**4. LWA in microstrip**

Microstrip antenna technology has been the most rapidly developing topic in antennas during the last twenty years [10]. Microstrip is an open structure that consists of a very thin metallic strip or patch of a width, w, separated from a ground plate by a dielectric sheet called substrate (Fig. 9). The thickness of the conductor, t, is much less than a wavelength, and may be of various shapes. The height of the substrate, h, is usually very thin compared to the wavelength (.0003 ≤ h ≤ 0.05 ) [11]. The substrate is designed to have a known relative permittivity, *<sup>r</sup>* , that is homogeneous within specified temperature limits.

Fig. 9. Geometry of a microstrip transmission line.

The antenna can be excited directly by a microstrip line, by a coaxial cable, or a combination of the two. The antenna can also be fed from a microstrip line without direct contact through electromagnetic coupling. Feeding by electromagnetic coupling through an aperture in the ground plane tends to improve bandwidth. To maximize efficiency, the impedance of the feed must be matched to the input impedance of the antenna. There are a variety of stubs, shunts, and other devices used for matching. The major disadvantages of microstrip are lower gain, very narrow bandwidth, low efficiency and low power handling ability. In addition, antennas made with microstrip typically have poor polarization purity and poor scan performance [12].

Operating above the cutoff frequency, the field lines of microstrip extend throughout the substrate as well as into the free space region above the substrate, as seen in Fig. 10. The phase velocity of the field in the free space surrounding the structure is the speed of light, c, and the phase velocity of the field in the substrate is given by Equation (14)

$$w\_p = \frac{c}{\sqrt{\varepsilon\_r}}\tag{14}$$

This difference in phase velocity at the interface between the substrate and free space makes the TEM mode impossible. Instead, the fundamental mode for microstrip is a quasi-TEM mode, in which both the electric and magnetic fields have a component in the direction of propagation. Likewise, a higher order mode in microstrip is not purely TE or TM, but a hybrid combination of the two. The nth higher order mode is termed the *TEn* mode. The fundamental mode of microstrip, as seen in Fig. 10, does not radiate since the fields produced do not decouple from the structure. If the fundamental mode is not allowed to propagate, the next higher order mode will dominate. Fig. 11 shows the fields due to the first higher order mode, *TE*<sup>10</sup> . A phase reversal, or null, appears along the centerline, allowing the fields to decouple and radiate.

called substrate (Fig. 9). The thickness of the conductor, t, is much less than a wavelength, and may be of various shapes. The height of the substrate, h, is usually very thin compared

The antenna can be excited directly by a microstrip line, by a coaxial cable, or a combination of the two. The antenna can also be fed from a microstrip line without direct contact through electromagnetic coupling. Feeding by electromagnetic coupling through an aperture in the ground plane tends to improve bandwidth. To maximize efficiency, the impedance of the feed must be matched to the input impedance of the antenna. There are a variety of stubs, shunts, and other devices used for matching. The major disadvantages of microstrip are lower gain, very narrow bandwidth, low efficiency and low power handling ability. In addition, antennas made with microstrip typically have poor polarization purity and poor

Operating above the cutoff frequency, the field lines of microstrip extend throughout the substrate as well as into the free space region above the substrate, as seen in Fig. 10. The phase velocity of the field in the free space surrounding the structure is the speed of light, c,

*p*

*v*

*r c*

(14)

This difference in phase velocity at the interface between the substrate and free space makes the TEM mode impossible. Instead, the fundamental mode for microstrip is a quasi-TEM mode, in which both the electric and magnetic fields have a component in the direction of propagation. Likewise, a higher order mode in microstrip is not purely TE or TM, but a hybrid combination of the two. The nth higher order mode is termed the *TEn* mode. The fundamental mode of microstrip, as seen in Fig. 10, does not radiate since the fields produced do not decouple from the structure. If the fundamental mode is not allowed to propagate, the next higher order mode will dominate. Fig. 11 shows the fields due to the first higher order mode, *TE*<sup>10</sup> . A phase reversal, or null, appears along the centerline,

and the phase velocity of the field in the substrate is given by Equation (14)

, that is homogeneous within specified temperature limits.

) [11]. The substrate is designed to have a known

to the wavelength (.0003

relative permittivity, *<sup>r</sup>*

scan performance [12].

Fig. 9. Geometry of a microstrip transmission line.

allowing the fields to decouple and radiate.

≤ h ≤ 0.05

Fig. 10. Field pattern associated with the fundamental mode of microstrip.

Fig. 11. Field pattern associated with the first higher order mode of microstrip.

Recently, there has been significant interest in the microstrip leaky-wave antenna which utilizes a higher order radiative microstrip mode. Since Menzel in 1979, published the first account of a travelling wave microstrip antenna that used a higher order mode to produce leaky waves [13], many microstrip leaky-wave antenna designs incorporating various modifications have been investigated. The design of Menzel antenna [13], can be seen in Fig. 12. Menzel's antenna uses seven slots cut from the conductor along the centerline to suppress the fundamental mode allowing leaky wave radiation via the first higher order mode. Menzel's antenna has been analyzed by a host of researchers over the past 25 years [14] and its performance is known and reproducible. Instead of transverse slots, we can uses a metal wall down the centerline of the antenna to block the fundamental mode. Symmetry along this metal wall invites the application of image theory. One entire side of the antenna

Fig. 12. Menzel's original antenna [13].

is now an image of the other side, making it redundant and unneeded. This property allows to design the resulting antenna half of the width of Menzel's antenna, as shown in Fig. 13.

Fig. 13. Half Width Leaky Wave Antenna.

As mentioned the microstrip structures do not radiate for the fundamental mode, therefore, a higher order mode must be excited to produce leaky waves. This method of producing radiation by exciting higher order modes in a transmission line has been documented since the 1950's [6]. By the 1970's, rectangular waveguides, circular waveguides, and coaxial cables were in use as leaky traveling wave antennas. However, until Menzel, the jump to microstrip had not been made. By looking at a cross section of microstrip excited in the fundamental mode, the E field is strongest in the center and tapers off to zero at the sides, as depicted in Fig 10. If the electric field down the centerline is suppressed, the fundamental mode will be prohibited, forcing the energy to propagate at the next higher mode, *TE*<sup>10</sup> . As seen in Fig. 11, *TE*10 mode causes E to be strongest at the edges. Menzel attempted to force the *TE*10 mode using several means. Feeding two equal magnitude waves 180° out of phase with a "T" or "Y" feed produced *TE*10 as desired, but did not fully eliminate the foundamental mode. Easier to produce and providing an even better response was given using transverse slots down the centerline (Fig. 12). The multiple feeds were not necessary to produce the *TE*10 mode when the fundamental mode was suppressed. Menzel demonstrated that the beam angle can be predictively steered by input frequency if the electrical length of the antenna is at least 3 . If the length is less than 3 , too little of the incident wave is being radiated and a resonance standing wave pattern is forcing the beam toward broadside. Qualitative analysis shows that the beamwidth of Menzel's antenna is not frequency dependent, however, it is inversely related to length. The 3 dB beamwidth approaches 10° for electrical length of over 6 and approaches nearly 90° for fractions of a wavelength. Menzel's gain varied from 7 dB for l = 0.2 to 14 dB for l = 4 . 7 dB is comparable to a similar sized resonant antenna. An antenna longer than l = 4 would have an even higher gain as the radiation aperture increases. Lee notes that Menzel assumed that his antenna should radiate simply because the phase constant due to his operating frequency was less than 0*k* [15]. If Menzel had considered the complex propagation constant, he would have realized that his antenna was operating in a leaky regime. The length would need to be roughly 220 mm, or more than twice as long as his design, to

is now an image of the other side, making it redundant and unneeded. This property allows to design the resulting antenna half of the width of Menzel's antenna, as shown in

As mentioned the microstrip structures do not radiate for the fundamental mode, therefore, a higher order mode must be excited to produce leaky waves. This method of producing radiation by exciting higher order modes in a transmission line has been documented since the 1950's [6]. By the 1970's, rectangular waveguides, circular waveguides, and coaxial cables were in use as leaky traveling wave antennas. However, until Menzel, the jump to microstrip had not been made. By looking at a cross section of microstrip excited in the fundamental mode, the E field is strongest in the center and tapers off to zero at the sides, as depicted in Fig 10. If the electric field down the centerline is suppressed, the fundamental mode will be prohibited, forcing the energy to propagate at the next higher mode, *TE*<sup>10</sup> . As seen in Fig. 11, *TE*10 mode causes E to be strongest at the edges. Menzel attempted to force the *TE*10 mode using several means. Feeding two equal magnitude waves 180° out of phase with a "T" or "Y" feed produced *TE*10 as desired, but did not fully eliminate the foundamental mode. Easier to produce and providing an even better response was given using transverse slots down the centerline (Fig. 12). The multiple feeds were not necessary to produce the *TE*10 mode when the fundamental mode was suppressed. Menzel demonstrated that the beam angle can be predictively steered by input frequency if the

incident wave is being radiated and a resonance standing wave pattern is forcing the beam toward broadside. Qualitative analysis shows that the beamwidth of Menzel's antenna is not frequency dependent, however, it is inversely related to length. The 3 dB beamwidth

an even higher gain as the radiation aperture increases. Lee notes that Menzel assumed that his antenna should radiate simply because the phase constant due to his operating frequency was less than 0*k* [15]. If Menzel had considered the complex propagation constant, he would have realized that his antenna was operating in a leaky regime. The length would need to be roughly 220 mm, or more than twice as long as his design, to

comparable to a similar sized resonant antenna. An antenna longer than l = 4

. If the length is less than 3

and approaches nearly 90° for fractions of a

to 14 dB for l = 4

, too little of the

. 7 dB is

would have

Fig. 13.

Fig. 13. Half Width Leaky Wave Antenna.

electrical length of the antenna is at least 3

approaches 10° for electrical length of over 6

wavelength. Menzel's gain varied from 7 dB for l = 0.2

radiate at 90% efficiency. Radiation patterns in Menzel's paper clearly show the presence of a large backlobe due to the reflected traveling wave.

Now this class of printed antennas that is particularly well suited for operation at mmwave frequencies, alleviate some of the problems associated with resonant antennas since they provide higher gain, broader bandwith performance, and frequency scanning capabilities. These microwave and millimeter leaky wave antennas, have the same properties of the waveguide leaky wave antennas described previously. In addition, when opening a waveguide to free space, a discrete spectrum is not enough to express an arbitrary solution [16].

In fact, when considering a closed region, all characteristic solutions, individuated by the associated eigenvalues, constitute a complete and orthogonal set of modes, whose linear combination can express any field satisfying boundary conditions. As soon as the region is not perfectly bounded, an arbitrary field solution cannot be expressed only using discrete eigenmodes but, generally, a continuous spectrum of modes, which don't necessarily have finite energy (e.g.: plane waves), must be considered, too.

Fortunately, for leaky wave antennas, an approximation that uses particular waves, called leaky, can be used instead of the continuous spectrum. Moreover, leaky waves are well described by dispersion constants (i.e.: leakage and phase constants) that strongly affect the radiated beam width and elevation.
