The space for the new antennas was inside this house's roof attic: 33 feet above ground level measuring 32 feet wide, 36 feet long along the north-south direction, and 8 feet high at the peak.Computer Assisted Low Profile Antenna Modeling I

Using A Personal Computer to Optimize Your Attic Antenna Projects

by Dr. Carol F. Milazzo, KP4MD (posted 13 June 1998)
E-mail: kp4md@arrl.net
 
 

INTRODUCTION

The advent of computer technology has greatly advanced many aspects of amateur radio. In technical areas such as antenna design, circuit design, and radio propagation, where one often depended on empirical estimations and trial and error methods, computer software can often help optimize results much more reliably. This article describes my experience with applying this software for low profile antenna modeling.

I was interested in comparing antenna models due to a recent move to a residential area with restrictive covenants in Omaha, Nebraska. The space available for the new antennas was inside a peaked roof attic 33 feet above ground level measuring 32 feet wide, 36 feet long along the north-south direction, and 8 feet high at the peak. I wanted an antenna for my weekly schedule between Omaha, Nebraska and New York City. The desirable features of the antenna were: gain to compensate for the losses due to being located indoors; broad bandwidth to minimize detuning effects of proximity to the roof; ability to handle the legal power limit, if necessary; ability to operate on multiple bands; and, if possible, rejection of signals from unwanted directions. A computer model offered the convenience of predicting the performance of different low profile antenna designs prior to physically building them.

NUMERICAL ELECTROMAGNETICS CODE

CONTENTS
Many modern antenna analysis programs have their origins in a very large and complicated FORTRAN program called the Numerical Electromagnetics Code or "NEC." NEC analyzes wire antennas by dividing them into a number of segments, calculating the current in each segment and summing the results. This provides information on the radiation pattern and impedance of the antenna for any selected frequency. NEC was written in the 1970's and was composed of tens of thousands of lines of computer code requiring the use of a mainframe computer inaccessible to most radio amateurs. In 1980, the team of John Rockway and Jim Logan successfully wrote a very simplified version called MININEC that had about 500 lines of BASIC and could run on a personal computer. Since that time, MININEC has evolved through several versions and enhancements to take advantage of the increased power of modern personal computers. MININEC provides the basis for a large portion of the recent amateur radio literature concerning antenna analysis.(1-39)For this study I obtained the following three freely available demonstration versions of antenna analysis software:

MININEC

Version 3 can be downloaded at ftp://ftp.funet.fi/pub/ham/antenna/NEC/mininec3.zip on the Internet. It is also widely available as freeware on many CD-ROMs and BBS's. It is provided as a BASIC listing and as a compiled BASIC executable DOS program and can run on any PC compatible computer with an 8080 or later CPU and at least 512k RAM. Like the original MININEC program, this version requires the user to work out an antenna model on paper, figure out the coordinates of the endpoints of each wire, and then enter these numbers into the program, along with the wire radius and wire connection data. The input and output consist of text and numerical tables with no graphics.(13)

ELNEC

A demo can be downloaded at ftp://ftp.funet.fi/pub/ham/antenna/elnecdem.exe. ELNEC is a compiled DOS program that can run on any PC compatible computer with an 8080 or later CPU, at least 512k RAM and a CGA/EGA/VGA/Hercules video adapter. This program by Roy Lewallen, W7EL, includes enhancements to the MININEC3 program allowing a simpler input of information with visual feedback (3-D graphics of antenna model, radiation pattern plots, graphs of impedance, VSWR, etc. vs. frequency). The free trial version limits the number of wire segments to 16 and does not allow printing of graphics from within the program; however, one can print graphic screens using the Print Screen key if one first runs the GRAPHICS.EXE program included with MS-DOS.(25)

NEC4WIN

A free demo of NEC4WIN95 can be downloaded here. This version requires Microsoft Windows 3.1 or later, or Windows NT or Windows 95 and a PC compatible computer with a 80386SX or later microprocessor. This program was written by Madjid Boukri, VE2GMI, and provides a Microsoft Windows interface to the MININEC3 program, is mouse driven and user friendly. The Windows graphics are superior to those of the DOS program. The free evaluation version is fully functional except on one point: you cannot reload the projects you created and saved. Only "demo" projects files can be loaded. You can however enter antennas, simulate them, save the projects, print all diagrams, etc. Projects are saved in ASCII and easily re-entered.

DESIGNING THE MODEL

I selected NEC4WIN as the most appropriate trial program for this project as the complexity of the antenna models exceeded the limits of the ELNEC demo program, and the graphic output of NEC4WIN was better suited for this study. I decided to compare the performance of my previous antenna (a 4-band crossed inverted vee) with the new proposed antennas. The antenna at my previous location was a combination of roof mounted inverted vees for 7.1 and 14.1 MHz, and an inverted vee with 60 uH loading inductors 1/4 of the distance from each end that resonated on both 3.6 MHz and 10.1 MHz. The feedline was a single 50 ohm coaxial cable. The center support was 34 feet above ground level with guy wire tie points 11 feet above ground. The main axis of the antenna was oriented north-south for the main lobes of radiation to be east and west. Other known data included the lengths of the wires and guy lines, distances between the tie down points, and average ground conductivity. Since this antenna had a complicated geometry, figuring the x, y, and z axis coordinates of the endpoints required using the Pythagorean Theorem for solving right triangles. I used a spreadsheet table to help recalculate the coordinates when adjusting wire lengths in the modeling process. The number of segments affects the accuracy of the calculations. The length of each segment is generally recommended to be on the order of .02 wavelengths. A larger number of segments provides greater accuracy, but this significantly slows the program and requires increasingly larger amounts of computer memory. Figure 1 shows the resulting antenna geometry data for the 4 band crossed inverted vee. Figure 2 shows a 3D view of the antenna.
 
Figure 1. Geometry Data of 4 Band Crossed Inverted Vee Antenna
Figure 2. 3D View of Crossed Inverted Vee Antenna

VALIDATING THE MODEL

An important part of the modeling process is the validation of the model. This assures the proper geometry and the polarity of each of the wires. Figure 1 shows the description of each wire with each endpoint with the greater y coordinate preceding the endpoint with the lesser y coordinate. This resulted in the proper calculated antenna current pattern. The program calculated the resonant frequencies of this antenna at 3.6 MHz, 7.0 MHz, and 10.15 MHz, near the observed resonances of the real antenna. Interestingly, there was no resonance near 14 MHz. This was also observed in the real antenna and was probably due to proximity effects between inverted vees in the particular configuration of this antenna.

ANALYZING THE MODEL

The VOACAP propagation program calculated the ionospheric path for the Omaha to New York circuit as an azimuth angle of 84.5º and an elevation angle varying from 12º to 30º depending on season, frequency, time of day and number of hops. As the best signals were predicted with a single F2 layer hop at 13º, this elevation was used for model analysis. The Miniprop propagation program confirmed these calculated angles. Figures 3 to 6 are the radiation patterns for the crossed inverted vees on 7.0 and 14.0 MHz. All azimuth plots were run for an elevation angle of 13º. The 14.0 MHz radiation patterns show the main lobe at 90º elevation. According to the modeling convention, 0º on the azimuth pattern represents the main lobe broadside to the antenna, which in this case would be facing due east (90º). The direction to New York City would then be 5.5º counterclockwise from 0º, i.e., at 354.5º on all azimuth radiation patterns. Figure 8 shows a null (calculated antenna gain of -8.81 dBi), showing very poor radiation in the desired direction.
 
Figure 3. Elevation Radiation Pattern for Crossed Inverted Vee Antenna at 7 MHz
Figure 4. Azimuth Radiation Pattern for Crossed Inverted Vee Antenna at 7 MHz
Figure 5. Elevation Radiation Pattern for Crossed Inverted Vee Antenna at 14 MHz
Figure 6. Azimuth Radiation Pattern for Crossed Inverted Vee Antenna at 14 MHz

COMPARING THE MODELS

The first comparison antenna modeled was a variation of a full wave horizontal loop called the "droopy loop" for 40 meters running along the corners of the attic, i.e., 36 feet long sides running north and south and a 18 foot diagonal wire from each of the attic corners up to the peaks on the north and south ends of the attic.(40) This feedpoint for this loop was at the center of the 36 foot wire on the east side. The next antenna modeled was a 20 meter full wave vertical rectangular loop 8 feet high and 28 feet wide fed at the center of the lower side. The last model was a 20 meter lazy H consisting of an 8 foot vertical radiator connected to the center of a 16 foot flat top, and a 36 foot horizontal wire counterpoise. I divided each loop into 72 equal segments for analysis. The loop design claimed broad bandwidth and multiple band operation.(14) The vertical loop also claimed low radiation angle and directionality. The lazy H antenna claimed omnidirectional low radiation angle.(38) Figures 5 and 6 are views of these models. The y-axis was oriented north-south; and the x-axis was oriented east-west. I oriented all directional antennas for maximum radiation in the east and west directions.
 
Figure 7. 3D View of 40 Meter Droopy Loop and 20 Meter Vertical Loop Antennas
Figure 8. View of 20 Meter Lazy H Antenna

The calculated radiation patterns of these models on 7 MHz and 14 MHz are in figures 9 to 16.

Figure 9. Elevation Radiation Pattern for 40 Meter Droopy Loop at 7 MHz
Figure 10. Azimuth Radiation Pattern for 40 Meter Droopy Loop at 7 MHz
Figure 11. Elevation Radiation Pattern for 40 Meter Droopy Loop at 14 MHz
Figure 12. Azimuth Radiation Pattern for 40 Meter Droopy Loop at 14 MHz
Figure 13. Elevation Radiation Pattern for 20 Meter Vertical Loop at 14 MHz
Figure 14. Azimuth Radiation Pattern for 20 Meter Vertical Loop at 14 MHz
Figure 15. Elevation Radiation Pattern for 20 Meter Lazy H at 14 MHz
Figure 16. Azimuth Radiation Pattern for 20 Meter Lazy H at 14 MHz

Here are the calculated elevations of lowest major radiation lobes and antenna gains for the Omaha to New York circuit for all the modeled antennas:

ANTENNA
PARAMETER*
3.5 MHz†
7.0 MHz
10.0 MHz
14.0 MHz
18.0 MHz
21.0 MHz
24.0 MHz
28.0 MHz
Crossed inverted vees Maj. lobe elev. @ 0º az.
Gain dBi @
13º el. 354º az.
90º

-4.32

90º

-3.22

65º

-2.15

90º

-8.81

20º

+12.67

10º

+10.55

20º

+13.58

35º

+4.12

40 meter "droopy loop" Maj. lobe elev. @ 0º az.
Gain dBi @
13º el. 354º az.
90º‡

-2.69‡

85º

-3.41

70º

-5.28

25º

+3.45

25º

+6.17

80º

-16.68

15º

+5.6

15º

-1.12

20 meter vertical loop Maj. lobe elev. @ 0º az.
Gain dBi @
13º el. 354º az.
90º‡

-4.99‡

45º‡

-1.43‡

35º‡

+1.23‡

25º

+4.95

20º

+6.82

20º

+6.84

15º

+6.54

80º

-3.46

20 meter lazy H Maj. lobe elev. @ 0º az.
Gain dBi @
13º el. 354º az.
25º‡

-0.50‡

20º‡

-0.48‡

15º‡

+0.19‡

15º

-0.08

15º

-0.28

10º

-0.31

10º

-2.33

10º

-2.85

Table 1. Calculated Parameters for Baseline and Comparison Antenna Models.

*Parameters are the elevation of first major lobe above the horizon and the gain in the desired direction.

†MININEC may exaggerate gains for antennas lower than 1/4 wavelength above ground.

‡Performance of models below antenna design frequencies may be poorer than calculated due to inefficiencies from high VSWR.

The data for the 7 and 14 MHz were of most relevance as these were the phone bands on which the best openings were expected during this part of the sunspot cycle. Compared to the crossed inverted vee antenna, the radiation pattern of the 40 meter horizontal loop in the desired direction showed similar gain at 7.0 MHz, increased gain at 14.0 MHz and a somewhat omnidirectional pattern on all bands. The 20 meter vertical loop showed even greater gain at 14 MHz with attenuation of signals from the sides. When modeling both loops together, NEC4WIN calculated negligible induced currents from one loop to the other, predicting very little interaction as would be expected due to the loops being in perpendicular planes. The 20 meter lazy H had the lowest radiation angle but the least gain of all the proposed antennas at 14 MHz, probably due to it being a shortened radiator as compared to the full wavelength size of the loops.

COMPARING THE ANTENNAS

I chose to build both the 40 meter and 20 meter loops due to their overall advantage in gain and bandwidth over the lazy H. I used #14 gauge bare stranded copper wire for the 20 meter loop. As the 40 meter loop would run in close proximity to the corners of the attic, I chose insulated #12 gauge stranded copper wire for the that one. Ceramic end insulators tied to screw eyes supported the low antenna corners. I passed nylon cords through 3/4 inch pulleys in the attic peak to support the ceramic insulators for the high loop corners. I tied the feedpoint ends of the loops to center-type ceramic insulators and directly fed them with 90 foot lengths (an electrical wavelength at 7.2 MHz) of polyethylene dielectric RG-8/U coaxial cable. The electrical wavelength is equal to the free space wavelength multiplied by the velocity factor of the transmission line, which is 0.66 in the case of polyethylene dielectric RG-8/U. I chose this length because transmission lines measuring an electrical half-wavelength, or multiples thereof, duplicate the impedance at the load end of the antenna and eliminate the need for a matching transformer between the feedline and the antenna. A 90 foot length of transmission line provides this effect at 3.6, 7.2, 10.8, 14.4, 18, 21.6, 25.2, and 28.8 MHz-frequencies in or near several of the amateur HF bands. I avoided foam dielectric coaxial cable because: 1) it has a lower voltage rating that might be exceeded by higher VSWR's when using the legal power limit on the WARC bands; and, 2) the heating of the foam dielectric with high VSWR's can cause the center conductor to migrate through the dielectric forming impedance bumps and increasing losses, heating and possibly shorting the center conductor to the shield. In the event that your power levels will not exceed 100 watts or so, you should be able to use RG-58/U or foam dielectric cable, being sure to calculate the cable lengths using the appropriate velocity factor for your cable if you wish to use a multiple of an electrical half-wavelength. Open-wire transmission lines would simplify the feeding and matching of the antennas, but I could not use these in my indoor installation due to a limited space for threading the cables from the attic to the station in the basement and due to the presence of metal heating ducts within that space.

I took the following measurements at the transmitter end of the transmission lines. The observed resonant frequencies were reasonably close to the calculated frequencies despite expected differences due to proximity effects of the attic structures.

ANTENNA
CALCULATED RESONANT
FREQUENCY (MHz)
OBSERVED RESONANT 
FREQUENCY (MHz)
2:1 VSWR BANDWIDTH
OBSERVED (MHz)
40 meter "droopy loop"
7.12 MHz
7.04 MHz
0.6 MHz
20 meter vertical loop
14.16 MHz
14.00 MHz
1.6 MHz
Table 2. Calculated and Observed Resonant Frequencies and Bandwidths of Loop Antennas.

On the air tests using both loops gave good results on scheduled contacts as NEC4WIN predicted. Either loop could handle either 100 watts or 1 kW of power; however, a test transmission of 1 kW on 7 MHz using the droopy loop induced high RF currents in the house wiring, tripping all the ground-fault current interruptors and triggering the home security system. One should assure compliance with the latest safety guidelines for RF exposure if planning to use high power with this type of antenna.(41,42) On some 20 meter schedules, the signal on the vertical loop was consistently ½ to 1 S unit stronger than on the horizontal loop, just as NEC4WIN predicted. At other times, switching between the 40 meter loop and 20 meter loop gave an interesting diversity reception effect, with signals at times stronger by several S units on one antenna or the other. This inconsistent difference in gain between the loops was probably due to changes in the incident radiation angle under varying propagation conditions. The loops have given me good signal reports with contacts to both coasts during openings on all bands from 40 through 15 meters using an antenna tuner. The antenna tuner also allowed the use of the 40 meter loop for short skip contacts using 100 watts on 80 meters. It may be difficult to use higher power levels on 80 meters since the half wavelength of transmission line would duplicate the high impedance of antenna feedpoint at the tuner, producing very high RF voltages that could exceed the component ratings of the antenna tuner.

CONCLUSION

Computer antenna modeling offers a practical way to save time and effort in the selection of antennas for the operator's requirements prior to actual construction. Currently available software makes computer antenna modeling for antenna projects easily accessible to the average amateur radio operator.

BIBLIOGRAPHY: COMPUTER ANTENNA ANALYSIS

  1. "Modeling HF Antennas with MININEC", The ARRL Antenna Compendium, Vol. 3. [MININEC]
  2. "MN Antenna Analysis Software for the IBM PC", QST, Sep. 1988, p. 41. [MN]
  3. "K6STI's MN and Yagi Optimizer Antenna Analysis Software", QST, Aug. 1990, p. 41. [MN, YO]
  4. "MININEC: The Other Edge of The Sword", Lewallen, R, W7EL, QST, Feb, 1991, p. 18. [MININEC]
  5. "Antenna Software - AO 5.0", Beezley, B, K6STI, QST, Apr. 1993, p. 45. [AO]
  6. "QST Compares Antenna Modeling Software", Straw, D, N6BV, QST, Oct. 1995, p. 72.
  7. "The Convoluted Loop", Hart, T, W5QJR, Ham Radio, Apr. 1989, Vol. 22:4, pp. 89-97. [MININEC]
  8. "Ham Radio Techniques: The Yagi Optimizer Disk", Orr, W, W6SAI, Ham Radio, May 1989, Vol. 22:5, p.83. [YO]
  9. "Ham Radio Techniques: Antenna Gain", Orr, W, W6SAI, Ham Radio, Jan. 1990, Vol. 23:1, pp. 30-31. [MN]
  10. "Ham Radio Techniques: The MN Analysis Program (That was then, this is now)", Orr, W, W6SAI, Ham Radio, Feb. 1990, Vol. 23:2, pp. 34-39. [MN]
  11. "Ham Radio Techniques: 160 Meter Antenna Problems and Solutions", Orr, W, W6SAI, Ham Radio, Mar. 1990, Vol. 23:3, pp. 49-54. [MN]
  12. "Ham Radio Techniques: The Yagi Optimizer", Orr, W, W6SAI, Ham Radio, Apr. 1990, Vol. 23:4, pp. 68-71. [YO]
  13. "Using MININEC for Antenna Analysis: Elements of MININEC theory", Haviland, RP, W4MB, Communications Quarterly, Nov. 1990, pp. 16-22. [MININEC]
  14. "The Quad Antenna: Rectangular and Square Loops: Design and performance data for any square, rectangular or diamond loop", Haviland, RP, W4MB, Communications Quarterly, Vol. 1:1, Spring 1991, pp. 11-22. [MININEC]
  15. "Yagi Optimization and Observations on Frequency Offset and Element Taper Problems: Using computer programs for antenna analysis", Orr, W, W6SAI, Communications Quarterly, Vol. 1:1, Spring 1991, pp. 79-85. [MININEC, YO]
  16. "Antenna Angle of Radiation Considerations: Performance comparison of Quads and Yagis mounted at low heights: Part 1", Luetzelschwab, C, K9LA, Communications Quarterly, Vol 1:3, Summer 1991, pp. 37-42. [MN, YAGINEC]
  17. "The Triangle Antenna: An alternative horizontal omnidirectional antenna", Beesley, B, K6STI, Communications Quarterly, Vol 1:4. Fall 1991, pp. 49-60. [MN]
  18. "Antenna Angle of Radiation Considerations: Performance comparison of Quads and Yagis mounted at low heights: Part 2", Luetzelschwab, C, K9LA, Communications Quarterly, Vol 1:4, Fall 1991, pp. 61-67. [MN, YAGINEC]
  19. "Antenna Structure Interaction: Modeling with MININEC", Haviland, RP, W4MB, Communications Quarterly, Vol 1:4, Fall 1991, pp. 73-78. [MININEC]
  20. "The 160 Meter Semi Vertical: A case history", Elwell, H, N4UH, Communications Quarterly, Vol 2:1, Winter 1992, pp. 81-93. [MININEC]
  21. "Parasitic Elements for Pattern Shaping in Vertical Antennas: Enhances patter control using parasitic elements", Haviland, RP, W4MB, Communications Quarterly, Vol 2:3, Summer 1992, pp. 28-34. [MININEC]
  22. "Supergain Antennas: Possibilities and problems", Haviland, RP, W4MB, Communications Quarterly, Vol 2:3, Summer 1992, pp. 55-72. [MININEC]
  23. "The Effects of Antenna Height on Other Antenna Properties: a computer study", Cebik, LB, W4RNL, Communications Quarterly, Vol 2:4, Fall 1992, pp. 57-79. [ELNEC]
  24. "The Unidirectional Long Wire Antenna: A look at this useful alternative to the Yagi", Haviland, RP, W4MB, Communications Quarterly, Vol 3:4, Fall 1993, pp.35-41. [MININEC]
  25. "Comparing MININECS: A guide to choosing an antenna optimization program", Cebik, LB, W4RNL, Communications Quarterly, Vol 4:2, Spring 1994, pp.53-72. [AM, AO, ELNEC]
  26. "Modeling and Understanding Small Beams Part 1: The X-beam", Cebik, LB, W4RNL, Communications Quarterly, Vol 5:1, Winter 1995, pp. 33-50. [ELNEC]
  27. "Source Data Display Program for ELNEC: Use this stand-alone program to plot or print data using ELNEC files", Cefalo, TV, WA1SPI, Communications Quarterly, Vol 5:2, Spring 1995, pp. 31-36. [ELNEC]
  28. "Modeling and Understanding Small Beams Part 2: VK2ABQ squares and Moxon rectangles", Cebik, LB, W4RNL, Communications Quarterly, Vol 5:2, Spring 1995, pp. 55-70. [ELNEC]"
  29. "Understanding Elevated Vertical Antennas: Useful information about a popular antenna type", Shanney, B, KJ6GR, Communications Quarterly, Vol 5:2, Spring 1995, pp. 71-76. [MININEC]
  30. "Modeling and Understanding Small Beams Part 3: The EDZ family of antennas", Cebik, LB, W4RNL, Communications Quarterly, Vol 5:4, Fall 1995, pp. 53-65. [ELNEC]
  31. "Quarterly Review: NEC-WIN Basic for Windows", Cebik, LB, W4RNL, Communications Quarterly, Vol 6:1, Winter 1996, pp. 55-56. [NEC-WIN]
  32. "Quarterly Computing: NEC-WIN Basic for Windows", Thompson, B, AA1IP, Communications Quarterly, Vol 6:1, Winter 1996, pp. 86-88. [NEC-WIN]
  33. "Fractal and Shaped Dipoles: Some simple fractal dipoles, their benefits and limitations", Cohen, N, N1IR, Communications Quarterly, Vol 6:2, Spring 1996, pp. 25-36. [EZNEC]
  34. "Modeling and Understanding Small Beams Part 4: Linear loaded Yagis", Cebik, LB, W4RNL, Communications Quarterly, Vol 6:3, Summer 1996, pp. 85-106. [ELNEC]
  35. "Modeling and Understanding Small Beams Part 5: The ZL Special", Cebik, LB, W4RNL, Communications Quarterly, Vol 7:1, Winter 1997, pp. 72-90. [EZNEC]
  36. "Optimal Elevated Radial Vertical Antennas: Design minimizes effects of unequal radials' currents", Weber, D, K5IU, Communications Quarterly, Vol 7:2, Spring 1997, pp. 9-27. [NEC-WIN]
  37. "EZNEC For DOS: The marriage of ELNEC and NEC-2". Cebik, LB, W4RNL, Communications Quarterly, Vol 7:2, Spring 1997, pp. 28-30. [ELNEC, EZNEC]
  38. "The Lazy H Vertical: A versatile antenna for DX work", Severns, R, N6LF, Communications Quarterly, Vol 7:2, Spring 1997, pp. 31-40. [NEC-2]
  39. "Modeling and Understanding Small Beams Part 6: Fans, bowties, butterflies, and dragonflies", Cebik, LB, W4RNL, Communications Quarterly, Vol 7:2, Spring 1997, pp. 81-97. [ELNEC]
  40. "The Droopy Loop", Newton, P, KJ7MZ, QST, Vol 80:7,July 1996, pp. 57-58.
  41. "The FCC's New RF-Exposure Regulations", Hare, E, KA1CV, QST, Vol 81:1, January 1997, pp.47-49.
  42. "What's New About the FCC's New RF-Exposure Regulations?", Hare, E, W1RFI, QST, Vol 81:10, pp.51-52.

APPENDIX: NEC4WIN Antenna Model Files n4wmodel.zip

Crossed inverted vees inve802B.n4w

CM
CM NEC4WIN File
CM 80/40/30/20 meter crossed inverted vees
CM Resonated on 3.575, 7.1, 10.12 and 14.075 MHz
CM 82 segments
CM
CE
GND Reference
UNITS Feet
Height 34.5144
Over Perfect Ground
Circular Boundary
F 7.000
GW 1 2 0.000 0.164 0.000 0.000 -0.164 0.000 0.0066
GW 2 16 -16.4042 30.0919 -22.9987 0.000 0.164 0.000 0.0066
GW 3 16 0.000 -0.164 0.000 16.4042 -30.0919 -22.9987 0.0066
GW 4 16 13.2316 24.2684 -18.5499 0.000 0.164 0.000 0.0066
GW 5 16 0.000 -0.164 0.000 -13.2316 -24.2684 -18.5499 0.0066
GW 6 8 0.000 13.7631 -10.5184 0.000 0.164 0.000 0.0066
GW 7 8 0.000 -0.164 0.000 0.000 -13.7631 -10.5184 0.0066
S 1 1 100 0
LI 1 5 .1 60
LI 2 30 .1 60
Coax 50

40 Meter Droopy Loop hloop40.n4w

CM
CM NEC4WIN File
CM 40 meter droopy loop
CM For attic 8' high x 36' long x 32' wide
CM 72 segments
CM
CE
GND Reference
UNITS Feet
Height 32.8101
Over Ground 13 5 (Diel. - Cond. µSiemens)
Circular Boundary
F 7.000
GW 1 18 16.000 -18.000 0.000 16.000 18.000 0.000 0.0069
GW 2 9 16.000 18.000 0.000 0.000 18.000 8.000 0.0069
GW 3 9 0.000 18.000 8.000 -16.000 18.000 0.000 0.0069
GW 4 18 -16.000 18.000 0.000 -16.000 -18.000 0.000 0.0069
GW 5 9 -16.000 -18.000 0.000 0.000 -18.000 8.000 0.0069
GW 6 9 0.000 -18.000 8.000 16.000 -18.000 0.000 0.0069
S 1 9 100 0
Coax 50

20 Meter Vertical rectangular loop vloop20.n4w

CM
CM NEC4WIN File
CM 20 meter vertical rectangular loop
CM For attic 8' high x 36' long x 32' wide
CM 72 segments
CM
CE
GND Reference
UNITS Feet
Height 32.8086
Over Ground 13 5 (Diel. - Cond. µSiemens)
Circular Boundary
F 14.000
GW 1 28 0.000 14.000 0.000 0.000 -14.000 0.000 0.0052
GW 2 8 0.000 -14.000 0.000 0.000 -14.000 8.000 0.0052
GW 3 28 0.000 -14.000 8.000 0.000 14.000 8.000 0.0052
GW 4 8 0.000 14.000 8.000 0.000 14.000 0.000 0.0052
S 1 14 100 0
Coax 50

20 Meter Lazy H lzh20.n4w

CM
CM NEC4WIN File
CM 20 Meter Lazy H Antenna
CM 30 segments
CM
CE
GND Reference
UNITS Feet
Height 32.810
Over Ground 13 5 (Diel. - Cond. µSiemens)
Circular Boundary
F 14.000
GW 1 9 0.000 -18.000 0.000 0.000 0.000 0.000 0.0066
GW 2 9 0.000 18.000 0.000 0.000 0.000 0.000 0.0066
GW 3 4 0.000 0.000 0.000 0.000 0.000 8.000 0.0066
GW 4 4 0.000 0.000 8.000 0.000 -8.000 8.000 0.0066
GW 5 4 0.000 0.000 8.000 0.000 8.000 8.000 0.0066
S 1 18 100 0
Coax 50

CAPTIONS

Figure 1. Geometry Data of 4 Band Crossed Inverted Vee Antenna
Figure 2. 3D View of Crossed Inverted Vee Antenna
Figure 3. 3D View of 40 Meter Droopy Loop and 20 Meter Vertical Loop Antennas
Figure 4. View of 20 Meter Lazy H Antenna
Figure 5. Elevation Radiation Pattern for Crossed Inverted Vee Antenna at 7 MHz
Figure 6. Azimuth Radiation Pattern for Crossed Inverted Vee Antenna at 7 MHz
Figure 7. Elevation Radiation Pattern for Crossed Inverted Vee Antenna at 14 MHz
Figure 8. Azimuth Radiation Pattern for Crossed Inverted Vee Antenna at 14 MHz
Figure 9. Elevation Radiation Pattern for 40 Meter Droopy Loop at 7 MHz
Figure 10. Azimuth Radiation Pattern for 40 Meter Droopy Loop at 7 MHz
Figure 11 Elevation Radiation Pattern for 40 Meter Droopy Loop at 14 MHz
Figure 12. Azimuth Radiation Pattern for 40 Meter Droopy Loop at 14 MHz
Figure 13 Elevation Radiation Pattern for 20 Meter Vertical Loop at 14 MHz
Figure 14. Azimuth Radiation Pattern for 20 Meter Vertical Loop at 14 MHz
Figure 15 Elevation Radiation Pattern for 20 Meter Lazy H at 14 MHz
Figure 16. Azimuth Radiation Pattern for 20 Meter Lazy H at 14 MHz

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