analysys (31 March 2005)

 

Scope

This Standard defines the requirements to perform the worst case circuit performance analysis and to write the worst case circuit performance analysis report. It applies to all electrical and electronic equipment. This worst case analysis(WCA) method can also be applied at subsystem level or for a combination of systems/subsystems for space to justify electrical interface specifications and design margins for equipment. It applies to all project phases where electrical interface requirements are established and circuit design is carried out.

The worst case circuit performance is generally carried out when designing the circuit.For selected circuitry, preliminary worst case circuit performance analysis (WCCPA) is used to validate a conceptual design approach at PDR.

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