Choosing the element spacing in a phased array antenna is a fundamental design decision that involves a direct trade-off between the antenna’s maximum scan angle without generating grating lobes and the overall directivity and physical size of the array. There is no single “perfect” spacing; it’s a balancing act where improving one performance characteristic often comes at the expense of another. The optimal spacing is dictated by the specific application’s requirements for scan range, sidelobe levels, beamwidth, and size constraints.
To understand this trade-off, we first need to grasp the concept of grating lobes. These are unwanted, duplicate main beams that appear in directions other than the intended one when the array is scanned. They occur because the widely spaced elements create ambiguity in the wavefront detection. The condition for avoiding grating lobes for a broadside beam is generally given by d ≤ λ / (1 + |sinθ|), where ‘d’ is the element spacing, ‘λ’ is the wavelength, and ‘θ’ is the maximum scan angle. For a wide scan range, say ±60°, the spacing must be very small, typically d ≤ 0.54λ. If you only need to scan a few degrees off broadside, you can use a larger spacing, closer to a wavelength, without issues.
The most significant trade-off is between scan range and directivity. Let’s break down the two extremes:
Small Element Spacing (e.g., d < 0.5λ)
Pros: This configuration allows for a very wide scan range without the appearance of grating lobes. It’s essential for systems that need to cover a large field of view, such as ground-based radar for air traffic control or satellite communication terminals tracking moving satellites. The close packing also helps in controlling sidelobe levels, which is critical for reducing interference and improving target discrimination in radar.
Cons: The primary drawback is mutual coupling. When elements are very close together, the electromagnetic fields of each antenna element strongly interact with its neighbors. This changes the input impedance of each element, which can lead to mismatched power and reduced efficiency. It also makes the array’s behavior more complex to predict and requires sophisticated matching networks. Furthermore, a densely packed array has a smaller physical aperture for a given number of elements, resulting in a wider beamwidth and lower directivity. This means the beam is less “sharp” and has less gain. Finally, a high-density array is more expensive and complex to build due to the large number of elements and the associated transmit/receive (T/R) modules packed into a small area.
Large Element Spacing (e.g., d > 0.7λ)
Pros: The biggest advantage is higher directivity and gain for a given number of elements. With elements spread out, the array’s effective aperture is larger, producing a narrower, more powerful beam. This is desirable for long-range applications like astronomical radio telescopes or strategic radar systems where maximum power projection is key. Larger spacing also reduces mutual coupling, simplifying the design and improving impedance matching and bandwidth. From a cost and complexity perspective, fewer elements are needed to cover a large physical area, reducing the number of expensive T/R modules.
Cons: The major, and often unacceptable, drawback for scanning arrays is the emergence of grating lobes when the beam is steered away from broadside. These lobes represent a massive loss of energy into unwanted directions, drastically reducing the gain in the intended direction and causing false targets in radar systems. The scan range is therefore severely limited. Additionally, with fewer elements, it becomes more difficult to achieve low sidelobe levels using common amplitude tapers (e.g., Taylor or Chebyshev distributions), potentially increasing susceptibility to jamming or interference.
The following table summarizes these key trade-offs based on spacing:
| Element Spacing (d) | Primary Advantage | Primary Disadvantage | Typical Applications |
|---|---|---|---|
| < 0.5λ | Wide scan range (±60° or more), low sidelobes | High mutual coupling, lower gain, higher cost/element density | Airborne radar, satellite communications, electronic warfare |
| ~0.5λ to 0.7λ | Good balance of scan range (±45° to ±50°) and gain | Moderate mutual coupling, design complexity for optimization | Multi-function radars, 5G base stations |
| > 0.7λ to 1.0λ | High gain and directivity, low mutual coupling | Grating lobes appear at low scan angles, limited scan range | Fixed-beam or limited-scan systems, radio astronomy |
Beyond scan angle and directivity, spacing impacts several other critical performance metrics. One is bandwidth. An array’s impedance bandwidth is affected by mutual coupling. While larger spacing reduces coupling and can potentially widen the bandwidth, the overall bandwidth is also limited by the electrical phase shift across the array as frequency changes. For wideband systems, the spacing choice becomes even more critical to avoid beam squint (where the beam points in different directions at different frequencies).
Another consideration is beamwidth. The Half-Power Beamwidth (HPBW) for a large linear array is approximately HPBW ≈ 50.8° * (λ / L), where L is the total length of the array (L = N*d for N elements). If you increase the spacing ‘d’ while keeping the number of elements ‘N’ constant, the array length L increases, and the beamwidth narrows. However, if you keep the physical size of the array constant and increase the spacing, you are forced to use fewer elements (N = L/d), which can actually widen the beamwidth. This illustrates how interconnected these parameters are.
The choice of element type also interacts with the spacing decision. For example, using wider bandwidth elements like Vivaldi or spiral antennas can tolerate different mutual coupling regimes than simpler patch antennas. The design of Phased array antennas must therefore be a holistic process, where the element design and the array lattice are co-optimized. Furthermore, the arrangement of elements isn’t always a simple rectangular grid. Triangular lattices are often used because they allow for slightly larger element spacing (approximately 15% larger) for the same grating lobe performance compared to a rectangular grid, leading to a more efficient use of the aperture area.
In practice, for most electronic scanning systems, a spacing around half a wavelength (d ≈ λ/2) has become a common compromise. It provides a reasonable scan volume of about ±60 degrees from broadside (in the principal planes) before grating lobes appear at the horizon, while offering a good balance of gain, beamwidth, and manageable mutual coupling. This is why you see this spacing so frequently in literature and commercial systems. However, pushing the boundaries of performance—whether for ultra-wideband systems, extremely low sidelobes, or very wide scan angles—requires deviating from this rule of thumb and carefully navigating the intricate trade-offs outlined here.