Antenna Theory

From The Radio Amateur's Handbook, Fifty-Fifth Edition, 1978
Chapter 21 -- Radiation and Antennas

   A fundamental principle of nature is that changes in magnetic, electric, and gravitational fields cannot propagate at infinite velocity. In the case of ordinary circuits, the effects of this finite propagation velocity can usually be neglected. This is because circuit dimensions are small enough so that the fields produced in one part of the circuit almost cancel those produced in other parts. On the other hand, radiation would be impossible if it were not for the fact that the speed of light is finite.

   The manner in which energy is radiated from a circuit can be illustrated with the aid of Figs. 1 and 2. In Fig. 1, a dc voltage of 4 is applied to the upper electrode in the picture and -4 to the bottom one. Such a configuration is called a dipole although the electrodes do not have to be long thin conductors, necessarily. The actual shape is unimportant for this discussion except for the requirement of symmetry about the xy axis. The upper and lower members also have to be identical. Consequently, the field lines and equipotential contours will be symmetrical about xy. A three-dimensional view can be visualized by rotating the plot shown in Fig. I about this axis.

   At distances far removed from the dipole, "distortion" produced by the conductor shape becomes negligible. That is, the conductors can be considered as two point charges. The fields of a configuration of this type are well known and the strength varies as the inverse of the distance cubed. While the analysis only holds for the dc case, it is also reasonably valid for slowly varying ac voltages. However, since the intensity diminishes so rapidly with distance, such fields would not prove very useful for communication purposes. In fact, fields of this type represent energy storage similar to that of ordinary capacitors used in radio work.

Fig. 1 -- Static-field configuration of dipole. Solid lines indicate the direction of electric field and dashed lines show equipotential contours.


   If a rapidly varying ac voltage is applied to the dipole terminals, the plot illustrated in Fig. 1 is altered drastically because of the finite propagation velocity. It takes time for a change in field conditions at the dipole to reach a given point in space. The time interval is equal to the distance (between the dipole and the point) divided by the speed of light. Fig. 2 indicates how the static field is modified by this effect. Instead of building up instantaneously to the pattern of Fig. I, the field follows the moving charges on the dipole.

Fig, 2 - Modification of electric field when an ac voltage is applied to the antenna terminals, Inset shows charge on the dipole as a function of time.

   During the first quarter cycle, as charge builds up on the dipole, the field lines tend to spread out toward the position they would occupy under static conditions (as shown in Fig. 2A). However, during the next quarter cycle, the dipole is being discharged and some of the lines break away to form closed loops (Fig. 2B). The process repeats itself during the next two quarter cycles except that the upper half of the dipole is charged negatively. An illustration of the field plot just before a complete cycle is shown in Fig. 2C.

   On the other hand, if there were no delay effects, the field throughout space would follow the charge changes instantaneously. Once the source was turned off and the dipole discharged, the field would also be zero everywhere. This implies that all of the energy in the field would be returned to the dipole terminals. However, because of the time delay, "past history" is independent of present events. The effects of turning off the source could not propagate fast enough to affect variations in field that had occurred previously. Consequently, fields such as those of Fig. 2 will continue to propagate out into space in much the same manner as water waves on a pond are formed when an object that disturbs the surface is dropped in. The implication here is that energy is irretrievably lost from the dipole. This lost energy represents electromagnetic energy in the form of radiation such as radio or light waves.

Radiated Power

   Along with the energy lost or radiated from the dipole, a certain fraction is also returned during each rf cycle. Consequently, the fields near the antenna represent both energy storage and radiation components. However, at points far enough away, the fields can be considered to belong only to the radiation component. Since it is assumed that the rf energy propagates at the same velocity in all directions, the power flowing through any imaginary sphere of a set concentric with an origin at the antenna must be the same. This is illustrated by the dashed circles in Fig. 2C. The circles represent contours of constant delay time. . . .

Fig. 3 -- Transverse electromagnetic wave. Solid lines represent direction of electric field and dashed lines show direction of magnetic field. There are no field components in direction of power flow (arrow labeled S).

Radiation Resistance

   Considerable confusion can result if such factors as antenna gain, directivity, efficiency, size, and aperture are not regarded in their proper contests. For instance, experienced amateurs might balk at the fact that the directivity of a half-wavelength dipole is only 1.64 compared with 1.5 for a short dipole giving a difference of 0.4 dB. This would imply that a four-foot dipole on 80 meters for instance, would be just as good as a half-wave version which would correspond to approximately 135 feet! The old amateur-radio adage, "the bigger the better," in regard to antenna performance would seem to be misleading.

   However, another factor must be taken into account and that is the radiation resistance "seen" by the source or transmission line when connected to the antenna terminals. It will be recalled in the discussion concerning the radiation process shown in Fig. 2, energy was lost because some of the field lines broke away from the dipole and were propagated into space. In essence then, a "good" antenna configuration is one where the field extends faraway from the conductors. Considered from a slightly different point of view, antenna dimensions and associated field shape should be large at the wavelength of operation so that delay effects in the fields caused by currents on different parts of the conductors will be maximum. For instance, the parallel-plate capacitor shown in Fig. 5 would be a relatively poor radiator. Most of the field is confined between the plates and only the "fringing" field at the edge of the plates and beyond would contribute to a radiation component. (An exception would be if the dimensions of the capacitor were so large the circumference approached an appreciable fraction of a wave-length. Then, the radiation would be from the fields across the slot and the entire system would be a "dual" of an antenna made from solid conductors. This effect is often of an undesirable nature in regard to designing effective shields out of sheets that are not completely bonded or soldered together. "Leakage " of If energy will occur from the cracks.) A similar effect occurs with the so-called inverted-vee dipole. Instead of a straight dipole, the conductors are run off at an angle from the feed point. This permits the use of one high support with the ends of the antenna tied to lower supports near the ground. However, if the angle of the vee at the apex becomes too sharp, the fields tend to cancel rather than radiate.

   The result of any of these effects is that the radiation resistance of the antenna becomes very low in value. This means that a high current is required to produce the same radiated power in comparison with an antenna with a higher value of radiation resistance. As a consequence, the effect of losses in such devices as matching networks, ground systems, and similar areas where currents are required to produce the radiated field become significant. A point may be reached where more power is dissipated in the losses than radiated. In cases where the losses can be neglected, the gain and directivity are the same. But while the directivity may remain the same, the antenna gain will decrease as the effect of antenna loss increases. As pointed out earlier, a small-sized antenna has the capability of being a good performer, but considerable care must be taken to insure losses do 'not offset any advantages. Also, since the ratio of energy stored to energy lost in the form of radiation (per rf cycle) is- greater in a smaller antenna compared to a larger one (at the same frequency), the bandwidth becomes smaller. The ratio of energy stored to energy lost will be recognized as being proportional to the Q of ordinary circuit theory. Hence, a small antenna represents a high-Q system and less frequency variation is permitted before retuning will be required.



  Antenna Impedance

  Technically, antenna impedance is the ratio at any given point in the antenna of voltage to current at that point. Depending upon height above ground, the influence of surrounding objects and other factors, our quarter wave antenna with a near perfect ground exhibits a nominal input impedance of around 36 ohms. A half wave dipole antenna is nominally 75 ohms while a half wave folded dipole antenna is nominally 300 ohms. The two previous examples indicate why we have 75 ohm coaxial cable and 300 ohm ribbon line for TV antennas.

  A quarter wave antenna with drooping quarter wave radials exhibits a nominal 50 ohms impedance, one reason for the existence of 50 ohm coaxial cable.

  The quarter wave vertical antenna

  The quarter wave vertical antenna is usually the simplest to construct and erect although I know a great many people who would dispute that statement. In this context I am speaking of people (the majority) who have limited space to erect an antenna.

This image is copyright © by Ian C. Purdie VK2TIP - a quarter wave vertical antenna with drooping radials
  Figure 1. - a quarter wave vertical antenna with drooping radials

  In figure 1 we have depicted a quarter wave vertical antenna with drooping radials which would about   45 degrees from horizontal. These 45 degree drooping radials simulate an artificial ground and lead to an antenna impedance of about 50 ohms.

A quarter wave vertical antenna could also be erected directly on the ground and indeed many AM radio transmitting towers accomplish this especially where there is suitable marshy ground noted for good conductivity. An AM radio transmitting tower of a quarter wave length erected for say 810 Khz in the AM band would have a length of nearly 88 metres (288') in height.

This image is copyright © by Ian C. Purdie VK2TIP - a marconi antenna
  Figure 2. - a marconi antenna

  The formula for quarter wave is L = 71.25 metres / freq (mhz) and in feet L = 234 / freq (mhz).   Note the variance from the standard wavelength formula of 300 / freq. This is because we allow for "velocity factor" of 5% and our wavelength formula becomes 285 / freq.

  When a quarter wave antenna is erected and "worked" against a good rf ground(calledMarconi Antenna) the earth provides a "mirror" image of the missing half of the desired half wave antenna.

  In figure 2 above where I have depicted the Marconi Antenna imagine a duplicate of the quarter wave antenna being in existence from the top of the ground and extending down the page. This is the mirror image.

  Half wave dipole antenna

  The half wave dipole antenna becomes quite common where space permits. It can be erected vertically but is more often than not erected horizontally for practical reasons. I gave quite a good example of its use in my paper on radio telescopes from my original site. I have reproduced it in figure 3 below.

This image is copyright © by Ian C. Purdie VK2TIP - a half wave dipole antenna

Figure 3. - half wave dipole antenna

  This particular antenna was dimensioned for use at 30 Mhz. You will note that the left and right hand halves are merely quarter wave sections determined by the formula given earlier. The input impedance (affected by many factors) is nominally 50 ohms.

  As with all antennas, the height above ground and proximity to other objects such as buildings, trees, guttering etc. play an important part. However, reality says we must live with what we can achieve in the real world notwithstanding what theory may say.

  People erect half wave dipoles in attics constructed of fine gauge wire - far from ideal BUT they get reasonable results by living with less than the "ideal". A lesson in life we should always remember in more ways than one.

 Hex Beam


  The folded dipole antenna

  The folded dipole antenna is probably only ever seen as a TV antenna. It exhibits an impedance of 300 ohms whereas a half wave dipole is 75 ohms and I'm certain someone will be alert enough to ask "why 75 ohms, if figure 3 above is 50 ohms?".

Within the limits of my artistic skills I have depicted a folded dipole antenna below.

This image is copyright © by Ian C. Purdie VK2TIP - half wave folded dipole antenna
Figure 4. - half wave folded dipole

 One powerful advantage of a folded dipole antenna is that is has a wide bandwidth, in fact a one octave bandwidth. This is the reason it was often used as a TV antenna for multi channel use. Folded dipole antennas were mainly used in conjuction with Yagi antennas.


  The Yagi antenna

  The Yagi antenna or more correctly, the Yagi - Uda antenna was developed by Japanese scientists in the 1930's. It consists of a half wave dipole (sometimes a folded one, sometimes not), a rear "reflector" and may or may not have one or more forward "directors". These are collectively referred to as the "elements".

This image is copyright © by Ian C. Purdie VK2TIP - the Yagi antenna

Figure 5. - the Yagi antenna

  In figure 5 above I have reprinted a UHF Yagi antenna array from my radio telescopes page. You will note, not altogther clearly.

  However in figure 6 below, which happens to be a photograph of a neighbour's TV antenna, I can clearly point out details of a practical Yagi antenna.

  This particular antenna has been optimised for dual band operation. It is designed to pick up both VHF and UHF transmissions. Because I live in a regional of NSW in Australia, TV antennas tend to be single channel types designed either for higher gain or better directivity. Different examples will be presented later.

This image is copyright © by Ian C. Purdie VK2TIP - a practical Yagi TV antenna

Figure 6. - a practical Yagi TV antenna

  Looking from left to right on this dual band Yagi we have six UHF "director" elements which improve gain and directivity.     Next is the UHF half wave dipole which could have easily been a folded dipole but is in fact a plain half wave dipole.

  The next three much longer elements form a "phased array" for the VHF band. I am unsure of the function of the three remaining smaller elements, information is quite scant here but one would certainly be a UHF "reflector". Likely the other two also fulfill this function also.

  Note: This is a horizontally polarised antenna and is orientated roughly NNW, 315 degrees.

You will notice the effect of very strong storms from the sea have had in bending the second larger elements. In my locality storms are a problem but not as much as roosting parrots such as large sulphur crested cockatoos.

  UHF Yagi antenna

  In the photograph in figure 7 below you can see a classic UHF Yagi antenna. It has a total of nineteen "elements" comprising seventeen "directors", a fancy folded dipole with a "low-noise mast head amplifier" and a "reflector".

This image is copyright © by Ian C. Purdie VK2TIP - a vertically polarised UHF Yagi antenna

Figure 7. - a vertically polarised UHF Yagi antenna

This is a a vertically polarised UHF Yagi antenna and it is orientated WSW or 225 degrees. It does in fact pick up signals about 100 Km or 60 mile distant from Sydney.

This is the very same antenna I was suggesting to be used in the radio telescope array I depicted in figure 5 above.


Stacked half wave dipoles or a collinear array


The majority of TV antennas in my retirement village are stacked half wave dipoles. These consist of four sets of a half wave dipole and a reflector only, but mounted one above another. These antennas owe their origin to the days we only had VHF TV in the area. Surprising with the introduction of UHF they continued to function quite well in picking up UHF as well. This particular antenna is my one and I've never had the need to go to a UHF antenna. The top two elements normally are home to roosting "top knot" pidgeons, a pigeon native to Australia.
This image is copyright © by Ian C. Purdie VK2TIP - four stacked half wave dipoles collinear antenna
Figure 8. - four stacked half wave dipoles collinear antenna

To the left of the photograph are the "reflectors" and to the right are the four vertically stacked half wave dipoles. The wires connecting each half wave dipole are done in a "phased way". This comprises a collinear antenna array and is so arranged for improved gain.

Note this antenna is horizontally polarised.

The N4GG Array

Need a simple, nearly invisible wire antenna with reasonable gain, low angle radiation (for DXing) and multiband capabilities? Check out this long-overlooked design that requires no antenna tuner. PDF file.


Terminated Tilted Folded Dipole

Now here is a little gem. The terminated tilted folded dipole is bound to give a "rush of blood to the head" of any avid DX'er (that means long distance -dx- receive / transmit enthusiast).

The terminated tilted folded dipole is somewhat similar to the half wave folded dipole in figure 4 above yet the claims for its performance are quite astonishing. The terminated tilted folded dipole is claimed to have a bandwidth of something like 5 or 6 to one, been extensively tested and adopted by the US Navy, easy to construct from readily available materials and, has a feedpoint impedance of around 300 ohms.

This image is copyright © by Ian C. Purdie VK2TIP - Terminated Tilted Folded Dipole
Figure 11. - Terminated Tilted Folded Dipole


The dimensions "A" and "B" for a terminated tilted folded dipole are as follows:

Each leg "A" = [ 2 X pi ( 15.25 / Fo )] and;

Distance "B" = [ 2 X pi ( 0.915 / Fo )]

where in both instances 2 X pi = 6.28 and Fo is in Mhz.

There seems to be some debate about the exact formula, my friend L. B. Cebik (see next) says:

"The "Wide-Long" version coincides with standard construction formulations, since the antenna is about 300/F(MHz) long and 10/F(MHz) wide. (Excessively fussy cutting formulas for this antenna are largely superfluous, since strict resonance is not in question)."

My late friend L. B. Cebik (see later) has modeled this antenna. Unfortunately since his passing the original article is no longer available on his site. A copy exists here: Modeling the T2FD

Further comprehensive details on the claims for the amazing terminated tilted folded dipole antenna and its construction can be found at:




 80 meter Isotron


ARRL's Antenna Handbook is highly recommended.