![]() ![]() This case also shows a full 180° shift between elements provides a theoretical 90° shift in beam direction. For the case of d = λ/2, there is an approximate 3 to 1 slope near boresight, which is the π multiplier in Equation 2. Some interesting observations can be made from these graphs. This will maximize the antenna gain in that direction.įor a better appreciation of how the phase shift varies with the beam direction (θ), these equations are plotted for a variety of conditions in Figure 4. So, if our wavefront is arriving at θ = 30º, then if we shift the phase of the neighboring element by 95º, we will cause the individual signals of both elements to add coherently. If a 10.6 GHz wavefront is arriving at 30º from mechanical boresight, then what is the optimal phase shift between the two elements? Consider two antenna elements spaced 15 mm apart. Let’s work out an example with these equations. If the spacing between elements is exactly one half of the signal wavelength, then this can further be simplified to: The equations for ΔΦ can then be defined relative to θ, as shown in Figure 3c and repeated in Equation 1. If we think of L as a fraction of the wavelength, then a phase delay could be substituted in for that time delay. The time delay to steer our beam is equal to the time it will take for the wavefront to traverse that distance, L. This allows us to compute L, the delta distance of wave propagation, as L = dsin(θ). In Figure 3b, we see that the sum of θ + φ = 90 o. The beam is pointed in a direction off boresight, θ, which is an angle, φ, from the horizon. beam steering angle.įigure 3a defines the trigonometry between those elements, with each element separated by a distance (d). Where ΔΦ is the phase shift between those adjacent elements. To visualize the phase shift needed for beam steering, a set of right triangles can be drawn between adjacent elements, as shown in Figure 3. Phased array concept using RF phase shifters. ![]() A positive angle θ is defined to the right of boresight, and a negative angle is defined to the left of boresight. Note that we define the boresight direction (θ = 0º) as perpendicular to the face of the antenna. phase shift in the section on beam squint, but for now let’s look at a phase shift implementation, and then derive the calculation for beam steering with that phase shift.įigure 2 shows this phased array arrangement using phase shifters rather than time delay. We will discuss the impact of time delay vs. But time delay can also be emulated with a phase shift, which is common and practical in many implementations. ![]() In a phased array, time delay is the quantifiable delta needed for beam steering. That applied delay now misaligns the phase of the four signals, and the output of the combiner is significantly reduced. In Figure 1b, that same delay is applied however, in this case, the wavefront is perpendicular to the antenna elements. This coherent combining results in a larger signal at the output of the combiner. And in this case, that applied delay causes the four signals to arrive in phase at the point of combination. In Figure 1a, that time delay matches the time difference of the wavefront striking each element. A time delay is applied in the receive path after each antenna element, and then all four signals are summed together. Figure 1 provides a simple illustration of a wavefront striking four antenna elements from two different directions. Beam Directionįirst, let’s look at an intuitive example of steering a phased array beam. These articles are not intended to create antenna design engineers, but rather to help the engineer working on a subsystem or component used in a phased array to visualize how their effort may impact a phased array antenna pattern. As it turns out, there are many analogies between the behavior of phased array antennas and the discrete time sampled systems that the mixed-signal and digital engineers work with every day. As phased arrays begin to include more mixed-signal and digital content, there are many engineers who could benefit from a much more intuitive explanation of phased array antenna patterns. Phased array antenna design is not new, as the theory has been well developed over decades however, most of the literature is intended for antenna engineers well versed in the electromagnetic mathematics. With the proliferation of digital phased arrays in commercial and aerospace and defense applications, there are many engineers working on various aspects of the design who have limited phased array antenna familiarity. Phased Array Antenna Patterns-Part 1: Linear Array Beam Characteristics and Array Factor ![]()
0 Comments
Leave a Reply. |