Yield analysis with Excel's statistical circuit analysis
introduction
Designing circuits that operate in the real world is challenging. It is not enough to just make the circuit design meet the specification goal. It is also important to accurately predict the performance of the circuit under a certain range of conditions, including the true value of each component. This process is often referred to as circuit yield analysis. Once this performance is well understood, designers can effectively use the expected manufacturing tolerances to select circuits and components for design.
It is well known that a properly functioning circuit, even if the circuit parameters change, its construction, testing and support costs are relatively low.
This article describes the use of tolerances for yield analysis predictions, ie how many circuits built with different component values ​​can meet specifications. For an effective yield analysis, you must have:
* Better circuit models, including important components, spurs, etc.
* Better predictive component value change model
* Pass/Fail definition or specification
With these three inputs, you can perform some calculations to predict the circuit yield. The tools used to make these calculations vary in their utility, depending on the complexity of the problem and your insight. In Table 1 below, some methods are summarized.
Table 1. Yield analysis methods
This article describes how to use Microsoft Excel software for yield analysis, discusses some basic yield analysis concepts such as probability distribution functions (pdf), and explains how to generate random component values ​​to get the ideal probability distribution.
Determining yield using component values ​​and design equations
The circuit consists of components. These components together form a circuit whose overall performance follows certain rules or design equations. To perform yield analysis, designers must understand component value changes and design equations.
For example, for the simple gain circuit shown in Figure 1 below, the gain of the op amp can be easily calculated by knowing the resistance of RF and Rg (assuming an ideal operational amplifier). However, in the real world, if we build the circuit hundreds of times, the values ​​of the components Rf and Rg will be different each time the circuit is built. Next, when testing the circuit, you will find that the gain is different each time the circuit is built. In this example circuit, the component value change is the resistance tolerance. The design equation for gain is:
Gain = - Rf/Rg
For example, if we choose Rf = 1kΩ and Rg = 1kΩ, the gain is -1.
Figure 1. Example of an inverting op amp
Finally, the circuit specification may be: Gain = -1 ± 0.1V/V.
Component PDF and CDF
Often designers cannot predict the value that a component will appear. But with experience, we can predict how many components or how many times the product will run. The description of this performance is called a pdf or probability distribution function.
Pdf is a curve or function that describes the possible relationship between the possible value x of a random variable X and the probability of occurrence of a particular value. For example, in the example circuit herein, we describe the relationship between the Rf resistance value and the probability of occurrence of this resistance value in a batch of resistors.
Cdf is a cumulative distribution function, taking a probability that the random variable X is less than or equal to a certain value x. In other words, if we have a pdf distribution, we can use the integral to calculate cdf. You may have used a Gaussian or normal pdf defined by two parameters: the mean (center value) and the standard deviation (approximately equal to the peak width). Figure 2 depicts the normal distribution of pdf and cdf.
Figure 2. PDF and CDF examples
The normal distribution is suitable for many real-world situations and is easier to implement mathematically. However, please pay attention! A normal distribution may not describe a particular situation for you. For example, if you are using a 20% tolerance resistor, you will find that 5% of the resistors are completely removed and sold to others. The actual pdf in this case is shown in Figure 3.
Figure 3. Distribution of the various components of the classification
With this distribution, the probability that the resistance value matches the resistance label is zero! Your circuit will perform quite poorly compared to a circuit with a normally distributed component value. In addition, designers who get 5% resistance will find that their work is better than expected, because his distribution has a trade-off between the mantissas.
The lesson we get from it is that there are many useful distributions to choose from, and how to choose them is very important. Don't limit yourself to a normal distribution.
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