Using tolerance analysis method in product selection
Keywords:product selection? tolerance analysis method? DAC? RSS calculation? EVA tool?
By Bonnie Baker, Senior Applications Engineer and
Brad Nielsen, Analog and Power Applications Engineer
Texas Instruments Inc.
In making product selection decisions in an analog circuit, such as the bridge sensor circuit (Figure 1), you can solve the problem by selecting the best performing parts on the market for each socket. The confidence derived from this approach can give a sense of security that the circuit will work as expected without a redesign.
However, hunches only go so far when designers justify products in their application circuit, particularly when they look at the bottom line price on your BOMs. So, is it an appropriate fit to put the highest performance analog products before the ADC?
Designers can eliminate most electronics and sensor errors by using calibration in the digital domain. However, these techniques will never recover the codes that are lost in the lower and upper regions of the ADC transfer function.
These lost codes in single-supply application circuits are a product of offset, gain, rail-to-rail swings and noise errors near ground and the positive power supply. If the OEM designer does not account for device variations, these errors appear as yield losses from lot to lot. For a simple discussion, we will only evaluate the effects of offset errors of the various components in the circuit.
This article will discuss two tools that engineers can use to estimate the level of uncertainty with the product selection of components in circuits, namely root-sum-square (RSS) and extreme value analysis (EVA).
The first tool, RSS, will help quantify decisions with the product selection of the parts in the signal chain so designers choose the appropriate devices for the circuit. The EVA tool, the more conservative approach, will assess the worst-case effects of the performance specifications of the devices in the circuit. Both tools will help quantify decisions on the chosen products for the signal chain so the appropriate devices can be selected for the circuit in terms of performance and cost.
Sample configuration
The system in Figure 1 provides the ability to sense a maximum weight of 896g (2lb) with an accuracy of 1g.
Figure 1: This load cell circuit shows the RSS and EVA calculations when determining the dynamic range of this system. |
The second order low-pass filter reduces system noise and ensures a system bandwidth of 10Hz. The load cell (LCL-816G, Omega) output voltage response is a nominal 2mV/V. With a reference at the top of the load cell of 5V, the load cell range to the input of the instrumentation amplifier (INA326, TI) is 10mV. This voltage is gained through the INA326 and filtered with a second order low-pass filter, which uses the OPA350 microPOWER, CMOS, operational amplifier. The ADS7841, quad, 12bit SAR ADC receives the filtered signal and digitizes the signal, achieving an overall accuracy of 1g.
There are several fundamental areas of concern (dynamic range, accuracy, temperature and manufacturing processes) when selecting the sensor, instrumentation amplifier, filter amplifier and ADC. Engineers determine the maximum dynamic range by selecting the right number of bits for the ADC and then assess the range limitations of the various devices in the circuit. The performance of the ADC in the circuit usually determines the optimum dynamic range of the system. The primary characteristics that have a bearing on the converter's dynamic range is the resolution (or number of bits) and ADC accuracy. The ADC offset, gain, INL and DNL performance defines the converter's accuracy.
Designers can digitally calibrate system offset and gain errors in the mid-range of the conversion and calibrate the system's outer regions in the analog domain. The example discussed here will focus on how to deal with the outer-region (at both rails) offset errors of the devices in the system. Although this discussion is limited to room temperature offset errors, you can extend the techniques below to include gain errors, rail-to-rail amplifier I/O limitations and noise errors.
With the sensor signal conditioning circuit, the sensor itself, can have a significant impact of the system's dynamic range and overshadow the converter's impact. For instance, the sensor's offset error is 0.3mV/V (max). This error is multiplied by INA326's gain of 245V/V before it reaches the input of the ADC. Determine the dynamic range of the system by assessing the number of usable bits from the converter and the errors, including offset, from the analog signal chain before the converter. The potential offset error of the ADC and the analog signal path limit the dynamic range nearest the power supply voltages and ground (Figure 2).
Figure 2: The dynamic range of a system spans from the lowest voltage above the negative rail of the power supply to the highest voltage below the positive supply. |
The system designer will find the primary device information in the IC manufacturer's product data sheet documents. The manufacturer may provide more information on request, but the first pass feasibility exercise starts with this documentation. In our evaluation, we will use two types of device errorstypical and min/max.
The maximum specifications usually encompass a normal distribution population that is statistically two to five sigma above the typical specification. If there is sorting and/or grading out of a particular device, this may not be the case and the population of the device may not fit under a Gaussian curve. Examine the data sheet for these types of situations and exercise engineering judgment by inserting appropriate "fudge factors" in the calculations. Table 1 lists the typical and max/min specifications of the components in the circuit in Figure 1.
Table 1: Typical, maximum, and minimum data sheet specifications for components shown in Figure 1. |
RSS as evaluation tool
One way to determine the feasibility of the products in the application circuit is by using the RSS calculation with the maximums from the product data sheet. The specifications that engineers combine during this calculation must be uncorrelated to each other or statistically independent. For example, a potential specification error such as offset from part to part can combine to determine the outer dynamic range limitations of an application circuit as long as their variations over temperature or power supply do not track each other.
With the RSS calculation technique, the first order of business is to calculate these errors to one, single node in the circuit. By using engineering judgment, designers can accept or adjust the maximum values. For instance, if a product that is selected for the circuit has one or more grade-outs, the population will not fit into a normal distribution. Under these conditions, designers may want to increase a maximum value. Once this is done with every component in the signal chain, calculate the square-root-of-the-sum-of the squares of the maximum values. Then, calculate the RSS value to determine the dynamic range or rail-to-rail swing capability of the circuit.
In Figure 1, the maximum offset error of the load cell is 0.3mV/V. Since the excitation voltage at the top of the load cell is 5V, the maximum offset error at the differential output of the load cell is 1.5mV. After the gain (245V/V) of the instrumentation amplifier and filtering by the two-pole lower pass filter (with the OPA350), the maximum DC offset error of the load cell at the input of the ADC is 368mV (refer to Table 2). In this example, you also bring the instrumentation amplifier errors to the input of the ADC with the same type of calculations. The typical and maximum offset error of the INA326 is 20?V and 100?V, inclusive. These instrumentation amplifier errors at the input of the ADC are 4.9mV (typical) and 24.5mV (maximum). Table 2 shows these calculation results, along with the results from the other components in this circuit.
Table 2: Typical and maximum performance specifications of voltage offset and gain for the devices in Figure 1. |
Referring to Table 2, the RSS value at the negative rail (or ground) and positive supply rail of the circuit is 369mV. This calculation shows that the headroom is reduced by 369mV near either of the rails. The ideal dynamic range of the ADS7841, 12bits converter is 5V. The total possible reduction in the dynamic range, per Figure 2, is equal to (V_{ERR-P} + V_{ERR-G}) = (369mV + 369 mV) or 738mV. This reduces the ideal 5,000mV dynamic range of the system to 4,262 mV or ~85 percent. This calculation estimates the "worst-case" response of the system using RSS techniques.
Using EVA for evaluation
The EVA techniques is implemented when the calculation is performed using only the maximum values on the data sheet. An EVA analysis assumes that all components are always at their worst case tolerance. As such, most manufacturers would have a difficult time shipping products in a cost-effective manner. Manufacturers always want to provide a maximum value that allows them to ship product at a cost-effective price point. In general, yields less than three-sigma are extremely unsatisfactory, but not always.
With a yield of three-sigma for a given parameter, the failure rate for a specified parameter is only three in a thousand. That means that the probability of having a part near or at the specification limit is approximately three out of a 1000. In a circuit, the probability of having two devices near the specification limit is approximately one out of a million.
In Figure 1, the summed maximum offset error of the components in the signal chain is equal to 396mV (see Table 3). The estimated dynamic range, taking only the offset errors at room temperature into consideration and given the EVA calculations is equal to (V_{ERR-P} + V_{ERR-G}) = (396mV + 396mV) or 792 mV. This magnitude of possible error reduces the dynamic range by ~84.2 percent. If the offset errors of the instrumentation amplifier, filter amplifier or ADC where higher and closer to the load cell sensor offset error, the estimated dynamic range of the system would decrease dramatically. With this type of calculation, statistically, there are almost no anticipated failures.
RSS or EVA?
Manufacturers list maximum specifications on their datasheets. Unfortunately, little is known beyond the limits written in the product datasheet. Generally speaking, most manufacturers choose maximum limits to ensure a reasonable yield. Engineers often use the maximum limit of the given parameters to calculate the worst case performance of the circuit. There is an assumption in these calculations that the parameter of interest is statistically independent and the manufacturer is testing 100 percent of the devices on their production floor. It can also be assumed that the manufacturer is removing parts that exceed their stated maximum limits.
The RSS calculation will provide a good estimate that is better than just relying on the data sheet specifications for each individual device in the circuit. The RSS calculation combines non-correlated specifications to estimate the worst case. During the first product selection attempt, designers can use RSS calculations. This calculation will assist them in making a logical and economical product selection decisions. The EVA calculation is a more conservative evaluation that may provide a more reliable system, but also more costly because you will be using higher performance products in your circuit.
But a final word of caution, once you take this first step in product selection, make sure to use the same evaluation technique in quantifying the effects of the processes imposed on the devices found in the manufacturing process (such as solder reflow) and the end-of-life effects.
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