**Plate Dipoles and Prismatics Revisited**

**by David J. Jefferies and Dan Handelsman**

n
last month's issue No. 60 of * antenneX* for April 2002, we wrote
about the striking similarity in the simulated performance of plate dipoles, and their
two-dimensional equivalents, the P2s. That article, now in Archive V, is entitled Plate
Dipoles and Prismatics.

This month we consider the conditions under which antennas, which have sheet metal elements, may be replaced by their skeleton equivalents and we discuss the reasons for the wide-band performance of such antenna structures.

**DEVICE LIMITS**

A caveat for the reader is in order here. We are trying to get to grips with the general
principles which underpin the design of wide-band antennas, as opposed to compact
antennas. For those people who desire both properties in a single device, we should say
here that we think this is unlikely to be realized, at least for sensible antenna
efficiency. However, our current understanding of the kinds of wide-band antennas reported
here and last month helps to guide the design of other structures which may have similar
properties. Also (see the end of the article) we can compare and contrast these antenna
designs with highly resonant narrow-band antennas and come to some conclusions about the
likely designs of these different classes of antenna.

As usual we start from the premise that it is the conduction current that radiates. More specifically, before allowing for phase shifts and the phase delay to the far field point, the contribution to the E field at a remote point is proportional to the (size of the current) times (the element of length in which it flows) times (the frequency). To perform a proper sum, or integral, we must remember that these little contributions to the electric field must add vectorially; they have magnitude and phase, and it is the length of the resultant vector along the curve of E-field contributions that determines the size of the radiated field.

The total length of the resultant E vector (given these phase shifts) must be less than the total length of all the little component vectors if they were added together in a straight line. Thus, if we increase the size of the antenna compared to a wavelength, a law of diminishing returns sets in, as the extra elements of length of antenna rod in which the current flows don't give us a corresponding increase in the length of the resultant E vector. That is why antenna performance, radiated power and radiation resistance improve with size only up to the half-wavelength limit. Beyond this limit we find the current on the structure reverses and the little elemental E field contributions subtract from the total E vector instead of adding to it, which is what we want.

**ANTENNA LENGTH SYNTHESIS**

If we can't increase the length of the antenna, how about increasing the size in the other
two space dimensions? In essence, this is what Handelsman's Pn antennas do. In the case of
the P2 antenna and the plate dipole, we are only using one of the two available extra
dimensions.

The main feature of the plate dipole and the prismatic polyhedral antennas, which we would like to explain, is the exceptionally wide bandwidth. By bandwidth, we mean the frequency range over which the antenna structure (at its driving point terminals) is a reasonable match to a transmission line having a fixed characteristic impedance. For convenience we have taken the VSWR < 2 criterion as defining the bandwidth of these kind of antennas. Of course, this is an arbitrary choice; one could equally argue for another figure of merit, or even that the antennas are of arbitrarily small bandwidth as they are only exactly matched at a spot frequency. The VSWR = 2 level corresponds to a power reflection coefficient of 1/9th or about 11%. Thus over the bandwidth we have defined, more than 88% of the incident power is radiated by the antenna.

We still leave ourselves free to choose the characteristic impedance of the main feed line to maximize this defined bandwidth. We are not restricting ourselves to 50, 75, or 300 ohms only, although when the antenna is designed it may be desirable and necessary to choose one of these impedances for practical realizations.

The driving point impedance has a real part, comprising the radiation resistance plus
the loss resistance due to antenna heating, both of which may be transformed up or down by
a transmission line section or by a filter section comprising antenna inductance and stray
capacitance as DJ wrote about in an earlier
article for * antenneX*. The driving point impedance also has
an imaginary part which will go to zero at resonance. Even though the imaginary part of
the driving point impedance has gone to zero, this does not mean there is no stored
reactive energy in the antenna environs. However, for these wide-band antennas we see
cyclic variations in the imaginary part of the driving point impedance, and it is
reasonable to assume that at the maxima of these variations, the reactance times the
square of the driving current is a measure of the stored energy in the antenna near-field
region.

To achieve the VSWR<2 target, we need both the real and imaginary part of the driving point impedance to stay within certain bounds. Anything that reduces the size of the maximum and minimum values of the excursions will help. That includes reducing the amount of stored energy in the near-field region as a proportion of the radiated energy per radian of oscillation. In these figures we examine the fluctuations in R and X over a wide bandwidth, 200-1600MHz, for several antenna structures of interest.

Below, we show a dipole that is made from 1.5 cm diameter tubing and is 50 cms long. We notice that the excursions in R and X become smaller at the higher order resonances.

**Figure 2**

Next we look at the equivalent plate dipole. This antenna is 40 cms long by 10 cms wide and constructed from 1.5 cm diameter tubing with a space between top and bottom plates of 4.8 cms. The sheet-metal dipole is approximated by a grid of tubes that has a mesh size such that the lengths of the sides of the holes always exceed the rod diameter. We notice how the excursions of R and X at the lower resonances are tamed, which leads us to expect wider bandwidth.

**Figure 3**

Now we look at the two-dimensional prismatic polyhedral antenna, the P2, which has the same peripheral dimensions as the plate dipole above. It is striking how similar the R and X behavior is to the model of the plate dipole.

**Figure 4**

What we observe, in both the plate dipole scenario and in the prismatic polyhedral antennas, is that the bandpass encompasses both the "resonant fundamental" and its " harmonics". The excursions in driving point reactance for these antennas are much less than for their resonant dipole and monopole wire cousins.

Provided these excursions are sufficiently small, we satisfy the VSWR<2 criterion over a wide range of frequency. This does not mean the antennas are "perfectly wide-band", as if they were entirely non-resonant. Neither do they approximate to LPDA antennas.

Here is a figure showing the VSWR of the dipole of figure 2, when fed by a 75-ohm cable.

**Figure 5**

And below, we show the corresponding VSWR for the plate dipole

**Figure 6**

Finally, we see a very similar response for the VSWR behavior of the P2. All these antennas are fed by 75-ohm cable.

**Figure 7**

Now, as Handelsman has found, the currents in the vertical, radiating, elements of a Pn antenna (n = 2,3,4,5) are copies of each other, exactly the same at a given frequency and distance from the feed no matter which leg they are in. This "symmetry" means there can be little or no horizontal electric field or stored electric field energy in the space between the radiators. In effect, they act as if they were elements of a barrel antenna made of sheet metal void of any internal electric field. In addition, in the Pn antenna and presumably the plate dipole, the length of transmission line from main feed to radiating element transforms the intrinsic radiation resistance of the element by an amount that depends on the length of the section in wavelength measure.

As far as the intrinsic radiation resistance of the section is concerned, various factors enter. As the frequency increases, the contribution to radiated field strength rises as we saw above. However, the currents cycle along the structure with the wavelength, which is getting shorter. These two effects cooperate to keep down the excursions in the real part of the driving point impedance.

For, as the frequency gets larger, we have seen that the radiation (electric field strength) from a given size of current over a given length increases proportional to frequency Thus, one expects the power to increase as omega^2 (the square of the radiated field strength) and thus the radiation resistance contribution as omega^2 also as it is proportional to the total power which is radiated. However the length over which the current is in the same direction is shortening as 1/omega (the wavelength gets less as the frequency goes up) which decreases the radiated power by the same factor omega^2. Thus we get cancellation in the frequency dependence of the radiated power and the Rrad stays roughly the same as the frequency rises. There are similar arguments for the stored energy and therefore the frequency dependence of the reactance.

Just how the frequency variation of the intrinsic radiation resistance of the elements combines with the transformation effect of the horizontal feed sections remains unclear to us at the time of writing. What seems to happen is that the main feed driving point real impedance cycles as does the reactance. That strongly indicates to us resonant behavior in the feed and structure whose dimensions remain fixed as the wavelength changes by a factor of up to 4:1.

The local stored electromagnetic energy is found from integrating the square of the electric field, and the square of the magnetic field, over the volume of the near field region. As already remarked, the stored electric field energy is rather small inside a Pn, and also it is zero on the surface of a metal sheet such as might comprise a plate dipole, or even a sheet equivalent of a Pn polyhedral antenna.

Now, in a Pn the star junctions at top and bottom force a current zero on their wires by symmetry. As the frequency is raised the adjacent nulls (which are half a wavelength away along the wires from the star points) run up and down the vertical radiating sections. There will be current reversals on the structure at high frequencies that reduce the radiation resistance as the total current length contributing to the radiated power lessens. This effect serves to lessen the swings in radiation resistance. The current reversals also limit the local stored energy, and so we do not see the extremes of reactance that are apparent in a simple rod dipole.

The similarity between sheet metal antennas and the Pn antennas in behavior stems from the fact that energy is not stored in the space between the wires of the Pn frame, neither is it stored when this space is filled with a sheet of metal. We therefore arrive at the substantive equivalence between sheet metal antennas and their wire frame equivalents - where the wire frame is run along the boundary of the sheet.

Also, we might consider the Pn antennas to consist of n dipoles all having series inductance and capacitance which mutually cancel at resonance. Above resonance, the Pn behaves as if it has inductance L/n, where L is the inductance of a single elemental dipole. For the same total current in the structure, the stored magnetic energy is reduced. Another way of seeing this is that each elemental rod carries current I/n (there are n rods in total) and that makes the total stored nearby energy proportional to nL (I/n)^2, or n times less than that for the single rod antenna. Of course, as the frequency on a simple rod dipole is increased further towards the next overtone, the reactance falls again to zero. But in the Pn, our thesis is that the maximum excursion of this reactance is a lot less than it is in the simple rod, for the reasons stated.

Again, the same effect comes in to play when we model a sheet metal antenna by a collection of parallel wires.

Thus we have reason to believe that both the stored electric energy, and the stored magnetic energy, are less for the Pn prismatics and by extension for the plate dipole and the plate equivalents to the Pn for n>2.

Now, not only have we reduced the stored local energy but, by feed transformation, we have put up the radiation resistance. The Q is therefore reduced by a factor of up to n^2 (which is 16 for the archetypical P4 antenna). This makes the structures intrinsically wide-band.

Because the near-field region of the antenna structure extends out to a distance of about lambda/3 from the center and because a plate dipole or Pn antenna has diameter which is a significant fraction of this distance (and, as remarked, there is not much stored energy inside the region delimited by the conductors), most of the electric and magnetic energy outside the structure is associated with the radiating fields and only a little with the local fields.

**To summarize**, a prismatic polyhedral antenna may be regarded as a
skeleton equivalent to a sheet metal antenna. Perhaps it is not surprising that both kinds
of structure share similar properties. The total near-field stored energy is reduced by
splitting up the total antenna current among a number of different paths and also by
distributing the total antenna charge over a larger area of metal. Taken together with the
upwards transformation of radiation resistance, this lowers the Q factor so that the
fundamental and higher harmonic resonances broaden and merge, making the VSWR<2
bandwidth criterion satisfied over a frequency range which may be as high as several
octaves. Here is a plate dipole example.

**Figure 8**

**Now let's consider resonant antennas.** A short monopole above a ground
plane has low radiation resistance as Jefferies wrote about in ** antenneX**
in the article "Radiation Resistance of Wire and Rod Antennas". For this kind of
antenna the Q factor is very high and the bandwidth very small, which is a severe
limitation on their use for communications purposes at medium frequency and at HF. We
understand this to be for the reason that there is much stored energy compared to the
amount of energy radiated per radian of oscillation.

Another class of high Q antenna consists of patch antennas. These store energy in the dielectric between the patch and the ground plane and the radiation resistance is rather small as this energy can only leak out of a little area around the perimeter of the patch. Still another class of high Q antenna is the small tuned loop, which stores energy in the tuning capacitor and in the magnetic field of the loop yet has radiation resistance that decreases sharply (as [diameter/wavelength]^4) as the loop is made smaller.

So we return to the thesis that for wide-band antenna design, we need three factors. Low stored local energy, large radiation resistance (which means size approaching a half-wavelength, and multiple current paths) and the merging of the resulting broadened resonances so that the successive overtones of the antenna response run together. This seems to be most easily achieved by having structures with large surface area, but after Dan Handelsman's great achievement of giving life to the prismatic polygon antenna idea, we were led to realize that these areas of metal may be whittled away inside the perimeter, to leave just a skeletal structure, lightweight and with low wind loading.

**THE BIPLANE**

As an afterthought, George Sharp (KC5MU) invented the biplane compact antenna which may be
regarded as a shrunk, compact, double-sided patch antenna with radiation from the fringing
fields. It is shrunk by tuning the capacitance with an external inductor, which puts up
the field strength between the plates by a factor of Q, and uses air dielectric that
provides for less capacitance than on a classical patch antenna. This antenna
"benefits" (in the parlance of the realtor) from having large areas of metal
that we might expect serve to increase the ratio of radiation resistance to loss
resistance. One of George's biplane pictures appear below.

This antenna radiates from the fringing fields across the gaps between the plates; the
intrinsic radiation resistance is again quite low as for the classical patch antenna, but
this is transformed up by the LC section of the tuning inductor and the plate capacitance
to provide a reasonable match to the feed. We would expect the bandwidth of this antenna
to be quite small; however, the Q factor will be limited by I^R losses to be not more than
a few hundred, and at 80 meters (3.5 MHz), this will give a usable audio bandwidth for
voice communications.** **

Lest it be thought that extending the area of an antenna, particularly if it is
compact, is a panacaea for bandwidth problems, we offer the following caveat: Other
antennas having areas of metal are the CFA, and also the biplane. These are naturally
narrowband antennas, since the dimensions of the metal sheets are very much less than a
quarter wavelength. So we are not suggesting that constructing small antennas from sheets
of metal is necessarily going to be of significant benefit, in all cases.**-30-**

D.Jefferies email

Dr. David J. Jefferies

School of Electronic Engineering, Information Technology and Mathematics

University of Surrey

Guildford GU2 7XH

Surrey, England

Click Here for the Authors' Biography

BRIEF BIOGRAPHY OF AUTHOR

Dan Handelsman, N2DT

Dan Handelsman, N2DT was first licensed as WA2BCG in 1957at age 13. He became interested in antennas at that time when he had to figure out a way to operate from the 6th floor of his apartment house. This resulted in a mobile whip being stuck out from a window without a counterpoise. At that point he became an "expert" in TVI. He was licensed as N2DT in 1977 and is a DX'er and contester. He is now playing with experimental antennas and low power.

Professionally, he is a Pediatric Endocrinologist and holds M.D. and J.D. degrees and is Clinical Professor of Pediatrics at the New York Medical College. As far as his antenna work he is an "amateur" in the truest sense of the word (Dan's words!).

~ antenneX ~ May 2002 Online Issue #61 ~

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