Instrument& Circuits Lab
Instrument& Circuits Lab ECE 3041
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This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 3041 at Georgia Institute of Technology - Main Campus taught by Thomas Brewer in Fall. Since its upload, it has received 9 views. For similar materials see /class/233891/ece-3041-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Mathcad Tutorial Example 1 lnverting Systems of Equations Consider the following problem arising from the analysis of a circuit with two mesh currents R1 4 2 I1 E1 R2 R3 I2 E2 Given the Rs and Es determine the Is Solution First specify the numerical values of the Rs and Es using the colon on the keyboard viz R period 1 colon 1000 R1 1000 R2 2000 R3 800 E1 10 E2 20 Mathcad has the ability to add units of Ohms volts and amps but for beginners the numbers are enough The numbers below and to the right ofthe Rs and Es are subscripts To get these type a period on the keyboard after the R or E Create the matrices with the Insert Matrix Command the inverse with the carrot on the keyboard and a 1 as the exponent which yields Ill l lb L R1 iRzY E1 where the operator afterthelvector is the colon on the keyboard orthe second entry on the R2 R3 J LE2 Evaluation Toolbar To see the result simply type the l vector and the equal on the keyboard no colon which is the first entry on the Evaluation Toolbar I1 70015 12 70013 Rememberthat Mathcad works from top to bottom A variable must be defined before it is used Otherwise it will turn red One ofthe neat things about Mathcad is that ifthe user changes the numerical value of a variable the result will be automatically recomputed To insert units simply multiply the variable asterisk on keyboard and then click on the icon forthe measuring cup on the top of the command bar Select the appropriate unit and click on it For instance R1 1kg introduces the unit of k Ohms lfthe correct units are used for the Rs and Es the result for the Is will be expressed as amps Example 2 Two Dimensional Plots A topic of paramount importance to all ECE 3041 students is the step function response of the first order RC circuit which is given by vct E 1 7 exp itjj ut where E is the amplitude of the step function of voltage ut is the unit step function T RC is the time constant R is the resistance C the capacitance and veg is the capacitor voltage To plot this begin by defining the values of the parameters with the colon definition on the keyboard E 10 11 104 c 0110 6 ut ltIgtt 7 RC where ltIgtt is the unit step function Now define the function with the keyboard colon vct El 7 expitut Start the 2D graph by clicking on the icon forthe 2D graph on the graph toolbar or use the keyboard shortcut shift v00 5 I I I 7 71x1073 0 1x10 3 2x10 3 3x10 3 Fill in the place tools which are red with the desired numerical values The dependent variable goes on the y axis and the independent variable on the x axis in the middle The start and stop values are on the extreme positions on the axes Click outside of the plot and the plot will be made Use the positioning tools to make the plot the desired size To make multiple plots the capacitor voltage will now be plotted for several different values of R Define the capacitor voltage to be a function of both time and the resistance t R E 1 it t V s E 7 ex u C p RC Start the 2D graph again Step Function Response 1 I I I En g vct1000010 gt 8 c3920000 5 3 g vct5000 O I I I 3 71x1073 1x10 3 3x10 3 t Time Type the expression vctR with the desired value of R followed by a comma The Place marker will drop down for anotherfunction The legend forthe plot is shown below each and is also color coded To add labels to the plot put the pointer in the plot and double click and select label Example 3 Bode Plots Bode plots are plots ofthe magnitude of a complex transfer function in decibels versus frequency and the phase in degrees as a function of frequency The frequency is always plotted on a log scale and the gain or magnitude ofthe complex transfer function and the phase shift are plotted on a linear scale Considerthe complex transfer function for the firstorder highpass filter Ts Ki 1 57 where K is the high frequency gain s the complex frequency variable Ts is the ratio ofthe output complex phasorto the input complex phasor and T is the time constant which is the product of R times C To make the Bode plot define the parameters and express Ts as a function of either Tf or Tw The 3 dB frequency for this filterwill be picked to be 1kHz which fixes T f3 1000 1 T K 1 F 2 f 180 M Kw Mf 20IoglTltfgtl ltlgtf argltTltfgtgt 1 J27rfT 7r where Mf is the magnitude of Tf in decibels and f is the phase in degrees The absolute value operator is found on the calculator toolbar Both Mf and f can now be plotted as functions of f However instead of using the default number of points and spacing the number of points and logarithmic spacing will now be set by specifying the frequency as a vector which of course will make functions of it vectors N 1000 Define the number of points to be 1000 1 o N 7 1 Define ito be an index It starts with i0 and goes to iN1 Mathcad starts with array index 0 The keyboard sequence is i colon 0 semicolon N1 5 fsta 100 fStOP 10 The start and stop are subscripts obtained with the period on the keyboard 1 N71 f fstm Stop The i on the f is NOT a subscript It is an array index 1 fstalt The keyboard shortcut is the left square bracket On the Matrix toolbar is the the x sub n icon This defines N logarithmically spaced values of frequency Start the 2D graph with either the icon on the Graph toolbar or the on the keyboard Plot Mf versus f where the array index is entered instead ofjust f Note the plot is all scrunched up on the left This is because the default setting for both axes is linear Put the pointer inside the graph M f ii 10 double click and swrtch the x aXIs to log 7 U I I I I 2x104 6X10 1x105 fr I 39 And viola 0 Now a separate plot could be made for the phase However it39s easier to double click Mfi on the graph and enable the secondary y 7 10 aXIs Then enter the phase I I i U 100 1x103 1x104 1x105 fr I I IUU 01x 80 This is the Bode plot 3960 Mfl Mfr 10 40 quotquot39 c 20 7 U I l n U 100 1x103 1x10 1x105 Matlab Tuton39al Example 1 Inverting Systems of Equations a Last M To get started select mums HEJE ae Demos from the HElp menu gtgt R11DDD 2 gtgt xemvmm I euu15u eumzs 1 me multiplication and the vector I has the correct dimensions The verbiage quotTo get started is from the Matlab Command Wmdow and should not be typed unles t Help or Demos onewan s Example 2 Two Dxmensxonal Plots To get started select mm HEJE 0 Demos from the HElp menu mama gtgt cllnspaceLDDDU31DDDI mc EaR22x4R35 3 gtgt mmwncnw 2mm Ram gtgt pluLv1cv2cv31 H Scep Funcclun Response 1 Capaclcur VDJEBEE gtgt xlahelL Tlme H gt rgure1 He m mew Insevt Van s Deskkav Wmdaw HE D Dansmm wm m n S Ep Funcnun Peapunse CapamernMage SPICE for ECE 3041ECE3042 SPICE is an acronym for Simulation Programwith lntegrated Circuit Emphasis it is used to u r fu mainfram lphysically really bigl computers in the 1960s primarily atthe University ofCalifornia at Berkley Once the pc revolution began a programfor SPICE on pcs was developed and known as PSPICE There are many versions of SPICE available today Two are used in ECE 3041 and ECE 3042 Cadence laka ORCADl and National instruments lMultisiml Cadence There are two versions ofthe Cadence SPICE on the lab pcs One isthe professional version and L used e i e since it uses less ofthe pc s resources and is therefore faster Two method are available to IIUH e simulate a circuitwith Cadence text editor laka SPICE Input Deckl and Schematic Capture J Eithermay be used for r providesa program Text Editor Input To simulate a circuit with the text editor create a file using Notepad It must be saved with the ension quotCirquot such as MVFILECR SPICE is not Case sensitive so the examples will use upper case for clarity The first line is the title line Then t e elements ofthe circuit are specified Then control lines are used to specify the type of analysis that SPICE is to perform Afterthe file has been saved openthe PSPICECompiIer P5P Dlnk Clickopen fileand importthe file thatwas created Change the type offile being imported from DAT to CIR EJMYFILE PSpice AD Demo MYFILE active Elle Edit Mlew Simulation IraCe Blot TQolS Window Help 3 v a RENEE EleElLE l7 GEORGE F EURDELL VIIDACID R1 21w c 2 n n in AC DEC an in Ink FROEE no i an The name of the bogus Georgia Tech student GEORGE P BURDELLthe title line The next line says there is an independent AC voltage source from node one to zero with a value of 10 Volts it is pointless to specify the units The third line statesthat there is a resistor from node 1 to 2 with a value of 10k Ohms The fourth line statesthat there is a capacitorfrom node 2 to 0 with a value of 01U micro farads The final three lines are control lines and they begin with a period The fifth line is a control line that implements an AC analysis with the frequency plotted on a log scale DEC with 30 points per decade a start frequency of 10 Hz and a stop frequency of lOKHz The penultimate line states that a plot is requested and the final line states that the end of the control code has been reached To run the program click on the blue run button triangle found on practically everything indicating run A blank graph will result with a horizontal axis going from the start to the stop frequency in logarithmic increments Click on Trace Add Trace and then V2 the voltage at node 2 Switch the vertical axis from linearto log by clicking on the icon of log vertical lines At this point the plot may be annotated with cursors check sign and text abc Either print or copy to the clipboard for pasting into other applications To copy to clipboard click on Window and Copy to Clipboard Lu g Mm mmni m ll View Simmnm Jrve Vin ml wrmw m z dznie as a r i a Jenn Schematic Capture Start the deemati39c Capture 39 D We 65 Cii39Ck the Create npcurheht icph in the upper ieft The New Prpiectscreeri wiii cprrie upAiwaysseiectAhaipg pr Mixed ADgi39ve M Prpiect screeh wiii cprrie up seiect Create a Biahk Project New Project Name 32 a New Piaied ushg Anaiag m Mixedup TivlaiNew Useis E Oiwaavdwiwa gamma a MixedADviaiecl e I new Dime2A may he hiank I o Piagiahhapie LagicWizaid m envied ham an existing I iehpiaie O schemata mum i cmumpsanusuhasirmiwcadmium i defauit vaiue with the desired if it is desired to zpprri ih pr put pressi far in arid p fur put burst munznd gwe 2 nametu theswmu ztmn such strequency Sweep S1mulat1an Semngs Frequency Swe mm mm WWWquot mes um use mumquot 1 WWW Ana ysxs Awe VAE SWEEP Me At SweepName Lmeav sen Fvetiuency n mum a Lagamhmm WWW 1 g Decade emuDecade r DMame Eav aWmsl Ease EESDSSWSZZWI 39 mwm m Emma mm Enab ed w W DLaad B s Pmm W e Dmpm He mum meme dela ed k7an Dmm Wmmahan rm nanhneav cannaHed sum2 and semmanduclm up Ban22 pr He v 39 A wumhetextednurpmmusw dwscussed 0 Multisim Start Multisim by pressing the Multisim icon or Start Programs All Programs National Instruments Circuit Design Suite and Multisim To zoom in or out press F8 or F9 on the keyboard A blank workspace will appear Press Control W on the keyboard which will bring up the Select a Component screen Under the drop down Group select Sources Power Source and then Ground and then ok and place where desired Next select SignaVotageSource and AC Votage click ok and place where desired Next get a capacitor and resistor from the Group Basic and CapacitorRated and ResistorRated To rotate a component highlight it right click and choose rotate Components may be moved by highlighting left clicking and dragging To change the element values double click on the component and change the value To delete a component highlight it and press delete on the keyboard The components are wired together by moving the pointer near one end of a component and left clicking and moving the pointer to the side of the element to which it is to be connected To perform a simulation the type of simulation must be specified and the node voltages to be plotted Place the pointer on the junction between the resistor and capacitor and double click which will bring up the Net screen Check the Show box and the node will be displayed on the schematic The node number may be changed to any number other than 0 and may also be replaced with a text name such as out In the above figure the value of the AC magnitude has been changed to 10 but what is being displayed is the peak value which is only used in a transient analysis The node between the resistor and capacitor is being displayed and the default number of 2 is used Next click Simulate Analyses AC on the top lumbar Spemfy the start frequency step frequency Number uf pmms per decade and whether the t de whmh sthevu tzge at nude 1cm Add Next chck S mu zte V AC Analysis Fvequenty Pavamelevi gutput u Ana ys s Optmns Summaw startrrequtrsrm Hz v p equentHFiYoP m Sweeptype i Numberarpahtspemmae u m Vemm scab Laqanthrw v se eded Cursursmzy bese eded by hght chchrg uhthe mm and Se emng Shaw Cursurs Ems
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