Hansen-Woodyard condition

This title will undoubtedly raise a few eyebrows. As stated in many respectable textbooks, surface waves do not radiate—period. What is not always emphasized is the fact that the theory for surface waves in general is based on a two-dimensional model like for example an infinitely long dielectric coated wire. And as discussed in this chapter infinite array theory may reveal many fundamental properties about arrays in general but there are phenomena that occur only when the array is finite. The fact is that surfaces waves are associated with element currents. They will radiate on a finite structure in the same manner an antenna radiates, namely by adding the fields from each column in an end-fire array. Numerous examples of this kind of radiation pattern will be shown in Chapter 4. They are typically characterized by having a mainbeam in the direction of the X axis that is lower than the sidelobe level. The reason for this abnormality is simply that the phase delay from column to column exceeds that of the Hansen-Woodyard condition by a considerable amount [29]. They also have a much lower radiation resistance. 

Recall that 5 = 1.0 corresponds to the endfire condition, leading to a gain significantly below that of a Yagi-Uda array tuned to maximum gain (it is close to the Hansen-Woodyard condition). 

P.S. Actually, it is (or should be) well known that maximum directivity and gain are not necessarily obtained for the in-phase condition. For example, an endfire array of dipoles attains maximum endfire gain when the phases of the elements are delayed 3/A radians per element in addition to the simple endfire condition. This is called the Hansen-Woodyard condition [105]. The W8JK antenna by Kraus is another example [106]. 

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See also in sourсe #XX -- [ , , ]

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