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Antenna Theory for the Thinking Man

A treatment of tuned wire antennas as used on the HF amateur bands.

 

 

 

Where it all began: Faraday, Maxwell and Hertz

 

The electromagnetic wave and field concept (Excerpted and adopted from: http://www.uv.es/EBRIT/macro/macro_5002_7_23.html)

 

Faraday introduced the concept of field and of field lines of force that exist outside material bodies ... the region around and outside a magnet or an electric charge contains a field that describes at any location the force experienced by another small magnet or charge placed there. ... The concept of field, specifying as it does a certain possible action or force at any location in space, was the key to understanding electromagnetic phenomena. It should be mentioned parenthetically that the field concept also plays (in varied forms) a pivotal role in modern theories of particles and forces.

 

Besides introducing this important concept of electric and magnetic field lines of force, Faraday had the extraordinary insight that electrical and magnetic actions are not transmitted instantaneously but after a certain lag in time, which increases with distance from the source. Moreover, he realized the connection between magnetism and light after observing that a substance such as glass can rotate the plane of polarization of light in the presence of a magnetic field. This remarkable phenomenon is known as the Faraday Effect.

 

As noted above, Maxwell formulated a quantitative theory that linked the fundamental phenomena of electricity and magnetism and that predicted electromagnetic waves propagating with a speed, which, as well as one could determine at that time, was identical with the speed of light. He concluded his paper "On the Physical Lines of Force" (1861-62) by saying that electricity may be disseminated through space with properties identical with those of light.

 

In 1864 Maxwell wrote that the numerical factor linking the electrostatic and the magnetic units was very close to the speed of light and that these results "show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to [his] electromagnetic laws."

 

In 1884 Hertz derived Maxwell's theory by a new method and put its fundamental equations into their present-day form. In so doing, he clarified the equations, making the symmetry of electric and magnetic fields apparent. The German physicist Arnold Sommerfeld spoke for most of his learned colleagues when, after reading Hertz's paper, he remarked, "the shades fell from my eyes," and admitted that he understood electromagnetic theory for the first time.

 

[In 1888] Hertz made a second major contribution: he succeeded in generating electromagnetic radiation of radio and microwave frequencies, measuring their speed by a standing-wave method and proving that these waves have the properties of reflection, diffraction, refraction, and interference common to light. He showed that such electromagnetic waves can be polarized, that the electric and magnetic fields oscillate in directions that are mutually perpendicular and transverse to the direction of motion, and that their velocity is the same as the speed of light, as predicted by Maxwell's theory.

 

 Hertz's ingenious experiments not only settled the theoretical misconceptions in favor of Maxwell's electromagnetic field theory but also opened the way for building transmitters, antennas, coaxial cables, and detectors for radio-frequency electromagnetic radiation. In 1896 Marconi received the first patent for wireless telegraphy, and in 1901 he achieved transatlantic radio communication.

 

 The Faraday-Maxwell-Hertz theory of electromagnetic radiation [(commonly referred to as Maxwell's theory)] makes no reference to a medium in which the electromagnetic waves propagate. A wave of this kind is produced, for example, when a line of charges is moved back and forth along the line.

 

Moving charges represent an electric current. In this back-and-forth motion, the current flows in one direction and then in another. As a consequence of this reversal of current direction, the magnetic field around the current (discovered by Ørsted and Ampère) has to reverse its direction. The time-varying magnetic field produces perpendicular to it a time-varying electric field, as discovered by Faraday (Faraday's law of induction). These time-varying electric and magnetic fields spread out from their source, the oscillating current, at the speed of light in free space.

 

The oscillating current in this discussion is the oscillating current in a transmitting antenna, and the time-varying electric and magnetic fields that are perpendicular to one another propagate at the speed of light and constitute an electromagnetic wave. Its frequency is that of the oscillating charges in the antenna. Once generated, it is self-propagating because a time-varying electric field produces a time-varying magnetic field, and vice versa. Electromagnetic radiation travels through space by itself.

 

 

Summary of Maxwell’s Equations extracted from: http://www.physics.unomaha.edu/Sowell/phys2120/Lectures/EMWaves/EMWaves.pdf

 

Maxwell_Eq_01.GIF

 

Maxwell_Eq_02.GIF

 

Maxwell_Eq_03.GIF

 

Reiterating, if a charged particle is accelerating, (as opposed to stationary, static or non-moving) then EM waves are radiating outward from it. The following images demonstrate this effect. Note the bold arrow showing a ‘line of force’ expanding away from the accelerating charge as time progresses:

 

Maxwell_Eq_04.GIF

 

Animated, it takes on this appearance where ‘q’ is a charge oscillating (accelerating back and forth on a wire):

 

Charge_T_animated.gif

 

 

The following paper discusses the “E-field kink” diagrams shown above:

 

A MULTI-PERSPECTIVE EXAMINATION OF THE PHYSICS OF

ELECTROMAGNETIC RADIATION

 

E. K. Miller                                         G. J. Burke

3225 Calle Celestial                            Lawrence Livermore National Laboratory

Santa Fe, NM 87501-9613                 PO Box 808, Livermore, CA94550

505-820-7371, ekmiller@prodigy.net             925-422-8414, burke2@llnl.gov

 

ABSTRACT

 

Three different perspectives of electromagnetic radiation are presented here. The first employs the electric-field kink model, the second is based on a technique called FARS (Farfield Analysis of Radiation Sources), and the third uses time-domain solutions obtained from the TWTD (Thin-Wire Time Domain) model. The kink model demonstrates qualitatively that radiation is produced by “wriggling” a charge. The latter two provide more quantitative results, showing that radiation for a straight dipole can come not only from the source region and ends but also from along its length.

 

 

The following illustrations are from http://theses.gla.ac.uk/408/01/2008whytephd.pdf

 

 

 

Figure 2.4. Oscillating electric dipole consisting of two electric charges in simple harmonic

motion, showing propagation of an electric field and its detachment (radiation) from the dipole.

Arrows next to the dipole indicate current (I) direction.

 

 

 

 

 

Figure 2.5. Electric field lines for a λ/2 antenna at (a) t = 0, (b) t = T/8, (c) t = T/4 and (d) t = 3T/8

 

 

 

 

Animated it takes on the above appearance.

 

 

With all this as a background we can now take a look at a few ‘wire’ antennas.

 

The common denominator all these antennas have in common will be moving, accelerating charges on a wire (or tube or loop).

 

Theoretically, it makes little difference whether the loop is 1/10 or ¼ Lambda circumference for radiating purposes, but on the practical implementation level these factors will determine the voltages and currents seen on the antenna; the smaller the antenna (relative to the wavelength or Lambda) the higher the voltages and currents will be for a given RF power input.

 

 

Chapter 5 - Loop Antennas (chapter, pdf book)
by Glenn S. Smith
Georgia Institute of Technology

5.2 ELECTRICALLY SMALL LOOPS. . . . . . . . . . . . . . . . . . . . . . . 5-2

The axial current distribution in an electrically small loop is assumed to be uniform; that is, the current has the same value I0 at any point along the conductor. For single-turn loops and multiturn loops that are single-layer solenoidal coils, measurements suggest that this is a good assumption provided the total length of the conductor (N × circumference) is small compared with the wavelength in free space, typically < 0.1 Lambda.

 

5.3 ELECTRICALLY LARGE LOOPS. . . . . . . . . . . . . . . . . . . . . . . 5-9

 

As the electrical size of the loop antenna is increased, the current distribution in the loop departs from the simple uniform distribution of the electrically small loop. For single-turn loops, this departure has a significant effect on performance when the circumference is greater than about 0.1 Lambda.

 

5.4 SHIELDED-LOOP ANTENNA. . . . . . . . . . . . . . . . . . . . . . . . . 5-18

 

For certain applications it is desirable to position the terminals of the loop antenna precisely so as to produce geometrical symmetry for the loop and its connections about a plane perpendicular to the loop. This can often be accomplished by using the so-called shielded loop.

 

Small Loops: Loop circumference < 1/10 Lambda

Physically small antennas can work; special attention must be paid to construction details such as the size of the tuned loop itself AND the tuning capacitor ... low losses in the antennas itself are a MUST if the antenna is used for transmitting.

Practical Small Antenna Efficiency (from Ref 1 Mike Underhill below)

Commercial example: A loop with a 4 meter diameter:

Intermediate sized loops: Loop circumference 1/8 to 1/4 Lambda

General:

Practical Details of the 80 Meter G0CWT or Edington Loop

Excerpted and paraphrased text:

·         Loop consists of 64ft (19.5 meters) of wire.

·         The ends the loop are connected to the tuning/matching assembly consisting of 1) a wide spaced capacitor of about 300 pf in full mesh and 2) a simple ferrite matching transformer.

·         This transformer is wound through two ferrite tubes with nine turns for the primary winding tapped at three turns, and two turns for the secondary winding the ends of which are coupled one to the loop and the other to the capacitor the other end of the loop is taken to the capacitor.

·         As it is not a high Q loop the bandwidth is in the region of 40 kHz on 80 m and 14 kHz on 160 m.

Benefits:

·         Will fit on small city lot

·         Lower Q than small Loop means voltages and currents do not reach the high values seen on a small loop

·         Can be used on several octave related bands with proper tap switching on ferrite transformer

·         Intrinsically low feed line radiation owing to Balun function of ferrite matching transformer

Drawbacks:

·         Requires retuning of remote cap for frequency changes > 40 kHz (80 m) or 14 kHz (160 m)

·         Higher Q than large loop may require HV cap for QRO operation (albeit a lower voltage than a small loop)

·         Tapped primary needed on Ferrite matching transformer for different bands (not a biggie; a simple relay does the trick)

Example:

·         Quarter wave 160 m Edington Loop

·         Quarter wave 80-meter Edington Loop

·         Quarter wave 40-meter Edington Loop On 80 meters this loop can be operated as a 1/8 wave loop

Full wave Loops: Loop circumference ~ 1 Lamda

Benefits:

·         Simple concept; just ‘wire in the air’

·         Simple construction; just ‘wire’ (no caps, no tuning elements intrinsic to the antenna)

·         Can be used on several octave related bands

Drawbacks:

·         Lot size determines the lowest band for which this antenna is usable

·         For the ‘Top Band’ ¼ Lambda per side approx. ~125 feet - TOTAL loop circumference over 500 feet!

·         Needs some height to be effective

Example:

References:

1) Tuneable Coupled (Multi-) Mode Small Antennas — CFA, CFL, EH etc? (pdf file)
By Professor Mike Underhill -G3LHZ

2) All sorts of small antennas – they are better than you think – heuristics shows why! (pdf file)
By Professor Mike Underhill - G3LHZ