#### Phased Array Antenna

Figure 1: left two antenna elements fed in phase, right two antenna elements fed out of phase

Figure 1: left two antenna elements fed in phase, right two antenna elements fed out of phase

## What is a phased array antenna?

#### Phased Array Antenna

A phased array antenna is an array antenna whose single radiators can be fed with different phase shifts. As a result, the common antenna pattern can be steered electronically. The electronic steering is much more flexible and requires less maintenance than the mechanical steering of the antenna.

#### Functional principle

The principle of this antenna is based on the effect of interference, i.e. a phase-dependent superposition of two or (usually) several radiation sources. It can be observed that in-phase signals (same color in Figure 1) amplify each other and counter-phase signals cancel each other out. So if two radiators emit a signal in the same phase shift, a superposition is achieved - the signal is amplified in the main direction and attenuated in the secondary directions. Here in the left radiator group in Figure 1 both radiators are fed with the same phase. The signal is amplified in the main direction therefore.

In the second graphic in Figure 1, the signal from the upper radiator is transmitted phase-shifted by 22° (i.e., slightly delayed) than from the lower radiator. Therefore, the main direction of the signal emitted in common is slightly steered upwards.

Figure 1 shows radiators without reflectors. Therefore, the back lobe of the antenna pattern is as big as the main lobe. However, the back lobe has also steered upwards. Tip: Take a look at the image in the enlarged view and pay attention to the differences in the radiation characteristics of the lower radiator when switching the phase shifter.

Figure 2: Electronic swiveling of the antenna beam,
left: boresight, right: steered

If the signal to be transmitted is now routed through a phase-regulating module, the direction of radiation can be controlled electronically. However, this is not possible indefinitely, because the effectiveness of this antenna arrangement is greatest in a main direction perpendicular to the antenna field, while extreme tilting of the main direction increases the number and size of the unwanted sidelobes, while at the same time reducing the effective antenna area. The sine theorem can be used to calculate the necessary phase shift.

Any type of antenna can be used as a radiator in the phased array antenna. Significantly, the single radiators must be controlled with a variable phase shift and thus the main direction of the radiation can be changed continuously. To achieve high directivity, many radiators are used in the antenna field. The antenna of the AN/FPS-117, for example, consists of 1584 radiators whose received signal is still combined in an analog way to the antenna pattern. More modern multi-function radar sets, on the other hand, use the digital beamforming during the reception.

• high antenna gain with large side-lobe attenuation
• very fast change of beam direction (in range of microseconds)
• high beam agility
• arbitrary space scanning
• freely selectable dwell time
• multi-function operation by simultaneous generation of multiple beams
• failure of some components does not result in a complete system failure.
• limited scanning range (up to max. 120° in azimuth and elevation)[1]
• Deformation of the antenna pattern during beam steering
• low frequency agility
• very complex structure (computer, phase shifter, data bus to each radiator)
• high costs (still)

Notes:

1. The limitation of the scanning range can be overcome with a three-dimensional radiator distribution.
This arrangement of the radiators got the name crow’s nest antenna.
2. Inspired by this animation, Arthur Morales, an engineer at Embraer, developed a demonstration program: mlago.dev

#### Possible Arrangements

Figure 3: Linear array of a phased array antenna

Figure 3: Linear array of a phased array antenna

##### Linear Array

These phased array antennas consist of lines, which are commonly controlled by a single phase shifter. (Only one phase shifter is needed per group of radiators in this line.) A number of linear arrays arranged vertically on top of each other form a flat antenna.

• Disadvantage: beam steering only in a single plane;
• Examples given:

Figure 4: planar array of a phased array antenna

Figure 4: planar array of a phased array antenna

##### Planar Array

These phased array antennas consist completely of single elements with a phase shifter per element. The elements are arranged like a matrix, the flat arrangement of all elements forms the entire antenna.

Figure 5: Frequency Scanning Array

Figure 5: Frequency Scanning Array

##### Frequency Scanning Array

The frequency scanning array is a special case of the phased array antenna, in which the beam steering is controlled by the transmitter’s frequency without use of any phase shifter. The beam steering is a simple function of the frequency. This type of phased array antenna was often used in older radar sets.

A vertical antenna array is fed serially by a so called snake feed. At the main frequency F1, all radiators get a part of the power of the same phase through structurally identical detours, which cause a phase shift of n · 360°. All radiators therefore radiate with the same phase. The resulting beam is thus perpendicular to the antenna’s plane.

If the transmitter’s frequency is increased by a few percents, however, the constructively defined length of the detour lines is no longer correct. At a higher frequency, the wavelength decreases and the detour line is now a bit too long. There appears a phase shift from one radiator to the next radiator. The first radiator radiates this few percent earlier than the next neighboring radiator, etc. The resulting beam for the F2 frequency is thus steered upwards by the angle Θs.

Although this type of beam steering is very simple, it is limited to a few permanently installed frequencies. In addition to the susceptibility to interference, there are even more limitations to be accepted, e.g. this radar set cannot use pulse compression because its bandwidth is too low.

Feed systems

#### Calculation of the phase shift

How large must be the phase shift x = Δφ from one radiator to the next radiator to achieve a desired deflection angle?

A linear arrangement of isotropic single radiators is considered.

Between the radiators, between the respective beam of the deflection angle with the applied phase shift, a right-angled triangle can be drawn, whose shorter side lies on the beam. The hypotenuse is the distance between two radiators. The third side is an auxiliary line perpendicular to the beam direction of the previous radiator.

main direction
phase shifters

Figure 6: graphic derivation of the formula

main direction
phase shifters

Figure 6: graphic derivation of the formula

x = d · sin ΘS

(1)

This distance x can be set in relation to the wavelength:

(2)

• Δφ = phase shift between two successive elements
• d = distance between the radiating elements
• Θs = beam steering

Both equations together are the solution:

(3)

 Example given: A radar set operates at a wavelength of λ = 10 cm. The distance between the radiators is d = 15 cm. The delays caused by the feedline, we can neglect temporarily. The angle to be steered should be Θs= 40°. Task: How large must the phase shift φ8  of phase shifter no. 8 (outside left) be in order to achieve this angle?
 We start with the determination of the phase shift x from one radiator to the next radiator. Because of the angle function we need a calculator: Δφ =(360°·15 cm/10 cm)·sin(40°) = 347.1°. This means that radiator no. 8 needs the phase shift φ8  = 7 · 347,1 = 2429.7°. Due to the periodicity of the sinusoidal function, a phase shift of n· 360° = 0° is obtained. Therefore we can subtract 360° from the result until there is an angle between 0° and 360° and thus obtain a phase angle of φ8  = 269,7° for phase shifter no. 8 (outer left). However, no phase shifter will be able to realize this as accurately as this. With a 4-bit phase shifter, the phase shift can be made in steps of 11.25°. So in practice, a phase angle of φ8  = 270° will be used.

With serial feeding, part of this phase shift is already realized by the delay time in the feed line. In practice, an individually calibrated table with the phase shift data for each desired angle exists in the computer for the antenna control (extra for each transmission frequency).

By the way, Figure 6 also shows the reason why a phased array antenna focuses worse at larger angles. The auxiliary line perpendicular to the adjacent radiator is always smaller than the radiator distance d at an angle that differs from the main beam direction. If the distance “seen” from the deflected beam direction is smaller than the optimum distance d, the antenna quality must deteriorate, which results in a wider antenna pattern.