Two Element Horizontal Beams,
Volumes 1 and 2
by L. B. Cebik, W4RNL
Plus 207 Example Antenna Modeling Files,
and design & matching calculators in Quattro Pro & MS Excel-XLS spreadsheets

Volume 1: Phased Arrays
espite the high volume of amateur literature on 2-element horizontal beams, most amateurs do not have a clear set of performance expectations or a general idea of how they actually work. Cebik has divided the general subject into two parts, with Volume 1 devoted to phased 2-element arrays. Not all phased arrays, with both elements supplied energy directly from the source, are (uni-)directional. In fact, bi-directional arrays have a long service history that is far from over. After an introduction to phased arrays, the next two chapters give individual treatment to the famous W8JK flattop array and the equally famous lazy-H array. Both types of antennas are as serviceable today as they were when developed in the 1930s and 1940s.

The remaining 7 chapters provide a step-by-step progression ultimately into the details of phasing two elements to provide an understanding of how these antennas work and the limits of what they can do. The performance limits emerge from models with separate sources for each element. In principle, we can design phased arrays for maximum gain (and very poor front-to-back performance) or for the maximum possible front-to-back ratio (but modest, though usable forward gain). Next come the limits of performance that we can obtain from feeding only one element and developing performance by the geometry of the 2-element array (as a foreshadowing of the detailed analysis of parasitic beams covered in Volume 2).. Since most 2-element phased horizontal arrays use transmission lines to obtain the correct relative current magnitude and phase angle on each element, Cebik next explores the ZL Special array in several configurations, followed by the elements of analysis for the current-phasing conditions. More complex forms of phasing follow, including the HB9CB, the N7CL, and a little used alternative form involving longer elements. All of these arrays use design parameters that set them between the two ends of the performance scale set out in the initial step of the analysis.

The final two chapters cover practical matters, such as extended uses of the 2-element phased array as the driver section of larger beams and the conversion of uniform-diameter elements used in models into stepped-diameter elements actually used in the construction of practical HF beams. (Additional construction suggestions appear in Volume 2, which is devoted to parasitic or Yagi-Uda 2-element beams.)

The volume illustrates that fact that all 2-element horizontal beams are phased arrays, whether we feed both elements or only one of them. The first volume in this 2-volume set contains 217 pages with 170 illustrations and tables. Attached to the volume is a large collection (92) of EZNEC-format models used in the study for use by the reader, either to correlate to the text or to serve as the basis for a practical antenna project.

Volume 2: Parasitic Arrays
overs the performance and dimensional parameters of parasitic beams that have evolved from the initial work of Yagi and Uda in the 1920s. The very first chapter acquaints the reader with the basic and occasionally confusing language applied to the various performance categories applied to directional parasitic arrays, as well as to the fundamental properties of the -λ dipole on which the performance of all 2-element Yagis rests. The next chapter provides an overview of the performance expectations that we can have from full-sze 2-element driver-reflector arrays, the most common form of the beam.

Because radio amateurs are always seeking ways to shrink HF Yagis, the next two chapters examine the performance that we can obtain from various forms of element shortening techniques. Beginning with element end hats, the treatment also explores inductive loading in the form of center and mid-element load positions. It also includes notes on so-called linear loads that in fact are forms of center inductive loading using shorted transmission line stubs to produce the required inductive reactance. Part 1 concludes with a survey of methods used to improve 2-element performance, including the use of driver-director arrays that sacrifice operating bandwidth for added gain and front-to-back ratio.

Part 2 of the volume covers the three most common forms of matching the typically low 2-element Yagi feedpoint impedance to the usual 50-Ω coaxial cable of most amateur installations. Separate chapters look at the theory and practice involved in series matching systems, beta or hairpin matching systems, and the gamma match.

The final part of the volume provides the dimensions and performance details of very useful 2-element beams for each of the 5 upper-HF amateur bands using practical stepped-diameter tubing schedules. The chapter on full-size Yagis uses wide-band driver-reflector designs with a direct 50-Ω feed for each of the three wider bands. For the 2 narrow bands, the chapter provides similar information on driver-director designs and beta matches. The final chapter provides stepped-diameter dimensions for practical Moxon rectangles that save installation space and provide a 50-Ω feedpoint impedance. Within these final two chapters are extensive suggestions for applicable construction techniques. The collection provides the home antenna builder with alternatives to the many published 2-element designs available.

Like Volume 1, Volume 2 includes a collection of antenna models (115), most in EZNEC format, that track the antennas discussed in each chapter. The volume has 236 pages, with over 200 illustrations and tables.

The Author
Considered an expert on antennas, L. B. has published 20+ books with works on antennas for both the beginner and the advanced student. Among his books are two tutorials in the use of NEC antenna modeling software and compilations of his many shorter pieces and some 800 modeling files, all of which are available here in the Shopping Shack. His articles have appeared in virtually every amateur radio publication, with translations of some into several languages. Retired Professor from the University of Tennessee, Knoxville, LB is Technical & Educational Advisor to the ARRL and Technical Editor for antenneX.

Here is an index of the contents found in VOLUME 1



Introduction to 2-Element Arrays 5
Part I: Bi-Directional Arrays  
1 The W8JK "Flat-Top" Array 28
2 The Lazy-H Array 48
Part II: Directional Arrays  
3 The Limits of Performance 71
4 The Limits of Geometric Phasing 95
5 The Limits of a Single Phase Line: The ZL -Special 115
6 The Analysis of the ZL-Special 137
7 Removing the Limits by Element Matching 154
8 Extending the Uses of 2-Element Phased Arrays 176
9 Converting a Uniform- to a Stepped-Diameter Model 200
Other Publications 218

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Here is an index of the contents in VOLUME 2



Introduction to 2-Element Beams


Part I: 2-Element Parasitic Beams  
1 Methods, Units of Measure and the Dipole Standard of Reference 11
2 The Full-Size 2-Element Yagi 31
3 Shortened Dipoles and Capacity Hat Yagis 51
4 Loaded Yagi Elements 71
5 Strategies for Improving Forward and Rearward Performance 93
Part II: Beam-Matching  
6 Series Matching Systems 115
7 Beta/Hairpin Matching Systems 137
8 Gamma Matching Systems 153
Part III: Some Practical HF 2-Element Parasitic Beams  
9 Beams for 20 through 10 Meters 183
10 Stepped-Diameter Moxon Rectangles 209
Other Publications 237

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