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# PERF GLOBAL CONTEXT THTR 2

UCSB

GPA 3.6

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This 11 page Class Notes was uploaded by Kobe Dare on Thursday October 22, 2015. The Class Notes belongs to THTR 2 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/226857/thtr-2-university-of-california-santa-barbara in Theatre at University of California Santa Barbara.

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Date Created: 10/22/15

ECE 2 Circuits and Systems Spring 2009 Now your plot should look something like this 100 10 1 Current I mA 0 O o 0001 Diode Voltage V Volts The data seems to fall on a straight line which is what we d expect for an exponential dependence A couple of minor formatting issues can be addressed here rst note that the x axis intersects the yaxis at 1 mA on a log plot like this we d prefer to have the xaxis and labels lie along the bottom of the chart You can do this by going back to the Format axis dialog box by doubleclicking on the yaxis and typing in the appropriate intercept value for the xaxis ins the Value X axis crosses at box In this case the appropriate value is 0001 Note that you could also adjust the limits of the vertical scale if desired but in this example Excel has automatically chosen appropriate values So we now have something that looks like this 100 10 Current I mA 0 02 04 06 08 Diode Voltage V Volts Here I have also removed the line connecting the data points in preparation for the next step which is to add a second Model curve to compare the data against our diode model Just doubleclick on one of the data points and click the Line None box in the Patterns tab of the Format Data Series dialog CurveFitting or Trendines As you know diodes are usually modeled by a relationship of the form 11ququotkT71J 01 where n is the ideality factor 13 is the reverse saturation current and kT q 26 mV at room temperature How can we use the measured data to determine appropriate parameters for the saturation current and ideality factor for this diode There is an easy way to do this Page 5 of 12 ECE 2 Circuits and Systems Spring 2009 using the Trendline feature in Microsoft Excel Just rightclick on one of the data points in the chart and select Add Trendline you will then see a new dialog box appear as shown below Grab this corner with the cursor and drag it dovm one row to remove the 0 data point m min ulzsalala You can see that there are a few different options for curve tting the data but the important one Exponential is grayed out Why The reason is that our data set includes an 0 0 data point which you can never theoretically have on a simple exponential model So the trick here is to remove that data point from the plot the easiest way to do this is to just grab one of the top corners of the boxes enclosing the data and adjust the range to exclude this point Do that for both the current and volta e columns and now you should see all of the available curve tting options when you select Add Trendline again mm uam v Pr rdLmLo uara A E c D l E F l G l H l l J Drum Mnuelmg M r 1 1 outrun EA K nndReyesslm type mum U24 Am i n has n 32 y 33 3 gm WW 339 nus 043 39 39 z m Ell u 115 39 39 21 n z u 49 39 4 n 5 n 53 Pansy mammal MWIW Marius J i u 57 Based an shes 2 u a 5 u 55 m u 59 14 n as 2 l 7 E1 cm i3 Now select the exponential model and hit Okay Excel will nd the best t of the data to a model of the form I Ag and plot this on the chart as shown below Page 6 of12 ECE 2 Circuits and Systems Spring 2009 100 10 Current I mA 3 39o 3 0001 00001 Diode Voltage V Volts A pretty good fit in this case But we d really like to know what the curvefit parameters are right Doubleclick on the trendline and select the options tab to get the following s WM we reml momento summon Export Data gustam r 2 ln 2 2 z 1 Dtsvlav swan n an the v r Dlsplay amp quaved valuean than mt Here we want to select Display equation on chart You can also change the name of the trendline to Model Now with a few additional but minor formatting changes we have Current I mA 0 0 001 0 00m 0 2 o 4 o 6 o 8 Diode Voltage v Volts Page7 of12 ECE 2 circuits and Systems Spring 2009 e last step is to simply compute the parameters we want from the information Excel has provided In this case Excel has told us that IA2 is a pretty good t to the data when A548x10396 and 12 2128 Note that our vertical scale is in milliamps so the tting parameter A also has these units in other words A 5 5 nA Now oing back to our diode model in 01 we see that for 1 gtgt 1 the model reduces to 1 s 15qu W so we must have 1 s A 55 nA 02 i Z 2128 rtrT You can use Excel to compute the ideality factor from the last equation Assuming the data taken at room temperature 1 get rt s 18 which is comfortably in the range we d expect for real devices Plotting Multiple Data Series As an example of plotting multiple curves let s make a plot showing how the diode would behave at other temperatures using the model parameters just provided by our curve tting exercise Note that the saturation cunent 1 is temperature dependent approximately given by the relation 15Tocrze Egquot 03 where EE is the bandgap energy ofthe semiconductor 113 eV for silicon Ifwe know the saturation current at some reference temperature Tn then We can write 3 E M 1008 expeq7 efi 04 i i BelowI ve made some room in the original spreadsheet so that columns FGH will describe the 439 4 39 39 39 quot 39 F G9andH9 Ala chEIFlG Hl Diode Modeling Example m 3 Constants round BUD 5 48506 rom datar mng at 3 7 room temperature Measured at 300K Temperature K 290 and 310 llmA v u 0 1 BEN El 24 0 005 u 32 0 m n 35 u 02 u 39 005 043 Enter merlrst New comm PH 01 EIAE two points and n 2 n w d to 05 053 rrllrntherest l U 57 2 05 5 El SE in u Be 4 D m Page 8 ole ECE 2 Circuits and Systems Spring 2009 The tting constants for the diode saturation current and ideality factor and the measurement 39 F4 F6 as shown To temperature TD are included in define the voltages at which we ll in rement and ag downvwird to fill in the rest as s ge of 00 to 075 Volts should be fine ow w an enter the equation for the diode cunent in the appropriate boxes There is e te fonnulafrom 04 as shown below formulas are alvmys preceded by an a sign Note that the temperature is referenced as F599 this tells Excel that no matter which cell this formula ends up in when we drag it around we always want to kee the 9 row reference constant Similarly the measured diode saturation current at TB is referenced as m5 which tells quot thecl 39 39 39f 39 Without r o umn tam the dollar sign in front ofarow or column reference the reference will change according to the relative movement ofthe cell content FIEI v I Arm A E i 0 mi E i F e i H V Um Mme39mg Examp39e Equation in box Ft 0 tor m computing tne saturation mm 5 Bus current at 280K n 1 517 Measured at EUDK Temperature K EU EDD 313 i ImA v v i lErEIB a nun D DEM I 24 El D5 0 35 Last step grab tne corner mm D 39 D 2D or box around Ho and 335 n 43 325 drag across to H 0 at u 45 man I 2 I 49 El 35 n 5 u 53 u an t u 57 u 45 2 I E USU 5 u 55 055 H u as non I4 I BE EH35 n m 075 once the formula is entered you can grab the comer ofthe box around F10 and drag it to H10 to fill in the saturation current for the other temperatures Now enter the equation for the full diode current from 01 in box F11 as shown below Note that this time we reference the voltage as E11 because we want the voltage to change as we drag the formula dawn but we don t want it to change when we drag it szdeways Now grab the comer of the box surrounding F11 and drag it down to F26 the last cell in that 3 column you should now see the followm Pages ole ECE 2 circuits and Systems Spring 2009 S1U LEXPISE1 lmb39lu unmeazl39rwn 1 Dt E F e H Diode Modeling Example Euuattun tn bux Flt fu Eumputlng m 1m 3m ism SAEEUE n l an Measmed al 3UUK Tampevah e K mA v U U DUE I 24 UUUS 3932 U1 El 3E U U2 U 39 I US I 43 U 1 U 45 El 2 3945 U 5 U 53 1 57 step grab 2 5 the currieer bux 5 I E5 m 055 r unu Flt n 4 I55 dragduwnt a tu ml in the EEHS in this ul m drag Finally grab the box and drag to H26 to fill in the other columns Now each cell should compute the diode current for the voltage in the particular row andfor the temperature at the top ofthe particular column at the cell appears in Ifyou then click in any ofthese boxes you can see how the references to the voltage and temperature change as you move from cell to cell To plot all three ofthese curves together we could use the same procedure as before and select the range of data to plot E11 through H26 and then insert a new c an However doing it that m means we d have to go through all of the formatting stuff again somewhat easier alternative is to copy and paste a previously formatted graph like the one we ade for our measured data and then just change the source data for the plot To do this right click somewhere in the new chart and select Source Data click on the Series tab box to add anew data series then click the Add button For example after doing this and entering anew name Model at T290K 1 get the following Page 10 of12 ECE 2 circuits and Systems Spring 2009 7 mm sales Click here to add a The next step is to de ne where the xy data for this new series is located The easiest my is to click on the little spreadsheet symbols as shown above and then use the cursor to se c the appropriate cells in the spreadsheet Note that ifyou do it this way you have to rst delete the 1 entry in the Yvalues box otherwise you will get an error message N is for the other two data sets for T300K and T310K Now all ofthe data should be on the plot and we just need to do some formatting to polish it up Here is what 1 have on alog scale 100 10 del at Data at 300K Current I mA 020 030 040 050 060 070 080 Diode Voltage V Volts Note that Excel doesn t usually make very intelligent choices of colors and line widths for the plots For good quality reports and presentations you need to choose bold daxk colors an thicker line widths than the Excel defaults as 1 have done here Also note that the data point Page 11 ole

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