# A Review on Improved Design Techniques for High Performance Planar Waveguide Slot Arrays

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Early Work

_{20}internal one [24].

^{2}) computations of the mutual coupling matrix, at each step of the procedure, were out of reach for the computers available at the time. However, soon afterward, new and far more effective approaches to the mutual coupling computation [25,26] have allowed an increase in the size of the arrays. On the other hand, such large arrays require a more complex feeding network [27]. Therefore, the iterative approach was improved to handle arrays with several hundred slots, or even thousands, without trap problems, which could prevent convergence.

## 3. Waveguide Slot Models

- (a)
- (b)

- (a)
- An interesting work involving modification of the guiding structure was proposed in 1990 by Green et al. [46]. The properties of longitudinal radiating slots in the asymmetric ridge waveguide were investigated. This solution allows for suppressing the butterfly lobes [52], since all the radiating slots are centered with respect to the waveguide axis. Afterward, several configurations of longitudinal slots in the ridged waveguide have been presented, though most have different purposes, such as the RCS reduction of the ridged waveguide slot array using EBG radar absorbing material [53] or the improvement of radiating properties by using a ridged waveguide slot array with a high-impedance ground plane [54], just to cite some examples. However, using a ridged waveguide is not the only way to improve the slot (and slot array) performance. In fact, other valuable solutions are available in the recent literature. For example, in [45], a reconfigurable radiating slot is proposed by means of tuning the screws in the waveguide broad wall opposite to the slot. In [55], the radiating slot was printed in a copper-clad dielectric substrate which replaced the upper waveguide wall and allowed easy and low-cost replacement of the radiating slots when the pattern requirement changed. In [47] a gap waveguide cavity slot array was proposed where the conductor losses were reduced by using the cavity-based radiator with virtual electric walls, which replaced the traditional waveguide slot array. The E-plane waveguide was integrated with the cavity and split from the center broadside, giving robust assembly to the designed array at a low cost. In [48], a slot array antenna based on the use of groove gap waveguide technology was proposed, where glide-symmetric EBG holes instead of pins were used, showing a simpler solution in terms of manufacturing and assembly compared with the use of pins as the unit cell.
- (b)
- In [49] and [50], the radiating element was modified by adding in the external region a truncated waveguide radiating in free space, or a radiating patch, electromagnetically coupled to the waveguide slot. Both of these configurations allow for suppressing the butterfly lobes [52] and increasing the radiating element gain, and they are suitable to allow pressurization of the feeding waveguide. Different radiating characteristics are instead achieved with a slot doublet, which consists of two longitudinal slots cut on the opposite broad walls in the same vertical plane of the radiating waveguide [51,56].

## 4. Waveguide Slot Arrays

#### 4.1. Analysis and Synthesis of Longitudinal Slot Arrays

_{m}of radiating slots. The radiating slots are spaced λ

_{g}/2 apart, where λ

_{g}is the wavelength of the dominant mode of the waveguide carrying these slots. The radiating waveguides are fed by a transverse waveguide using, in the most typical configuration, a series-series coupling slot. In its typical equivalent circuital model, the radiating slots are represented through a shunt admittance on the transmission line equivalent to the waveguide [21]. Following [2], a waveguide array of shunt slots can be described by two design equations:

_{10}is the characteristic conductance of the equivalent transmission line for the fundamental TE

_{10}mode in the radiating waveguides; V

^{S}

_{n}is the (external) slot voltage at the slot center; K

_{1}, f

_{n}and α depend on the radiating waveguide geometry and on the slot offsets [11]; Y

^{A}

_{n}is the n-slot active admittance; V

_{n}is the mode voltage at the shunt element Y

^{A}

_{n}; and g

_{nm}is the normalized coupling coefficient between slot n and slot m.

_{10}mode of the waveguide. At any rate, we can easily include higher-order mode interactions by simply considering their effect as a further mutual coupling term, and this approach is accurately detailed in [24]. Typically, in order to obtain an accurate analysis of the WSA, we must solely consider the first higher-order mode TE

_{20}and only for adjacent slots.

_{m}is the current transformation ratio of the m

^{th}coupling slot and Y

^{IN}

_{m}is the input admittance of each waveguide. Obviously, the sum is only extended to the slots contained in the m

^{th}radiating waveguide.

^{S}

_{n}) and the input impedance Z

^{IN}at the input node of the array.

_{nm}consists of evaluating these coefficients using the results of the preceding iterative step, because slight variations in lengths and offsets only produce small changes in the coefficients of mutual coupling. By exploiting this choice, we can decouple the design equations, and therefore we are able to recompute the new lengths and offsets for each radiating slot independently.

#### 4.2. Design of a WSA in a Waveguide Partially Filled with a Dielectric Slab

_{0}in an empty waveguide, where λ

_{0}is the wavelength in free space). Therefore, the number of slots composing the array (i.e., the number of elements of the array) is limited in an empty waveguide, and in many cases, this could hinder obtaining a satisfying radiation pattern or an adequate aperture distribution. On the other hand, the presence of the dielectric sheet can allow a rise in the number of elements of the array, helping the designer to obtain a better radiation pattern.

_{n}of the design equations in the waveguide partially filled with the dielectric sheet [4].

#### 4.3. Design of a WSA in a Waveguide Covered with a Dielectric Slab

_{nm}in the second design’s Equation (2) can be computed as described in [22]. This expression cannot be used when the radiating waveguides are covered with a dielectric slab and must therefore be recomputed while including the effect of the external dielectric sheet. The resulting expression of the mutual coupling coefficient for a waveguide covered with a dielectric slab can be written as [6]

_{n}and M

_{m}are the normalized equivalent magnetic currents on the slot apertures “n” and “m”, respectively (as indicated in Figure 2b), F

_{ext}[M

_{n}] is the vector potential in the region external to the waveguide due to the equivalent magnetic current M

_{n}and k

^{2}= ω

^{2}εμ.

_{0}ρsin(ϕ) and v = k

_{0}ρcos(ϕ), Equation (4) can be computed by splitting the domain of integration into three subdomains:

_{0}mode (corresponding to the surface wave traveling into the dielectric layer) [6]. While in the subdomains (i) and (ii), the corresponding integrals in Equation (6) can be computed with a standard Gaussian quadrature after adequate changes of the variable [6]. The evaluation of the integral in the unbounded subdomain (iii) in particular requires attention and must be carefully evaluated by applying adequate mathematical concepts. We can write the integral (6) as

_{nm}, the distance between the “n-th” and “m-th” slots of the array. The convergence of this integral can be accelerated by resorting to the weighted average algorithm (WAA) together with the Shank’s transform, as described in detail in [6].

#### 4.4. Multilayer Dielectric Cover Effect in WSAs

_{1}, h

_{2}, h

_{3}and h

_{4}and relative permittivity equal to ε

_{r}

_{1}, ε

_{r}

_{2}, ε

_{r}

_{3}and ε

_{r}

_{4}.

_{1}) and second (h

_{2}) covering layers, respectively. In both figures, X

_{0}represents the offset of the slot with respect to the center of the radiating waveguide, as shown in Figure 7a.

_{1}and h

_{2}.

#### 4.5. Interaction between the Beam-Forming Network and the Radiating Waveguides

- The strong influence between the T-junction and the coupling slots which connect the radiating and feeding waveguide;
- The interaction between the coupling slot and the nearby radiating slots;
- The effect of the bent terminations.

_{L}and V

_{L}indicate the current and the voltage along the feeding waveguide, respectively, immediately to the left (subscript LX) or to the right (subscript DX) of the slot couplers near the T-junction. I

_{C}and V

_{C}indicate the current and the voltage, respectively, in the slot couplers near the T-junction. I

_{AT}(or V

_{AT}) is the feeding known term at the T-junction. The radiating waveguides farthest from the T-junction are replaced in Figure 13b by their input impedance (i.e., the impedance seen looking at the input port of their slot coupler). The T-junction can therefore be modeled by the following hybrid matrix, which corresponds to the equivalent circuit of Figure 13b:

_{ij}are the impedances, Y

_{ij}are the admittances and S

_{ij}and A

_{ij}are adimensional coefficients. All these coefficients of the 5 × 5 hybrid matrix are calculated using a method of moments (MoM) procedure which allows for analyzing the structure of Figure 13a.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Waveguide slot models: (

**a**) Typical broad-wall radiating slots; (

**b**) slot doublet; and (

**c**) waveguide longitudinal slot with cavity.

**Figure 2.**Geometry of a typical planar waveguide slot array with longitudinal radiating slots. (

**a**) 3D view. (

**b**) Top view.

**Figure 3.**Side view of waveguide slot arrays (WSAs) with waveguides partially filled with a dielectric slab. (

**a**) “Comb-like” structure with copper-clad laminate as a “cover”. (

**b**) “Comb-like” structure with a dielectric slab and slotted wall as a “cover”. (

**c**) Array model used in the synthesis procedure.

**Figure 4.**(

**a**) Simulated far-field pattern requiring a Taylor nominal pattern and having a sidelobe level SLL = −20 dB (E-plane) for (i) an array having a common dielectric layer and (ii) an array approximate model considering separate radiating waveguides. (

**b**) Simulated far-field pattern requiring nominal uniform distribution (H-plane) for (i) an array having a common dielectric layer and (ii) an array approximate model considering separate radiating waveguides. (

**c**) Frequency response for (i) an array having a common dielectric layer and (ii) an array approximate model considering separate radiating waveguides.

**Figure 6.**(

**a**) Far-field pattern simulated with HFSS in the H-plane, with a nominal Chebychev pattern with −30 dB sidelobes. The continuous line refers to “dielectric coupling”, while the dashed line refers to “free space coupling”. (

**b**) Far-field pattern simulated with HFSS in the E-plane with a nominal uniform pattern. The continuous line refers to “dielectric coupling”, while the dashed line refers to “free space coupling”. The cross-polar components are not reported because their level was below −45 dB. (

**c**) Frequency response simulated with HFSS. The continuous line refers to “dielectric coupling”, while the dashed line refers to “free space coupling”.

**Figure 7.**Radiating slot geometry in a waveguide with a multilayer dielectric cover using four dielectric layers. (

**a**) Top view. (

**b**) Side view.

**Figure 8.**Three-layer case. The continuous lines represent the resonant length of the slot with respect to the thickness h

_{1}of the first covering layer. The dashed lines represent the conductance at resonance, normalized to the waveguide fundamental mode admittance with respect to the thickness h

_{1}of the first covering layer. Frequency = 9 GHz.

**Figure 9.**Three-layer case. The continuous lines represent the resonant length of the slot with respect to the thickness h

_{2}of the second covering layer. The dashed lines represent the conductance at resonance, normalized to the waveguide fundamental mode admittance with respect to the thickness h

_{2}of the second covering layer. Frequency = 9 GHz.

**Figure 11.**Gain of an array with 6 × 6 elements and a dielectric cover and of an array with 8 × 8 elements radiating in free space (HFSS simulations). (

**a**) E-plane. (

**b**) H-plane. (

**c**) Simulated frequency responses of the 6 × 6 and 8 × 8 designed arrays using HFSS.

**Figure 12.**Gain of an array with 8 × 8 elements and a dielectric cover and of an array with 10 × 10 elements radiating in free space (HFSS simulations). (

**a**) E-plane. (

**b**) H-plane. (

**c**) Simulated frequency responses of the 8 × 8 and 10 × 10 designed arrays using HFSS.

**Figure 13.**(

**a**) Subarray fed by a T-junction (side view and top view). (

**b**) Five-port circuital and matrix models of the T-junction.

**Figure 15.**E-plane far-field pattern of the monopulse WSA. The short bend length is equal to 12.4 mm, and the analysis model with the T-junction was performed using a straight shorted termination for the feeding waveguides with an impedance of 200 Ω.

Advantages of WSAs | Drawbacks of WSAs |
---|---|

Low power dissipation and low losses | Small, useful bandwidth (resonant antennas) |

High mechanical strength | High realization cost |

Massive realization | Low flexibility |

Small size | Weak reconfigurability |

Easily unfoldable | - |

High power handling capability | - |

High radiation efficiency | - |

Advantages | |||||
---|---|---|---|---|---|

WSA Configuration | Pressurization | Thermal Insulation | Gain Enhancement | Aerodynamic Purposes | Flexibility |

Standard WSA | - | - | - | - | - |

WSA with waveguides covered with dielectric slab | Yes | Yes | - | Yes | Yes |

WSA with waveguides partially filled with dielectric slab | Yes | - | - | - | Yes |

WSA with multilayer dielectric cover | Yes | Yes | Yes | Yes | Yes |

**Table 3.**Comparison of the state-of-the-art works, considering several WSAs with different configurations.

Ref. | Freq (GHz) | No. of Elements | Aperture Size (λ_{0}^{2}) | RLBW (−10 dB) | ARBW (3 dB) | GBW (3 dB) | PG | η | SLL (dB) |
---|---|---|---|---|---|---|---|---|---|

[34] | 30 | 10 × 1 | 0.9 × 6 | 4% | 8% | 4% | 16.3dBi | 98% | −18.5 |

[47] | 120 | 8 × 8 | 5.67 × 5.67 | 13.3% | - | 13.3% | 25 dBi | 75% | −13 |

[48] | 28.6 | 4 × 9 | 4.3 × 8.6 | 7% | - | 7% | 24.8 dBi | 75% | −11.5 |

[62] | 30 | 4 × 4 | 3.5 × 3.5 | 40.21% | 36.51% | 37.02% | 19 dBic | - | −13 |

[63] | 29 | 4 × 4 | 10.25 × 8.7 | 29.6% | 25.4% | 19% | 20.3 dBic | 57.9% | −10 |

[64] | 30 | 8 × 8 | 6.12 × 6.12 | 27.6% | 32.7% | 30% | 25.2 dBic | 75.2% | −13 |

[65] | 28 | 4 × 4 | 7 × 5 | 27.7% | 27.8% | 25.3% | 20.2 dBic | 78% | −10 |

[69] | 28 | 8 × 8 | 7.6 × 7.6 | 28% | - | 25.2% | 26.4 dBi | 60% | −13 |

[70] | 60 | 16 × 16 | 15.4 × 15.6 | 11.4% | - | 11% | 33.5 dBi | 83.6% | −14.9 |

[71] | 12 | 8 × 8 | 7.4 × 7.4 | 36.9% | - | 31.9% | 23.4 dBi | 60% | −21.3 |

[72] | 60 | 8 × 8 | 7.6 × 6.9 | 30% | - | 29.1% | 27.5 dBi | 80% | - |

[73] | 78.5 | 32 × 32 | 29.56 × 29.56 | 19% | - | 19% | 38.4 dBi | 76.4% | −13 |

[74] | 62 | 16 × 16 | 7 × 6.4 | 16% | - | 16% | 32.5 dBi | 70% | −13 |

[75] | 130 | 32 × 32 | 30.43 × 30.43 | 12% | - | 12% | 38 dBi | 60% | −13 |

[81] | 9 | 8 × 8 | 5.92 × 7.8 | 2% | - | 2% | 27.1 dBi | 67% | −20 |

[84] | 9.3 | 64 × 24 | 55.8 × 17 | 4.3% | - | 4.3% | 37.7 dBi | 50% | −22.5 |

[85] | 35 | 22 × 1 | 22.68.57 × 2.92 | 3.7% | 3.7% | 3.7% | 23.3 dBic | 75% | −28 |

[86] | 94 | 16 × 16 | 17.23 × 17.23 | 21% | - | 21% | 30.5 dBi | 60% | −20 |

[87] | 40 | 22 × 20 | 17.23 × 17.23 | 3.75% | - | 3.75% | 31.8 dBi | - | −30 |

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**MDPI and ACS Style**

Casula, G.A.; Mazzarella, G.; Montisci, G.; Muntoni, G.
A Review on Improved Design Techniques for High Performance Planar Waveguide Slot Arrays. *Electronics* **2021**, *10*, 1311.
https://doi.org/10.3390/electronics10111311

**AMA Style**

Casula GA, Mazzarella G, Montisci G, Muntoni G.
A Review on Improved Design Techniques for High Performance Planar Waveguide Slot Arrays. *Electronics*. 2021; 10(11):1311.
https://doi.org/10.3390/electronics10111311

**Chicago/Turabian Style**

Casula, Giovanni Andrea, Giuseppe Mazzarella, Giorgio Montisci, and Giacomo Muntoni.
2021. "A Review on Improved Design Techniques for High Performance Planar Waveguide Slot Arrays" *Electronics* 10, no. 11: 1311.
https://doi.org/10.3390/electronics10111311