3.3 Polarizations

in radial direction. The feeder is a part of RLSA antennas used to feed signals from a

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

Figure 2 shows the wave propagation mechanism including TEM cavity mode and TEM coaxial mode. The feeder placed in the centre of the antenna cavity feeds the electromagnetic power (indicated by the arrows). The feeder is an ordinary SMA feeder, which is modified by adding a head disc. The head disc has a function to convert the electromagnetic power from a TEM coaxial mode into a TEM cavity mode (a radial mode), so that the electromagnetic power fed by the feeder will propagate in a TEM mode and in a radial direction within the antenna cavity.

When the power passes the slot pair, some amount of the power escapes through

the slot pair and radiates as illustrated in Figure 3. Hence, the slot pair can be considered as one antenna element. Since there are many slot pairs (thousands in normal-size RLSA antennas), all the slot pairs will form an array antenna. There-

fore, this is the reason why 'array' word is included in the name of RLSA.

(a) The component of RLSA antennas. (b) The magnified view of the feeder [39].

Illustration of the TEM cavity mode and the TEM coaxial mode [39].

transmission line into the antenna.

3.2 How RLSA antennas work

Figure 1.

Figure 2.

188

A slot pair, which represents a signal source in RLSA antennas, is located in the top surface of the radiating element of a RLSA antenna. A linear polarization in the RLSA antenna can be produced by combining two signals from the slot pair. Figure 4a shows the illustration of the slot pair. The signal from Slot 1 and the signal from Slot 2 have a phase difference of 180° or phi radians since Slot 1 and Slot 2 have the distance of half wavelength (0.5λgÞ to each other. Since the orientation of Slot 1 and Slot 2 is perpendicular to each other, the signals from Slot 1 (at y axis) and Slot 2 (at x axis) are also perpendicular to each other, as shown in Figure 4b.

Figure 4b shows that when Signal 1 is increasing in positive values, Signal 2 is decreasing in negative values. Since their position is perpendicular to each other, the resulting wave becomes a line in Quadrant II. When Signal 1 is decreasing towards zero and Signal 2 is increasing towards zero, the resulting signal will be a line in Quadrant II but with a shorter length compared to the line in the previous case. When Signal 1 is decreasing in negative values and Signal 2 is increasing in positive values, then the resulting signal will be a line in Quadrant IV. When Signal 1 is increasing towards zero and Signal 2 is decreasing towards zero, then the resulting signal will be a line in Quadrant IV but with the shorter length compared to the line in the previous case. Now, we can understand that the resulting signal of Signal 1 and Signal 2 results in a signal that looks like a straight line where the

Figure 3. Illustration of the power escaping from the slot pairs [39].

Figure 4. Polarization establishment in a linearly polarized RLSA [39]. (a) slot pair position (b) signal of each slot.

length changes as a function of time; this is the reason why its name is 'linear polarizations'.

### 3.4 Orientation of the slot in RLSA antennas

Figure 5 shows the position of the slots (indicated by 'A' and 'B') and the squint of the inclination angles of the slots (indicated by 'θ1 and θ2). The slot pair must be located in the correct position on the radiating surface of RLSA antennas. The slot pair must be located in different and unique positions in order to prevent overlapping between them.

Equations (1) and (2) express the squint of the slots obtained by the beamsquint technique [4, 14–17, 39–43]:

$$\theta\_1 = \frac{\pi}{4} + \frac{1}{2} \left\{ \arctan \left( \frac{\cos \left( \theta\_T \right)}{\tan \left( \phi\_T \right)} \right) - \left( \phi - \phi\_T \right) \right\} \tag{1}$$

$$\theta\_2 = \frac{3\pi}{4} + \frac{1}{2} \left\{ \arctan \left( \frac{\cos \left( \theta\_T \right)}{\tan \left( \phi\_T \right)} \right) - \left( \phi - \phi\_T \right) \right\} \tag{2}$$

where θ<sup>1</sup> is the inclination angle of Slot 1; θ<sup>2</sup> is the inclination angle of Slot 2; θ<sup>T</sup> is the beamsquint angle in elevated direction; ϕ is the azimuth angle of Slot 1 and Slot 2 position; and ϕ<sup>T</sup> is the beamsquint angle in azimuth direction.

#### 3.5 Arrangement of slot pairs

Figure 6 shows the geometrical arrangement of a slot pair or also called a unit radiator. The arrangement of the unit radiator in the radiating surface of RLSA antennas must be carefully calculated and drawn since a little deviation of the unit radiator position will rapidly decrease the performance of RLSA antennas.

Based on Figure 6, the distance of a particular unit radiator from the centre point of RLSA antennas is expressed in Eq. (3) [4, 14–17, 39–43]:

$$\rho\_{\rho} = \frac{n\lambda\_{\text{g}}}{1 - \xi \sin \theta\_T \cos \left(\phi - \phi\_T\right)}\tag{3}$$

Equation (4) expresses the distance between two adjacent unit radiators located

Equation (5) expresses the distance between two adjacent unit radiators in a

<sup>S</sup><sup>ϕ</sup> <sup>¼</sup> <sup>2</sup>πλ<sup>g</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>ξ</sup><sup>2</sup> sin <sup>θ</sup><sup>T</sup> <sup>2</sup> p

where λ<sup>g</sup> is the length of the wavelength inside the cavity of RLSA antennas; ε<sup>r</sup> is

The parameters of Sρ, Sϕ, ρρ,ρ1, and ρ<sup>2</sup> are shown in Figure 7. Since the distance from the centre of the unit radiator to Slot 1 or Slot 2 is 'λg=4', Eqs. (5)–(7) express

ρρ<sup>1</sup> <sup>¼</sup> ð Þ <sup>n</sup> � <sup>1</sup> <sup>þ</sup> <sup>q</sup> � <sup>0</sup>:<sup>25</sup> <sup>λ</sup><sup>g</sup>

ρρ<sup>2</sup> <sup>¼</sup> ð Þ <sup>n</sup> � <sup>1</sup> <sup>þ</sup> <sup>q</sup> <sup>þ</sup> <sup>0</sup>:<sup>25</sup> <sup>λ</sup><sup>g</sup>

n is the ring numbers (1,2,3, etc.); q is the integer numbers (1, 2, 3, etc.) that express the distance of the innermost ring from the centre of RLSA antennas; and p

<sup>1</sup> � <sup>ξ</sup>sinθ<sup>T</sup> cos <sup>ϕ</sup> � <sup>ϕ</sup><sup>T</sup> ð Þ (4)

<sup>1</sup> � <sup>ξ</sup>sinθ<sup>T</sup> cos <sup>ϕ</sup> � <sup>ϕ</sup><sup>T</sup> ð Þ (6)

<sup>1</sup> � <sup>ξ</sup>sinθ<sup>T</sup> cos <sup>ϕ</sup> � <sup>ϕ</sup><sup>T</sup> ð Þ (7)

(5)

q p

in two different rings (the distance in the radial direction) [4, 14–17, 39–43]:

<sup>S</sup><sup>ρ</sup> <sup>¼</sup> <sup>λ</sup><sup>g</sup>

same ring (the distance in the azimuth direction) [4, 14–17, 39–43]:

the distance of slots from the centre of antennas [4, 14–17, 39–43]:

the relative permittivity of the cavity of RLSA antennas.

Figure 6.

191

Geometrical arrangement of a unit radiator [39].

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

is the number of unit radiators in the innermost ring.

Where <sup>ξ</sup> <sup>¼</sup> <sup>1</sup> p

Figure 5. Slot pair geometry [39].

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

length changes as a function of time; this is the reason why its name is 'linear

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

pair must be located in different and unique positions in order to prevent

<sup>2</sup> arctan

<sup>2</sup> arctan

2 position; and ϕ<sup>T</sup> is the beamsquint angle in azimuth direction.

point of RLSA antennas is expressed in Eq. (3) [4, 14–17, 39–43]:

Figure 5 shows the position of the slots (indicated by 'A' and 'B') and the squint of the inclination angles of the slots (indicated by 'θ1 and θ2). The slot pair must be located in the correct position on the radiating surface of RLSA antennas. The slot

Equations (1) and (2) express the squint of the slots obtained by the beamsquint

cosð Þ θ<sup>T</sup> tan ϕ<sup>T</sup> ð Þ � �

cosð Þ θ<sup>T</sup> tan ϕ<sup>T</sup> ð Þ � �

where θ<sup>1</sup> is the inclination angle of Slot 1; θ<sup>2</sup> is the inclination angle of Slot 2; θ<sup>T</sup> is the beamsquint angle in elevated direction; ϕ is the azimuth angle of Slot 1 and Slot

Figure 6 shows the geometrical arrangement of a slot pair or also called a unit radiator. The arrangement of the unit radiator in the radiating surface of RLSA antennas must be carefully calculated and drawn since a little deviation of the unit

Based on Figure 6, the distance of a particular unit radiator from the centre

radiator position will rapidly decrease the performance of RLSA antennas.

ρρ <sup>¼</sup> <sup>n</sup>λ<sup>g</sup>

� �

� �

� ϕ � ϕ<sup>T</sup> ð Þ

� ϕ � ϕ<sup>T</sup> ð Þ

<sup>1</sup> � <sup>ξ</sup>sinθ<sup>T</sup> cos <sup>ϕ</sup> � <sup>ϕ</sup><sup>T</sup> ð Þ (3)

(1)

(2)

3.4 Orientation of the slot in RLSA antennas

<sup>θ</sup><sup>1</sup> <sup>¼</sup> <sup>π</sup> 4 þ 1

<sup>θ</sup><sup>2</sup> <sup>¼</sup> <sup>3</sup><sup>π</sup> 4 þ 1

polarizations'.

overlapping between them.

technique [4, 14–17, 39–43]:

3.5 Arrangement of slot pairs

Where <sup>ξ</sup> <sup>¼</sup> <sup>1</sup>

Figure 5.

190

Slot pair geometry [39].

ffiffiffi εr: p

Figure 6. Geometrical arrangement of a unit radiator [39].

Equation (4) expresses the distance between two adjacent unit radiators located in two different rings (the distance in the radial direction) [4, 14–17, 39–43]:

$$S\_{\rho} = \frac{\lambda\_{\text{g}}}{1 - \xi \sin \theta\_T \cos \left(\phi - \phi\_T\right)}\tag{4}$$

Equation (5) expresses the distance between two adjacent unit radiators in a same ring (the distance in the azimuth direction) [4, 14–17, 39–43]:

$$S\_{\phi} = \frac{2\pi\lambda\_{\text{g}}}{\sqrt{1-\xi^2\sin\theta\_T^2}}\frac{q}{p} \tag{5}$$

where λ<sup>g</sup> is the length of the wavelength inside the cavity of RLSA antennas; ε<sup>r</sup> is the relative permittivity of the cavity of RLSA antennas.

n is the ring numbers (1,2,3, etc.); q is the integer numbers (1, 2, 3, etc.) that express the distance of the innermost ring from the centre of RLSA antennas; and p is the number of unit radiators in the innermost ring.

The parameters of Sρ, Sϕ, ρρ,ρ1, and ρ<sup>2</sup> are shown in Figure 7. Since the distance from the centre of the unit radiator to Slot 1 or Slot 2 is 'λg=4', Eqs. (5)–(7) express the distance of slots from the centre of antennas [4, 14–17, 39–43]:

$$\rho\_{\rho1} = \frac{(n - 1 + q - 0.25)\lambda\_{\text{g}}}{1 - \xi \sin \theta\_T \cos \left(\phi - \phi\_T\right)}\tag{6}$$

$$\rho\_{\rho2} = \frac{(n - 1 + q + 0.25)\lambda\_{\text{g}}}{1 - \xi \sin \theta\_T \cos \left(\phi - \phi\_T\right)}\tag{7}$$

Figure 7. Definition of some slot parameters [39].

#### 3.6 Length of slots

The length of the slots on the radiating surface of RLSA antennas must be varied in order to achieve a uniform aperture illumination. The farther a slot from the centre of the antenna, the longer the length of the slot will be. The length of the slot is the function of ρ that is the distance of the slot from the centre of the antennas, as expressed by Eq. (8) [42]:

$$L\_{rad} = \left(4.9876 \times 10^{-3} \rho\right) \frac{12.5 \times 10^9}{f\_0} \tag{8}$$

Equation (9) shows that the amount of the remaining power depends on the number of rings (n), which is also proportional to the number of slots. For small-RLSA antennas, which have a small number of slots, the amount of the remaining power at the antenna perimeter will be high. Part of this remaining power will be reflected back to the feeder and result in a high signal reflection, thus increasing the reflection coefficient. For normal-size RLSA antennas, which have thousands of slots, the remaining power at the antenna perimeter is very small so that its effect to

(a) Top view of RLSA. (b) Cut view of a RLSA antenna and the power flow mechanism inside the RLSA cavity [39].

Figure 9 shows the front cut view of a RLSA antenna and the signal flow within the cavity of the RLSA antenna. The grey arrows represent the signals that flow from the centre of the RLSA antenna to the antenna perimeter, and the black arrows represent the reflected signal from the slots. Figure 9 shows that since the distance between the slots (d) is λg/2, the signal from slot 'A' will travel for λg/2 to reach 'B'. At 'B', some of the signal will be reflected back and travel for another λg/2 to reach 'A'. Therefore, the reflected signal from slot 'A' and slot 'B' will have a different

the signal reflection is neglected.

Illustration of the reflected signals from the slot [39].

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

Figure 8.

Figure 9.

193

4.2 Signal reflection due to the reflected signal from slots

The formula in Eq. (8) is an approximate formula. To get an accurate formula, we need to do some measurements and experiments.

### 4. Reflection in small-RLSA antennas

#### 4.1 Signal reflection due to remaining power

The power (P) comes from the feeder, which is located at the centre of the antenna, and flows towards the antenna perimeter, as illustrated in Figure 8b. When the power passes the slots, some amount of the power radiates through the slots. The power inside the cavity will decrease every time the power passes the slots and will continue to decrease until the power reaches the antenna perimeter. Equation (9) expresses the remaining power (PR) at the antenna perimeter [42]:

$$P(P\_R) = P\left(\mathbb{1} - a\right)^n \tag{9}$$

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

Figure 8.

(a) Top view of RLSA. (b) Cut view of a RLSA antenna and the power flow mechanism inside the RLSA cavity [39].

#### Figure 9.

3.6 Length of slots

Definition of some slot parameters [39].

Figure 7.

192

expressed by Eq. (8) [42]:

The length of the slots on the radiating surface of RLSA antennas must be varied

<sup>ρ</sup> <sup>12</sup>:<sup>5</sup> <sup>x</sup>10<sup>9</sup>

The formula in Eq. (8) is an approximate formula. To get an accurate formula,

The power (P) comes from the feeder, which is located at the centre of the antenna, and flows towards the antenna perimeter, as illustrated in Figure 8b. When the power passes the slots, some amount of the power radiates through the slots. The power inside the cavity will decrease every time the power passes the slots and will continue to decrease until the power reaches the antenna perimeter. Equa-

tion (9) expresses the remaining power (PR) at the antenna perimeter [42]:

f 0

ð Þ¼ PR P 1ð Þ � <sup>α</sup> <sup>n</sup> (9)

(8)

in order to achieve a uniform aperture illumination. The farther a slot from the centre of the antenna, the longer the length of the slot will be. The length of the slot is the function of ρ that is the distance of the slot from the centre of the antennas, as

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

Lrad <sup>¼</sup> <sup>4</sup>:<sup>9876</sup> � <sup>10</sup>�<sup>3</sup>

we need to do some measurements and experiments.

4. Reflection in small-RLSA antennas

4.1 Signal reflection due to remaining power

Illustration of the reflected signals from the slot [39].

Equation (9) shows that the amount of the remaining power depends on the number of rings (n), which is also proportional to the number of slots. For small-RLSA antennas, which have a small number of slots, the amount of the remaining power at the antenna perimeter will be high. Part of this remaining power will be reflected back to the feeder and result in a high signal reflection, thus increasing the reflection coefficient. For normal-size RLSA antennas, which have thousands of slots, the remaining power at the antenna perimeter is very small so that its effect to the signal reflection is neglected.

#### 4.2 Signal reflection due to the reflected signal from slots

Figure 9 shows the front cut view of a RLSA antenna and the signal flow within the cavity of the RLSA antenna. The grey arrows represent the signals that flow from the centre of the RLSA antenna to the antenna perimeter, and the black arrows represent the reflected signal from the slots. Figure 9 shows that since the distance between the slots (d) is λg/2, the signal from slot 'A' will travel for λg/2 to reach 'B'. At 'B', some of the signal will be reflected back and travel for another λg/2 to reach 'A'. Therefore, the reflected signal from slot 'A' and slot 'B' will have a different

phase of λg/2 + λg/2 = λ<sup>g</sup> or 360° (or can be said there is no phase difference), so that they will strengthen each other and result in a high signal reflection [42].

### 5. Extreme beamsquint technique

The ability of beamsquint technique in minimizing the reflected signal from the slots depends on one condition, that is, the number of ring must be sufficient. As an example, Figure 10a and b shows the reflected signals of a three-ring RLSA antenna and the reflected signals of a two-ring RLSA antenna, respectively. Since every ring consists of two slots, hence, there are six reflected signals for the three-ring RLSA antenna and four reflected signals for the two-ring RLSA antenna. It is assumed that the amplitude of all reflected signals is the same in order to simplify the analysis. From Figure 10a, it can be observed that all the graph space is covered by the reflected signals; hence the combination of all reflected signals will cancel out each other, and the minimum signal reflection is obtained. In contrast, from Figure 10b, it can be seen that not all graph space (the area pointed by 'A') is covered by the reflected signals; hence the combined signal will be greater than the combined signal in Figure 10a.

From the example in the previous paragraph, it can be concluded that a smaller number of ring will decrease the ability of beamsquint technique in cancelling the reflected signal. Therefore, this is the reason why the reflection coefficient of small-RLSA antennas, which have few numbers of rings (less than 2), is high and why the normal beamsquint technique fails to minimize the reflection coefficient of small-RLSA antennas. The next section will explain how the proposed extreme beamsquint technique can reduce the high reflection coefficient of small-RLSA antennas by increasing the number of ring.

The position of the ring in radial direction (Sρ) can be expressed by Eq. (10) [21]:

$$S\_{\rho} = \frac{r\lambda\_{\text{g}}}{1 - \xi \sin \theta\_T \cos \left(\phi - \phi\_T\right)}\tag{10}$$

It illustrates that the beamsquint technique performs the ring in the shape of ellipse rather than in the shape of circular. From Figure 11b, it can be observed that the position of the ring at the left-hand side will move closer to the centre of the antenna as the beamsquint increases. In contrast, the position of the ring at the right-hand side will move farther from the centre of the antenna as the beamsquint

(a) Illustration of some parameters of ring position. (b) Plot of the ring for beamsquint of 20, 30 and 60°. (c) Plot of various ring numbers for beamsquint angle of 20°. (d) Plot of various ring numbers for beamsquint

Still based on Eq. 3, by utilizing ϕ<sup>T</sup> ¼ 0 and ϕ = 0 to 360°, the rings are plotted for various ring numbers both for the beamsquint angle of 20° and 800 as shown in Figure 11c and d, respectively. From these figures, it can be observed that at the left-hand side, the distance between rings for beamsquint angle of 80° is shorter than the distance between the rings for beamsquint angle of 20°. Due to the shorter distance between rings, the beamsquint angle of 80° has more rings (nine rings) that can be plotted in the antenna area compared to the beamsquint angle of 20° (six rings). Based on the previous examples and explanations, it can be concluded that the higher beamsquint angle can yield more rings. This fact is very useful to include additional rings for the small-RLSA antenna, which originally has a low number of rings (less than 2). The extra number of rings will have more ability to minimize the

increases.

195

Figure 11.

angle of 80° [39].

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

θ<sup>T</sup> is the beamsquint angle, ϕ is the position of slots in azimuth, ϕ<sup>T</sup> is the azimuth angle of beamsquint and r is the ring number. Figure 11a illustrates the definition of all this parameters.

Based on Eq. (10), by utilizing r = 1, ϕ<sup>T</sup> ¼ 0 and ϕ = 0–360°, the rings for beamsquint angle of 10°, 30° and 60° are plotted as shown in Figure 11b.

#### Figure 10. (a) Reflected signal of a three-ring RLSA antenna. (b) Reflected signal of a two-ring RLSA antenna [39].

Radial Line Slot Array (RLSA) Antennas DOI: http://dx.doi.org/10.5772/intechopen.87164

phase of λg/2 + λg/2 = λ<sup>g</sup> or 360° (or can be said there is no phase difference), so that

The ability of beamsquint technique in minimizing the reflected signal from the slots depends on one condition, that is, the number of ring must be sufficient. As an example, Figure 10a and b shows the reflected signals of a three-ring RLSA antenna and the reflected signals of a two-ring RLSA antenna, respectively. Since every ring consists of two slots, hence, there are six reflected signals for the three-ring RLSA antenna and four reflected signals for the two-ring RLSA antenna. It is assumed that the amplitude of all reflected signals is the same in order to simplify the analysis. From Figure 10a, it can be observed that all the graph space is covered by the reflected signals; hence the combination of all reflected signals will cancel out each other, and the minimum signal reflection is obtained. In contrast, from Figure 10b, it can be seen that not all graph space (the area pointed by 'A') is covered by the reflected signals; hence the combined signal will be greater than the combined

From the example in the previous paragraph, it can be concluded that a smaller number of ring will decrease the ability of beamsquint technique in cancelling the reflected signal. Therefore, this is the reason why the reflection coefficient of small-RLSA antennas, which have few numbers of rings (less than 2), is high and why the normal beamsquint technique fails to minimize the reflection coefficient of small-

The position of the ring in radial direction (Sρ) can be expressed by Eq. (10) [21]:

<sup>1</sup> � <sup>ξ</sup> sin <sup>θ</sup><sup>T</sup> cos <sup>ϕ</sup> � <sup>ϕ</sup><sup>T</sup> ð Þ (10)

RLSA antennas. The next section will explain how the proposed extreme beamsquint technique can reduce the high reflection coefficient of small-RLSA

<sup>S</sup><sup>ρ</sup> <sup>¼</sup> <sup>r</sup>λ<sup>g</sup>

θ<sup>T</sup> is the beamsquint angle, ϕ is the position of slots in azimuth, ϕ<sup>T</sup> is the azimuth angle of beamsquint and r is the ring number. Figure 11a illustrates the

Based on Eq. (10), by utilizing r = 1, ϕ<sup>T</sup> ¼ 0 and ϕ = 0–360°, the rings for beamsquint angle of 10°, 30° and 60° are plotted as shown in Figure 11b.

(a) Reflected signal of a three-ring RLSA antenna. (b) Reflected signal of a two-ring RLSA antenna [39].

they will strengthen each other and result in a high signal reflection [42].

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

5. Extreme beamsquint technique

antennas by increasing the number of ring.

definition of all this parameters.

Figure 10.

194

signal in Figure 10a.

Figure 11.

(a) Illustration of some parameters of ring position. (b) Plot of the ring for beamsquint of 20, 30 and 60°. (c) Plot of various ring numbers for beamsquint angle of 20°. (d) Plot of various ring numbers for beamsquint angle of 80° [39].

It illustrates that the beamsquint technique performs the ring in the shape of ellipse rather than in the shape of circular. From Figure 11b, it can be observed that the position of the ring at the left-hand side will move closer to the centre of the antenna as the beamsquint increases. In contrast, the position of the ring at the right-hand side will move farther from the centre of the antenna as the beamsquint increases.

Still based on Eq. 3, by utilizing ϕ<sup>T</sup> ¼ 0 and ϕ = 0 to 360°, the rings are plotted for various ring numbers both for the beamsquint angle of 20° and 800 as shown in Figure 11c and d, respectively. From these figures, it can be observed that at the left-hand side, the distance between rings for beamsquint angle of 80° is shorter than the distance between the rings for beamsquint angle of 20°. Due to the shorter distance between rings, the beamsquint angle of 80° has more rings (nine rings) that can be plotted in the antenna area compared to the beamsquint angle of 20° (six rings). Based on the previous examples and explanations, it can be concluded that the higher beamsquint angle can yield more rings. This fact is very useful to include additional rings for the small-RLSA antenna, which originally has a low number of rings (less than 2). The extra number of rings will have more ability to minimize the reflection coefficient of small-RLSA antenna. The use of extra high beamsquint angle underlies the naming of extreme beamsquint technique.
