This Instructors’ Manual provides solutions to most of the problems in Antennas: for All Applications, THIRD EDITION. All problems are solved for which answers appear in Appendix F of the text, and in addition, solutions are given for a large fraction of the other problems. Including multiple parts, there are 600 problems in the text andsolutions are presented here for the majority of them.
Many of the problem titles are supplemented by key words or phrases alluding to the solution procedure. Answers are indicated. Many tips on solutions are included which can be passed on to students.
Although an objective of problem solving is to obtain an answer, we have endeavored to also provide insights as to how many of theproblems are related to engineering situations in the real world.
The Manual includes an index to assist in finding problems by topic or principle and to facilitate finding closely-related problems.
This Manual was prepared with the assistance of Dr. Erich Pacht.
Professor John D. Kraus
Dept. of Electrical Engineering
Ohio State University
2015 Neil AveColumbus, Ohio 43210
Dr. Ronald J. Marhefka
Senior Research Scientist/Adjunct Professor
The Ohio State University
1320 Kinnear Road
Columbus, Ohio 43212
Table of Contents
Chapter 2. Antenna Basics 1
Chapter 3. The Antenna Family 17
Chapter 4. Point Sources 19
Chapter 5.Arrays of Point Sources, Part I 23
Chapter 5. Arrays of Point Sources, Part II 29
Chapter 6. The Electric Dipole and Thin Linear Antennas 35
Chapter 7. The Loop Antenna 47
Chapter 8. End-Fire Antennas: The Helical Beam Antenna and the Yagi-Uda
Array, Part I 53
Chapter 8. The Helical Antenna: Axial and Other Modes, Part II 55
Chapter 9. Slot, Patch and HornAntennas 57
Chapter 10. Flat Sheet, Corner and Parabolic Reflector Antennas 65
Chapter 11. Broadband and Frequency-Independent Antennas 75
Chapter 12. Antenna Temperature, Remote Sensing and Radar Cross Section 81
Chapter 13. Self and Mutual Impedances 103
Chapter 14. The Cylindrical Antenna and the Moment Method (MM) 105
Chapter 15. The Fourier Transform Relation BetweenAperture Distribution
and Far-Field Pattern 107
Chapter 16. Arrays of Dipoles and of Aperture 109
Chapter 17. Lens Antennas 121
Chapter 18. Frequency-Selective Surfaces and Periodic Structures
By Ben A. Munk 125
Chapter 19. Practical Design Considerations of Large Aperture Antennas 127
Chapter 21. Antennas for Special Applications 135
Chapter 23. Baluns, etc. By Ben A.Munk 143
Chapter 24. Antenna Measurements. By Arto Lehto and
Pertti Vainikainen 147
Chapter 2. Antenna Basics
Show that the directivity D of an antenna may be written
Note that area/steradian, so or (watts/steradian) = (watts/meter2) meter2
Calculate the approximate directivity from the half-power beam widths of a unidirectional antenna if the normalized power pattern is given by: (a) Pn = cos , (b) Pn = cos2 , (c) Pn = cos3 , and (d) Pn = cosn . In all cases these patterns are unidirectional (+z direction) with Pn having a value only for zenith angles 0 90 and Pn = 0 for 90 180. The patterns are independent of theazimuth angle .
(a) , (ans.)
(b) , (ans.)
(c) , (ans.)
(d) , (ans.)
*2-7-3. Approximate directivities.
Calculate the approximate directivities from the half-power beam widths of the three unidirectional antennas having power patterns as follows:
P(,) = Pm sin sin2
P(,) = Pm sin sin3
P(,) = Pm sin2 sin3