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Practical Log-Periodic Antenna Designs
May 4, 1964 Electronics Magazine

May 4, 1964 Electronics

May 4, 1964 Electronics Cover - RF Cafe[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 hand-held 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 on-hand 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 Log-Periodic Antenna Designs

George J. Monser - RF Cafe

The author:

George J. Monser is an engineering specialist at Sylvania Electronic Systems-West 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.

Log-periodic dipole structure uses transmission-line booms - RF Cafe

Log-periodic dipole structure uses transmission-line 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 log-periodic structure - RF Cafe

Pyramidal log-periodic structure (left) shows basic relation ships between two plates (angleψandαand ratio τ).

Antenna becomes a log-periodic dipole array - RF Cafe

The antenna becomes a log-periodic 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 - RF Cafe

Choice of angular parameters and their effect on antenna directive gain referred to that of a half-wave dipole antenna.

Practical angular parameter variations - RF Cafe

Practical angular parameter variations and their effect on H-plane beamwidth between 3·db points for an antenna having a 60°° E-plane beamwidth.

Chart of basic plate configuration - RF Cafe

Chart of basic plate configuration is developed in normalized form for a 10-to-1 frequency band log periodic antenna employing two similar plates. Length of the lowest frequency element is determined as a quarter-wave 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 - RF Cafe

Illustrative chart shows that when the design ratio is multiplied by itself the number of elements is thinned out (left) by first placing alternate even-ordered elements on the same side of the boom.

Conversion chart shows how the log-periodic rod model - RF Cafe

Conversion chart shows how the log-periodic rod model can be converted to a tooth or profile log-periodic type (left) or to a shark-tooth or zig-zag model, (right).

Chart showing thinned-out plate - RF Cafe

Chart showing thinned-out 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 10-to-1 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 log-periodic 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 plate-separation 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 front-to-back ratios for this type of antenna are generally satisfactory, except at the low end of the band. Units are frequently over-designed to remedy this situation.

The basic design concepts were then re-evaluated 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 10-to-1 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 even-ordered 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 thinning-out 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 log-periodic 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 50-ohm 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 half-wave 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, f0 = 50 Mc; λ0, = 984/50 = 19.7 feet; and λ0/4 = 4.9 feet, which is the value of L0 provided no over-design is used.

The next element, L1 = (18/20) (4.9) = 4.41 feet (where 18/20 are multiplying factors from the left-hand reduced angle a chart. Similarly, L2 = (16/20) (4.9), L3 = (14.4/20) (4.9), etc.

The process is continued until element L20 is obtained. The ratio L20/L0 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, R0 = 2 L0. Similarly, R1 = 2 L1, R2 = 2 L2, 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 half-wave 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 - RF Cafe

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 zig-zag.

Chart for reduced angle α - RF Cafe

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.



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