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A microstrip patch antenna separated from a ground plane by a dielectric substrate is fed by a microstrip transmission line and the four vertical dielectric substrate walls serve as the radiating apertures for the energy. There are two apertures on the sides and two apertures at the front and back. The figure below shows the geometry of one aperture..
In this scenario the vector r represents the radiated energy. Θ and Φ represent the direction of this vector expressed in spherical coordinates. The radiation pattern for this geometry may be very accurately determined using numerical methods [10], but to solve for it in closed form requires some assumptions [11]. The general idea is that each radiating aperture may be modelled as a magnetic dipole. This model also assumes the length of the antenna is one-half wavelength, so the fields in the front and back apertures are reversed. Note the feed points are intentionally chosen so higher-order modes are not excited. Given these assumptions, the rectangular radiating apertures reduce to magnetic dipoles, each with the magnetic current
Im.
Applying a far-field approximation, defining V_0=hE_x as the voltage gradient in the slot, and assuming k_0 h≪1 gives the equation for the direction of the radiated energy. Solving this equation for varying values of Θ and Φ generates a plot of the antenna coverage pattern. Figure 5 shows a sample antenna coverage pattern plot. Different antenna configurations produce different plots and multiple antennas may be used in concert. For example, multiple antennas could be arranged linearly, as two-dimensional arrays, meandering lines, etc. [13].
Regardless of whether there are single or multiple antenna elements, a fixed antenna design produces a fixed radiation pattern. Choosing this fixed pattern involves tradeoffs and there will be some places where the antenna is more sensitive than others. For example, the pattern in Figure 5 shows “blind spots” at about +/- 40°. An antenna pattern generally focused in front of the door would typically be less sensitive directly towards the sides of the door and immediately underneath the sensor. To eliminate blind spots and these weaker detection areas, it would be good to be able to steer the radiating energy.
The most recognizably common methods for steering antennas are mechanical, such as by mounting the antenna to a pan and tilt mechanism. The apparent physical configuration of the antenna could also be changed electrically by using high-frequency diodes to short and effectively eliminate antenna elements from the configuration. This can be used to change the radiation pattern or frequency characteristics (or both) of the antenna [12]. Finally, phased array technology may be used to steer the radiation pattern. The idea behind a phased antenna array is that different antenna elements are purposely driven out of phase from one another. For example, Figure 6 shows a linear phased antenna geometry. In this figure the antenna elements are equally spaced a distance, d, apart. θs represents the desired steering angle for the antenna
sensitivity.
The basic calculations to determine the required phase shift between two successive antennas as a function of desired steering angle are straight forward:
x=d〖cosθ〗_s The phase shift caused by the wave having to travel the extra distance x to the next element is:
kx=2π/λ x which gives: ϕ_s=kd〖cosθ〗_s where ϕ_s is the phase shift between two successive antenna elements required to achieve the desired steering angle θ_s
[15].
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