Resonances in Infinite Linear Arrays of Cylindrical Dipoles

Resonances in Infinite Linear Arrays of Cylindrical Dipoles:

A Two-Term Theory Approach

Ioannis Psarros and George Fikioris

Department of Electrical and Computer Engineering,

National Technical University,

9 Iroon Polytechniou street, GR 157-73 Zografou, Athens, Greece.

Email: giannispsar@yahoo.com, Tel: +210 772-2866, Fax: +210 772-2281

Suggested Topic Number: 8 (Antenna Theory and Measurement)

A number of papers (e.g. [1]), as well as two chapters in the recent book [2] are devoted to the phenomenon of resonances in circular arrays of cylindrical dipoles. Only one of the many array elements is driven; near resonance, the single driving-point conductance is very large, while the driving-point susceptance varies rapidly from very large, positive values to very large, negative ones, passing through zero. The distribution of currents around the resonant array can be thought of as a slow traveling wave. In the aforementioned works, the theoretical tool of study is “two-term theory,” which is an approximate solution to the coupled integral equations for the currents along the array elements. Another recent work [3] has indicated that moment-method analyses of resonant circular arrays presents difficulties.

The present paper has two parts. In the first, we extend the two-term theory to apply to infinite linear arrays. This is straightforward except for difficulties arising from the slow convergence of certain infinite summations. These difficulties are successfully dealt with. As a result, the final two-term theory formulas are quite simple in form and do not require much running time when programmed in a computer. (The same is true for the corresponding formulas for finite arrays.)

In the second part, we use the new theory to study resonance phenomena in infinite linear arrays. Two cases are considered, the uniform case, as well as the case of a single driven element. Resonances are seen to occur for short elements, when the inter-element...