Q3Antenna And Wave Propagation

(a) Advantages of Array Antennas

Increased directivity/gain: a single antenna element typically has only modest directivity (e.g., a half-wave dipole's directivity is only about 1.64, or 2.15 dB), whereas arranging multiple identical elements into an array, with their individual fields combining constructively in a desired direction, substantially increases the overall directivity/gain achievable from the combined structure — directivity of a uniform array generally increases with the number of elements N and their spacing (in wavelengths), enabling array antennas to achieve the high-gain, narrow-beamwidth performance required for long-distance point-to-point communication, radar, and satellite links, which would be impractical to achieve with any single simple radiating element alone.

Beam-steering capability: by controlling the relative excitation phase applied to each individual array element (rather than physically/mechanically repositioning the antenna structure), the direction of the array's main radiation beam can be electronically steered to point in essentially any desired direction within the array's practical scan range — this electronic beam-steering capability, central to phased-array antenna operation, allows extremely rapid beam repositioning (in microseconds, as needed for scanning radar target tracking) that would be entirely impossible with a mechanically-steered single antenna, and also permits simultaneous or rapidly time-multiplexed multi-target tracking and multi-user beamforming (as used in modern 5G base stations).

Side-lobe level control: by deliberately tapering (non-uniformly weighting) the relative excitation amplitude applied across the array's individual elements (e.g., using a binomial, Dolph-Tchebyscheff, or Taylor amplitude distribution, rather than uniform excitation), the level of the array's unwanted side lobes (secondary radiation peaks away from the main beam direction) can be substantially suppressed compared to a uniformly-excited array, at the cost of some increase in the main beam's width — this side-lobe control capability is essential in radar and communication applications where minimizing interference/clutter/unwanted signal reception from directions away from the intended main-beam direction is important, and is a design freedom available only to multi-element arrays, not to single antenna elements.

No moving parts (for electronic steering): because beam steering in a phased array is achieved purely through electronic control of element excitation phase (via solid-state or ferrite phase shifters), rather than mechanically rotating or repositioning the physical antenna structure, phased array antennas eliminate the need for the bulky, slow, and mechanically-wearing rotating mounts/gimbals required by traditional mechanically-steered dish or reflector antennas — this greatly improves system reliability (fewer moving mechanical parts to wear out or fail), reduces maintenance requirements, and, as noted above, allows vastly faster beam repositioning than any mechanical system could achieve.

Principle of Pattern Multiplication

The principle of pattern multiplication states that the total far-field radiation pattern of an array of N identical, identically-oriented antenna elements is given by the product of the element factor (the individual radiation pattern of a single element in isolation) and the array factor (the pattern that would result from an array of isotropic point sources having the same geometric arrangement, spacing, and excitation amplitude/phase distribution as the actual array):

This principle allows the array factor (governed purely by the number of elements, their spacing, and their excitation amplitude/phase distribution) to be analyzed entirely independently of the specific element type used (dipole, patch, horn, etc.), greatly simplifying both the analysis of existing arrays and the systematic design of new arrays for a desired overall pattern shape, beamwidth, and side-lobe performance.

A further practical benefit of pattern multiplication is that it clarifies how the choice of individual radiating element interacts with the array geometry to shape the overall pattern: since the total pattern is a product of the element factor and the array factor, any direction in which either factor goes to zero produces a null in the overall composite pattern, meaning the designer can deliberately choose an element with a pattern null in a particular direction to reinforce a null that the array factor already produces there, or conversely select an element whose own pattern remains strong in directions where additional array-factor side lobes appear, thereby suppressing those side lobes in the final combined pattern. This decomposition is also what permits antenna engineers to first optimize the array factor alone (choosing N, spacing, and amplitude/phase weighting to meet a target beamwidth and side-lobe specification using the comparatively simple isotropic-source mathematics) and only afterward select or design the physical element (dipole, patch, slot, horn) to be used at each array location, confident that the final composite pattern will simply be the product of the two, provided all elements in the array share an identical orientation and pattern shape — a condition that holds for the great majority of practical uniform arrays.

Radiation Pattern of a 3-Element Array, Spacing lambda/2

For a uniform linear array of N=3 isotropic elements with spacing d=lambda/2 and all elements fed in phase (psi=0, the broadside condition), the array factor is:

The array factor reaches its maximum value (AF=1) at theta=90 degrees (broadside to the array axis, where psi_t=0), and falls to zero (nulls) at angles where 3*psi_t/2 is a non-zero integer multiple of pi but psi_t/2 is not itself a multiple of pi — for this 3-element, lambda/2-spaced broadside array, nulls occur at theta=arccos(2/3)=48.19 degrees and its mirror-image angle 131.81 degrees (measuring from the array axis), while a smaller secondary side lobe appears between the main beam and these nulls.

(b) Numerical: Directivity of Broadside Stacked Antenna

Given: height=10.5 m, length=21 m, operating frequency f=3.5 GHz.

Step 1 - Wavelength:

Step 2 - Aperture area: a broadside stacked antenna array (elements stacked both vertically and horizontally to form a planar radiating aperture) is treated, for directivity calculation purposes, as an aperture antenna with a physical radiating area equal to the product of its height and length:

Step 3 - Directivity: the directivity of an aperture-type antenna is given by the standard aperture-antenna directivity formula:

Substituting A=220.5 m^2 and lambda=0.08571 m:

Step 4 - Directivity in dB:

Result: the directivity of the broadside stacked antenna is D0=377148.20, equivalent to approximately 55.77 dB, a very high directivity value characteristic of a large-aperture antenna structure (220.5 m^2, many wavelengths in extent at 3.5 GHz) — this result illustrates the general aperture-antenna design principle that directivity scales directly with the physical aperture area expressed in square wavelengths (A/lambda^2), meaning either a larger physical aperture or a higher operating frequency (shorter wavelength, for the same physical aperture) both directly increase the achievable directivity, a fundamental trade-off underlying the design of all large aperture-type antennas including stacked dipole arrays, reflector dishes, and phased array panels.