School of Electrical Engineering EI2400 Applied Antenna Theory Lecture 10: Leaky wave antennas
Leaky wave antenna (I) It is an antenna which is made of a waveguide (or transmission line) which leaks progressively the transmitted fields. KTH School of Electrical Engineering www.ee.kth.se 2
Leaky wave antenna (II) They continuously loose energy due to radiation. The fields decay along the structure in the direction that they wave travels. The earliest example of such an antenna is a rectangular waveguide with a continuous slit cut along its side. (Hansen 1940) KTH School of Electrical Engineering www.ee.kth.se 3
Attenuation of the waves Since part of the propagated waves are radiated, the intensity of the waves inside of the waveguides is attenuated with the distance. KTH School of Electrical Engineering www.ee.kth.se 4
Attenuation of the waves Since part of the propagated waves are radiated, the intensity of the waves inside of the waveguides is attenuated with the distance. KTH School of Electrical Engineering www.ee.kth.se 5
Radiation and losses Because of the leakage, the leaky waveguide has a complex propagation wave number, with a phase constant β and a leakage constant α. α is large or small depending on whether the leakage per unit length is large or small. - A large α implies that the large leakage rate produces a short effective aperture, so that the radiated beam has a large beamwidth. - Conversely, a low value of α results in a long effective aperture and a narrow beam, provided the physical aperture is sufficiently long. KTH School of Electrical Engineering www.ee.kth.se 6
Directivity versus size A typical leaky-wave antenna might be about 20 wavelengths long, so that the beamwidth of the radiation would be about 4 or so if the beam direction is about 45 from the leaky waveguide axis. 1 L / r cos 0 KTH School of Electrical Engineering www.ee.kth.se 7
Direction of radiation (I) The angle of radiation is determined by the phase of the wave which is propagating inside of the waveguide. γ Propagating wave (β 2 ) Propagating wave (β 1 ) cos 0 1 / 2 KTH School of Electrical Engineering www.ee.kth.se 8
Direction of radiation (II) Because the phase constant β changes with frequency, the beam direction also changes with frequency. f 1 f 2 The leaky-wave antenna can be used to scan by varying the frequency. TE 10 f 3 KTH School of Electrical Engineering www.ee.kth.se 9
Direction of radiation (III) All leaky-wave line sources can scan in principle from broadside to end fire. In practice, however, you cannot get too close to end fire or to broadside, but how near those limits can be approached depends on the specific structure. f 1 f 2 f 3 cos 0 1 / 2 KTH School of Electrical Engineering www.ee.kth.se 10
Uniform implementation A hole (or a number of holes) is made in a conventional waveguide: KTH School of Electrical Engineering www.ee.kth.se 11
Periodic implementation We can design the leaky wave by a periodic repetition of metallic strips. Difference between uniform and periodic leaky-wave antennas: - The dominant mode on the former is a fast wave that therefore radiates whenever the structure is open. - On the other hand, the dominant mode on a periodic leaky-wave antenna is a slow wave that does not radiate even though the structure is open. KTH School of Electrical Engineering www.ee.kth.se 12
Periodic implementation The condition to have a leaky wave radiation is: d d 2 n n 0 n 0 2 n / d When the periodic array of strips is added, the periodicity introduces an infinity of space harmonics KTH School of Electrical Engineering www.ee.kth.se 13
Side lobes Side lobe levels are only produced when the structure is finite: 10 150 F. Schwering and S. T. Peng, Design of Dielectric Grating Antennas for Millimeter Wave Applications, IEEE Trans. Microwave Theory Tech., vol. MTT-31 (February 1983): 199 209. KTH School of Electrical Engineering www.ee.kth.se 14
Amplitude Tapering A structure with a large aperture length has both a high radiation efficiency and small sidelobes. - But the aperture efficiency is very poor in that the directivity will be much lower than a uniformly illuminated aperture of the same length. Therefore, in practice, the aperture is usually tapered so that the attenuation constant α is a function of z, in order to realize a specified aperture illumination. G. Goussetis, V. Fusco, J.L. Gomez-Tornero, M. Vigueras and A. Martinez-Ros, LEAKY WAVE ANTENNAS. KTH School of Electrical Engineering www.ee.kth.se 15
Examples (I) Long Slits in Rectangular Waveguide: - The slit is shown tapered (in exaggerated fashion) to remind us that in the design the slit width is varied to control the sidelobes in the radiation pattern. KTH School of Electrical Engineering www.ee.kth.se 16
Examples (II) Closely Spaced Holes in Rectangular Waveguide: - Since the holes perturb the initially closed guide much less than the long slit does, the resulting value of α is much smaller. - It can be used to obtain a very narrow radiated beam. KTH School of Electrical Engineering www.ee.kth.se 17
Examples (III) Array of Closely Spaced Wide Transverse Strips: - The antenna consists of a parallel-plate waveguide operated in its first higher-order (TE11) mode, with its upper plate composed of an array of closely spaced transverse strips. KTH School of Electrical Engineering www.ee.kth.se 18
Examples (IV) Periodic Dielectric Waveguides: - Periodic dielectric waveguides are uniform dielectric waveguides with a periodic surface perturbation. KTH School of Electrical Engineering www.ee.kth.se 19
Rotationally symmetric leaky waves One of the main differences between this type of structure and the ones considered previously is that the leaky wave on this structure is a two-dimensional (2D) cylindrical wave, which propagates outward radially from the source along the interface. The beam may be a pencil beam at broadside, or a conical beam pointing at an angle θ. KTH School of Electrical Engineering www.ee.kth.se 20