EEE119 Digital Systems Engineering - Component Tolerance Modelling and Analysis Using MATLAB
1. Introduction
In this assignment you will be introduced to the concept of component tolerances and examine the effects of component variation on a number of different circuits by using extreme value analysis and by using MATLAB to perform Monte Carlo analysis. All electronic components are subject to variation, and it is essential that the systems engineer accounts for these variations during the design process, so their system meets the specification under normal operating conditions. By the end of this assignment, you should have learnt the importance of accounting for the effects of component variation during the design process in order to maximise yield.
The assignment is a self-learning exercise and should be attempted individually. It is the responsibility of the student to allocate sufficient time to complete the required tasks by the deadline. The student is reminded that this assignment contributes ~ 20% of the final grade for EEE119 Coursework. Assessment of this work will be in the form of an assignment written in the style of a technical report in which you should describe your investigations, simulation experiments and the results, and findings of these experiments.
You should also include any recommendations and conclusions that you draw from this work. The deadline for the report is by 23.59 on Friday 20th May 2022 which time an electronic copy must be submitted to Turnitin. Reports submitted to Turnitin after this date will be penalised.
You have been introduced to MATLAB. Appendix A1 contains a list of MATLAB functions which you may find useful. Further details regarding MATLAB/Simulink can be found on the EEE119 Blackboard page. The MATLAB/Simulink software is available through the University's Managed Desktop Service that is available in the Student Computer Rooms (inc. Information Commons and the Diamond). MATLAB is also available as a software download on MUSE should you wish to use your own computer. You may use GNU Octave [1], a free alternative to MATLAB, should you wish.
The remainder of this document is divided into 4 sections:
• Section 2 introduces the concept of yield and component tolerance
• Section 3 describes component tolerance analysis techniques
• Section 4 describes the individual exercises
• Section 5 describes the report requirements
2. Yield and Component Tolerances
Yield is a performance measure for manufacturing processes and is defined as:
3.1 Extreme Value Analysis
3. Component Tolerance Analysis
This section introduces the principles of component tolerance analysis which will be used subsequently to analyse the performance of a number of circuits in section 4.
With Extreme Value Analysis (EVA), one compares the performance of a circuit evaluated with nominal component values with the performance of the circuit when the component values take on their extreme tolerance values. By way of example, consider a circuit consisting of two series connected resistors ?1 and ?2 whose combined value is ??, ??=?1+?2. To evaluate the performance of this circuit when subject to component tolerances, consider a perturbation in the value of resistor i such that ??→??(1±Δ??) where Δ?? represents the resistor's tolerance (i.e. 0.05 or 5%). Assuming ?1 and ?2 have similar component tolerances (ΔR=Δ?1=Δ?2) then, ??(1±Δ??)=?1(1±ΔR)+?1(1±ΔR). Taking the extreme positive value reveals Δ??=ΔR, i.e. the tolerance remains unchanged in this example. Although this technique can be applied to most component parameters it quickly becomes cumbersome for large circuits since the number of interacting components increase making it difficult to extract useful information. Furthermore, for certain circuits one has to make a judgement on whether to use a positive or negative tolerance value to maximise effects.
3.2 Monte Carlo analysis
In Monte Carlo analysis many hundreds or thousands of circuit evaluations (simulations) are evaluated to determine the effects of component tolerance on yield. Each simulation uses a randomly chosen set of component values that exist in the range permitted by the tolerance bounds and the components' values are obtained from probability distributions. Thus, many different component value scenarios are evaluated allowing a more in depth understanding of cause and effect.
Returning once again to our resistor example and using x to represent a randomly generated number in the range 0 to 1. If the resistor values obey a uniform distribution (i.e. each resistor value has an equal chance of appearing), the value of the resistor, ? _, for a single simulation can be determined using ?=_????[_1_+_2_(_?−0_._5_)_Δ?]_ _where ???? _is the nominal or mean resistor value and ΔR_ _is the component tolerance. Figure 1 shows a histogram of resistor values for a 1kΩ ±5% tolerance resistor generated using the uniform probability distribution described above. The MATLAB program code used to generate the Figure 1 is given in Appendix A2 where the random number ? _was generated using the MATLAB rand function.
