**Prismatic Polyhedron Antenna Measurements
at Low GHz Frequencies
David J. Jefferies
D.Jefferies
email**

he Prismatic polyhedral class of
antennas was developed in 2000 and 2001 by Dan Handelsman, N2DT, who holds the patent on
this class of antennas. It has been discussed in the pages of *antenneX* in various articles, but mainly in the
context of simulation "virtual experiments".
The following articles are of especial interest:

#57 From the Shack: A New Antenna -
The Prismatic Polygon by Dan Handelsman |

#01 Archive V: Prismatic
Rectangle on 80 Meters by Dan Handelsman |

#18 Archive V: Creating
Ultra Wideband Antennas by Dan Handelsman |

#32 Archive V: Practical
Wideband HF Antennas by Dan Handelsman |

#49 Archive V: Plate
Dipoles and Prismatics by Dan Handelsman & David Jefferies |

#56 Archive V: Plate
Dipoles and Prismatics - 2 by David Jefferies & Dan Handelsman |

* To recap*,
this class of antennas offers wide bandwidth, up to 5:1 in frequency range (for a P6), and
a reasonable match to a 50 or 75 ohm feed. The antennas have nearly circular radiation patterns in
azimuth, and although they can squint at the top end of the frequency range, their
elevation patterns are also most often benign.

So that we can be aware of what we are
talking about, four antennas in this class, called a P1, P2, P3, and P4, designed for
frequencies around 1500MHz, are shown in the photograph in **Figure 1**. Notice that the P1, which has just one
vertical radiator, is just a dipole. You may click on each of the "P" versions
in Figure 1 for a larger view of each one. The scales shown in the pictures are in cm.

In this short report, we present the results of construction and measurement of a range of antennas for the low GHz band of frequencies, where mobile telephones operate. To cover the range of frequencies for a tri-band mobile phone, we need a bandwidth of nearly 3:1. This is easily achieved by most of the antennas in this class that we investigated.

Dan Handelsman was commissioned to construct a P4 antenna and send it for measurement. His study using the simulations indicated that the design and construction was going to be quite critical. As a result, we went ahead and built our own range of antennas, and discovered, perhaps serendipitously, that the fabrication of wide-band antennas of this type is not especially critical. This relaxation in the tight tolerances that are suggested by the simulations is not unexpected, and is commonplace in simulation exercises which seem to provide overly restrictive construction goals. When the antenna design is constructed, one can find performance which exceeds that indicated from extrapolation of simulation information.

While I went on an extended summer trip to Australia, my MSc student, Peter Apalos, was given the task of constructing some of the designs and measuring their bandwidth and properties on a network analyser whose upper frequency reached 3GHz. Thus, the measurements reported here are the (mostly unaided) efforts of Apalos and are condensed and adapted from a report he wrote in partial fulfillment of the requirements for an MSc at the University of Surrey in summer 2002.

To keep the report short, we present photographs of each of the individual antennas followed by a plot of their VSWR performance up to 3GHz, which was the limiting frequency of the network analyser used to take the data. In each case the reference impedance level was 50 ohms, and the antennas were each fed by an unbalanced 50 ohm coaxial cable through a BNC socket.

**P1** shows the reference
dipole. The rod diameter is 6 mm and the overall length is 96.5 mm, plus or minus 2 mm. It
is soldered to a standard BNC connector, 50 ohms characteristic impedance. The
corresponding VSWR plot is shown in **Figure 2**.
We notice the minimum VSWR is 1.3:1 which puts the resonant characteristic impedance of
this fat dipole at about 50*1.3 = 65 ohms, which is about what we would expect for a
dipole having rods of this diameter. For a thin dipole we would have expected the resonant
impedance to be closer to 72 ohms. We also notice the large bandwidth between VSWR=2
points on the curve. This bandwidth is 404 MHz and the centre frequency is 1500 MHz, so
the percentage fractional bandwidth is nearly 27%. We recall that at VSWR = 2, eleven
percent of the power incident on the antenna is reflected, and 89% is transmitted; that
is, it is radiated.

**P2** shows the antenna,
which was made from 1.2-cm diameter rod. Various other diameters of rod were used to
construct P2 antennas, but this 1.2 cm rod version performed best in the measurements
which are shown in **Figure 3**. The construction
details are as follows: the height of the antenna is 11.3, plus or minus 0.2 cm between
rod centrelines; the width of the antenna is 4.1 cm, plus or minus 0.2 cm between rod
centrelines; the transmission line is made from 0.3 cm diameter rod with 1.0 cm spacing,
and each length of line is 1.8cm long from the BNC connector at the centre to the edge of
the main rod. In **Figure 3**, the VSWR=2 crossing
points are at 900 MHz and 2820 MHz, which makes the ratio of top frequency to bottom
frequency 3.13 to 1.

**P3** shows a photograph
of the antenna constructed on a triangular base. In this case the rod diameters were 0.6
cm. The overall height was 10.5 cm, plus or minus 0.2 cm, between the centrelines of the
triangular frame rods, and the spacing of the radiators (parallel vertical rods) was 4.0
cm, plus or minus 0.3 cm. The transmission line was made from 0.1-cm diameter wire, spaced
by 0.9 cm, plus or minus 0.2 cm. The lengths of the lines were 2.5 cm, plus or minus 0.3
cm. **Figure 4** shows the VSWR plot for this
antenna. The network analyser top frequency did not encompass the upper VSWR=2 crossing
point. The VSWR=2 crossing at the lower frequency was 784 MHz so the ratio of top
frequency to bottom frequency is greater than 3.8 to 1, and probably greater than 4 to 1.

**P4** shows a photograph
of the (hastily constructed) antenna made as an afterthought when time had nearly run out
on the project. This antenna was significantly more difficult to construct than the others
in the sequence. The end footprint should have been a square, but in this case turned out
to be rectangular with dimensions between rod centrelines of 4.3 cm by 3.8 cm, again plus
or minus 0.2 cm on each measurement. The height was again 10.5 cm plus or minus 0.2 cm.
The transmission lines were made from 1-mm diameter wire, spaced 1.0 cm, plus or minus 0.2
cm, and having lengths 2.5 cm, plus or minus 0.3 cm. The rod diameters in the main part of
the antenna structure were again 0.6 cm. The results of measuring this antenna are shown
in **Figure 5**, where we see VSWR=2 crossing
points of 722 MHz and 2396 MHz, which gives a ratio of upper frequency to lower frequency
of 3.32 to 1.

It is possible that this P4 design was in no way optimum. Certainly, it did not follow the inventor's specifications for a scaled P4 antenna at this frequency band. Nevertheless, it is still satisfying that with rather limited attention to accuracy, the antenna produced still has a bandwidth in excess of 3:1 at VSWR=2 with respect to a transmission line feed impedance of 50 ohms.

For all these antennas, SMITH chart plots were obtained showing the characteristic cycling in R and X that Dan Handelsman finds in his simulations. Radiation pattern measurements at the centre of the bands show nearly omnidirectional characteristics in the azimuth plane, and nearly dipole-like characteristics in the elevation plane.

An approximation to the P2 antenna,
consisting of two coupled dipoles, was also constructed and measured and turned out to
provide a VSWR=2 upper/lower frequency ratio of 2.6 to 1. The P2, on the other hand, shows
an extended lower frequency response. However, it is possible that the mere act of
constructing an array of dipoles and letting them couple through the transmission line
feeds, provides a significant degree of broad-banding for the antenna structure, without
the added refinement and complication of top-loading and bottom-loading with the
connecting rods. **-30-**

Dr. David J. JefferiesD.Jefferies email

School of Electronics and Physical Sciences

University of Surrey

Guildford GU2 7XH

Surrey, England

Click Here for the Authors' Biography

~ antenneX ~ November 2002 Online Issue #67 ~

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