May 4, 1964 Electronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Electronics,
published 1930  1988. All copyrights hereby acknowledged.

Designing a
log
periodic antenna is a piece of cake. Just punch in your computer program
(e.g. DIY LPDA Calc) or smartphone app (e.g.
LPDA Designer) a few parameters for
frequency range, power handling, directivity, impedance, etc., and out pops boom
and element lengths, diameters, and spacings  and probably radiation gain
profiles for elevation and azimuth. That is the way it's done today. However,
when Dwight Isbell and Raymond DuHamel of the University of Illinois came up
with the log periodic concept in 1958, they did not have the convenience of a
computer or even a handheld calculator. Slide rules and logarithm tables were
the order of the day. After trudging through the equations for building the
antenna, calculating enough points to plot the radiation pattern on polar
(circular) graph paper could consume the better part of a morning or afternoon.
With any luck you didn't make any mistakes so the onhand data would give you
confidence to build and test your design. Mr. George Monser provides some
background information into log periodic antenna design in a 1964 (only 5 years
since its invention) Electronics magazine article, along with a couple charts that facilitates
the design without making a lot of calculations.
Practical LogPeriodic Antenna Designs
The author: George J. Monser is an engineering specialist
at Sylvania Electronic SystemsWest active in the preparation of technical proposals
and studies dealing in advanced direction finding techniques for which his previous
experience in radar and antenna work has prepared him. He received his Bachelor
of Science degree in Electrical Engineering from Cornell University and his Master
of Science degree in Electrical Engineering from West Virginia University. His list
of published papers includes several that have appeared in Electronics. He is a
registered professional engineer in Arizona and West Virginia.
By George J. Monser
Sylvania Electric Products Co., Mountain View, Calif.
Logperiodic dipole structure uses transmissionline booms that are formed from
6·inch steel tubes. These are tapered down to reduce the wind area by telescoping
in smaller sections of tubing. Wind sails on this type of antenna are necessary
because the centroid of the wind area does not correspond with the center of gravity.
Pyramidal logperiodic structure (left) shows basic relation
ships between two plates (angleψandαand
ratio τ).
The antenna becomes a logperiodic dipole array when ψ, the angle
between plates, is reduced almost to zero, (right). The infinite balun (inset) is
a practical method of feeding the antenna.
Choice of angular parameters and their effect on antenna directive
gain referred to that of a halfwave dipole antenna.
Practical angular parameter variations and their effect on Hplane
beamwidth between 3·db points for an antenna having a 60°° Eplane beamwidth.
Chart of basic plate configuration is developed in normalized
form for a 10to1 frequency band log periodic antenna employing two similar plates.
Length of the lowest frequency element is determined as a quarterwave distance
corrected for velocity factor. Other simplified or specialized configurations are
derived in later figures.
Illustrative chart shows that when the design ratio is multiplied
by itself the number of elements is thinned out (left) by first placing alternate
evenordered elements on the same side of the boom.
Conversion chart shows how the logperiodic rod model can be
converted to a tooth or profile logperiodic type (left) or to a sharktooth or
zigzag model, (right).
Chart showing thinnedout plate that has been simplified by reduction
in the number of radiating elements. Here, the elements to the left of the boom
are dashed.
A graphic technique based upon angular dimensions establishes
gain and beamwidth and converts dipoles to toothed types.
Antennas that exhibit essentially constant performance over a frequency range
of 10to1 are being used increasingly for civil as well as military communications.
Despite this widespread application, simple design data for one of the most useful
types  the log periodic  has not been available until now.
The design constants of such structures, which evolved in a general way from
a basic structure described in the literature nearly a decade ago, can be expressed
in terms of angles. When so defined, the antenna possesses a unique property: The
dimensions of significance are logarithmically related and when an antenna is designed
according to these criteria, it appears electrically similar throughout its operating
band. The only dissimilarities are seen near the band edges. The band edges are,
in turn, delineated by the structure size and the fineness with which the unit can
be fabricated.
The pictorial sketch (right) is generally used as the starting point in classical
discussion of this antenna type. It is termed pyramidal logperiodic because of
its geometry. The two identical structures are said to be set complementary to each
other because if the angle of separation (ψ) between the
plates is made nearly 0° (plates being parallel to each other), the structure
appears as it does at the right of the figure with corresponding elements diametrically
opposite or complementary. A popular feed technique, the infinite balun, is also
shown. The important design parameters illustrated areψthe separation angle
between the plates,αthe spread angle for each plate and τ the ratio between
successive element length or the ratio of successive distances measured from the
apex. A third angle β, not shown, represents a spread angle for each boom in proceeding
from the apex to the rear of the antenna. In general, β is not a significant design
constant.
To find simple design methods, considerable experimental data from many sources
was reviewed. It was seen that, within variational tolerances, antenna gain and
beamwidth could be represented as shown in the graphs (left) that show gain as related
to plateseparation angle. These graphs indicate that several choices are generally
afforded the engineer in selecting his design constants to meet the performance
criteria. Minor lobe structure and fronttoback ratios for this type of antenna
are generally satisfactory, except at the low end of the band. Units are frequently
overdesigned to remedy this situation.
The basic design concepts were then reevaluated and the rest of the charts were
developed. In these charts, combinations of design constants were made that permitted
easy design variations. On each chart, one of the plates like that in the first
illustration, is developed and displayed in normalized form over an approximately
10to1 frequency band.
When the design ratio
τ is multiplied
by itself, the result is equivalent to thinning out the antenna, that is, reducing
the number of its radiating elements. The first step in such a development is shown
above in the illustrative chart (right). Alternate evenordered elements have been
placed on the other side of the boom. A further variation from the basic design
illustrative chart (right) shows that by using a smaller value of
τ with the
other design constants unchanged, fewer elements are required for a given bandwidth.
However, when such a thinningout procedure is applied, the antenna with fewer radiating
elements tends to show more variations in performance across the band.
The illustrations in the conversion chart below show one method for converting
the rod model to provide profile layouts. The areas indicated by the lettered designators
are sometimes completely filled and a small spreading angle β is provided for
each plate. This type of solid geometrical pattern is more familiar at very high
frequencies.
Antenna Impedance
For logperiodic dipole arrays the impedance values range from, about 60 to 100
ohms. Spacing between the feeders (booms) is generally set to give an impedance
in the order of 100 ohms. As
ψ is increased
from 0° to 50°, the impedance increases to approximately 160 ohms. Thus,
although a higher gain appears to be provided for ψ, greater than 0°, a
poorer match (more losses) to a 50ohm line may result, unless a suitable matching
transformer is used. That is, if a matching transformer is not provided, the difference
in the measured gains may not be so great. Two design examples illustrate the use
of these charts.
Frequency range is 6.5 to 40 Mc with a maximum vswr of 2 to 1. A tapered transformer
is used inside one boom.
Design Example 1:
Suppose it is desired to design a receiving antenna to operate from 50 Mc to
400 Mc and provide about 8 db gain referred to that of a halfwave dipole.
From the chart for gain vs separation angle, one suitable set of values is: α
= 60°, ψ= 45°. The value of τ = 0.9 assures reasonable limits on
the impedance fluctuations across the band. Selectingα= .53 0, which allows
some safety in the gain, the chart (above) for reduced angle a can be used.
Then, f_{0} = 50 Mc; λ_{0}, = 984/50 = 19.7 feet; and λ_{0}/4
= 4.9 feet, which is the value of L_{0} provided no overdesign is used.
The next element, L_{1} = (18/20) (4.9) = 4.41 feet (where 18/20 are
multiplying factors from the lefthand reduced angle a chart. Similarly, L_{2}
= (16/20) (4.9), L_{3} = (14.4/20) (4.9), etc.
The process is continued until element L_{20} is obtained. The ratio
L_{20}/L_{0} is slightly less than 50/400, the required frequency
interval.
To find the element locations, measured from the apex, it is observed from inspection
of the reduced angle a chart that the boom multipliers are twice the value of the
element multipliers. Thus for the lowest frequency element, R_{0} = 2 L_{0}.
Similarly, R_{1} = 2 L_{1}, R_{2} = 2 L_{2}, etc.
Design Example 2:
Suppose it is desired to design an antenna to operate from 100 Me to 900 Mc
and provide 6 db gain over a halfwave antenna. From the chart for gain vs separation
angle: α
= 90°, if ψ = 40° and τ = 0.9. Then the basic plate chart is used and the
steps used in example 1 are followed, beginning with a different fo and Ao. Here,
fo = 100 Mc and Ao = 9.84 feet. Also the boom multipliers and the element multipliers
that must be applied are equal so that element locations (measured from the apex)
are equal to the length of the particular element.
For the design from 100 Mc to 500 Me (instead of 900 Me) the smallest frequency
element would occur sooner, leaving a considerable boom length without elements.
This unused boom section can be removed or the design continued above 500 Me as
desired.
Pyramidal log periodic dipole built by Antenna Products Co. for
Project Mercury uses an offset straight element rather than either the common tooth
design or the zigzag.
Chart for reduced angle α. Additional simplification in
a single plate for which the angle α. has been reduced from 90° to 53°
(left) and to 37° (right). Elements to the left of the boom are represented
by dashed lines to the right.
Posted July 11, 2019
