Homework answers / question archive / EN1093 Coursework – JFET Data Analysis This coursework (CW) will be marked out of 100 and will contribute 20% to the overall EN1093 module mark

EN1093 Coursework – JFET Data Analysis This coursework (CW) will be marked out of 100 and will contribute 20% to the overall EN1093 module mark

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EN1093 Coursework – JFET Data Analysis This coursework (CW) will be marked out of 100 and will contribute 20% to the overall EN1093 module mark. It involves 2 main tasks with mark allocations shown. The technical work will comprise 90% of the total mark for CW (i.e. 25% + 65% for tasks 1 + 2); the remaining 10% will be based on the presentation of your submission (format, annotation, correctness of writing, etc.) CW will be set in week 7 of the Spring semester and the guidance on its completion will be offered in each of weeks 7-11. The submission deadline for CW will be Sunday 6:00 p.m. in week 11 of the Spring Semester, via Learning Central. That means that you will have 5 weeks to complete it. You need to use Matlab for completing CW. Your coursework submission should consist of a single report (in pdf format) which answers the three tasks. You’ll first need to create a wordprocessed document, into which you import the graphs and main analytical results from your Matlab output, in addition to adding your Matlab code with good comments as an appendix; for your submission, you must create a pdf from this document. To repeat, your submission should be a single pdf – no other file format is acceptable. Any work submitted after the week 11 deadline without good reason will automatically receive a mark of zero. Everyone should generate their own data files so no submissions should generate identical values. All cases of plagiarism will end in a mark of zero, so don’t risk it. In preparation for CW, please familiarise yourself with the following: Topics in Matlab and statistical data analysis (covered in the EN1093 lectures) ? Importing data files into Matlab ? Defining data vectors from data matrices in Matlab ? Plotting multiple point and line graphs in Matlab ? Fitting straight lines and parabolas to data in Matlab ? Solution of linear simultaneous equations for finding the point where straight lines cross ? Calculation of mean and standard deviation ? Calculation of the standard error when data is averaged Topics in Electronics (covered in EN1072 laboratories) ? The theory of operation of a 4-bit DAC using op-amp circuits ? The basic operation of an n-channel JFET ? The output characteristic of a JFET ? The transfer characteristic of a JFET ? The linear and saturation modes of a JFET ? The transconductance of a JFET, and how it can be modelled ? The pinch-off voltage of a JFET It is really important that you familiarise yourself with the JFET data file format that you have generated in the EN1072 laboratory, and understand what data appears in each of the columns. If you haven’t got the JFET data file needed, please email me for figuring out further solutions. Dr Yue Zhou March 2022 Task 1 Theoretical Analysis (25 marks) The structure of the DAC used in the experiment is shown in the figure below: Therefore, the relationship between the output voltage ? ?????? and the input voltage ? ????? can be expressed as ? ?????? = ? ? ? ????? ? ( ?0 ?0 + ?1 ?1 + ?2 ?2 + ?3 ?3 ) = 3.2 ? ( ?0 8 + ?1 4 + ?2 2 + ?3 1 ) ? where ?3, ?2, ?1, ?0 are binary bits which take the values of 0 or 1. In this Task 1, it is assumed that the resistors ?3 and ? come from a batch of resistors of which the resistance values are normally distributed, with the nominal value being 10 ?Ω and the tolerance band being 5%. The resistance values of all the other resistors in the figure are assumed exactly accurate with no error. 1.1 If a number of resistors (the number equals to the last 4 digits of your student number) are taken out from the batch of resistors where ?3 and ? come from, what will the resistance values be for them? (Use MATLAB to simulate this process and obtain the resistance values) (5 marks) 1.2 Estimate how many of the resistors you take out in 1.1 have the resistance between 9.8 ?Ω and 10.2 ?Ω (Use the CDF Table method you learn to calculate, by hand or by MATLAB), and compare the calculation result with the number obtained in 1.1. (10 marks) 1.3 Considering ?3 and ? equal to 10 ± 5% ?Ω and (?3, ?2, ?1, ?0) = (1, 0, 1, 0) , estimate the error of ? ?????? because of the errors in ?3 and ?. (10 marks) R r3 r2= r1= r0= V V output input Task 2 Experimental Data Analysis (65 marks) 2.1 DAC Output Investigations (15 marks) The output voltage of your 4-bit DAC ranges from 0 V to around 6 V, in 15 steps of around 0.4 V. Any discrepancies will depend on the differences between actual and nominal values of the five resistors used in the DAC circuit. Investigate this in more detail through the following tasks. 2.1.1 Calculate your predicted DAC output voltages V1 from the formula V1 = mVmax /15 (where m = 0, 1, 2 … 15, and Vmax is your maximum DAC output voltage). Plot a graph of your actual DAC output voltages V2 (on the vertical axis) against V1 (on the horizontal axis). (5 marks) 2.1.2 Investigate your DAC behaviour in more detail by plotting a graph of the “error” in voltage ?V =V2 −V1 against V1 . What sort of error is this? Explain it in terms of the resistance values of your DAC circuit. (10 marks) 2.2 JFET Output Characteristic Investigations (25 marks) A JFET’s output characteristic is the family of plots of drain current ID as a function of drainsource voltage VDS for various values of gate-source voltage VGS (negative for an n channel JFET). 2.2.1 Plot the output characteristic of your JFET, varying VGS in steps of 0.5 V. (5 marks) 2.2.2 The gradient of the output characteristic in its saturation mode is used to calculate the JFET’s series resistance R0 . By using linear regression over a suitable portion of the output characteristic, calculate R0 for VGS = −1.0 V. Comment on your result. (5 marks) 2.2.3 The initial gradient of the output characteristic in its linear mode is used to calculate the channel resistance of the JFET. Calculate the channel resistance for VGS = −1.0 V. Compare your result with the value of R0 from task 2.2.2 above. (5 marks) 2.2.4 The “knee voltage” is the value of VDS at the boundary between the linear and saturation modes of the JFET. It can be defined to be the value of VDS at the intersection of the straight lines generated in tasks 2.2 and 2.3. Calculate the knee voltage for VGS = −1.0 V. Explain what happens to the knee voltage as VGS gets more negative. (10 marks) 2.3 JFET Transfer Characteristic Investigations (25 marks) The transfer characteristic of a JFET is the plot of drain current ID in the saturation mode as a function of gate-source voltage VGS . The transconductance gm is the gradient of this characteristic. 2.3.1 Plot the transfer characteristic of your JFET. Fit a parabola to your data and hence deduce an approximate formula for the JFET’s transconductance gm as a function of VGS . Use it to calculate the transconductance when VGS = −1.0 V and to estimate the pinch-off voltage of your device (i.e. the value of VGS at which ID reduces to zero). (10 marks) 2.3.2 Generate four additional datasets with the same JFET and repeat task 2.3.1. Quote your best estimates (with standard errors) of the transconductance when VGS = −1.0 V and pinchoff voltage from these 5 datasets. What is the origin of the error in this data? (7 marks) 2.3.3 Generate four additional datasets with four different JFETs and repeat task 2.3.1. Quote your best estimates (with standard errors) of the transconductance when VGS = −1.0 V and pinch-off voltage from these 5 datasets. What now is the origin of the error in this data? (8 marks)