300 Lab Manual (Pspice and Mathcad)

 

  

Developed

by Ronald H. Rockland, Ph.D.

EET 300

Computer Applications Manual

TABLE OF CONTENTS INTRODUCTION.........................................................................................................................................5

LESSON 1 – INTRODUCTION TO MATHCAD ...................... ....................... ........................ .................. 7 STARTING STARTING MATHCAD........................ MATHCAD...................................... ............................ ............................ ............................ ............................ ............................ ........................... ........................... ................ .. 8 ARITHMETIC ARITHMETIC OPERATIONS OPERATIONS ............................ ......................................... ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 9 ENTERING ENTERING FORMULAS FORMULAS ............................ .......................................... ............................ ............................ ............................ ............................ .......................... ......................... ....................... .......... 10 COMPLEX COMPLEX NUMBERS NUMBERS ........................... ........................................ ........................... ............................ ............................ ............................ ............................ ............................ .......................... ............ 11 AUTOMATIC AUTOMATIC MODE ............................ .......................................... ............................ ............................ ............................ ........................... ........................... ............................ ............................ .............. 11 INSERT INSERT FUNCTION........... FUNCTION......................... ............................ ............................ ............................ ............................ ............................ ........................... ......................... .......................... ..................... ....... 13 UNIT CONVERSION CONVERSION .......................... ........................................ ............................ ............................ ............................ ............................ ............................ .......................... .......................... ................. ... 14 USING THE MATH PALETTE....................... PALETTE.................................... ........................... ............................ ............................ ............................ ........................... ........................... ................... ..... 15 COPYING COPYING FROM MATHCAD MATHCAD TO WORD ........................... ......................................... ............................ ............................ ............................ ............................ ...................... ........ 16

ASSIGNMENT 1 .................................. ................ ................................... ................................... .................................... ................................... ....................................... ...................... 16 SETTING UP A FUNCTION FUNCTION IN MATHCAD................. MATHCAD............................... ............................ ............................ ............................ ............................ ........................ ............... ..... 17 INTEGRATION INTEGRATION AND DIFFERENTIATI DIFFERENTIATION ON - MATHCAD................... MATHCAD................................. ............................ ........................... ........................... .................... ...... 18 GREEK SYMBOLS.............. SYMBOLS............................ ............................ ........................... ........................... ............................ ............................ ............................ ........................... ........................... ................... ..... 20

ASSIGNMENT 2 .................................. ................ ................................... ................................... .................................... ................................... ....................................... ...................... 20 GRAPHING GRAPHING IN MATHCAD....................... MATHCAD..................................... ............................ ............................ ............................ ............................ ............................ .......................... ...................... .......... 21

ASSIGNMENT 3 .................................. ................ ................................... ................................... .................................... ................................... ....................................... ...................... 23 LESSON 2 – INTRODUCTION TO PSPICE .................... ........................ ....................... ....................... ..24 OVERVIEW OVERVIEW ............................ .......................................... ............................ ............................ ............................ ............................ ............................ ............................ ............................ ........................... ............... 25 USING SCHEMATICS SCHEMATICS ............................ .......................................... ............................ ............................ ............................ ............................ ........................... ........................... .......................... ............ 27 SEARCHING SEARCHING FOR PARTS................................. PARTS............................................... ............................ ............................ ............................ ............................ ......................... ......................... ................. ... 30 ARRANGING ARRANGING PARTS................. PARTS............................... ............................ ............................ ............................ ............................ ............................ .......................... .......................... .......................... ............ 31 CONNECTING CONNECTING PARTS ............................ .......................................... ............................ ............................ ............................ ........................... ........................... ........................... ......................... ............ 33 CHANGING CHANGING PARTS ATTRIBUTES................. ATTRIBUTES............................... ............................ ............................ ............................ ............................ ............................ .......................... ............... ... 34

Page 2

EET 300


SAVING SAVING A SCHEMATIC SCHEMATIC FILE.................. FILE................................ ............................ ............................ ............................ ............................ ........................... ........................ ....................... ............ 37 COPY/PASTING COPY/PASTING PARTS....................... PARTS..................................... ............................ ............................ ............................ ............................ ............................ ........................... ........................... .............. 38 UNDO/REDO UNDO/REDO ............................ .......................................... ............................ ............................ ............................ ............................ ............................ .......................... .......................... ........................... ............... 40 REDRAW REDRAW AND ZOOMING ZOOMING .......................... ........................................ ............................ ............................ ............................ ............................ ........................... .......................... .................... ....... 41 WORKING WORKING WITH WORD 97.................................... 97.................................................. ............................ ............................ ............................ ............................ .............................. ..................... ..... 43 MEASUREME MEASUREMENTS NTS - DC ANALYSIS....................... ANALYSIS.................................... ........................... ............................ ............................ ............................ .......................... ...................... .......... 45 EXPLANATION EXPLANATION OF PROBLEMS............ PROBLEMS.......................... ............................ ............................ ............................ ........................... ........................... ........................... ......................... ............ 48

PROBLEM

1.....................................................................................................................................49

LESSON 3 - TRANSIENT ANALYSIS ANALYSIS WITH RC AND RL CIRCUITS ...................... ....................... ...50 PULSE VOLTAGE VOLTAGE SOURCE ........................... ......................................... ........................... ........................... ............................ ............................ .......................... .......................... ................... ..... 51 UNIT STEP.......................... STEP........................................ ............................ ............................ ............................ ............................ ............................ ........................... ........................... ............................ ................... ..... 52 SETTING UP THE TRANSIENT TRANSIENT ANALYSIS.... ANALYSIS.................. ............................ ............................ ............................ ............................ ............................ ......................... ............. .. 53 PERFORMING PERFORMING THE TRANSIENT TRANSIENT ANALYSIS............ ANALYSIS.......................... ............................ ............................ ............................ ............................ .......................... ................ .... 55 CHANGING CHANGING BACKGROUND BACKGROUND COLORS COLORS IN PROBE ........................... ......................................... ............................ ........................... ........................... ...................... ........ 56 SPECIAL SPECIAL MARKERS MARKERS ............................ .......................................... ........................... ........................... ............................ ............................ ............................ ............................ ............................ .............. 59 MODIFYING MODIFYING GRAPHS ........................... ......................................... ............................ ............................ ............................ ............................ ............................ ........................... ......................... ............ 61 PRINTING PRINTING AND COPYING COPYING GRAPHS GRAPHS ............................ .......................................... ............................ ............................ ............................ ............................ ......................... .............. ... 64 SWEEPING SWEEPING A COMPONENT COMPONENT VALUE............. VALUE........................... ............................ ............................ ............................ ............................ ............................ .......................... ............... ... 65 USING THE VPWL SOURCE.......................... SOURCE........................................ ............................ ............................ ............................ ............................ ......................... ......................... ................... ..... 68 USING THE DIFFERENTIATO DIFFERENTIATOR R AND INTEGRATOR INTEGRATOR ............................ .......................................... ............................ ............................ ............................ .............. 70 WORKING WORKING WITH CUSTOM AXIS ............................ .......................................... ............................ ............................ ............................ ............................ ............................ ................... ..... 72

PROBLEMS 2-5 .................................... .................. ................................... ................................... .................................... ................................... ................................... .....................75 ...75 LESSON 4 – LAPLACE TRANSFORMS USING MATHCAD...............................................................77 LAPLACE LAPLACE TRANSFORMS TRANSFORMS ........................... ......................................... ............................ ............................ ............................ ........................... .......................... ........................... ..................... ....... 78

ASSIGNMENT 4 .................................. ................ ................................... ................................... .................................... ................................... ....................................... ...................... 79 ROOTS OF AN EQUATION EQUATION ........................... ......................................... ............................ ........................... ........................... ............................ ......................... ......................... ..................... ....... 80

PROBLEMS 6-7 .................................... .................. ................................... ................................... .................................... ................................... ................................... .....................81 ...81 LESSON 5 – LAPLACE TRANSFORM IN IN PSPICE PSPICE ...................... ........................ ....................... ...........82

Page 3

EET 300


USING THE LAPLACE LAPLACE COMPONENT COMPONENT .......................... ........................................ ............................ ............................ ............................ ............................ ........................... ............... 83

PROBLEMS 8-9 .................................... .................. ................................... ................................... .................................... ................................... ................................... .....................84 ...84 LESSON 6 – SINUSOIDAL STEADY STATE IN PSPICE......................................................................86 MEASURING MEASURING DIFFERENCES DIFFERENCES WITH CURSORS CURSORS ........................... ......................................... ............................ ............................ ............................ ......................... ........... 87 MARKING MARKING SPECIFIC SPECIFIC VALUES VALUES ON THE GRAPH ............................ .......................................... ............................ ............................ ............................ ...................... ........ 89 GENERATING GENERATING MULTIPLE MULTIPLE PLOTS .......................... ........................................ ............................ ............................ ............................ ............................ ........................... .................... ....... 91 USING THE VSIN SOURCE......................... SOURCE....................................... ............................ ............................ ............................ ............................ ......................... ....................... ...................... .......... 92 SIMULATING SIMULATING A BODE PLOT ............................ ......................................... ........................... ............................ ............................ ............................ ........................... ........................... .............. 93

PROBLEMS 10-11 ................................... ................. ................................... ................................... .................................... ................................... ................................... .................. 95 LESSON 7 – FOURIER ANALYSIS ..................... ....................... ....................... ........................ ......... .....98 FOURIER FOURIER ANALYSIS ANALYSIS - MATHCAD MATHCAD ........................... ......................................... ............................ ............................ ............................ ............................ ......................... .................. ....... 99 FOURIER FOURIER ANALYSIS ANALYSIS - PSPICE........................... PSPICE......................................... ............................ ............................ ............................ ............................ ......................... ....................... ............ 101

PROBLEMS 12-13 .................. ........................... .................. .................. .................. .................. .................. .................. .................. .................. ................... ................... ............103 ...103 APPENDIX - PROBLEMS IN THE TEXTBOOK ...................... ....................... ....................... ..............104 .............. 104

INDEX ................. ................. .................. .................. ................. .................. ..................... ................. .......107

Page 4

EET 300


INTRODUCTION

T

his manual is intended to reinforce concepts brought up in class discussions for EET 300, and will help you you understand two relevant computer applications. One of these applications is called PSpice®, and is a registered trademark of Cadence Corporation. PSpice is a simulation program that can help you understand basic circuit theory and related topics to EET300. The other application is called MathCAD®, which is a registered trademark of Mathsoft, Inc., and is an equation solving application that allows you to view equations as you would normally write them. Although Mathcad might seem similar to Equation Editor, found in Microsoft Office products, MathCAD has far more capabilities. This manual is intended to help students get started using both programs. Additional information can be found in the online help documentation that comes with these programs. In addition, for Mathcad I would suggest a book by Ronald W. Larsen, entitled Introduction to MathCAD, Prentice Hall. Many of the MathCAD books I have reviewed use very abstract examples, and can be more confusing that Mathsoft’s own guides. This book is small enough to go go through fairly quickly, yet thorough enough to cover most topics. PSpice is a circuit simulation software, and the output of various circuits can be analyzed, with respect to both time and frequency. MathCAD is a mathematical analysis tool, and can be used to create your own examples, solve them theoretically, and then confirm those answers by having MathCAD solve the examples. MathCAD will be value for certain topics that will be covered in the EET 300 course, such as complex numbers, adding sinusoids, integration and differentiation of various functions, Laplace and inverse Laplace transforms and solving algebraic equations. MathCAD can also be used to create the graph of a theoretical derivation of a circuit, and then you can use this graph to compare it to the output from PSpice. This manual will be oriented to using version 8.0 of PSpice. Versions higher than 8.0 have changed dramatically, and are not as easy to use. The system requirements for this version is any 486 or Pentium (Pentium 133 or higher would be preferable), 16 MB RAM, Microsoft® Windows® 95, and a CD-ROM drive. You will be told during the first class how to obtain a copy of PSpice. The same procedures that are written in this manual can be used for versions 6.1 and higher of PSpice. For these earlier versions, some of the toolbars, command words, or dialog boxes will appear slightly different. However, the functionality of the program is the same as described in this manual. Many of the standard features of Schematics and Probe will be covered within the first two lessons. Additional features that are specific to the other lessons will be covered in the respective sections. Exercises are given throughout this manual to help reinforce the concepts, and problems are given at the end of each lesson that are required by each student to complete. Mathsoft, through its website www.mathsoft.com www.mathsoft.com,, provides a free product called MathCAD Explorer. This product demonstrates most of the features of MathCAD 8.0, although you can’t save any files, nor use the OLE features of MathCAD in products such as Microsoft® Word. However, this Explorer version will allow you at each session to work with the full product features, open worksheets that have been created, modify them, and print them. MathCAD

Page 5

EET 300


Explorer allows you to also create new worksheets and copy/paste the results to a Word document. This version also comes with a complete Help file. You will be given standard worksheets to modify, along with a blank worksheet to use. The purpose the Mathcad portion of this manual is to help you you learn MathCAD quickly. Only certain topics that will be useful to EET 300 students are covered. The discussion on each area will be very limited – only how to do something and illustrations as to how to accomplish that task. The worksheets that are in this manual can be downloaded from my my home page. You can open them using MathCAD Explorer, and change the functions to see different results. I would encourage most students to modify these worksheets, and thus create additional examples. Do not use Mathcad as a substitute for deriving equations – you need to get the practice. Rather, use Mathcad as a means to verify that the derivation is correct. The best way to study a technical course, such as EET 300, is to continuously solve examples. Both these applications will help you do that, as well as visualize an answer that might otherwise be just an equation. In this manual, items to be clicked are bolded and keys that are to be pressed are enclosed in arrow brackets < >. Tips that are general general in nature are preceded with a  symbol, and programs are italicized. When the word “choose” is seen followed by a bolded expression (usually with a comma between words) this means to click on the menu bar. The word click will refer to pressing the left mouse button, unless otherwise stated. To help you learn PSpice, I have included examples that you can experiment with as you are reading the specific sections. These examples are not to be handed in to me. The explanation of the problems that you need to hand is on page 48, and the problems start on the next page. The Mathcad assignments are noted after each section, and start on page 16. Both the PSpice problems and the Mathcad assignments are to be handed in, according to the schedule you will receive on the first day of class. In some cases, you you will be asked to use Mathcad to plot the theoretical work, and compare it to PSpice. This will be part of the PSpice problem. All the Mathcad worksheets that are in bold can be downloaded from my website, http://www-ec.njit.edu/~rockland.. http://www-ec.njit.edu/~rockland

Page 6

EET 300


LESSON 1 – INTRODUCTION TO MATHCAD M ATHCAD You will Learn:



How start Mathcad.



How to enter and move text.



How to enter a formula, and define a variable.



How to work with arithmetic calculations



How to work with complex numbers



How to use the automatic mode

Page 7

EET 300


STARTING MATHCAD When you open up a file in MathCAD, you are actually in a workbook. If you have MathCAD Explorer, you will see text (hyperlinks) above. In both cases just click anywhere in a blank section of the page. You will see a small red cross, which is a placeholder for the beginning of entering text or an equation.

Entering and Moving Text 1- To enter text, rather than an equation, equation, type a quotation quotation mark, and then start start typing the text. You will see text being typed, and a box surrounding the text. The font, if you haven’t changed it, will say Normal, which is Arial 10 pt. If you press , you can type a second line of text. To start typing somewhere else in the worksheet, click somewhere else in the worksheet. 2- If you want want to move the text, move the mouse pointer over over the edge of the text box. You will see an open hand. 3- Click and hold the mouse button, and drag this text box to a new position.

This is the method for moving any text or formula box.

 If you want to move to a new area, and start typing in a formula, just click on another blank area, and start typing without the quote. If you you just type in letters and then a space, MathCAD assumes that you want a text box, and will convert the letters you typed to a text format. When you type type a formula, the font is called variables, and is Times Roman 10 pt. For both text and equations, the font can be changed.

Page 8

EET 300


ARITHMETIC OPERATIONS Various mathematical operations can be performed on both numbers and variables. This include addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^). The difference between MathCAD and most other solution oriented applications is that MathCAD is a WYSIWIG application (What You See Is What You Get). When you type with a /, you you get a fraction that looks like an equation editor fraction. When you type with an asterisk as a multiply sign, you get a dot between the two numbers or variables. When you type a ^, the exponent is in 2 superscript (i.e. 3 rather than 3^2).

Arithmetic Calculations 1- Type in the first number, type in the the appropriate arithmetic arithmetic operation, operation, and then continue continue until you are finished. 2- Type in an an equal sign (=), and then press . MathCAD will will calculate the results.

Example: 7

8

=

15

7 .8

=

56

7

8

=

1

7

=

8

Page 9

0.875

7

8

=

5.765 10

6

EET 300


ENTERING FORMULAS MathCAD expects you to first define variables before you use them in an equation or calculation, such as determining an integral or multiplying complex numbers. To define a variable, y you ou need to type a series of letters (there are certain limitations on naming variables – see the Help section for that limitation). The process of defining a variable is actually called assigning.

Defining a Variable 1- Type in the variable name. One caution is not to use something that might be a unit, such as deg, or an operation, such as integ. 2- Type in a colon (:). You will see the variable name and then a colon followed by an equal sign. This is the assignment equality.

3- Type in the rest of the the definition for the variable. variable. . If you want a subscript as part of the variable name, type a period before typing the subscript.



You must define all variables before you you use them in an equation. Otherwise, you will see one of the elements in the final equation with a red color. This indicates that one of the variables is not defined. Mathcad works from top down and from left to right. You must define the variable above and/or to the left of where you are using the variable in an equation.

Page 10

EET 300


COMPLEX NUMBERS To understand how to manipulate complex numbers, you should define several different complex numbers before performing the operation. When you type type in a complex number, you you must type the imaginary quantity before you type in the j, such as 5 + 3j, as opposed to 5+j3. If you type an imaginary number such as 5+j3, you will get an error. Note: if you are just typing in a j, such as 1+j, make sure you type it as 1+1*j. When typing in complex expressions, it is important to understand how MathCAD determines what portion of the expression to use. Try typing typing in a blank area the expression B*C (do not press ). You will notice that a blue line appears to the right of the letter C, indicating the next position to type. You should also notice that there is a bottom cursor, or underline, which is currently under the letter C. If you typed in a slash (/) followed by the letter D, you will see the following expression C B

.

D

Delete this expression (by depressing the mouse button, dragging over the expression, and pressing the delete key). Retype the same expression B*C below. This time, press the spacebar. Notice that the bottom blue underline is under both the B and the C term. When you type type in a slash (/) followed by the letter D, you will now see the following expression B .C D

Make sure you observe where the blue underline is prior to typing typing in an equation. Also, if you already typed an equation, and want to edit it, simply click inside the equation and press the space bar the appropriate number of times. Before looking at a sample worksheet, there is another feature of Mathcad that you should be aware of - the Automatic Mode.

AUTOMATIC MODE The automatic mode allows you to redo an expression, or redefine a variable, and automatically recalculate the results below. When you start Mathcad, you are in automatic mode, and can verify it by looking at the lower right hand side of the Mathcad window (the message line). The word Auto should appear. This automatic mode applies to calculations as well as graphs, and is very useful when you want to see how changes in one variable affect another, or affect a graphical output. An example of both setting up the complex numbers, as well as observing what the automatic mode will do, can be seen from the worksheet Complex Numbers.m Nu mbers.mcd cd, as shown on the following page.

Page 11

EET 300


A

5

5j

B

2

3j

C

6

j

D A

2

=

D B .C

5j

0.517 1.207i

=

3.793 1.483i

D A

C .D B

=

9.462 + 2.308i

The advantage of setting up a worksheet in this manner is that you can go back to one of the expressions, click and drag over the numbers to the right of the equal sign, type in a new complex number, and when you click outside that area, or press , all the expressions will be recalculated automatically. In this manner, you you can set up your your own problems, try to solve them on your own first, and then look at the answers. This should be your approach to all other worksheets.

Page 12

EET 300


INSERT FUNCTION

There are many instances where you need a specific function to perform a calculation, such as statistical analysis (mean, median, variance) or complex numbers (real and imaginary). To do so, you can use the insert function button on the toolbar.

Inserting a Function 1- Click in the worksheet where you want to insert the function.

2- Click on the function button, button, located located in the the toolbar. The Insert Function dialog box will open. 3- Choose the appropriate appropriate function. function. You can type in the first letter of of the function, function, and the dialog box will point point to the first word with that letter. You might want to look at Help so that that you know what function to choose.

For example, if you want to calculate the magnitude and phase angle, you might need to use the Im (A) and Re(A) functions. Note that A does not mean that this will only work with the variable A that you defined above – you can write the function as Re(B), Re (B/C), etc.

An example of using the Re and Im functions is given below:

To convert from rectangular to polar, you need to derive magnitude and phase

magA

Re ( A )

2

Im( A )

2

phaseA

atan

Im( A ) Re( A )

ma A

=

7.071

haseA

=

0.785

Page 13

EET 300


UNIT CONVERSION There might be instances where you need to display units that are different from the actual function. For example, phase would normally be calculated as radians, but it is easier to visualize phase in degrees. Mathcad automatically will apply the necessary conversion factors, if you “tell it” what units you want.

Unit Conversion 1- Click in the result to see the unit placeholder. For example, in the example on the previous page, phaseA is in the radians. When you type phaseA =, what you will see is . Note the mark after the 0.785 – this this is the placeholder. placeholder. 2- Move the mouse over the placeholder, and click. You will now see the placeholder underlined. 3- Type any combination of units in the unit placeholder. You will will see the placeholder, a small diamond marker, and the units you typed in. 4- Click outside the expression expression to redisplay the result in terms of the the selected units. You will will know see the phase as

phaseA = 45 deg .

5- If you change the variable A, the phase will be recalculated recalculat ed automatically in degrees.

The example on the previous page now looks like the following: magA

magA

Re( A )

=

2

Im( A )

2

7.071

phaseA

phaseA

Page 14

atan

=

Im( A ) Re( A )

45 deg

EET 300


USING THE MATH PALETTE One of the most useful features in MathCAD is the Math Palette. This is a series of buttons, which will allow you to get most of the features of MathCAD, as well as type in equations with the appropriate symbols. By clicking on any of the buttons in the Math Palette, you will produce additional Palettes (buttons) for specific functions. If the Math Palette is not visible, choose View from the menu bar, and see if the word Math Palette has a checkmark. If not, click the word Math Palette. Usually it is floating, but sometimes it can “anchor” in one of the other toolbars. Many of the button functions can be accomplished by using shortcut keys.

Arithmetic Arithmetic Palette – for trig, roots, factorial, exponential

Evaluation and Boolean Palette – for logical expressions Vector and Matrix Palette – for matrix algebra and vectors

Graph Palette – for graphing functions

Programming Programming Palette – for setting up programs in MathCAD

Calculus Palette – for integration and differentiation

Symbolic Keyword Palette – for solving equations, Laplace and Fourier analysis

Greek Symbol Palette- for getting all the s mbols

For example, instead of defining the magnitude as the square root of the sum of the squares, you can define magnitude as the absolute value. That button can be found in the Arithmetic palette. Also, instead of defining the phase angle in terms of the arctangent, you can use the function arg(A), found by using the insert function button. The previous example could then be expressed as the following:

magA1

phaseA1

A

phaseA1

magA1 = 7.071

Page 15

arg( A )

=

45 deg

EET 300


COPYING FROM MATHCAD TO WORD In many cases, you might want to include mathematical expressions in your Word document or your PowerPoint presentation. MathCAD can be easier to work with than Equation Editor can. One reason is that you can solve an equation, rather than having to type in the solution as well. The second reason is that when you type in a ^ followed by a number, MathCAD will automatically create the correct expression without you having to click on a superscript icon and type in the number.

Copying from MathCAD to Word 1- Open the MathCAD file you you want to copy. 2- Move the mouse pointer above and to the left of the area you want to copy. Click and hold the mouse button, and drag it down and to the right, until you have enclosed the expressions you want to copy. You will see dotted lines around each area that will be copied. 3- Choose EDIT…COPY from the menu bar. 4- Go to your Word document, and click where you want to paste. Choose Paste…Special from the menu bar, and uncheck the box marked Float over Text. 5- Click the OK button. You might need to resize the object you copied. To do so, click once on the object, move the mouse button to the lower right black box (selection handle) and click and hold the mouse button until you are satisfied with the size of the object.

ASSIGNMENT 1 1. Let A1=3+j2, A2=-1+j4, B=2-j2. Determine C=(A1 x B)/A2 theoretically (show full calculations on a sheet of paper) and then confirm using MathCAD. Theoretical results can be in pencil, MathCAD results must have printout. 2. Develop the formulas, using MathCAD, to change from rectangular to polar, and from polar to rectangular. Try using the variable in example 1, showing the two forms of the all the complex numbers above. 3. Copy the results of problem 2 to Word. Before you copy the results, type in your your name, class, date, and retype the description of problem 2.

Page 16

EET 300


SETTING UP A FUNCTION IN MATHCAD In many operations, such as integration and differentiation, you need to first define a function, which may be dependent on one or more variables. Once you have defined a function, such as v(t), and then performed the mathematical operation below, such as integration, modify the original function and, by pressing , a new result will automatically be calculated.

Setting up a Function 1- Click anywhere in the worksheet, and type a letter, or expression, followed by a parenthesis. Inside the parenthesis should be the independent variable. For example, f(x) or v out(t). If you want to define a function that is dependent on more than one variable, separate each variable with a comma (such as f(t,x). 2- Type in the colon symbol, which will will set up the assignment equality, :=. 3- Type in the expression expression with the independent variable(s).

The example below shows several functions: f( t )

sin ( 2 .t )

g( t )

1

f( t , x)

3 t

2

t

x

 Mathcad is case sensitive, so the variable t and the variable T are not the same.

If you you get an error (the expression is in red) make sure that there are no other variables that are not defined above the function. In the example below, u appears to be a variable. However, it is defined before the function that uses it. u

g( t )

3

1

Page 17

3 .u t

EET 300


INTEGRATION AND DIFFERENTIATION - MATHCAD To experiment with both integration and differentiation, you need to set up a variable (by assigning it to an expression), and then solve for the expression symbolically. When you click outside the expression, or press , MathCAD will solve the expression in terms of the independent variable. If you you back to the original expression and change it, MathCAD will automatically recalculate the new solution.

Integration and Differentiation 1- Set up the expression, with the variable on the left side of the assignment equality, such as v(t), type in a colon to get the assignment equality, and then type in the expression. 2- Click somewhere below the expression in item 1, and using the Calculus Palette, click either the indefinite integral or derivative. 3- You will see placeholders for both the expression and the variable. You can either use the mouse to go from one placeholder to another, or use . For an indefinite indefinit e integral, you should have something that looks like the following:

f( t ) d t

For differentiation, you should have something that looks like the following:

d dt

f( t )

4- After you type either expression, hold down and press the period. This will cause an arrow to appear to the right of the expression. This is called Symbolic Evaluation, and can also be accomplished by opening up the Symbolic Keyword Palette and clicking on the appropriate button. However, the shortcut is easier to use, and you will use it a lot 5- Press or click outside the formula box, and the expression will be evaluated. By setting a worksheet up in this manner, you can easily change the original expression, and test out your integration integration and differentiation differentiation skills. If you want a definite integral, integral, you need to type in the limits, and then type an equal sign after the expression, expression, rather than solve for it symbolically. Note that when you open a palette, and hold the mouse over a button, a tooltip appears. This will not only tell you the purpose of the function, but also the shortcut key.

Page 18

EET 300


From the worksheet Integration and Differentiation.mcd Differentiation.mcd

Integration Integration and Differentiation First, define the variable f( t )

sin ( t )

then, type in both an integral and a derivative sign on the function, followed by the symbolic evaluation symbol, plus a period.

f( t ) d t

d dt

f( t )

cos ( t )

cos ( t )

You can now go back and change f(t)'s expression, and MathCAD will recalculate everything

Page 19

EET 300


GREEK SYMBOLS In this course, you will be using symbols such as Ω and ω. While you can use the Greek Symbol Palette, a shortcut method would be to type in a letter, followed by (hold down both and the letter G at the same time). This will produce the Greek letter equivalent. The problem is trying to remember what equivalents are. Some of the more common ones that will be used in EET 300 are listed below. Since the symbol symbol π is used all the time, Mathcad has a simple shortcut for that symbol -
.

English Letter

Greek Symbol

w

ω

W

Ω

t

τ

a

α

m

µ

q

θ

For Greek symbols that are different from the above, use the Greek Symbol Palette.

ASSIGNMENT 2 1. Look at all the buttons on the Math Palette. Which palette does the function absolute value appear? Which palette does the function complex appear? What is the help definition of both functions? 2. Integrate and differentiate the following functions: e , 2cos (3t), 2cos (2 πt), e sin(2ωt) and xsin(x). Discuss any difficulties you had with any of these three functions. Try to do these functions theoretically first. -2t

-3t

3. Integrate sin(t) from 0 to 2 π. (Hint- there is a definite integral in one of the palettes). -t

4. Do the second derivative of sin(t) and e . (Hint- there is a way of doing higher order derivatives in one of the palettes).

Page 20

EET 300


GRAPHING IN MATHCAD You can graph the results of your calculations very easy using Mathcad. When you graph a function, you first need to set up a range for the independent variable. There are three parts to this range – the initial value, the increment, and the final value. An increment can be left off, but the default will be 1, and it might be produce a graph that looks unusual. Try to use increments that make sense. This range can also be used to produce a non-graphical result of the function vs. the independent variable. When you are graphing functions that would involve sine or cosine, you might want to have as the final value (or increments) some function of pi.. If you are not sure of the range, then you can initially graph without defining the range for the independent variable. Usually you will get a graph that is centered around the origin. Once you observe the graph, you can insert the range for the independent variable in a location that is below where you define the function, but above where the graph is placed.

Setting up a Range for an Independent Variable 1- Below the variable expression which used the independent variable, type the variable, such as t, followed by the assignment expression (colon). 2- Type in a number, which which will be be the initial initial point for the graph. 3- Type a comma followed by a number or expression that represents the increment. 4- Type a semicolon, which will produce two dots, followed by a number or expression that -t represents the final value. For example, if you wanted to plot e from 0 to 4, with an increment of .01, then the variable t would look like

t

0 , .0 .01.. 4

5- Press .

Graphing 1- Below the range range and the definition of of the function, type the function, function, such as f(t), followed by the @ sign (<2>). You will see see the outlines outlines of a graph. 2- Click anywhere outside that graph, and the graph will be produced. You can also type the @ sign first, and then type in the placeholders in the graph the function and the independent variable.

Page 21

EET 300


3- If you want to resize the graph, click once on the graph, point to the lower right hand side of the graph (on top of the small black box) and the mouse pointer will change to a double arrow. Drag it to the right and down, and and the graph will will enlarge. 4- If you want want to graph two functions, functions, click next next to the first function function in the graph, graph, make sure the underline is under the entire expression, and type in a comma, followed by the new function. Note – If you want to just graph the function, you do not have to initially define the range for the independent variable, such as t. You will get a graph, and then based on that graph, insert just above the graph the range, as described in the previous page.

From the worksheet Graphing.mcd

Graphing Examples f( t ) g( t )

sin ( t ) cos ( t )

0 , .0 .01.π

t

..

2 .π

1

0.5

f( t ) g( t )

0

0.5

1 0

2

Page 22

4 t

6

8

EET 300


ASSIGNMENT 3 1.

Do problem 2-36 in the text theoretically. Then plot the addition of the two functions using MathCAD, as well as the result of solving problem 2-36 (on a separate graph). They should be the same graph. (a) Are they the same graph? (b) What are some of the difficulties you encountered in the MathCAD assignment? (Hintyou might want to plot each of the two functions separately first). (c) How would you determine the phase angle from the resulting graph in this example?

2.

For extra credit, plot the product of these two functions, describe what you observe, and could you mathematically have determined the plot? If so, how?

Page 23

EET 300


LESSON 2 – INTRODUCTION TO PSPICE You will Learn:



How start PSpice.



How to add parts to a schematic.



How to search for a part.



How to move and rotate parts.



How to connect parts.



How to change the attributes of a part.



How to save a schematic file.



How to copy and paste a part.



How to use the Undo/Redo feature



How to use Redraw and the Zooming feature



How to incorporate schematics in Word 97



How to perform simple DC analysis measurements

Page 24

EET 300


OVERVIEW The three main programs that will be used in the evaluation software are Schematics, PSpice and Probe. Schematics is the program that builds circuits by having you “draw” them on a monitor, and save them to a file with an .sch extension. PSpice is the software that is used to analyze the circuit created by Schematics , and to generate solutions. To graph these solutions a third application, called Probe, will be used.

Getting Started 1- Click on the Start button. The pop up menu appears. 2- Point to the word Programs. Programs . A pop up menu appears. 3- Point to the word DesignLab Eval 8. You will see the pop up menu with all of the evaluation evaluation programs. 4- Point to the word Schematics and click. The Schematics window Schematics window will open.

You will see a Windows based program, MicroSim Schematics (will change with OrCad version), with a menu bar and icons both below the menu bar and on the left side of the page. You will also see a blank area with blue letters on the top and left side of the page. To start drawing a schematic, part need to be placed on the page. In version 8.0, you will see on the Taskbar two additional programs, which are minimized. These programs are MicroSim Message Viewer and DesignLab Design Manager . Additional descriptions of these programs will be provided later on. You will also see a status bar on the bottom of the window. This will be used for prompts and cursor coordinates.

Page 25

EET 300


Tool Bars

Status Bar

Schematics window

Page 26

EET 300


USING SCHEMATICS Schematics is a schematic capture front-end program that provides a convenient system for:

· creating and managing circuit drawings · setting up and running simulations using PSpice · evaluating simulation results using Probe An important prerequisite to building a schematic is the availability of the necessary parts (in the form of symbols) for assembly. Schematics has an extensive symbol libraries and a fully integrated symbol editor for creating your own symbols or modifying modifying existing symbols. For the labs you will be using the existing symbols. A schematic consists of symbols, attributes, wires, buses and text items. Parts are electrical devices that make up a circuit, such as resistors, operational amplifiers, diodes, voltage sources and digital gates. gates. The graphical representation of a part is a symbol. symbol. You can add additional text to the schematic.

Adding Parts To A Schematic 1- Choose Draw…Get New Part from the menu bar, or click on the Get New Part button located in the toolbar. The Part Browser Basic dialog box appears. The description for the button is in the Tooltips, which are the yellow background words just under the mouse pointer. A more detailed description appears in the status bar, located at the bottom of the window. 2- Either type the the first letter of the part in the Part Name field or scroll scroll down the list list until you see the part part name or number. number. If you type in the first letter the scroll scroll list below will will automatically go to a part with that letter. 3- Select the part by clicking clickin g on the appropriate name in the list box. The part will appear in the Part Name field. 4- To place a part on the drawing drawing page, first click on the Place and Close button. Then move the part to approximately where you want it, and click on the left mouse button. The part will appear to be attached to the mouse icon. Once you click on the left mouse button the part will appear on the page, and still attached to the mouse icon. You can place multiple instances of this part by clicking on the left mouse button each time. When you are placing a part, you will see a package reference (which will designate that part) and a value attribute (which shows the value of that part). 5- When you are are finished, finished, click on the the right mouse mouse button. The part will will no longer longer appear appear to be attached to the mouse icon.

Page 27

EET 300


6- If you want another part, then repeat items items 2-5. Otherwise, click on the Close button. If you only want one part from this dialog box, after choosing it you can click on the Place and Close button. The Part Browser Basic dialog box closes.

 You can click on the Place button in the Part Browser dialog box, rather than the

Place and you to choose another part without opening the dialog box. Close button. This will enable you However, you might find this as difficult, since you will have to move each part after placing it.

 The dialog box above will be different for Versions 6.0 and 6.1.

Starting with Version 6.2, it

will be the same.

 If you click on the Advanced button, you will see a picture of the part, before placing it (see dialog box on right). To get back to the original shape of the dialog box, click on the Basic button.

Page 28

EET 300


Adding Parts To A Schematic Using The Get Recent Part List 1- Click on the drop drop down list, list, located on the right side of of the first line of tools.

2- Click on the item you want want to place. 3- Move the mouse onto the drawing page. If you want the part rotated before you you place it, then press prior to clicking on the left mouse button. 4- To place the part, click click on the left mouse button. Continue to click on the left mouse mouse button to place multiple copies. copies. When you are finished placing placing that part, click on the right mouse button.

 The recent part list shows the most recent parts that you use (the last 10 parts), and would probably be a good source for many of your schematics.

EXERCISE 1-

Open Schematics .

2-

From the Get Recent Parts Dialog box, obtain a resistor and place it on the page, by moving the mouse pointer onto the page and clicking on the left mouse button. Note that R1 is the package reference, and 1k is the value attribute (the default value).

3-

Move the mouse pointer to the right of the first resistor and place a second resistor. Note that this second resistor has a package reference R2.

4-

Click on the right mouse button to stop placing resistors.

5-

Click on the Get New Part icon, and find a part called VDC. Place it to the left of R1. It will be easiest to click on the Place and Close button in Part Browser dialog box.

Page 29

EET 300


SEARCHING FOR PARTS There might be times where you do not know the abbreviation of the part, and are having a problem finding the part. You can use a description search to find a part (or group of parts) that has that characteristic.

Using The Description Search Feature Of The Part Browser Dialog Box 1- Open the part browser dialog box, by clicking on the Get New Part button located in the toolbar.

.

2- In the description description search field, enter a general general description description of the part (i.e. ground, ground, power power supply). 3- Click on the Search button. A list of those parts, which contain the phrase you entered, will appear.

EXERCISE 1-

In the current drawing page, page, open the Part Browser dialog box. Make sure the Advanced button has been clicked.

2-

In the description search field, type in the word ground, and click on the search field.

3-

Click on each of the ground parts, and observe the description and picture.

Page 30

EET 300


ARRANGING PARTS Once you have all the parts on the drawing page, page, they need to be arranged. This includes moving them relative to one another and rotating the parts to get the correct orientation. By default, voltage and current sources are placed vertically and passive components (RCL) are placed horizontally. You can also delete parts that were accidentally placed on the drawing page.

Moving Parts 1- Double click on the Visio icon. 2- Select the part by by clicking clicking it. The part part will will turn red. Caution: Caution: Only single-click, do not double-click the part. 3- Move the mouse icon over the part. You will see the mouse icon change, and a double/double white arrow will appear on the lower right of the mouse icon. With the mouse icon on the part, click and hold the part, and move it to the position you want. The part will not move smoothly, but rather snap into position based on the grids (grids are used to make the parts line up). If the grid is not visible, and you want it visible, then select Options…Display Options…Display Options and click in the checkbox next to Grid On. When you paste these circuits to another application application (to be discussed later) it is recommended to turn the grid off 4- If you want to move more than one part at a time, select the first part, and hold down while selecting additional parts. Another way to select multiple parts is to position the mouse pointer to the left and above the group of parts you want to select, click and hold and draw a box around those parts. All the parts within the box will turn red.

 You can also move a label (either a value or the part number) by repeating items 1 and 2 above.

Page 31

EET 300


Rotating Parts 1- Select the part part by clicking it. The part part will turn red. red. o

2- Press . The part will rotate 90 counterclockwise each time you press this key combination. combination. This is very useful for passive passive components. components. After selecting a part but prior to clicking on the left mouse, you can also use to rotate the part prior to placing it on the drawing page.

Deleting Parts 1- Select the part part by clicking it. The part part will turn red. red. 2- Press . . If you want to delete multiple parts at once, select the first part, hold , , and select additional additional parts. Once all the parts are selected, selected, press . .

EXERCISE 1-

In the schematic you just created, select both resistors and move them down about 1inch.

2-

Move R1 so that it to the right of the voltage source, and horizontal.

3-

Move and rotate R2 so that it is to the right of R1 and vertical.

4-

Add one additional resistor, and then delete it.

Page 32

EET 300


CONNECTING PARTS Parts and ports contain one or more pins to which connections are made. Electrical connections are formed by wire and bus segments joining pins and other wire and bus segments. Attaching pins directly to pins also forms connections. Schematics represent each such electrical connection by a junction. Junctions are made visible when three or more connected items converge at the junction. Junctions are created and removed automatically.

Connecting Parts 1- Either click on the Draw Wire button in the toolbar icon changes to a pencil.

, or press . . The mouse

2- Place the tip of the pencil on one of the parts you want to connect, and click the left mouse button. This will anchor the drawing wire at that point. 3- Move the mouse until it is on the next part you want to connect to. The parts will look like they are connected. 4- Click at that that point. The wire will now now anchor anchor at the the next next point. Note: Note: If you need to make a bend in the wire, simply move the mouse in that direction. The wire will continue to be drawn until you click it. 5- You can now move the pencil to a new point, and connect two new parts. 6- When you are finished finished connecting, connecting, click on the the right mouse button button to deselect deselect the Draw Wire tool.



In most circuits, you will need to add a ground. This can be found in the parts dialog box as AGND or EGND.

 Once the parts are connected, you can still move them.

They will remain connected. However, make certain that in the Display Options dialog box (choose Options, Display Options in the menu bar) the Rubberband checkbox is checked.

Page 33

EET 300


CHANGING PARTS ATTRIBUTES Each part has a single or multiple set of values. Parts such as resistors, capacitors, inductors and VDC have just a single value that needs to be changed. The default value is shown in a box next to the part. For example, resistors will have a default value of 1 k Ω, voltage sources will have a default value of 0V. Certain complex sources, such as VSIN, VPULSE, VSRC, etc. must have several values defined before you can begin the analysis.

Changing Single Values 1- Double click on the value of the part. The Set Attribute Attribut e Value dialog box opens. 2- With the value highlighted, highlight ed, type over with a number. You do not have to put in the appropriate units (unless you want to put in mV as opposed to V). 3- Click OK. OK.

Set Attribute Value dialog box

 Be careful with abbreviations after parts.

PSpice will not recognize 5M as 5 M Ω − use 5000k instead. The same thing is true about .01F – write it as 10000 µF.

Page 34

EET 300


Changing Complex Values 1- Double-click on on the p part, art, or select select the part and click on on the Edit Attributes button in the toolbar

. A dialog box will open with the part name.

2- Click on the appropriate line you wish to change. The name and value will appear above in the designated boxes. 3- Double-click in the Value Box field, and type over the appropriate number. 4- Press . . You must do this, or the value value will not change. 5- Continue repeating repeating items 2-4 2-4 until you are are finished changing changing all the attributes. 6- Click OK. OK.

PartName dialog box

Page 35

EET 300


EXERCISE 1-

In the schematic you just created, connect all the parts together, and add an AGND part.

2-

Change the value of R2 to 2k.

3-

Change the VDC value, using the PartName dialog box, to 5 V, and change the Package reference Designator attribute (PKGREF) from V1 to Vin.

Page 36

EET 300


SAVING A SCHEMATIC FILE Prior to any simulation, you you must save the schematic. You can save a file by using the current name, drive and folder ( File, Save), or change the name, drive or folder to create a file that is separate from the original ( File, Save As). When you first create a schematic file Schematics automatically opens the Save As dialog box.

Saving A Schematic File 1- Choose File, Save to save an existing file as itself, or click on the Save button in the toolbar. If you haven’t saved the file before, the Save As dialog box will open. If you have already saved the file, the changes will be saved with the same file name. 2- If you want to save this file with a different differ ent name, drive or folder, choose File, Save As. As . 3- If the Save As As dialog box appears, fill in the the name of the schematic in the the File name field field in the Save As dialog box, and choose both the drive and folder. 4- Click on the Save button.

Save As Dialog Box

Page 37

EET 300


COPY/PASTING PARTS To add multiple copies of a part, you can repeatedly click on the left mouse button after selecting that part from the Parts Browser dialog box. If you you have placed a specific part on the schematic, and you want to add additional copies, you can also copy that part. Since this copy will be the same value as the original, it can be very useful when you are have a several values you need to set, such as a voltage source. You can also copy from one file, and paste that same part to a new file.

Copying A Part 1- Select the part. The color of the part becomes becomes red. 2- Copy and paste the part (using shortcut keys, menu bar, or the toolbar). You will see that part on the end of the mouse pointer. 3- Position the mouse pointer where you want the part, and click on the left mouse button. If you want another instance of this part, click again. 4- When you are completed completed with with pasting, click on on the right mouse mouse button.

Page 38

EET 300


EXERCISE 1- Start a new schematic, and draw the circuit as shown below.

2- Add two more 2k resistors by copying and pasting.

3- Save this file as THEV1.

Page 39

EET 300


UNDO/REDO Schematics keeps a record of each edit you apply to your schematic. Because of this, you can undo (or reverse) each edit, up to the last time you saved the schematic. If you you used undo too much, you can redo (or reapply) the edits. Both Undo and Redo apply only to design changes that alter the contents of a schematic page.

Undo/Redo 1- Choose Edit, Undo, Undo, or press , , or click on the Undo button on the toolbar

.

2- To reverse any undo action, choose Edit, Redo, Redo, or press , , or click on the Redo button on the toolbar.

EXERCISE 1-

Save the file you just created as RESISTOR (note that the program will automatically put in the extension).

2-

Once saved, add a resistor to the drawing page, delete it, undo that deletion, and redo that deletion. When you are finished with these tasks, you should have the original drawing.

3-

Keep this file open.

Page 40

EET 300


REDRAW AND ZOOMING If there are additional lines in the schematic that shouldn’t be there, or lines that are missing, the drawing might need to be refreshed. The redraw feature accomplishes this. When working on a design, you can zoom in or zoom out to view a larger or smaller portion of the schematic window.

Using Redraw 1- To refresh refresh your drawing, choose View, Redraw, Redraw , or click on the Redraw button in the toolbar. 2- Click on the appropriate line you wish to change. The name and value will appear above in the designated boxes. 3- Double-click in the value box field, and type over the appropriate number.

Zoom Out

Zoom To Fit Page

Zoom Area

Zoom In

Zoom Button in the Toolbar

Page 41

EET 300


Button

Function

Menu Bar Method

Zoom In

Click on this button to zoom in on the circuit.

Choose View, In and click on the portion of the circuit you want to zoom in on.

Zoom Out

Click on this button to zoom out.

Choose View, Out and click on the portion of the circuit where you want to zoom out.

Zoom Area

Click on this button, and then click and hold the left mouse button down to draw a box around the area you want to zoom in on. When you release the mouse button, that area will fill the entire drawing page.

Choose View, Area and then click and hold the left mouse button down to draw a box around the area you want to zoom in on. When you you release the mouse button, that area will fill the entire drawing page.

Zoom to Fit Page

Click on this button and the circuit will fill the entire drawing page. This is useful if you zoomed in on an area too far and you want to see the entire circuit.

Choose View, Fit and the circuit will fill the entire drawing page. This is useful if you zoomed in on an area too far and you want to see the entire circuit.

 You can also choose View, Entire Page from the menu bar. entire drawing page, including border and title block.

Page 42

This will enable you you to see the

EET 300


WORKING WITH WORD 97 If you want to incorporate a schematic into your report, the best way would be to copy/paste the schematic into your Word document.

Copying Schematics Into Word 97 1- Choose Options, Display Options, Options, and click off Grid On. 2- In the Schematics window, Schematics window, point the mouse above and to the left of the schematic. 3- Click and hold the mouse button, and drag to the right and below the schematic. You will see a rectangular box surrounding your schematic. Make sure this box surrounds the entire schematic, and there is about ½ inch border between the box and the parts. 4- Choose Edit, Copy to Clipboard. Clipboard. The schematic can now be pasted into another Window application, application, such as Word W ord 97. 5- In Word 97, choose Edit, Paste Special. Special . The Paste Special dialog box appears. 6- In the right side of this dialog box, you will see a checkbox with the description descripti on Float over text . Make sure the checkbox is not checked, then click the OK button. You need to do this this to prevent the schematic schematic from having a frame around it. Without a frame, you can position position the schematic using using the formatting toolbar – left, center, center, or right. If you didn’t uncheck this box, you could move the schematic anywhere in the page. However, this can cause problems. 7- If you click once in the schematic, you will see 9 small boxes around the picture, as well well as a Picture toolbar. You can move the mouse to the lower right box, click and hold the mouse button down, and then you can resize the schematic by dragging diagonally. 8- You will will see a line around around the schematic. schematic. If you want want to get rid of the line, click on on the cropping button in the Picture toolbar, , and then move the mouse pointer over the four middle boxes boxes in the picture, click and drag then then inwards. When you click outside the picture, you should not see the lines.

 It might be easier to first crop the picture and then resize it.

Page 43

EET 300


EXERCISE 1-

Open both PSpice and Word 97. If you you have another word processing application, you can still perform this exercise. However, you will need to understand how to crop a picture.

2-

In PSpice, place a VDC part and two resistors. Drag a box around those three parts, paste them into your word processing program, and center the drawing in the page.

3-

Using the cropping tool, get rid of the outside border lines

Page 44

EET 300


MEASUREMENTS - DC ANALYSIS If you want to measure DC levels (i.e. for experiments involving Ohm’s law or Kirchoff’s law) you can use two parts to view these levels. These parts are placed on the schematic drawing the same way any other part is placed. VIEWPOINT is a voltage viewing point, which will show the value after the circuit is simulated. You place VIEWPOINT on a node. IPROBE is a current probe, which will show the value after the circuit is simulated. You need to put this part between two parts, so that current flowing in that branch can be measured. If you have measurements that are time-varying (i.e. a sinusoid) then you need to run Probe. This section will deal with simple DC analysis.

DC Analysis 1- Place VIEWPOINT VIEWPOI NT and/or IPULSE in the appropriate points. You place the VIEWPOINT VIEWPO INT part at a node. To place the IPULSE part, you will have to break the circuit. 2- Save the drawing. 3- Choose Analysis…Simulate from the menu bar, or click on the Simulate button in the toolbar. 4- If there are no errors, you will see the PSpice dialog box and hear a click. Move the mouse anywhere in the schematic page and click the left mouse button. You will see the values on the VIEWPOINT or IPULSE parts. If there is an error, you will see an Error dialog dialog box. If you click on the OK button, you will bring up the MicroSim MicroSim Message Viewer dialog box. Anything with a red Error message needs to be corrected.

Page 45

EET 300


PSpiceAD dialog box

MicroSim Message Viewer

Page 46

EET 300


EXERCISE 1-

In the RESISTOR file, add a VIEWPOINT and IPROBE part.

2-

If there were no errors, you should see the PSpiceAD dialog box

3-

Close the PSpiceAD dialog box. The schematic should now show numbers for both the voltage and current through R2.

4-

Change the value of R2 to 5K, run the simulation again, and observe the new values.

5-

Delete the AGND part, and run the simulation again. You should see an error, which needs to be fixed by adding the AGND part.

6-

Save this file.

Page 47

EET 300


EXPLANATION OF PROBLEMS At the end of each chapter there will be several problems based on what was covered in the chapter. Besides doing the required steps, you are encouraged to experiment by

• • • •

Changing values of components Adding/deleting components Changing the measuring points Changing the amplitude or type of input

You will be required to hand in a report based on these problems. This report should include the following: 1. A title page page with your name 2. An introductory section detailing what you you think you will be accomplishing in this exercise, what new concepts you will be learning, and what if any additional items you tried. 3. Detailed calculations (similar to a pre-lab) which will demonstrate what you expect to see. This may involve mathematical proof of responses. 4. Printouts of the schematic(s) and of the responses. These printouts should be pasted into the Word document, as opposed to being printed out. If there is a problem doing this, see me during office hours. 5. A brief conclusion as to the observations, how close they came to the “pre-lab” calculations, and how do you think this exercise could have been changed.

Page 48

EET 300


PROBLEM 1 1-

Place the following components on a new drawing page: 4 Resistors, VDC and AGND.

2-

Move and rotate the components so they appear as in the figure below.

3-

Wire the components together.

4-

Change the values to the components as follows: V 1=100, R1=7.5k, R2=5k, R3=3k and R4=2k. (Note that you do not have to put in Ω for the resistors). You might have to move the value box away or nearer the part.

5-

Add two VIEWPOINT objects to the drawing- one attached to the right of R 1, the other on top of R 4. You should have the figure below.

6-

First calculate the voltage at the two VIEWPOINT VIEWPOINT objects. Show the calculations.

7-

Save the drawing first, as CHAP3-1.

8-

Run a simulation, and compare the values to those from item 6.

9-

Change R2 to 2k, and R4 to 4k. Calculate first, and then run the simulation again.

10-

Save this again and close out of this file.

Page 49

EET 300


LESSON 3 - TRANSIENT ANALYSIS WITH RC AND RL CIRCUITS You will Learn:



How to use the pulse voltage source.



How to set up and perform a transient analysis.



How to use special markers for the schematic.



How to modify the graph appearance.



How to print graphs.



How to copy and paste the schematic or graph to another program.



How to sweep a component value.



How to use the VPWL source.



How to use the Differentiator and Integrator parts.



How to work with custom axis.

Page 50

EET 300


PULSE VOLTAGE SOURCE In analyzing a circuit that has a voltage source switched at t=0, you can simulate this by using a pulse voltage source (VPULSE). Various parameters must be set for this source.

Setting A Pulse Voltage Source 1- Select from the Part Browser Browser dialog dialog box box VPULSE. VPULSE. 2- Place it on the drawing page. 3- Double-click Double-cli ck on the part. The VPULSE dialog box opens. 4- Type in zero for V1 (unless you want a positive and negative pulse). Type in the desired amplitude (don’t need the unit V) for V2. 5- Type in values for TR and and TF, at at least 1/100

th

of the pulse width.

Unless you are going to choose an extremely narrow pulse, a choice of 1ns for each of the two values would be appropriate. Do not have a space between the value and the units . 6- Type in a value for PW. 7- Type in a value for the PER. This value will depend on whether you want to see multiple cycles (then type in a value 2 or 3 times the pulse width) or only one cycle (then type in a value at least 10 times the pulse width). 8- Click OK.

Page 51

EET 300


UNIT STEP In many instances, you will be required to set up a circuit with a unit step function. This function would also be used to solve initial and steady state conditions in circuits, where you have a DC source and a switch that closes at DC. The VPULSE part can be used to set up a Unit Step.

Setting up a Unit Step Input 1- Follow the procedure on the preceding page for setting up a VPULSE part. 2- When you are setting setting up the value value of PW, this value value must be at least least 5 times the time constant of the system. If you do not know the time constant of the system, you can set the value of the PW to several seconds. The circuit will view this “wide” pulse as a switched DC, or a unit step function.

Page 52

EET 300


SETTING UP THE TRANSIENT ANALYSIS To run a transient analysis on the pulse waveform, the Transient dialog box must be filled in.

Transient Dialog Box 1- Choose Analysis…Setup from the menu bar, or click on the Setup Analysis Analysis button in the toolbar

. The Analysis Setup dialog box opens.

2- Click on the Transient button in the Analysis Setup dialog box. The Transient dialog box opens. 3- Type in the appropriate appropriate values values for the Final Time. If you want to see multiple waveforms, then the Final Time should be at least twice the value of PER. If you want to see an expanded view of the rise time, then the Final Time value should be approximately approximatel y 1.2 times the PW. You do not have to change the Print Step value unless you only have a resistive circuit (do not set it to zero). If you need to change the Print Step value (because the analysis is incrementing too slowly), th make sure Print Step is at least 1/100 of the Final Time. 4- Click OK, OK, and then Close. Close.

Page 53

EET 300


Analysis Setup Dialog Box

Transient dialog box

Page 54

EET 300


PERFORMING THE TRANSIENT ANALYSIS Once the VPULSE part, the Transient Dialog box, and the rest of the circuit are set up, transient analysis can be performed. Since usually both the input and output need to be observed, this can be set before running the simulation.

Performing The Transient Analysis Analysis 1- Save the schematic. Place markers on the schematic to indicate the points for which you want to see simulation waveforms displayed in Probe . Placement can occur occur before or after after simulation takes place. place. Use Mark Voltage/Level markers for this part. 2- Choose Analysis…Simulate from the menu bar, or click on the Simulate icon in the toolbar. If there are no errors, you will see the PSpice dialog box, and on the bottom of this dialog box you will see numbers changing. When the iterations are completed, you will hear a click, followed by a display of the Probe window. Probe window. 3- If there are errors, you need to choose File…View Messages from the menu bar. Read the error messages and take appropriate action. 4- If you want to modify the schematic, click on the Schematic button in the Taskbar (Windows (Wi ndows 95). Then repeat step 2. You do not have to repeat step 2 if you are only adding additional markers .

 When the graph appears, you will see a window with PROBE in the title bar, and in Windows 95/98 the Taskbar will contain the Probe button. You will also see at the bottom of the graph a color indicating which point on the circuit you are looking at, i.e. for a resistor R1, V(R1:1) represents the left side of the resistor (if you are looking at a horizontal resistor) while V(R1:2) is the right side of the resistor.

Page 55

EET 300


CHANGING BACKGROUND COLORS IN PROBE The default colors in Probe are a black background with a white axis. Although this might be acceptable when viewing on a monitor, it is very difficult to see when you copy to a Word document (to be shown later). You can change the default colors so that you have a white background.

Color Change In Probe 1- Locate the file called msim_evl.ini in the C:/windows C:/windows directory. directory. It is not the file called msim_ev.ini. (must have have evl after the underline). underline). You can use either either Windows Explorer Explorer or use the Find feature of Windows 95. 2- If you double double click on the icon icon to the left of the file name, this file should should open open in Notepad. Notepad. If it doesn't, then open it in Notepad (although you can also open it in Word). Make sure that PSpice is closed. 3- In Notepad, choose Search…Find, Search…Find , type in the words PROBE DISPLAY COLORS, COLORS, and then click the FIND NEXT button. You should go to the section you need to modify. 4- In the next several lines, you are going to change the Background, Foreground and Trace_1 and Trace_3 values. The original Trace_1 value is BRIGHTGREEN, BRIGHTGR EEN, which is very hard to see on top of a white background. The first 5 lines of the PROBE DISPLAY COLORS COLORS section should look like the following: [PROBE DISPLAY COLORS] NUMTRACECOLORS=6 BACKGROUND=BRIGHTWHITE FOREGROUND=BLACK TRACE_1=BRIGHTBLUE TRACE_2=BRIGHTRED TRACE_3=BRIGHTGREEN 5- Save these changes, and then reopen PSpice.

Page 56

EET 300


EXERCISE 1-

Place VPULSE, AGND, R and C parts on the drawing page, move and connect them so you get the schematic as seen below. Make sure you change the C1 value to 1 uF.

2-

Setup VPULSE for a pulse width (PW) of 1ms, a period (PER) of 5ms, V1= 0 and V2 = 5. Make sure you put in appropriate values for TR and TF.

3-

Go to Setup Analysis, and in the Transient analysis set Final Time to 10ms.

4-

Place a voltage marker at the input (at the top of V1) and the output (at the top of the capacitor).

5-

Save this file as RC.

6-

Click on the Simulate button in the toolbar. If there are no errors, you should see the PSpiceAD window come up, various numbers change on the bottom, and then the Probe graph window appear, with graphs showing both the input and the output (see next diagram). If you you have a black background, change the setting in the msim_evl.ini file, as detailed in the previous page.

Page 57

EET 300


7-

Go back to the Schematics window, change the value of the capacitor to 0.2uF, and run the simulation again.

8-


Page 58

EET 300


SPECIAL MARKERS Instead of using markers, which will name the trace based on the part it is attached to, you can use a special part called a BUBBLE. You can give this part any name, and it can be used to mark the traces as Vin, Vout, etc.

Using Bubbles 1- Click on the Get a new part button in the toolbar, and choose Bubble from the drop down list. 2- Place the bubble bubble part at the point(s) point(s) of interest (delete the Voltage/Level Voltage/Level markers). 3- Double-click on each bubble. The Set Attribute Value dialog appears. Type in the name for the bubble. 4- Click on Analysis…Simulate to run PSpice . If the setup was done properly, Probe should Probe should run and you will see a blank graph. 5- In the Probe menu Probe menu bar, choose Trace…Add. Trace…Add. The Add Traces dialog box appears. 6- From the left-hand column of this box click on the appropriate name. You can hold down while clicking to choose choose multiple traces. You will see the traces traces listed in the Trace Expression field at the bottom of this dialog box. 7- Once you have all the traces listed, click OK. OK. You can repeat items 5 and 6 to add traces.

 You can delete any trace by clicking on the legend for the trace (located in the lower left portion of the graph) and pressing .

 The Add Traces dialog box can also be used to display complex functions of voltages and currents, i.e. power.

 If you you use the bubble part, label it with names such as input or output. next to the name.

Page 59

Probe will add the V

EET 300


EXERCISE 1-

Delete, in the previous schematic, the Voltage/Level markers, and place a Bubble part on top of the VPULSE and the capacitor.

2-

Double-click on each of the Bubble parts, and put in the label Vin and Vout.

3-

Run the simulation. You should get a blank graph in the Probe window.

4-

In the menu bar of the Probe window, choose Trace, Add, select Vin and click OK.

5-

Repeat item 4 for Vout. You should now have a graph that is labeled with Vin and Vout.

6-


Page 60

EET 300


MODIFYING GRAPHS There are many ways to modify the graphs. Changes include axis setting, adding labels to a curve, or adding a cursor to the plot.

Changing Axis 1- Choose Plot and either X Axis Settings or Y Axis Settings. Settings. A dialog box will appear. 2- To change the scale, click in the radio box next to the words User Defined, Defined, and enter the new scale below. To go back to the original setting, select Auto Range in the Data Range field. 3- You can add an Axis Title as well, by typing in that field. 4- Click OK. OK.

Page 61

EET 300


Adding Labels To Curve 1- Choose Tools, Label. Label. You will see a drop down list. 2- If you want a text label then choose Text, Text, and type in the desired text in the dialog box. To choose just text you can also click on the Text Label button in the toolbar. When you click OK, OK, the mouse pointer will change to a pencil. You can move the mouse around and place the text anywhere you want, and then click the left mouse button to fix the position. 3- You can also use other Label items, such as lines, arrows and boxes. To use an arrow, choose Arrow from the drop down list, move the mouse away from the point of the graph you want the arrow to point to. Click, and then move the mouse towards the point you want the arrow to show. Note that an arrow is always at the line end. 4- If you typed text, and want to modify or delete it, double click on the text. The dialog box will appear, and either edit what is in the dialog box or delete it, and then click OK. OK.

Adding A Cursor To The Plot 1- Choose Tools, Cursor, Display, Display, or click on the Toggle Cursor button in the toolbar. A display box appears in the lower right hand corner of the graph, entitled Probe Cursor. Probe Cursor. This will show values for both axes. 2- Click with the left mouse button anywhere in the graph. A dotted vertical white white line appears (this is the cursor). If the graph is anything but a pulse, pulse, you may see a horizontal horizontal and vertical dotted line. You can click and drag the cursor over the curve, and observe the changes in the values in the Probe Cursor Probe Cursor display box. 3- To select which which trace the cursor cursor is measuring, click click on the icon next to the axis axis label (located in the lower left part of the graph).

Page 62

EET 300


EXERCISE 1-

In the Probe graph you have opened, change the X-axis to 5 ms.

2-

Add an arrow, pointing to the peak of the output.

3-

Add a label entitled Maximum.

4-

Add a cursor to Vout.

Page 63

EET 300


PRINTING AND COPYING GRAPHS There are two ways to get hardcopy of your graphs: printing them or copy them to another application (such as Word).

Printing Graphs 1- In the Probe window, Probe window, choose File…Print from the menu bar. If a graph does not appear, make sure that the appropriate printer is chosen (one that can print graphs as well as text). You can see what printer is chosen by choosing File, Printer, Select from the menu bar..

Copying Graphs 1- In the Probe window, Probe window, choose Tools, Copy to Clipboard. Clipboard. The graph can now be pasted into another Window application application,, such as Word. If you are using Word 97, then you should should use Edit, Paste Special, Special , and uncheck the “Float over text” checkbox. 2- Select a new new folder in the Choose a Drawing Template dialog box and click on the Open button. The folder represents represents a group of templates. templates.

EXERCISE 1-

Print the graph directly from Probe.

2-

Open a new Word document, and type the word Schematic and then press .

3-

Copy and paste the schematic to this new document.

4-

Press , and then type the word Graph. Press .

5-

Copy and paste the graph in the Probe window to this document.

Page 64

EET 300


SWEEPING A COMPONENT VALUE There are tests that might require you you to sweep a component through a range of values. To do this, a three-step process is needed.

Changing the Component Value to A Variable 1- Double click click on the Value Attribute Attribute (the components components magnitude). magnitude). The Set Attribute Value Value dialog box opens. 2- Type in an expression, such as RLOAD or ROUT, ROUT, make sure you encase this expression in curly braces braces {}, and then click OK. OK. You might want to move this label, by pointing to the label and clicking and hold and drag this label to a new position.

Defining the Value as A Variable 1- Click on the Get New Part butto button n on on the the too toolba lbar. r.

. The Part Part Brows Browser er dialo dialog g box box ope opens ns..

2- Select from the list the PARAM part. 3- Click on the Place and Close button, move the mouse pointer to an empty area (i.e. above and to the right of the schematic) and click on the left mouse button. 4- Click on the right mouse mouse button. 5- Point to the word PARAMETERS, PARAMETERS, and double click on it. The PartName dialog box opens. 6- Enter the name you chose for this component in the NAME1 field, and enter the original value of this component in the VALUE1 field. 7- Click OK. OK.

Page 65

EET 300


Global Sweep 1- Click on the Setup Analysis button in the toolbar. opens.

The Analysis Setup dialog box

2- Click on the DC Sweep button. The DC Sweep dialog box opens. 3- Select Global Parameter in the Swept Var. Type field. 4- Enter the name of the component and the range of the sweep (the start value, end value, and the increment). 5- Click OK, OK, and then click Close. Close.

DC Sweep dialog box

Page 66

EET 300


EXERCISE 1-

Draw the circuit below, defining the last resistor as a variable RLOAD.

2-

Setup the sweep with Start Value of 100, End Value of 100k, and Increment of 100.

3-

Add a voltage level marker at the top of R4.

4-

Run the simulation.

5-

Add a cursor to the graph, and measure the voltage amplitude. See how it approaches a certain value.

6-

Try doing the same thing using a Current/Level marker.

Page 67

EET 300


USING THE VPWL SOURCE When you want to create a custom voltage source, you can use the VPWL part. This will allow you to define different voltage levels for up to 10 different time points. This source can be very useful in creating a linear voltage waveform to analyze RMS, average, integration and differentiation of piecewise linear voltage waveforms.

Setting Up the VPWL Source 1- Set up up a circuit with with a VPWL source. source. 2- Double click on the VPWL VPWL source. The PartName PartName dialog dialog box box opens. opens. 3- Enter the values values for the voltage, voltage, and the the time that voltage voltage occurs. 4- To view the waveform, place a resistor across the source (use the default value) and an AGND part. Place a Voltage marker marker at the top of the resistor, and run a transient transient analysis. Make sure that the Final Time is set so you can see the entire waveform.

 To create most waveforms, you might want to start at 0, which means that V1 and T1 should be 0.

 If you want to create a square wave, then T1=T2.

Page 68

EET 300


EXERCISE 1-

Set up a VPWL source with the following parameters: T1=0, V1=0, T2=2, V2=2, T3=4, V3=0.

2-

Add a resistor and AGND part.

3-

Set the transient analysis analysis to the following: Print Step = 1 ms, Final Time=5s. Add a voltage marker to the top of R1.

4-

Save this file with a name WAVEFORM, and run the analysis. You should see an triangular waveform, with an amplitude of 2V and a pulse width of 4s.

5-


Page 69

EET 300


USING THE DIFFERENTIATOR AND INTEGRATOR In working with mathematical expressions such as differentiation and integration, you can add a part to the schematic that will accomplish these expressions. These are single input, single output parts.

Using Mathematical Parts 1- Click on the Get New Part button. 2- Select either either the part DIFFER (for differentiation) differentiation) or INTEG (for integration). integration). 3- If you are just viewing the effects of differentiation or integration on a waveform, place this type of part immediately after the source, and place a resistor (use the default value) as an output. Make sure you use an AGND part.

EXERCISE 1-

Using the VPWL source you just created, insert a DIFFER part between the source and the resistor.

2-

Add another voltage probe, so you have one before and after the DIFFER part.

3-

Run a simulation. Compare the output to what you you would expect the differentiated waveform to look like.

Page 70

EET 300

4-


Repeat steps 1-3 with the INTEG INTEG part. Note: You can also replace parts by clicking on that part, choosing Edit, Replace and then typing in the part name.

Page 71

EET 300


WORKING WITH CUSTOM AXIS Besides being able to plot standard values such as input or output voltages or currents, Probe allows you to plot calculated plots (i.e. voltage times current) or functions (i.e. derivative of the output voltage waveform). You also have functions which will be useful for plotting Bode plots (log) and also for finding average and rms values.

Generating A Custom Axis 1- In the Probe window, Probe window, choose Trace, Add. Add. The Add Traces dialog box appears. 2- To create a simple simple expression expression (i.e. Vout/Vin), Vout/Vin), click on the first Variable Variable in the expression expression.. You will see it appear in the Trace Expression field (located at the bottom of the dialog box). 3- Click on a Function (located on on the right right half of the dialog box). box). This function will appear appear after the first variable. 4- Continue to add the appropriate appropriat e Variables and Functions. If you are using a function with a parenthesis ( ), make sure that the cursor is in the middle of the parenthesis before clicking on a Variable (i.e. LOG10 (Vout)).

Page 72

EET 300


Some of the expressions you may need for the labs in this course are as follows:

Function

Meaning

AVG(x)

Running average of x over the range of the x-axis variable.

AVGX(a,b)

Running average of x for a range – from the point a on the x-axis to the point b on the x-axis.

D(x)

Derivative of x with respect to the x-axis variable.

DB(x)

Magnitude in decibels of x.

LOG10(x)

log (x)

LOG(x)

ln(x)

P(x)

Phase of x (in degrees)

PWR (x,y)

x

RMS(x)

Running RMS average of x over the range of the x-axis variable.

S(x)

Integral of x over the range of the x-axis variable.

y

 Note that you could do differentiation and integration using functions as well as the parts.

Page 73

EET 300


EXERCISE 1-

From the previous exercise, delete the integrated waveform (leave the original triangular waveform alone).

2-

Add the average waveform to this plot, using the function (the voltage should be V(R1:2). Note that this waveform is the average at each instant of time.

3-

Try adding the RMS value as well. See if you can explain the differences.

Page 74

EET 300


PROBLEMS 2-5 PROBLEM 2 1-

Create a waveform with the following characteristics, using the VPWL source: T1=0, V1=0, T2=1, V2=1, T3=2, V3=1, T4=4, V4=0.

2-

Integrate and differentiate the waveform, both theoretically and using PSpice.

3-

Create the figure shown in Fig. P2-60 (only the first two waveforms) using the VPWL source. Differentiate and integrate this waveform theortically and with PSpice.

PROBLEM 3 1-

Create a voltage waveform, using the VPWL source, with the following parameters: T1=0, V1=0; T2=3, V2=5; T3=6, V3=0. Place a 1k resistor across this source. Note that V and s are assumed units if they are not specified.

2-

Place a BUBBLE part at the output (across the resistor), call that part Vout,.

3-

Use the Set Up button to run a Transient Analysis. Set the Print Step to 2ms and the Final Time to 10s. Run the simulation.

4-

Add the trace Vout to the graph and observe the waveform.

5-

Add another plot to this graph, and add a trace to that new plot with the function AVG(Vout).

6-

Place a cursor on the upper graph, and move the cursor until it is at 6s. Read the value of the upper graph, and compare it to the calculated average for this triangular waveform.

Page 75

EET 300


PROBLEM 4 1-

Place the following components on a new drawing page: 1 Resistor, VSIN, 1 Capacitor and AGND.

2-

Move and rotate the components, and wire them together. Also add two voltage markersone at the input, and one at the output.

3-

Change the capacitor value to 1u.

4-

Set the values of VSIN as follows: VOFF=0, VAMPL=10V, FREQ=1000.

5-

Set the Transient values to 1us for the Print Step, and 2 ms for the Final time.

6-

Run the simulation and observe the two curves. Which voltage (input or output) leads, and approximately by how much. How do you you calculate phase?

7-

Replace the position of the resistors and capacitors. What happens to the phase relationship between the input and output voltage.

PROBLEM 5 1-

Solve problem 4-17 for the voltage and current waveforms, using PSpice. Estimate theoretically what the initial and steady state condition should be. Does it conform to the Probe waveform?

Page 76

EET 300


LESSON 4 – LAPLACE TRANSFORMS USING MATHCAD You will Learn:



How to perform the Laplace transform and inverse transform in Mathcad.



How to solve for the roots of an equation.

Page 77

EET 300


LAPLACE TRANSFORMS

MathCAD can enable you to perform both Laplace transforms and inverse Laplace transforms. The best way to accomplish this is to use the Symbolic Keyword Palette.

Laplace Transforms 1- Set up a variable, such as v(t), and assign it to an expression, such as sin(t). 2- Type the variable variable below, and click on the laplace button located in the Symbolic Keyword Palette. You will see the word laplace, followed by a comma, a placeholder and an arrow. 3- The placeholde placeholderr is for the variable. Type in t, and press press . . You will will see the transform. 4- You can now change the original expression, and see a new transform.

Inverse Transform 1- Set up a variable, such as V(s), and assign it to an expression that is a function of s. Remember that the order of the denominator must be greater than the order of the numerator. 2- Type the variable variable below, and click on the invlaplace button located in the Symbolic Keyword Palette. You will see the word invlaplace, followed by a comma, a placeholder and an arrow. 3- The placeholder is for the variable. Type in s, and press . You will see the inverse transform. 4- You can now change the original expression, and see a new transform.

Page 78

EET 300


From the worksheet Laplace Transform.mcd

Laplace Transforms v( t )

sin ( t ) 1

v ( t ) laplace , t s

2

1

Now, look at the inverse transform. If we type the same expression as above, we should get the original function sin(t)

1

V( s ) s

2

1

V( s ) invlaplace , s

sin ( t )

ASSIGNMENT 4 1.

Solve equation 5-48 theoretically, and show the solution with MathCAD. Are they different, and if so why?

2.

Practice with other examples in the textbook.

Page 79

EET 300


ROOTS OF AN EQUATION

When you need to solve the inverse Laplace transform, you will need to factor the roots of an equation. MathCAD enables you to type type in an equation, and solve for the roots, whether they are real or imaginary. The equation you will be solving in EET300 will generally be of the order 2

a .x

b .x

c

Solving for the roots of an Equation 1- Define the coefficients of each each order, order, for example a, b, and and c. 2- Type in the equation. 3- From the Symbolic Keyword Palette, click on the solve button. You will see the word solve, followed by a comma, a placeholder and an arrow. 5- Type in the independent variable, such as x in the example above, and press . You will see the solution. 6- You can now change the original expression, and see a new solution.

From the worksheet Quadratic Equation.mcd

 Consider the General form of a second order polynomial 2

a .x

b .x

c

To solve this equation, first define a, b and c a

1

b

2

c

3

Then to solve the equation 2

a .x

b .x

c solve

,

x

1

i

.

2

1

i

.

2

For any other second order polynomial, change a, b or c

Page 80

EET 300



Draw the circuit in Figure 6-49 in PSpice.

2-

Derive the output v(t) theoretically, using Laplace transforms. Do not use Mathcad for the transforms (do it by hand).

3-

From the output v(t) you derived theoretically, use Mathcad to plot this voltage, and paste this plot in Word.

4-

Use a VPULSE generator in place of the 10V source and switch with the following parameters: V1=0 and V2=10 TR and TF = .01us PW=10 and PER=20

5-

Run the simulation with the Setup dialog box as Transient, Print Step= 20ms, and Final Time=7000ms. Copy this plot to word

6-

Observe what happens and compare it to the theoretical analysis from step 3.

PROBLEM 7 1-

Analyze, both theoretically and with PSpice, problem 6-25.

2-

Try to do problem 6-26. See if you can determine how to do it with PSpice (you (you should be able to do it theoretically, and use Mathcad to plot the final output voltage).

Page 81

EET 300


LESSON 5 – LAPLACE TRANSFORM IN PSPICE

You will Learn:



How to use the Laplace component in a circuit

Page 82

EET 300


USING THE LAPLACE COMPONENT You can analyze the effect of a system with a specific Laplace transform by utilizing the Laplace component. This component allows you to specify both a numerator and denominator. To analyze the effect of the transform, you need to have an input (either a pulse or sine wave), the setup (either an AC sweep or transient), a resistive load on the output, and a ground. The resistive load will not be part of the circuit in analyzing the response. Therefore, the response you will observe will be strictly due to the Laplace component, and not as a result of voltage division between the resistor and the Laplace component.

Using the Laplace Component 1- Set up a circuit with a VPULSE source, a LAPLACE component in series, a resistor in series with the LAPLACE component, and a ground (AGND). 2- Double click on the VPULSE component and set up the parameters (see Lesson 2). Note: Note: You want to set up the pulse width parameters based on the time constants of the 1 transform. For example, example, if the the transform is , then you want to specify the PW (pulse s +1 width) of the VPULSE component as 1s (1 second), if you want to see the entire response. 3- Double click on the LAPLACE component and specify the numerator and denominator. If 2 3 you want higher order, type in s*s to represent s , and s*s*s to represent s . 4- Place a voltage marker on the input, and another one on the output. 5- Type in the appropriate appropriate values values for the Print Print Step and Final Time in the Transient setup. setup. Make sure that the Final Time is no more than 1000-2000 times the Print Step (otherwise the simulation will take a long time). 6- Run the Simulation. You should see the output in the Probe window that represents the Laplace transform.

 Do not include the resistor in the analysis of the circuit (i.e. use the resistor as a voltage divider). Only consider the Laplace transform block.

Page 83

EET 300


PROBLEMS 8-9 PROBLEM 8 1- Setup up the circuit as shown below, with the LAPLACE component set to the default of 1 , and the resistor set to 1, and the VPULSE component set to 1us for the rise and fall s +1 time, 1s for the PW, and 10s for the PER. Make sure that you use the AGND component. Also, set V1 to 0, V2 to 5.

2- Place two voltage markers (one on the input, and one on the output). 3- In the Transient setup, set the PRINT STEP to 10ms, and the FINAL TIME to 5s. 4- Run the simulation. The graph should appear as shown below. Verify theoretically that this is the correct answer, by plotting your theoretical answer with Mathcad, and comparing to PSpice.

Page 84

EET 300


PROBLEM 9 1. Set the LAPLACE component to

1

, and run the simulation. Observe the graph, graph, and s+2 describe the differences between Exercise 1.

2. Develop the theoretical solution to transform

 5  , and compare to the graph in step 1.   s + 2  s  1

3. Put another LAPLACE component in series, and set it to the same value as in step 1 of Exercise 2. Run the simulation, observe the graph, graph, develop the theoretical solution to the transform, and compare. Make sure you have voltage markers at the input and at each output of the LAPLACE component. 4. Change the second LAPLACE component to

1 s +1

, run the simulation, observe the graph,

and develop the theoretical solution. 5. Change the denominator in the first LAPLACE component to s, run the simulation, observe the graph, and develop the solution. Comment on why you are seeing the specific graph. 6. Repeat items 2-4 with a VSIN component. Set the frequency to 1 Hz (see page 92 for additional information on the VSIN component). You should do the theoretical work as well as the PSpice examples, and plot the theoretical results with Mathcad. You must do the theoretical results by hand (not use Mathcad to perform the transforms).

Page 85

EET 300


LESSON 6 – SINUSOIDAL STEADY STATE IN PSPICE You will Learn:



How to measure differences with cursors



How to delete a trace



How to mark specific values on the graph



How to generate multiple plots on a graph



How to use the VSIN source



How to simulate a Bode plot

Page 86

EET 300


MEASURING DIFFERENCES WITH CURSORS There are actually two cursors that you can activate; one with the left mouse button and one with the right mouse button. By moving moving these cursors around, you can measure both time and amplitude differences.

Setting Up Multiple Cursors in Probe 1- With the Probe window Probe window open, click on the Toggle Cursor button in the toolbar.

.

2- If you have two waveforms, you can associate a cursor with each waveform. Point to the legend symbol , located in the lower left portion of the graph, and click on one of the legend symbols with the left mouse button. You will see a closely spaced dotted line around that legend. This is cursor A1, as seen in the Probe Cursor display box. 3- Point to the other legend symbol, and click with the right mouse button. You will see a loosely spaced dotted line around that symbol. This is cursor A2, as seen in the Probe Cursor display box.

 You can have two cursors even if there is only one waveform (i.e. output voltage).

If you you click on the left mouse, you will bring up cursor A1. If you click on the right mouse, you you will bring up cursor A2.

 If you click and hold on the title bar of the Probe Cursor display box, you can reposition it.

Page 87

EET 300


Moving Cursors 1- Position the mouse pointer to the place on the waveform where you want the cursor. Click on either the left or right mouse button (depending on whether you want A1 or A2 cursor).. 2- To move the cursor position, click and hold on either button, and drag the mouse to the desired direction. 3- For finer cursor movement, movement, press the the right or left arrow key for the A1 cursor, cursor, and right or left arrow key for the A2 cursor.

 The difference calculation is A2 (the right mouse button cursor) minus A1 (the left mouse button cursor). You might want to position the appropriate cursors to get a positive difference.

Deleting A Trace 1- Click on the legend name (not the symbol) of the trace you want to remove. It will change to a red color. 2- Press . . The trace is removed. removed.

EXERCISE 1-

Open up the RC.sch file you created in the exercise on page 57. If you do not have this file, recreate it.

2-

Perform a simulation, and add traces for Vin and Vout.

3-

Assign A1 cursor to Vin, and A2 cursor to Vout.

4-

Move either cursor and observe the changes in the Probe Cursor display box.

5-

Delete the Vin trace, and change the X-axis to 2 ms.

6-

Measure the time difference between t=0 and the point where the voltage is 63% of maximum. You will need both cursors. Compare that value to the rise time.

7-

Move the Probe Cursor display box to the middle right portion of the graph. Keep this file open

Page 88

EET 300


MARKING SPECIFIC VALUES ON THE GRAPH If there are specific points on a graph you wish to mark, you you can do so using the cursor. You can also reposition these marked points.

Marking Coordinate Values 1- Activate the cursor by clicking on the Toggle Cursor button in the toolbar.

.

2- Move the cursor to a specific point. 3- Choose Tools, Cursor, Freeze from the menu bar. 4- Click on the Mark Label button in the toolbar. The x and y coordinates will be displayed near that point, along with a line pointing to the specific point.

Moving the Marked Coordinate Values 1- Choose Tools, Cursor, Freeze. Freeze . 2- Click and hold on the marked coordinate values that you want to move, and drag them to the new location. 3- Double-click Double-clic k in the value box field, and type over the appropriate number.

Removing the Marked Coordinate Values 1- Choose Tools, Cursor, Freeze. Freeze . 2- Click on the marked coordinate values you want to remove, and press .

Page 89

EET 300


EXERCISE 1-

From the previous example, move the right cursor (A2) to the Y-axis.

2-

Position the A1 cursor somewhere on the graph, and mark the coordinate values.

3-

Do that two additional times.

4- Keep this plot opened.

Page 90

EET 300


GENERATING MULTIPLE PLOTS If you start to add too many plots to a single graph, it can become confusing. One way to overcome this would be to generate multiple plots within a single Probe window. These plots can either share the same X-axis or have individual X-axes (allows you to zoom in on one plot at a time). You can have up to four individual plots in a Probe window.

Generating Multiple Plots in A Probe Window 1- Choose Plot, Add Plot. Plot. 2- Choose Trace, Add and select the trace you want to add to this plot. 3- Click anywhere anywhere in the the desired plot to select select it. You will see SEL>> SEL>> is to the left of the selected plot.. 4- To delete a plot, select it and choose choose Plot, Delete Plot. Plot . 5- To create a separate X-axis for a new plot, select that plot and choose Plot, Unsync Plot. Plot. The new plot will now have a separate X-axis, and there will be a cursor separating the plots. You can scroll horizontally on the new plot.

EXERCISE 1-

In the open Probe window, add an additional plot.

2-

Select Vin as the trace to add to this new plot.

3-

Select the original plot (Vout).

Page 91

EET 300


USING THE VSIN SOURCE You can analyze the frequency response of a circuit to a sinusoid by utilizing the VSIN part. By placing the markers at appropriate points in the circuit, and running a transient response, you can observe the amplitude and phase changes for a particular frequency.

Analyzing Analyzing the Response of A Circuit to A Specific Sinusoidal Frequency Frequ ency 1- Set up a circuit with a VSIN source. 2- Double click on the VSIN source. The PartName dialog box opens. 3- Enter the following values for these values in the dialog box: VOFF – 0 VAMPL – Peak amplitude for the sine wave (5V is a good value to use) FREQ – Choose the value you which to observe (don’t need to include the units) 4- Place Voltage/Level markers at the appropriate places in the circuit. Place at least one at the input and one at the output. You may want to use the bubble part so that you can mark these parts Vin and Vout. 5- Choose Analysis…Setup. Analysis…Setup . The Analysis Setup dialog box opens. 6- Click on the Transient button, and fill in the appropriate values for the Print Step and Final Time in the dialog box. For amplitude and phase analysis, you want to observe at least 2-3 complete waveforms. 1 Therefore, select a value for Final Time that is 2-4 times the period of the input ( ). frequency 7- Choose Analysis…Simulate, Analysis…Simulate , or click on the Simulate button in the toolbar and observe the graph in the Probe window. Probe window. You should be able to use the cursor to measure the amplitude change and phase change of the output. If you use the BUBBLE part, you will need to add those traces to the graph. 8- To select a different frequency, go back to the Schematic window Schematic window and double click on the VSIN source. Change the value of the frequency and run the simulation again.

Page 92

EET 300


SIMULATING A BODE PLOT You can perform a Bode plot (amplitude and phase) vs. frequency in PSpice. You will need to create two plots.

Viewing Amplitude Amplitude Vs. Swept Frequency 1- Set up a circuit with a VSIN part. 2- Double click on the VSIN part. The PartName dialog box opens. 3- Enter the following values for these values in the dialog box: VOFF – 0 VAC – same value as VAMPL VAMPL – Peak amplitude for the sine wave (5V is a good value to use) FREQ – Choose the value you which to observe (don’t need to include the units) 4- Choose Analysis…Setup. Analysis…Setup . If Transient is selected, you might want to deselect it by clicking in the check box, and then select AC Sweep. Sweep. Specify the Start Freq., End Freq., Freq., and Total Pts. (you many initially want want to leave this value alone). You may have to experiment with these values, if you have not tried to calculate the Bode plot theoretically from the circuit. 5- Choose Analysis…Simulate. Analysis…Simulate . If you didn’t deselect Transient (as in step 4), you will get a small dialog box, entitled Analysis Type. Click on the AC button. If you deselected Transient, this box will not appear. You will get a plot with frequency as the X-axis. If you choose Plot, X Axis Settings, you will see that the scale is log. 6- In the Probe window Probe window choose Trace, Add. Add. The Add Traces dialog box opens. 7- Select DB() DB() in the Function Function or Macro field. field. The cursor will will be in the middle of the parenthesis. 8- Select Vout from the Variables Variables field, and then move move the cursor one position position to the left (using the arrow keys on the keyboard or the mouse). You want to have the cursor inside the right most parentheses. parentheses. 9- Select the “ / ” operator operator from the Function Function or Macro Macro field, and then then select Vin from the Variable field. 10- Click on OK. OK. You will see a plot of dB vs. frequency.

Page 93

EET 300


AC Sweep and Noise Analysis Dialog Box

Viewing Phase Vs. Swept Frequency 1- Choose Plot, Add Plot. Plot. A second plot in the Probe window Probe window is selected. 2- In the Probe window Probe window choose Trace, Add. Add. The Add Traces dialog box opens. 3- Select P() in the Function Function or Macro Macro field. The cursor will will be in the middle of the parenthesis. parenthesis. 4- Select Vout from the Variables field. 5- Type in a – sign, and then then select P() P() again. 6- Select Vin from the Variables field. 7- Click on OK. OK. You will see a plot of angle (d) vs. frequency.

Page 94

EET 300



Setup an RC circuit, as shown below. Set the frequency to 10Hz, the VAMPL to 5 V, the Final time to 40 ms, and run the simulation (make sure to save this file first). Measure the ratio of the peak output waveform to the peak input waveform, and record it. Measure the phase difference between the input and output.

o

Note that to measure phase differences, 360 represents the time interval between two consecutive peaks for the input waveform (period of the input). Therefore, to measure the phase differences between output and input, measure the time differences between the two peaks, and o divide 360 by that number, and then multiply multiply that result by the period. That will be the phase shift at that frequency. It might also be easier to change the value of the X-axis setting to 20 ms.

2-

Change the frequency to 100Hz, and repeat step 1. Do the same thing for 250Hz, 500Hz, 1000Hz, and 5000Hz.

Page 95

EET 300


3-

Take the values of the amplitude ratio (output/input), convert those values to decibels, and plot the result vs. frequency on semi-log paper.

4-

Plot the phase measurements vs. frequency on semi-log paper.

5-

Try repeating the same thing with the circuit as shown below (save this file with a different name)

6- Go back to the original file in item 1, and leave that open.

PROBLEM 2 1-

Develop a theoretical Bode plot (amplitude and phase) for the RC circuit that is open from the previous exercise. Use breakpoint analysis. What type of filter is this?

Page 96

EET 300


2-

Determine the break frequency from this plot. How would you do it, and how does it compare to the calculated break frequency?

3-

Replace the VSIN in the schematic with a VPULSE (set PW equal to 1 ms, PER to 5 ms). What happens to the output waveform, and how does it compare to the frequency response of this circuit? Determine the output theoretically using Laplace transforms

4-

Reverse the capacitor and resistor, and develop a new Bode plot for this circuit. What type of filter is this? Repeat items 3 & 4 for this new circuit. In all cases, do a theoretical Bode plot as well.

Page 97

EET 300


LESSON 7 – FOURIER ANALYSIS You will Learn:



How to understand Fourier analysis using Mathcad



How to do a Fourier analysis with PSpice

Page 98

EET 300


FOURIER ANALYSIS - MATHCAD One of the basic concepts in Fourier analysis is an understanding of how combining harmonics of a sinusoidal waveform can produce other periodic waveforms. A Mathcad worksheet, Recursive Fourier Analysis.mcd, was created to demonstrate this principal (see next page). Note the use of functions such as odd and even. Look them up in Mathcad help, to understand why they were used.

Page 99

EET 300


Demonstration of Fourier series First, create variables for odd harmonics, harmonics, even harmonics, and all harmonics. Odd harmonic variable would be 1 for an odd number, and 0 for an even number. The even harmonic variable would be 1 for an even number, and 0 for an odd number. The all variable would be 1 for odd or even.

odd ( i)

mod( i , 2 )

even( i)

mod( i

1 , 2)

all( i)

1

For a specific time function, determine whether there are only odd, even, or all harmonics

odde oddeve ven n( i)

odd ( i)

Select how many harmonics you want to view

n

5

Create a function that that is based on the Fourier Fourier series from calculations or from Table 9-2

g( i , t)

2 . sin( i. π .t ) i. π

Determine the resulting time time function, placing the appropriate odd/even function function in the summation sign

n g( i , t) . od odd ( i)

f( t ) i= 0

Determine the time axis (based on the fundamental frequency)

t

0 , .01 .. 4

1

0.5 f( t )

0

0.5

1 0

1

2 t

Page 100

3

4

EET 300


FOURIER ANALYSIS - PSPICE You can perform Fourier analysis on any waveform, whether you have generated it using a simple source or the waveform is the output from a circuit.

Fourier Analysis of A Simple Waveform 1- Set up the circuit circuit with a source, source, a resistive resistive load, a ground ground and a voltage voltage marker. 2- Set up the transient analysis. If you set up the combination of pulse width, period and Final Time in the analysis so that you only see one waveform, you will see a Fourier Transform. If you change the parameters (most likely lik ely the Final Time) so that there are repetitive waveforms in the plot, you will be approaching a Fourier series. 3- Simulate the circuit, and ge generate nerate a plot.

4- Choose Trace, Fourier or click on the Fourier button in the toolbar. 5- To view the lower harmonics, change the X-axis settings.

 You can also look at the Fourier analysis of any circuit using the same procedure.

If you set up the voltage markers to show the input and outputs, you can then observe how the circuit is affecting the frequency content of the input signal.

EXERCISE 1-

Set up a circuit with a VPULSE part, a resistor (use the default value) and an AGND part.

2-

Set the VPULSE part to the following parameters: V1=0, V2=5, PW=1, PER=5.

3-

Run a transient analysis with a Final Time of 5 s.

4-

Change the plot to a Fourier analysis, and change the X-axis setting to user defined, 0 to 40Hz.

Page 101

EET 300


5-

Change the X axis settings to a maximum of 10 Hz, and observe the difference in the graph.

6-

Derive theoretically and compare.

7-

Change the PER to 2, and change the Final Time in the transient analysis to 20.

8-

Generate the waveform, and then generate the Fourier Fourier plot. Because you see many waveforms on the plot, the Fourier plot will appear more like a line plot, or more like the Fourier series.

9-

Add a 100 uF capacitor in series with the resistor, and place a voltage probe at the input and output. Change the PER back to 5, change the Final Time back to 5, and run the transient analysis. Change the plot to a Fourier analysis, and compare the input and output spectra.

Page 102

EET 300



Generate a square wave, PW=1s and PER=10s.

2-

Set the Final Time to 2s, and generate a Fourier plot. How much less is the 5 harmonic from the fundamental.

3-

Decrease both PW and Final Time by 1/10, and generate a new Fourier plot. Compare the two (you might want to look at only the first 10 harmonics).

4-

Repeat item 3 once more.

5-

Repeat items 1-4 with a triangular waveform and a sawtooth pulse (see pg. 414). Compare the three waveforms, both theoretical and from the PSpice experiment.

6-

Change the PER to 2s, and the Final Time to 10s for the square wave. Generate a Fourier plot. How is it different from the one in item 2?

7-

Change the Final Time to 40s for the square wave, and repeat item 6. What is happening?

th

PROBLEM 13 1-

Generate plots for both the input and output for the circuits in Examples 6-49 and 6-50 (page 257). Make sure that you set the Final Time so that you have only one waveform appear on the plot.

2-

Generate a Fourier plot, with the input and output superimposed. Compare the input and output plots for both circuits. What does the Fourier transform show, and is it correct?

Page 103

EET 300


APPENDIX - PROBLEMS IN THE TEXTBOOK

The textbook, in the back of each chapter, has examples in either PSpice or Matlab. However, the examples in Matlab can be accomplished in MathCAD. Three examples are shown in the next several pages. Try to set them up on your your own, and then modify them.

blem - Matlab example 4-1, p. 153, using Mathcad t

)

10

75 8 .e

z 0 , 1 .. 400

2 8 ..63 z = 7.04

Capacitor Voltage of Example 4-7

50

100

150

200

250

t time seconds seconds

Page 104

300

350

400

EET 300


Problem - Matlab example 5-1, p. 201, using Mathcad (s

F( s ) s

f( t )

t

2

4) 3 s

2

F ( s ) invlaplace

0 .01 ,

..

,

s

2 ex exp ( 2 t ) .

.

3 ex exp ( .

t)

5

1.5

1 f( t ) 0.5

0 0

1

2

Page 105

3

4

5

EET 300


Plotting Impulse response of a transfer function Problem 7-1, p. 305, using MathCad First define the transfer function, G(s) 1

G( s ) s

2

. 1.4142s

1

Then, create a variable f(t), which is defined by using the invlaplace keyword When you click on that keyword, you will have two placeholders. placeholders. In the one to the left of invlaplace, type in G(s). In the placeholder to the right of G(s), type the variable s. Then press return - you will get the time function

f( t )

G( s ) invlaplace , s

.exp( .7071.t ) .sin( .7071135 .t2) 1.4142000002601225741 .70711356230 62308063 80637816 78162

Define the appropriate time period - note: you might have to experiement. However, if you see an exponent, such as the number .7071, take the inverse of that number, and multiple by 5. That is 5 time constants. Set the initial value of t to 0, the increment to at least 0.01 of the final value, and set the final value to about 10 time constants (if you know them). t

0 , .0 .01.. 10

Then type below this f(t)@, and then press return. You will get the graph. graph. If you change anything above, such as the G(s) term or the time period, the graph will change. Impulse Response of Filter for ex. 7-3

0.6

0.4 e s n o p s e r

f( t ) 0.2

0

0.2 0

2

4

6 t time (s)

Page 106

8

10

EET 300


INDEX Laplace Transforms - Mathcad, 79 Adding cursor to plot, 63 Adding labels to curve, 63 Adding parts to schematics, 27 Analysis Setup Dialog Box, 55 Automatic mode, 11

Marking coordinate values, 90 Math palette, 15 Message Viewer, 47 Moving parts in PSpice, 32 Multiple cursors, 88 Multiple plots in PSpice, 92

Bode Plot, 94 Bubbles, 60

Overview, 25 Calculations in Mathcad, 9 Changing axis, 62 Changing colors in Probe, 57 Changing parts attributes, 35 Complex numbers, 11 Connecting parts, 34 Copying graphs, 65 Copying Mathcad to Word, 16 Copying schematics into Word, 44 Copying/pasting Copying/pasting parts, 39 Custom axis, 73

Part Browser Dialog Box, 28 Parts browser dialog box, 30 Printing graphs, 65 Pulse voltage source, 52 Redraw, 42 Roots of an equation, 81 Rotating parts, 33 Saving a schematic file, 38 Schematics window, 26 Setting up functions in Mathcad, 17 Sweeping a component value, 66

DC Analysis, 46 Defining a variable, 10 Deleting parts, 33

Text in Mathcad, 8 Transient analysis, 54

Fourier analysis - Mathcad, 100 Fourier analysis - PSpice, 102 Functions, 74

Undo/Redo, 41 Unit conversion, 14 Unit step, 53 Using math parts in PSpice, 71

Graphing in Mathcad, 21 Greek symbols, 20

Viewpoint, 46 VPWL, 69 VSin source, 93

Inserting a function, 13 Integration and Differentiation, 18 Introduction, 5 Ipulse, 46

Zoom, 43 Laplace Component - PSpice, 84

Page 107

300 Lab Manual (Pspice and Mathcad)

Recommend Documents