PC-assisted instruction of introductory electromagnetics

IEEE TRANSACTIONS ON EDUCATION, VOL. 33, NO. I , FEBRUARY 1990 51

PC-Assisted Instruction of Introductory Elec tromag neic s

N. NARAYANA RAO, FELLOW, IEEE

Absfruct-A comprehensive, user-interactive software package for the IBM PC or compatible, resulting from an ongoing effort by the author to enhance the teaching and learning processes in the instruction of introductory electromagnetics courses is described.' The associated topics are distributed throughout the realm of introductory electromagnetics, ranging from coordinate systems to antenna fundamentals. The PC-assisted instruction involves the use of the software in the classroom integrated with the lecture-discussion of the subject matter, as well as outside the classroom by the student at hislher own pace and leisure. Following brief descriptions of the 15 programs of the software package, four examples are presented in detail to illustrate the teaching and learning nature of the software. Student responses to the PC-assisted instruction are included.

I. INTRODUCTION LECTROMAGNETICS has long been considered to E be a very difficult subject by the students, primarily

for the following reasons: a) electromagnetic concepts are perceived to be abstract, and b) the understanding of electromagnetic phenomena involves visualization in space and time. Consequently, the degree of undergraduate student motivation to learn the subject matter is one of the lowest of the areas of electrical engineering, in spite of the fundamental importance of field theory. Fortunately, the advent of the personal computer as a pedagogical tool has provided a unique opportunity to develop materials toward the goal of rectifying this situation. In this paper, we describe a comprehensive, user-interactive software package developed by the author in this context for PC- assisted instruction of topics distributed throughout the realm of introductory electromagnetics, ranging from coordinate systems to antenna fundamentals, and extending the author's earlier contribution [ 11. The software is writ- ten for the IBM PC or compatible with a minimum of 256 kbytes of memory, a color graphics card, a color graphics monitor, and preferably a math coprocessor chip. The programs are coded in Basic and then compiled and saved as executable files, along with a run-time module.

At the University of Illinois, a sequence of two courses in electromagnetics is required for the undergraduate elec-

Manuscript received November 30, 1988; revised April 18, 198Y. The author is with the Department of Electrical and Computer Engi-

IEEE Log Number 89299 18. ' The software package described in this paper is available by writing to

the author at the address given below, enclosing two blank 5 I /4 in double- sided, double density diskettes, or one blank 3 1 /2 in double-sided, double density diskette: Prof. N. Narayana Rao, Dep. Elec. Comput. Eng., Uni- versity of Illinois at Urbana-Champaign, 1406 West Green Street, Urbana, IL 61801.

neering, University of Illinois, Urbana, IL 61801.

rrical engineering majors. Each course is of one semester duration and carries a credit of three hours. The first of these two courses is also required for the computer engineering majors. Accordingly, the material in these two courses is packaged such that the first course is not merely a prerequisite for the second course, but also serves as a useful terminal course for computer engineering students. In addition, concurrently with each of these two courses, a one credit-hour elective course devoted to the solution of electromagnetics problems using the personal computer is offered. The software package is designed for the two-semester sequence as well as for the concurrent one credit-hour elective courses, for use in the classroom integrated with the lecture-discussions of the subject matter, as well as outside the classroom by the student at his/ her own pace and leisure.

11. NATURE AND SCOPE OF TOPICS The software package consists of 15 programs, includ-

ing a preview program. The preview program serves the purpose of introducing at the outset the types of problems illustrative of the topics and subtopics associated with the remaining 14 programs. Each of these 14 programs gen- erally consists of brief introduction(s) to topic(s) under study and then presents for each topic a number of examples associated with the topic and provides opportunity to the user to run examples by inputting hidher own data, thereby enabling student involvement in the teaching and learning process.

The topical headings and brief descriptions of the 15 programs are given in the following:

I) Preview: Introduces briefly four topics as exten- sions of knowledge the student may have gained from prerequisite courses. These topics are a) capacitance of a parallel-plate capacitor, b) transmission line versus lumped circuit, c) total internal reflection of light, and d) an it- erative procedure associated with the numerical solution of B two-dimensional partial differential equation.

2) Conversion of Vector from Cartesian Coordinates to Spherical Coordinates: Considers first a multitude of special cases, with the aid of diagrams, in order to pro- vide drill on the directions of the components (directions of unit vectors) in the spherical coordinate system and then examples involving all three components in the spherical coordinate system.

3) Polarization of Sinusoidally Time- Varying Fields: Introduces the linearly polarized sinusoidally

0018-9359/90/0200-0051$01 .OO O 1990 IEEE

I

52 IEEE TRANSACTIONS ON EDUCATION, VOL. 33. NO. I . FEBRUARY 1990

time-varying vector and then demonstrates the different cases of polarization, that is, a) linear, b) circular (both right- and left-circular), and c) elliptical (both right- and left-elliptical), as resulting from the superposition of two linearly polarized vectors, differing in directions by 90°, and depending upon their amplitudes and the difference between their phase angles.

4) Direction Lines of Electric Field due to Point Charges: Illustrates the procedure for plotting a direction line of electric field and then considers examples of constructing field maps for pairs of point charges, involving both the like-charge case and the unlike-charge case, and zero-field point situations.

5) Motion of Electron in Crossed Electric and Mag- netic Fields: Presents a number of cases in which the traces of electron motion in a region of crossed electric and magnetic fields are plotted and their parametric de- pendence is illustrated.

6) Plotting of Equipotentials due to Point Charges: Constructs maps of equipotential lines for several cases of pairs of point charges, involving both the like-charge case and the unlike-charge case, and including situations of equipotential lines surrounding only one or the other of the two charges, as well as those involving the surrounding of both charges.

7) Solution of Laplace’s Equation and Plotting of Equipotentials: Demonstrates the numerical solution of Laplace’s equation in two dimensions to determine the distribution of the electrostatic potential in a charge-free region, from a knowledge of the potentials along the boundaries of the region, and then extends to the plotting of equipotentials in that region for several cases in which three sides of the charge-free region are kept at zero potential and the potential variation along the fourth side is specified.

8) Charge Distribution and Capacitance by Method of Moments: Illustrates application of the method of moments in the analysis of field problems by considering several examples in which the approximate charge distributions on conductors held at known potentials are determined: a) thin, straight wire, b) thin, bent wire, c) thin, square-shaped conductor, and d) two parallel, square- shaped conductors (including computation of capacitance of the arrangement).

9) Illustration of the Traveling Wave Con- cept: Demonstrates the concept of a traveling wave by considering propagation in one dimension along the positive z and negative z directions, involving the unit step function.

10) Time-Domain Analysis for a Transmission-Line System: Considers wave propagation on a terminated lossless line, excited by a direct voltage source, and de- picts the transient bouncing of the voltage and current waves along the line for several cases, one of which is the case of a short-circuited line.

11) Sinusoidal Steady-State Analysis of Transmission- Line Systems: Considers three associated topics. These are a) computation of resonant frequencies of a system involving two short-circuited lines, including a graphical

construction pertinent to the solution of the characteristic equation for resonance, b) plotting of standing wave patterns along a line and computation of associated parameters, and c) computation of time-average power flow along a line.

12) Transmission-Line Matching and Frequency Re- sponse: Considers first the solution of the matching problem for three cases, viz., a) quarter-wave transformer, b) single stub, and c) double stub, and then extends to the investigation of the frequency response of a transmission line system, applying it to all three cases and in addition to the case of an alternated transformer.

13) Construction and Applications of the Smith Chart: Reviews construction of the Smith chart, defines a number of procedures pertinent to the application of the chart for the sinusoidal steady-state solution of problems involving transmission lines and those involving transmission line analogies, and carries out solutions for several examples using these procedures.

14) Guided Modes in a Dielectric Slab Wave- guide: Computes the allowed values of angles of inci- dence for guided modes in a symmetric dielectric slab waveguide, including graphical constructions pertinent to the solutions of the associated transcendental equations.

15) Topics in Antennas and Antenna Arrays: a) Hert- zian dipole fields and associated parameters, including computation of the complete electromagnetic field, depic- tion of the radiation patterns, and discussion of radiation resistance and directivity; b) linear antenna characteristics, involving the plotting of radiation patterns and computation of radiation resistance and directivity for a number of cases; and c) group patterns for uniform linear arrays, involving the plotting of single patterns using the polar representation, as well as a series of patterns using the rectangular representation.

111. ILLUSTRATIVE EXAMPLES

We shall now present four examples to illustrate the teaching and learning nature of the software. Theoretical details pertinent to the solution techniques associated with the problems are not included because they can be found extensively in textbooks and journal articles (for example, [ I l l .

A. Direction Lines of Electric Field due to Point Charges

First the basic procedure of plotting a direction line is illustrated by considering two point charges Q l = 2Q and Q2 = -Q located at ( - 1 , 0 ) and ( 1, 0), respectively, in the xz-plane where Q is positive, and plotting the direction line through the point P ( 0 , 1 ) by tracing the path followed by a test charge released at point P. To do this, the electric field at point P is computed and the test charge is moved by a small distance 0.1 along the direction of the field, by striking a key, to reach a new point. The procedure is continued by computing the field at the new point and moving the test charge by 0.1 along the direc-

RAO: INTRODUCTORY ELECTROMAGNETIC3 53

tion of the field by striking a key, and so on, until the direction line is completed due to termination on the charge Q2. The current location of the test charge and the direction of the field are displayed for each step.

For considering examples, the basic procedure is modified slightly as follows. Instead of moving the test charge by 0.1 from its current location, say point A , to a new location, say point B, along the direction of the electric field at point A, it is moved by 0.1 to a point C along a direction which bisects the directions of the fields at points A and B. The modified procedure is applied to plot sets of direction lines for electric field of pairs of point charges located at points ( - 1,O) and ( 1, 0), thereby constructing field maps. The plotting of a direction line begins at one of the point charges and terminates when the line reaches to within a distance of 0.1 from the second point charge, or if it goes beyond a specified rectangular region. In this manner, direction lines beginning at points around each point charge and at 30" intervals on a circle of radius 0.1 are plotted. Three examples are considered as follows.

Example I: Q l = 2Q at ( -1 ,O) and Q2 = - Q a t (1 , 0). The rectangular region is one having corners at ( -3, 2) , (3, 2 ) , (3, -2) , and ( -3, -2). The completed field map is shown in Fig. l(a). For this example, the field lines originating at each point charge either terminate on the second charge or go out of the boundary of the rectangular region.

Example 2: Q l = 4Q at ( -1 , 0) and Q2 = Q at ( 1 , 0). Region of map is rectangle having comers at ( -3, 4 ) , (3 , 4 ) , (3, 0), and ( -3 , 0), as shown in Fig. l(b). This takes advantage of the symmetry of the field map about the axis through the charges, illustrated in Fig. l(a). For this example, a zero field point exists within the region at ( 1/3, o), between the two charges. For direction lines passing through this point, the test charge gets trapped at that point and the user is instructed to strike a key to untrap it by displacing it by 0.01 right angle to the axis and continue plotting of the line, which will then terminate at a point on the boundary of the region.

Example 3: Q l = 9Q at ( -1 ,O) and Q2 = - Q a t (1, 0). Region of map same as for example 2. The completed field map is shown in Fig. l(c). For this example, a zero field point exists within the region at (2 , 0), to the right of Q2. For direction line to the right of Q2, the test charge gets trapped at that point and the user is instructed to strike a key to untrap it as in example 2 and continue plotting of the line, which will then terminate on Q l . By striking a key, the field line to the right of the zero field point (along the axis through the charges) is completed. Also for this example, the user is given the opportunity for plotting additional field lines from either charge. Three such lines are shown in Fig. l(c). Two of these are from Q l at angles 40" and 45" and the third is from Q2 at 10".

User Examples: Finally, the user is given the opportunity to run examples by inputting values for the point charges. For all user examples, the locations of the charges and the extent of the rectangular region are the same as for examples 2 and 3 above. Also, since only the relative values of the two point charges and their relative

signs are pertinent to the construction of the field map, the magnitude of Q2 is assumed to be Q and Q l is assumed to be positive, so that it is only necessary to spec- ify a) whether the charges are like or unlike, and b) the ratio of Q l to Q (restricted to be from 1 to 100, limited by the step size of 0.1). For each example, after the field map is completed, the user is given the opportunity for plotting additional field lines, as in example 3. The completed field map for the case of like charges and Q l / Q equal to 81 is shown in Fig. l(d). The map also includes two additional field lines originating from Ql at 5" and 15" angles. The important concept that at distances far from the charges the field lines appear to originate from a single charge is clearly evident in this example.

B. Charge Distribution and Capacitance by Method of Moments

In this program, the application of the method of moments in the analysis of field problems is illustrated sys- tematically by considering several examples in which the approximate charge distributions on conductors held at known potentials are determined, and then extended to the computation of the capacitance of a parallel-plate capacitor.

Example I-Thin, Straight Wire: In this example, a thin straight wire of length L and radius U (<< L), and held at a potential of 1 V is considered. The wire is divided into a number of segments of equal lengths and the charge density in each segment is assumed to be uniform. If n is the number of segments, then from considerations of symmetry there are only INT ( ( n + 1 ) /2 ) charge densities to be determined, where INT stands for "integer part of." Choosing n = 5 so that there are only three unknown charge densities to be determined, the setting up of the 3 X 3 matrix equation and its solution by inversion are illustrated for the case of L = 1 m and a = 1 mm. To obtain a more accurate solution, a value of 40 is assumed for n and the solution is repeated to obtain the 20 unknown charge densities. In each case, a plot of the charge distribution is shown in addition to listing the charge density values. The plot for n = 40 is shown in Fig. 2(a), where the height of the first rectangle is 2046 C/m2, E being the permittivity.

Example 2-Thin, Bent Wire: In this example, the thin wire of example 1 is considered to be bent in the middle. The angle subtended by the two halves at the bend is de- noted to be ALPHA. The two halves are divided into an equal number of segments of equal lengths. Therefore, n is even; however, from considerations of symmetry, there are only n / 2 unknowns, namely, the charge densities of the segments in one half of the wire. The solution is illustrated by considering L = l m, a = l mm, ALPHA = 15", and n = 6, and solving for the three unkowns. To obtain a more accurate solution, a value of 40 is assumed for n and the solution is repeated to obtain the 20 unknown charge densities. Again, as in example 1, for each case a plot of the charge distribution is shown in addition to the listing of the charge density values. Also for the n = 40 case, the plot of the charge distribution is compared

I

IEEE TRANSACTIONS ON EDUCATION, VOL. 33. NO. I . FEBRUARY 1990

(a)

(-3.4) Example 3 . (3.4) ( -3 .4 ) (3 .4 )

(-3.8) 9 1 92 (3 .8 ) ( -3 .0 ) 91 92 ( 3 . 8 )

(c) (d) Fig. 1. Electric field maps for pairs of point charges for four cases: (a) Ql

= 2Q and Q2 = -Q. (b) Q l = 4Q and Q2 = Q. (c) Q l = 9Q and Q2 = -Q, and (d) user example with Ql = S l Q and Q2 = Q. For each part of the figure, the x axis is directed to the right and the z axis is directed upwards

n

(c) Fig. 2. (a) Charge distribution along a thin, straight wire of length 1 m

and radius I mm, and held at a potential of I V. The height of the first rectangle is 204t C/m'. (b) Comparison of the distribution in (a) with that along the same wire but bent in the middle so that the angle ALPHA subtended at the bend is 15". (c) Same as in (b), except for a user example involving bent wire with ALPHA = 0.1".

with that for the case of the straight wire. This comparison is shown in Fig. 2(b) where it is understood that for the bent wire, the charge distribution represents that for the two halves of the wire, although the wire is shown to be straight.

Before proceeding further, the user is given the opportunity to obtain the charge density distribution for another value of ALPHA and compare it with that for the case of the straight wire. Recalling that L = 1 m, a = 1 mm, and n = 40, the only input parameter is ALPHA in degrees. An interesting case is ALPHA equal to a very small value, say 0.1 O , because the situation then corresponds essentially to that of a straight wire half the length of that in example 1 and hence the resulting charge density distribution should be such that each half is similar to that for the straight wire case. This is indeed the result, as shown in Fig. 2(c). Further user examples consist of obtaining the charge distribution for different sets of values for the parameters L / a , AI .PHA, and n.

Example 5-Thin, Square-Shaped Conductor: In this example, a thin, square-shaped conductor of sides w and held at a potential of 1 V is considered. The conductor is divided into a number of squares of equal area and the charge density in each square is assumed to be uniform. If each side is divided into n equal parts, then there are n X n squares. However, from considerations of symmetry, there are only m ( m + 1 ) / 2 charge densities to be determined where m is equal to INT ( ( n + 1 ) /2 ) . Choosing n = 4, so that there are only three unknown charge densities to be determined, the setting up of the 3 X 3 matrix equation and its solution by inversion are illustrated. For a more accurate solution, a value of n = 8 is considered and the solution for the ten independent charge densities is found.

RAO: INTRODUCTORY ELECTROMAGNETICS 55

square 11 : 13.4348 square 12 : 9.1077 square 13 i 8.5077 square 14 . 8.2752 square 22 : 4.8904 square 23 : 4.4469 square 24 : 4.2804 square 33 * 3.9895 square 34 i 3.8191 square 44 : 3.6472 (1 i n Coulombs i s 6.4272 times the permi t t i v l t y . C = 3.2136 times permittivity C/CFN = 3.2136

square 11 : 20009.36 square 12 : 20007.61 square 13 : 20007.4 square 14 : 29607.28 square 22 : 20005.52 square 23 . 20005.17 sqLmre 24 i 20005.04 square 33 ' 20004.79 square 34 20004.62 square 44 : 20004.39

Q i n Coulombs is 4.4704 times the permi t t iv 1 t y . Q i n Coulombs is 20006.14

t ines the permit t iv i ty . c = 18003.87 t ines permittivity C = 2.2352 times permittivity

C/CFN = 1.0003 C/CFN = 2235.209

(C) (d) Fig. 3. (a) Parallel-plate capacitor for method of moments analysis. (b)

Results of method of moments analysis for the arrangement in (a) for w = 1 m and k = 1 . (c) Same as in (b) except for a user example with k = 0.0001. (d) same as in (b) except for a user example with k = IOOO.

Example &Two Parallel, Square-Shaped Conduc- tors: This example extends example 3 by considering two parallel, square-shaped conductors, thereby leading to the arrangement of a parallel-plate capacitor. The size of each plate is assumed to be w X w and the separation between the plates is assumed to be kw, as shown in Fig. 3(a). For a potential difference applied between the plates, the higher potential plate will be positively charged whereas the lower potential plate will be negatively charged, with identical distributions of charge density. Hence, it suf- fices to find the charge density distribution on one conductor, by considering the potentials on the two plates to be equal in magnitude and opposite in sign. Here, the positively charged plate with a potential of 1 V is considered.

Choosing first n = 4 as in the case of the single conductor, the setting up of the 3 X 3 matrix equation for the three independent charge densities and its solution by inversion are illustrated for the case of w = 1 m and k = 1. Proceeding further, the total charge (Q) on the conductor, the capacitance (C = Q/2) of the parallel-plate arrangement, and its ratio to the capacitance [CFN = e w / k ] of the same arrangement computed by ignoring fringing of the field, are obtained. To obtain a more accurate solution, a value of n = 8 is considered, as shown for the upper conductor in Fig. 3(a), and the solution is repeated by computing the ten independent charge densities, the total charge Q on the conductor, the capacitance C, and the ratio C/CFN. The resulting output is shown in Fig. 3(b) where the squares are designated by their row and column numbers and the charge densities in C/m2 are the correspondingly listed numbers times E.

The user is then given the opportunity to input sets of values for the parameters and carry out the analysis. A

value of w = 1 m is assumed for all examples since it is the ratio k that governs the charge density distribution and the value of C/CFN. Thus, the input parameters are k (must be > 0) and the number of squares n (an integer from 1 through 8). Two cases of interest are as follows:

(a) k = 0.0001, n = 8. This corresponds to spacing between the plates very small compared to the dimensions of the plates. Hence fringing of the field is negligible, the charge distribution is nearly uniform, and C/CFN is al- most equal to unity, as shown by the output reproduced in Fig. 3(c).

(b) k = 1000, n = 8. This corresponds to spacing between the plates very large compared to the dimensions of the plates so that the capacitance C is essentially equal to half that of an isolated conductor identical to the plates. The output is reproduced in Fig. 3(d).

C. Time-Domain Analysis for a Transmission-Line System

This program considers wave propagation on a terminated lossless transmission line, excited by a direct voltage source. The line is assumed to be extending along the z direction, with the source end at z = 0 and the load end at z = 1, as shown in Fig. 4. The pertinent quantities are

VO = Source voltage in volts RG = Source resistance in ohms RL = Load resistance in ohms ZO = Characteristic impedance in ohms

T = One-way travel time on the line

Following a brief discussion of the voltage and current waves progressing on the line following its excitation, three examples, one of which is that of a short-circuited

I

56 IEEE TRANSACTIONS ON EDUCATION. VOL. 33. NO. I . FEBRUARY 1990

l - 7 3 vo

z.0 2.1

Fig. 4. A lossless transmission-line system for time-domain analysis

For t / T = 9 For t / T = 1.1 U = 144 U f o r 1 > z/l > .9

88 U f o r E < z/l < .9 U = 8 0 U f o r 0 < z/l < .9

Z/l

1 = .16 A f o r 1 > z / l > .9 8 A fop E < r/ l < .9

1 = .8 B for E < z/l < ,9

- z / 1

For t / T = 2.1 In the s t e a d y state, U = fB. R Z - E O f p $,:/? <. .1 U = 97.29729 U f o r E < z/l < 1 U = 185.6 U for E < z/l < .1 U = 97.29729 U f o r E < z/l < 1

144 U f o r 1 > z/l > .1

I =-.224 A f o r E < z/l < .I I .1E81881 I( f o r E < z/l < 1 .16 A f o r 1 > z/l > .1

3 1 ~ 3 1 I E 1 1 P Z / l

-3j j , , , , , , , , , , Z/l - E .2 .4 .6 . 8 1 @ .2 .4 .6 . 8 1

Fig. 5 . Four screen5 from a series of screens demonstrating the phenomenon of transient bouncing of voltage and current waves between the source and load ends following the excitation of the transmission-line system of Fig. 4, for a user example involving VO = 100 V. RG = 25 Q , RL = 900 Q. and ZO = 100 Q.

line, are considered to illustrate the phenomenon. For each example, the input parameters are VO, RG, RL, and ZO. The switch is closed at t = 0 and the resulting transient phenomenon is presented as a series of plots for line voltage and current at intervals of t/Tequal to 0.1, up to t / T equal to 6. The line voltage and current values are displayed above the plots for each value of time. The wave motion is interrupted at 0.1 ( z / l ) from each end of the line and continued with the strike of a key to permit discussion of the reflection and re-reflection of the waves at the two ends. Finally, the steady-state line voltage and current distributions are displayed.

After completion of the third example, the user is given the opportunity to input sets of values for the parameters to run examples. Four screens from the user example for VO = 100 V, RG = 25 Q , RL = 900 Q , and ZO = 100 Q are shown in Fig. 5 , in which (a) represents the incident wave situation ( t / T = 0.9) , (b) represents the superposition of the incident and reflected waves ( t / T = l . l ) , (c) represents the superposition of the incident, reflected, and re-reflected waves ( t / T = 2.1 ), and finally (d) represents the steady-state situation. The vertical scales for these plots are such that one division corresponds to 49 V for the voltage and 0.27 A for the current. The transient bouncing of the waves between the source and load ends

of the line following the excitation of the line is clearly demonstrated by the series of plots.

D. Construction and Applications of the Smith Chart Following a discussion of the construction of the Smith

chart and several pertinent features, the application of the chart is considered by means of several examples involving lossless lines. This is done by first defining 18 different procedures, available in the program. Each procedure is identified by a two-letter code. The first letter refers to the action. For example, the letter “I” refers to LO- CATE. The second letter completes the description of the procedure. For example, the letter “c” refers to COOR- DINATES. Thus the code “IC” means LOCATE CO- ORDINATES. The 18 different codes together with their expansions and a 19th code used to terminate the solution of a problem are listed in Fig. 6(a), with SWR representing standing-wave ratio and r representing real part of the normalized line impedance. During the solution of a problem, a directory of code letters with their representations is listed beside the chart for reference, as shown for example in Fig. 6(b), with 1 representing the first letter of the code and 2 representing the second letter.

Four examples are considered. For each example, first the problem is defined and then the sequence of steps to


IC ; l i :

PC . ms : dr : ax : ds : du : mu : MO : m z : tc :

3 i

ac : ru : mr i 4: i

locate coordinates locate inverse move tonard mo ve to ward OF

locus part locus

I Line 3 Line2 zll zLQ 203 20 2

draw r=l c moue to r= moue to in moue to ze transf o r m add to coo

.rcle . clrcle ‘ini ty :oordinates *di nat es S O

rotate r=l circle move along constant real part locus Pint value of SUR P erminate solution

m - moue p - print r - rotate t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SUR circle

6.Find SUR value <procedure -ps-) SUR = 4.695953 Procedure completed Strike any key to continue

(b) Fig. 6. (a) Expansions for the codes representing the various procedures

for the application of the Smith chart. (b) The final screen in the series of screens pertinent to the example of finding the SWR value in line 3 of the system of Fig. 7 , for ZL = (50 + j 5 0 ) 0, ZO1 = 100 0, 202 = 50 Q , 203 = 75 0, L1 = 0 . 3 X, and L2 = 0.2 A.

be carried out for its solution are outlined, and followed by the carrying out of the steps. The examples are 1) finding the input impedance of a line terminated by a complex load, 2) finding the length of a short-circuited stub to re- alize a specified normalized input susceptance, 3) finding the SWR in the line farthest to the load in a system of three lines in cascade, and 4) the solution of the single- stub matching problem.

Fig. 6(b) shows the screen giving the required SWR value for example 3. The transmission-line system for this example is shown in Fig. 7. The values assumed are: ZL = (50 + j 5 0 ) 52 , ZO1 = 100 Q , 202 = 50 Q , 203 = 75 Q , L1 = 0.3 A, and L2 = 0.2 A. The solution consists of the following steps, beginning with the normalized impedance of (0.5 + j . 5 ) .

1) Locate the normalized load impedance coordinates (procedure “IC”). 2) Move along the SWR circle toward the generator by

LI (procedure “mg”). 3) Transform the coordinates located in step 2 by mul-

tiplying by the ratio ZOl/ZO2, that is, 2 (procedure ‘‘tc”). 4) Move along the new SWR circle toward the gener-

ator by L2 (procedure “mg”). 5) Transform the coordinates located in step 4 by mul-

tiplying by the ratio Z02/203, that is, 2 / 3 (procedure ‘‘tc”).

Fig. 7 . PL2-t - 4

A system of three lines in cascade for finding the SWR in line 3 using the Smith chart.

6 ZO j b 2 0 j b l o Z L O

Fig. 8. Double-stub matching system for illustrating the solution of a user example by using the Smith chart.

6) Find the SWR value corresponding to the coordinates located in step 5 (procedure “ps”).

These steps are identified in Fig. 6(b) by the corresponding numbers.

User examples involve identifying first the sequence of procedures to solve the problem of interest and then carrying out the procedures. Let us, for example, consider the solution of the double-stub matching problem. The situation is illustrated in Fig. 8 where the problem is to find the normalized susceptances bl and b2, and hence the stub lengths for realizing them, in order to achieve a match between the line and the load. Assuming values of ZL = (30 + j40) Q , ZO = 50 Q , 01 = 0.05 A, and 02 = 0.375 A, the solution consists of the following sequence of steps, where x stands for imaginary part and WL stands for A. 1) Locate coordinates for normalized load impedance

(0.6 + j . 8 ) ; (procedure “IC”). 2) Locate inverse (procedure “li”). 3) Move toward generator by 01 = 0.05 (WL); (pro-

4) Draw r = 1 circle (procedure “du”). 5 ) Rotate r = 1 circle by 012 = 0.375(WL); (pro-

cedure “ru”). 6) Move along constant real part locus to reach a point

on the circle of step 5 (procedure “mr”). Record change in x.

7) Move along SWR circle toward generator by 012 = 0.375(WL) to reach point on r = 1 circle (procedure “ms”).

8) Print coordinates (procedure ‘‘pc”). Record imaginary part.

9) Locate coordinates corresponding to r = 0 and x = value recorded in step 6 (procedure “lc”). 10) Move to infinity (procedure “mo”). Distance

moved gives length of stub 1. 11) Locate coordinates corresponding to r = 0 and x

= negative of value recorded in step 8 (procedure “IC”). 12) Move to infinity (procedure “mo”). Distance

moved gives length of stub 2.

cedure ‘‘mg’ ’).

- I 1

I

58

Pt re E t “,I : d - draw 1 - locate m - move P - print

IEEE TRANSACTIONS ON EDUCATION. VOL. 33. NO. I . FEBRUARY 1990

f t Zen t ~ 5 1 : d - draw 1 - locate m - moue

E - i-otate t - transform

2.c - coordinates g - generator-- i - inverse 1 - load o - infinity r - real part s - SYR circle U - r=1 circle x - imag. part z - zero

mg

Procedure completed Strike any key to continue

f t re? t S 9 : d - draw 1 - locate m - moue P - print r - rotate t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SUR circle U - p=l circle x - imag. part z - zero

Procedure Change in

bein x z-7. carried 386

out is: mr

Procedure completed Strike any key to continue

1 - locate m - moue P - Print E - i-otate t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SYR cgrcle U - r=1 circle x - imau. part z - zero -

Procedure being carried out is: ms Distance moved = .376 * YL toward generator Procedure completed Strike any key to continue

g 1 t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SHR circle U - r=l circle x - imag. part z - zero

Procedure being carried out is: mr Strike 1 for increasing x d for decreasing X, or s to stob

(b)

P ~ ~ e E t Z ~ ~ : d - draw 1 - locate m - moue P - print r - rotate t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SYR circle U - r=l circle x - imag. part z - zero

$~~,P~$uy,;:t;i carried out is: ms

load or, s to stop generator. or 1 toward

PtfeEtgi: d - draw 1 - locate m - move P - print r - rotate t - transform

2.c - coordinates g - generator i - inverse 1 - load o - infinity r - real part s - SYR circle U - r=l circle x - imag. part z - zero

Procedure being carried out is: pc Real part = 1.013 Imaginary part = 3.024 Procedure completed Strike any key to continue

Fig. 9. A few screens in the seriea of screens pertinent to the solution of the double-stub matching problem associated with the system of Fig. 8, for ZL = (30 + j40) Q. ZO = SO Q , DI = 0.05 X, and D2 = 0.375 A.

Fig. 9 shows a few screens encountered in the process of carrying out these steps. In particular, (c) and ( f ) give the values of 6 , and -b2, respectively.

IV. CONCLUSION The comprehensive, user-interactive software package

described in this paper is a result of an ongoing effort by the author to enhance the teaching and learning processes in the instruction of the introductory electromagnetics courses at the University of Illinois at Urbana-Cham- paign. The key words here are “teaching,” the process of giving individual guidance to the learner, “learning,” the process of gaining knowledge of a subject by study, instruction, or experience, and “instruction,” the process of providing, in a systematic way, the necessary infor-

mation or knowledge about a subject. The question is: how does this software enhance these processes? First, its use in the classroom, integrated with the lecture-discussion of the subject matter, enables the instructor to illustrate in a systematic manner a number of built-in examples pertinent to the topic under study. Second, it facilitates instructor-student interaction by allowing user examples to be run on the topic during the lecture session. Third, it allows the students to “explore” individually on their own and hence enhance their learning of the subject matter, without being inhibited by the classroom atmo- sphere.

The above assertions are borne out by typical comments from student responses to the PC-assisted instruction pointing out to characteristics such as a) simplifying dif-

I --

I


ficult concepts by being able to show many examples in a short time, b) making it easier lo visualize a dynamic

board or in the book, c) enabling the students to partici-

plicated calculations without waiting SO the teacher can

Descriptions of computer programs relating to topics of more specific nature (for example, [2]-[4]) and of courses

131 S. R. H. Hoole and P. R. P. Hoole, “Finite element programs for teaching electromagnetics,” lEEE Trans. Educ . , vol. E-29, pp. 21- 26, Feb. 1986.

interactive computer graphics in a first course in applied electromagnetics.” IEEE Trans. Educ . . vol. E-30, pp. 5-8, Feb. 1987.

ilton, “A new course on computational methods in electroniagnetics.”

Process that cannot be done with a drawing on the chalk- [4] P. L. Levin, J . F. Hoburg, and z. J . Cendes, “Charge simulation and

pate in the instmction7 and dl going through a lot Of ‘Om- [ 5 ] M , F, Iskander, M , D. Morrison, W , C , Datwyler, and M, S. Ham.

take the time to explain. IEEE Trans. Educ . , vol. E-31, pp. 101-115, May 1988.

dealing specifically with numerical methods (for exarn- ple, [5]) have appeared in literature. It is the author’s be- lief that these endeavors, as well as the one reported in this paper, constitute the necessary ingredients for achiev- ing enhanced undergraduate student motivation for learning electromagnetics.

REFERENCES [ I ] N. N. Rao, Elements of Engineering Electromagnetics. 2nd ed. En-

glewood Cliffs, NJ: Prentice-Hall, 1987. [2] J . F. Hoburg and J. L. Davis, “A student-oriented finite element pro-

gram for electrostatic potential problems,” IEEE Trans. Educ., vol. E-26, pp. 138-142, Nov. 1983.

N. Narayana Rao (SM’83-F’89) was born in Kakumanu, Andhra Pradesh, India He received the Ph D degree from the University of Wdshing- ton, Seattle, in 1965

He joined the faculty of the Department of Electrical and Computer Engineering of the Uni- versity of Illinois at Urbana-Champaign in 1965, where he is currently Professor and Associate Head. His primary interests have been in the areas of ionospheric propagation and electromagnetics education He has authored three textbooks in in-

troductory electromagnetics, the latest of which is Elemenrs ofEngmeertng Electromagnetics, Second Edition.

Dr Rao is a member of ASEE, Eta Kappa Nu. and U.S. Commission G of URSI.

T

Date post:	21-Sep-2016
Category:	Documents
Upload:	nn
View:	214 times
Download:	2 times

PC-assisted instruction of introductory electromagnetics

Documents