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Gain of a Quarter Wave Ground Plane Antenna?

Oct 9th 2017, 10:39


Joined: Feb 17th 2012, 16:31
Total Topics: 0
Total Posts: 0
What is the gain of a quarter wave ground plane antenna?
Simple question? Everyone has an opinion. Which one is correct?
Assumption: a dipole is 2.15 dBi.

-0.85 dBi
“...the "1/4 wave" antenna has 0.85 dB loss as compared to an isotropic source.”
A Discussion of Antenna Theory by Paul Graham (K9ERG)

1.15 dBi
“Gain is slightly lower than a dipole (about 1 dB less)...” [2.15 - 1]
US Naval Academy EE302 Lesson 13: Antenna Fundamentals, page 19.

2.15 dBi
“The performance of a quarter wave antenna (either well grounded or using a counterpoise) is essentially the same as a half-wave dipole antenna.”
US Naval Academy EE302 Lesson 13: Antenna Fundamentals, page 21.

2.15 dBi
“λ/2 dipole has 2.15 dBi gain – Ground-plane gain equivalent to λ/2 dipole”
Antennas 101

2.15 dBi
“A monopole over an infinite ground plane is theoretically the same (identical gain, pattern, etc., in the half-space above the ground plane) as the dipole in free space.”
Antenna System Guide, NIJ Guide 202-00 - NCJRS

2.2 dBi
“The following discussion of antenna types assumes an “adequate´ ground plane is present...A single radiating element approximately 1/4 wavelength long. Directivity 2.2 dBi, 0 dBd.
Antenna Basic Concepts

5.15 dBi
“If the directivity of a dipole of length 2L has a directivity of D1 [decibels], then the directivity of a monopole antenna of length L will have a directivity of D1+3 [decibels].” [2.15 + 3]
The Monopole Antenna

5.16 dBi
“Thus, the gain of a quarter-wave monopole should have twice the gain of a corresponding
half-wave dipole, or 5.16 dB.”
Dipole and Monopole Antenna Gain Effective Area for Communication Formulas

5.19 dBi
“...a quarter-wave monopole, the most common type, will have a gain of 2.19 + 3 = 5.19 dBi...”
Wikipedia entry for Monopole antenna.

5.31 dBi
“Therefore, we deduce the antenna gain of a quarter-wave monopole antenna above virtual ground as 5.31 dB which is little bit more than twice the gain of a center-fed half-wave dipole antenna that is 2.16 dB.”
Radiation Characteristics of a Quarter-Wave Monopole Antenna above Virtual Ground

73, Steve J. Noll, WA6EJO

Oct 11th 2017, 13:44


Super Moderator

Joined: Apr 4th 1998, 00:00
Total Topics: 0
Total Posts: 0
The wide variety of opinions suggest the answer is not so simple.

Traditionally, it took three years of engineering school to learn how to calculate the impedance of a highly simplified dipole. First year you learned single variable calculus. Second year you got to handle real engineering problems with two variable calculus. Third year you took the hardest classes, which included solving antenna problems with calculus. Senior classes were typically easier, as they expected you to to be pre-occupied with finding a job.

The first edition of Antennas by Kraus, W8JK is now a free download. It is well worth studying if you want to understand the tradeoffs made to calculate antenna gain from first principles. For instance, the antenna element is usually infinitely thin with zero conductor loss, something that is impossible with real antennas. But, nobody has been able to solve the equations if you try to solve for a real conductor diameter.
Fortunately for hams, method of moments computer programs can give good answers provided care is taken in setting up the proper models. A distinct advantage of computer models is that they specify exactly what is being modeled--what exactly is a "ground plane antenna"?
One approach is to consider it half of an ideal dipole above an infinite perfect ground. This is useful because it provides a clever way to get an answer. The difficulty with this approach is answer is that it is often misleading. You can argue that the answer is pretty good for tiny little atolls in the Pacific surrounded by salt water, but most hams have ground conditions that are significantly worse than this "best case" scenario. And getting from an idealistic best case to what you really want can be hard to understand if you insist on solving calculus problems to get there.

So, for most hams, the most useful answer they can get is to learn how to use modeling programs to best approximate the antennas and ground conditions they actually have. While it is nice to know what you could get if you moved to beach front property, most hams would benefit more if they could obtain comparisons between more realistic antenna options.

Zack Lau W1VT
ARRL Senior Lab Engineer

Aug 9th 2022, 18:23


Joined: Feb 17th 2012, 16:31
Total Topics: 0
Total Posts: 0
I finally answered my own question. Claims of -0.85 dBi to +5.31 dBi are just nuts! I decided to measure it myself using the two-identical antenna technique and the Friis equation. I made two ¼-wave ground plane antennas for 449.9 MHz. Tuned to 1.01:1 SWR. Excited with approx 5W. Received with a HP 478A/432C microwave power meter. The measurement was extremely difficult due to the reflection effects for omnidirectional antennas. If ever there was a time to use a RF anechoic chamber or two mountaintops, this was it! It took 39 gain readings to get the confidence to say that the gain of a ¼-wave ground plane is 1.32 dBi +/-0.4 dBi. To verify my technique and math I then measured the gain of the only other two identical antennas I had at hand, Two Seavey Engineering SGA-20 standard gain horns. Performed at 2.4 GHz I came within about 3% of the specified gain.

73, Steve J. Noll WA6EJO

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