Introduction to Traveling-Wave antennas.pdf

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2 Introduction to TWAA periodic leaky-wave antenna structure is one that consists of a uniform structurethat supports a slow (non radiating) wave that has been periodically modulatedin some fashion. Since a slow wave radiates at discontinuities, the periodic modulations(discontinuities) cause the wave to radiate continuously along the length ofthe structure. From a more sophisticated point of view, the periodic modulation createsa guided wave that consists of an infinite number of space harmonics (Floquetmodes). Although the main (n = 0) space harmonic is a slow wave, one of the spaceharmonics (usually the n = −1) is designed to be a fast wave, and hence a radiatingwave.A typical example of a uniform leaky-wave antenna is a rectangular waveguidewith a longitudinal slot. This simple structure illustrates the basic properties commonto all uniform leaky-wave antennas.√The fundamental TE 10 waveguide mode is a fast wave, with β = ko 2 − ( ) 2πalower than k o . The radiation causes the wavenumber k z of the propagating modewithin the open waveguide structure to become complex. By means of an applicationof the stationary-phase principle, it can be found in fact that:βk o=cv ph= λ oλg ≃ sin θ m (1)where θ m is the angle of maximum radiation taken from broadside. As is typical fora uniform LWA, the beam cannot be scanned too close to broadside (θ m = 0), sincethis corresponds to the cutoff frequency of the waveguide. In addition, the beamcannot be scanned too close to endfire (θ m = 90 ◦ ) since this requires operation atfrequencies significantly above cutoff, where higher-order modes can propagate, atleast for an air-filled waveguide. Scanning is limited to the forward quadrant only(0 < θ m < π ), for a wave traveling in the positive z direction.2Figure 1: Slotted guide (patented by W. W. Hansen in 1940)This one-dimensional (1D) leaky-wave aperture distribution results in a “fanbeam” having a narrow beam in the xz plane (H plane), and a broad beam in thecross-plane. A pencil beam can be created by using an array of such 1D radiators.Unlike the slow-wave structure, a very narrow beam can be created at any angleby choosing a sufficiently small value of α. A simple formula for the beam width,European School of Antennas
3 Introduction to TWAmeasured between half power points (3dB), is:1∆θ ≃L(2)λ ocos θ mwhere L is the length of the leaky-wave antenna, and ∆θ is expressed in radians. For90% of the power radiated it can be assumed:L≃ 0.18αλ o k o⇒ ∆θ ∝ α k oSince leakage occurs over the length of the slit in the waveguiding structure, thewhole length constitutes the antenna’s effective aperture unless the leakage rate is sogreat that the power has effectively leaked away before reaching the end of the slit.A large attenuation constant implies a short effective aperture, so that the radiatedbeam has a large beamwidth. Conversely, a low value of α results in a longeffective aperture and a narrow beam, provided the physical aperture is sufficientlylong.Since power is radiated continuously along the length, the aperture field of a leakywaveantenna with strictly uniform geometry has an exponential decay (usually slow),so that the sidelobe behavior is poor. The presence of the sidelobes is essentially dueto the fact that the structure is finite along z.When we change the cross-sectional geometry of the guiding structure to modifythe value of α at some point z, however, it is likely that the value of β at that pointis also modified slightly. However, since β must not be changed, the geometry mustbe further altered to restore the value of β, thereby changing α somewhat as well.In practice, this difficulty may require a two-step process. The practice is then tovary the value of α slowly along the length in a specified way while maintaining βconstant (that is the angle of maximum radiation), so as to adjust the amplitude ofthe aperture distribution A(z) to yield the desired sidelobe performance.We can divide uniform leaky-wave antennas into air-filled ones and partiallydielectric-filled ones. In the first case, since the transverse wavenumber k t is then aconstant with frequency, the beamwidth of the radiation remains exactly constantas the beam is scanned by varying the frequency. In fact, since:where:cos 2 θ m = 1 −( βk o) 2(3)k 2 o = k 2 t + β 2 ⇒( βk o) 2= 1 −(ktk o) 2⇒ cos θ m = k t⇒ ∆θ ≃ 2πk o k t L = λ cLEuropean School of Antennas
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