International Journal of Antennas and Propagation
Volume 2018 (2018), Article ID 1893650, 13 pages
https://doi.org/10.1155/2018/1893650

Research Article

Analytical Model for Predesigning Probe-Fed Hybrid Microstrip Antennas

Nilson R. Rabelo,¹ J. C. da S. Lacava,¹ Alexis F. Tinoco Salazar,² P. C. Ribeiro Filho,¹ D. C. Nascimento,¹ Rubén D. León Vásquez,² and Sidnei J. S. Sant’Anna³

¹Laboratório de Antenas e Propagação (LAP), Instituto Tecnológico de Aeronáutica (ITA), Praça Mal. Eduardo Gomes 50, 12228-900 São José dos Campos, SP, Brazil
²Departamento de Eléctrica y Electrónica (DEE), Centro de Investigaciones Científicas y Tecnológicas del Ejército (CICTE), Universidad de las Fuerzas Armadas (ESPE), Av. General Rumiñahui s/n, Sangolquí, Ecuador
³Divisão de Processamento de Imagem (DPI), Instituto Nacional de Pesquisas Espaciais (INPE), Av. Dos Astronautas 1758, 12227-010 São José dos Campos, SP, Brazil

Correspondence should be addressed to Alexis F. Tinoco Salazar; aftinoco@espe.edu.ec

Received 13 September 2017; Accepted 5 December 2017; Published 28 February 2018

Academic Editor: Miguel Ferrando Bataller

Copyright © 2018 Nilson R. Rabelo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Based on the equivalent resonant cavity model, an effective analysis methodology of probe-fed hybrid microstrip antennas is carried out in this paper, resulting in a better understanding of the parameter interrelations affecting their behavior. With that, a new design criterion focused on establishing uniform radiation patterns with balanced 3 dB angles is proposed and implemented. Results obtained with the proposed model closely matched HFSS simulations. Measurements made on a prototype antenna, manufactured with substrate integrated waveguide (SIW) technology, also showed excellent agreement, thus validating the use of the cavity model for predesigning hybrid microstrip antennas in a simple, visible, and time- and cost-effective way.

1. Introduction

Microstrip antennas and arrays can be accurately designed using modern electromagnetic simulators such as CST [1] and HFSS [2]. However, as their focus is on analysis, the development process becomes more simple and time- and cost-effective when the geometry under study is predesigned in the first place. In this context, to predesign means the determination of preliminary antenna dimensions before implementation in the simulators. Once in the software environment—which incorporates significant effects, such as dielectric and ground plane truncation, that are not taken into account in more basic models—the antenna can then be more comprehensively analyzed and its dimensions optimized to meet project specifications. Naturally, the closer the predesigned dimensions are to the optimal ones, the faster the analysis-synthesis process will converge.

Although Deschamps [3] proposed the concept of microstrip radiators back in 1953, it was only in the 1970s, with the production of low-loss microwave laminates that this type of antenna started gained popularity [4] and a number of practical applications came about [5]. Nowadays, their peculiar characteristics are established [6–8] and they are found as customary components in modern communication systems [9]. Analytical methods, such as the transmission line [10], resonant cavity [11], and electric surface current [12] models, have been extensively used for predesigning planar, cylindrical, and spherical microstrip antennas [6–8, 13–15].

The conventional probe-fed linearly polarized antenna, comprising a metallic rectangular patch printed on top of a grounded planar dielectric layer, is certainly the most popular microstrip radiator [16], but at the cost of high levels of cross-polarization in the H plane, as recently revisited [5]. A convenient way to overcome this limitation consists of using a hybrid microstrip patch, as described in [9, 16–21]. In this publication, hybrid microstrip antennas fed by a coaxial probe are predesigned via the cavity model. Although this model had been previously utilized [9, 16, 18, 22, 23], the systematic determination of adequate design criteria has not been fully carried out yet. Such is the primary goal of this work.

To validate our predesigning procedure, HFSS simulations were run, and excellent agreement with our results confirms the effectiveness of the equivalent resonant cavity model for thin hybrid antennas. Since the implementation of vertical electric walls in microstrip structures is not straightforward, a prototype antenna was manufactured using the substrate integrated waveguide (SIW) technique [24]. Here again, an excellent match between predesigned and experimental results was observed.

2. Cavity Model

Differently, from their conventional counterpart, hybrid microstrip antennas fed by coaxial probes can exhibit low cross-polarization level in the H plane, as recently reported in [9, 16–19, 25, 26]. That outstanding behavior is obtained by connecting two opposite edges of a rectangular patch to the antenna ground plane. The typical geometry, proposed by Penard and Daniel [23], is shown in Figure 1, where aa and ba denote the patch dimensions and h is the thickness of the substrate, ε of electric permittivity, and μ₀ of magnetic permeability. Note the antenna is fed, at coordinates ya and za, by a SMA (subminiature version A) connector whose characteristic impedance is 50 Ω.

(a)

(b)

Figure 1: Hybrid microstrip antenna: (a) top view and (b) lateral view.

The resonant cavity model, used for the analysis of conventional microstrip radiators [11], is applied here to the hybrid antenna. In this model, the region between the patch and the ground plane is considered equivalent to a cavity made up of electric walls at , , , and and magnetic walls at and , as illustrated in Figure 2. The equivalent cavity dimension along the z-axis shall be made greater than the actual antenna dimension (i.e., a > aa) to account for the fringing effect at the edges [10]. On the other hand, since the walls at and are electrically grounded to the bottom wall, the dimensions along the y-axis of the equivalent cavity and the actual antenna are the same (i.e., ba = b).

Figure 2: Equivalent cavity excited by a strip of uniform current density.

By modeling the coaxial feeder by a vertical strip of uniform current density,

located at the point (yc, zc); as illustrated in Figure 2, the electric field amplitude of the resonant mode {m, n} inside the cavity is given by

where

with and if and if , ω is the angular frequency and is the current on the feeding strip.

Therefore, the total electric field inside the resonant cavity excited by a uniform current density strip is given by the following expression:

where

Consequently, the cavity input impedance becomes

However, this equation does not properly describe the input impedance of a microstrip antenna. According to [11], more accurate results are obtained if the cavity wavenumber k is replaced with the effective wavenumber , given by

where

with denoting the effective loss tangent, tanθ the loss tangent of the substrate, σ the electrical conductivity of the cavity electric walls, δmn their skin depth, calculated at the resonant frequency of the {m, n} mode, k₀ the wavenumber, and η₀ the intrinsic impedance of vacuum, and the parameter Iint directly proportional to the radiated power of the {m, n} antenna mode is obtained from the far radiation field of the hybrid microstrip antenna. Here, as in [27], equivalent magnetic sources, positioned along the ungrounded patch walls, lead to the following expression [9, 28]:

where

Thus, the input impedance of the hybrid microstrip antenna is calculated from

3. Antenna Analysis

In this section, the electromagnetic behavior of the hybrid microstrip antenna is analyzed with the purpose of establishing an effective predesigning procedure. As mentioned in [16, 28], is the first resonant mode. Since its electric field does not vary along the z-axis, the fringing fields are in phase opposition, thus producing a null in the broadside direction of the antenna radiation pattern (perpendicularly to the yz plane of Figure 1). In addition, its input impedance does not vary with zc, what makes impedance matching difficult. Given these undesirable characteristics, this first resonant mode is not adequate for the usual operation of microstrip antennas. On the other hand, the mode presents a cosinusoidal distribution along the z-axis over the length a of the patch, thus permitting matching the antenna to the coaxial probe feeder. Since its fringing fields are in phase, the radiation pattern maximum occurs in the broadside direction. These characteristics make the mode of operation to hybrid microstrip antenna.

Since the resonant frequency of the mode is a function of both physical dimensions of the patch, antennas with different values of a and b can be designed for operation on a given frequency. Design criteria are therefore required for determining the patch dimensions a and b and the position (yc, zc) of the coaxial probe feeder, to guarantee the proper operation of the antenna. For this purpose, three different hybrid radiators (HB₁, HB₂, and HB₃), designed to operate at 2.45 GHz, the central frequency of the ISM (industrial, scientific, and medical 2.4–2.5 GHz) band, are compared. The dimensions of their respective equivalent resonant cavities are shown in Table 1, noting that HB₁ has a rectangular patch, with b > a; HB₂ patch is square, with b = a; and HB₃ has also a rectangular patch, but now with b < a. The substrate used for all three radiators is 1.524 mm thick Arlon CuClad 250GX (εr = 2.55 ± 0.04 and tanθ = 0.0022) microwave laminate.

Table 1: Dimensions of the equivalent resonant cavities.

Dimension
HB₁
HB₂
HB₃

a (mm)
40.00
54.19
133.30

b (mm)
133.30
54.19
40.00

Initially, the resonant frequencies of the modes that are the closest to are calculated from (4) and shown in Table 2. Thus, in the case of the HB₁ antenna, modes {2, 0} and {2, 1} are the closest to . For HB₂, modes {1, 0} and {2, 0} are closest to , whereas, in the HB₃ case, modes {1, 0} and {1, 2} are the closest.

Table 2: Resonant modes closest to (calculated in Mathematica [29]).

Frequency (GHz)
HB₁ (b > a)
HB₂ (b = a)
HB₃ (b < a)

f₁₀
0.7042
1.7322
2.3467

f₁₁
2.4501
2.4497
2.4501

f₂₀
1.4084
3.4644
4.6934

f₁₂
4.7460
3.8734
2.7369

f₂₁
2.7369
3.8734
4.7460

Also from Table 2, the frequency offset Δf between the mode and its closest one is promptly determined. It is, for the HB₁ antenna, Δf₁ = 286.8 MHz; for HB₂, Δf₂ = 717.5 MHz; and for HB₃, Δf₃ = 103.4 MHz. The frequency bandwidth of conventional microstrip antennas operating in the fundamental mode is known to be roughly 1% [6–8] or approximately 25 MHz in the ISM band. Hence, in practical terms, the proximity of modes , , , and to the one will not significantly affect the operating frequency bandwidth of electrically thin hybrid antennas. Thus, from the perspective of modal interference, any one of the three designed antennas could be used. Nonetheless, a simple way to suppress modes and consists of placing the feeder at yc = b/2, where their electric field is minimal [9, 16, 28]. In such case, only modes {1, 0} and {1, 2} need to be controlled in the antenna design.

Consequently, the input impedance at the operation mode can be rewritten from (12) as

where

With that, the next step consisted of determining the value of zc such that the input impedance matches the 50 Ω characteristic impedance of the feeding probe SMA connector (Figure 1). Plots of Zin and the absolute value of the reflection coefficient, also obtained in Mathematica from (13) and (14) (for ℓp = 1.3 mm), are shown in Figures 3–5 for the three antennas.

Figure 3: HB₁ input impedance and reflection coefficient module.

Figure 4: HB₂ input impedance and reflection coefficient module.

Figure 5: HB₃ input impedance and reflection coefficient module.

In addition, the resulting frequency bandwidth (BW) and quality factor (Q) are presented in Table 3, both calculated at 2.45 GHz.

Table 3: Electrical characteristics of the antennas under analysis.

HB₁ (b > a)
HB₂ (b = a)
HB₃ (b < a)

Zin (Ω) (2.45 GHz)
50.05 + i10.72
49.94 + i10.61
50.04 + i6.89

zc (mm)
9.72
21.33
52.66

BW (%)
2.29
0.84
0.47

Q
29.19
79.67
141.35

As shown in Table 3 and in Figures 3–5, the three hybrid antennas exhibit inductive input impedances at the design frequency (2.45 GHz), as expected from a coaxial probe feed. It is also noticed that the bandwidth for the HB₁ antenna is larger than that for the HB₂ antenna and that for the HB₂ antenna is larger than that for the HB₃ one. This is directly related to side b being longer than side a—for the larger the b dimension is, the smaller the input impedance will be at the antenna edges, that is, at zc = 0 or at zc = a, resulting in a smoother dependence of Zin with zc. Besides compromising the antenna impedance matching at the design frequency, an inductive Zin, makes for an asymmetrical bandwidth around the center frequency, thus reducing its symmetrical operating bandwidth (i.e., |Γ| < −10 dB for the same frequency spacing both left and right of the design frequency). As shown in Figures 3–5, the bandwidth comes from 56 down to 38 MHz, for HB₁; from 21 down to 14 MHz, for HB₂; and from 12 to 10 MHz, for HB₃. Besides, the larger the antenna bandwidth, the lower its Q factor, as expected from the product BW × Q = 0.6667. Thus, from the point of view of frequency bandwidth, the design of hybrid antennas should achieve a < b. The effect of this criterion on the radiation pattern of hybrid antennas is analyzed next.

Since now only modes {1, 0} and {1, 2} need to be controlled, the far electric field can be rewritten from (10) and (11) as [9, 28]

where

Since the z-axis of the adopted rectangular coordinate system is normal to the magnetic currents at the ungrounded edges of the patch (Figure 1), the Eθ component in (15) defines the copolarization of the hybrid antenna, whereas the cross-polarization is given by Eϕ. Implementing (15) in Mathematica, radiation patterns for the HB₁, HB₂, and HB₃ antennas were plotted at 2.45 GHz as shown in Figures 6–8. It is noticed that the patterns are asymmetrical in the E (xz) and yz planes.

Figure 6: Normalized radiation pattern of the HB₁ antenna.

Figure 7: Normalized radiation pattern of the HB₂ antenna.

Figure 8: Normalized radiation pattern of the HB₃ antenna.

Analysis of Figure 1 indicates that the coaxial feeder location introduces an asymmetry in the antenna geometry, by making the field distribution asymmetrical within the equivalent resonant cavity, which what reflects in the radiated field. One also notices, however, that in the H (xy) plane the antenna is perfectly symmetrical. The 3D radiation patterns in Figure 9 permit a clearer visualization.

(a) HB₁ antenna

(b) HB₂ antenna

(c) HB₃ antenna

Figure 9: 3D radiation patterns of HB₁, HB₂, and HB₃ antennas.

Shown in Table 4 are the results from the Mathematica simulation of the directivity (D) and radiation efficiency (RE) of the antennas under analysis. One notes that HB₁ and HB₂ are equally directive. Nonetheless, the total field structure in HB₂ is more uniform, with better balanced 3 dB angles, circa 69o in the E (xz) plane, and 80.5o in the H (xy) plane, as opposed to the wide discrepancy between those angles for antenna HB₁, that is, 99.88° in the E (xz) plane and 53.5° in the H (xy) plane. It is also noticed in Figure 9 that the radiation pattern of HB₃ shows considerable secondary lobes, which what makes its directivity less than that of the HB₁ and HB₂ antennas.

Table 4: Directivity and radiation efficiency.

HB₁ (b > a)
HB₂ (b = a)
HB₃ (b < a)

D (dB)
8.33
8.23
7.39

Dcop (dB)
8.98
8.84
8.85

RE (%)
90.4
74.1
50.9

Another relevant parameter is the copolarization directivity Dcop, promptly calculated in the adopted coordinate system. In this case, only the Eθ component is taken into account. The difference between Dcop and the directivity D is due to the intensity of the antenna cross-field (component Eϕ), which varies substantially from one antenna to another (Figure 9(B)), although it is null on the E and H planes. This means a hybrid microstrip antenna does not exhibit cross-polarization on the main radiation planes xz and xy, differently from the significant cross-polarization level on the H plane of a conventional antenna [5]. Such is a relevant property of hybrid antennas. Also shown in Table 4 are the results obtained for the radiation efficiency; that is, the HB₁ antenna outweighs both, whereas HB₃ is the worst.

From these considerations, if the goal is to provide an operation equivalent to the conventional antenna, the hybrid antenna design should go for a modified square patch, with b ≥ a, for, in this case, the antenna directivity will be in the order of 8 dB, its radiation efficiency close to 80%, frequency bandwidth around 1%, and 3 dB angles balanced in the E and H planes. The complete antenna design will be accomplished in the next section.

4. Antenna Design

Given the condition b ≥ a, a hybrid antenna (HB) was designed for operation in the same frequency (2.45 GHz) of the antennas that were analyzed in the previous section. For the substrate, the 1.524 mm thick Arlon CuClad 250GX (εr = 2.55 and tanθ = 0.0022) was used again. Through Mathematica, the following dimensions were obtained: , , , and . In this case, the resonant modes closest to are at f₁₀ = 1.575 GHz and at f₂₀ = 3.150 GHz. For a frequency bandwidth in the order of 1%, the antenna design is good enough in this respect.

Input impedance and the reflection coefficient module, for ℓp = 1.3 mm, are plotted in Figure 10. As expected, the HB input impedance turns out to be inductive at the design frequency (Zin = 50.30 + i13.99 Ω), so the best matching occurs above 2.45 GHz. Consequently, the symmetrical passband of the antenna, in relation to the central operating frequency, goes down from 25 MHz to 14 MHz, as shown in Figure 10.

Figure 10: HB input impedance and reflection coefficient module.

Results for the radiation patterns in the principal planes, at 2.45 GHz, are shown in Figure 11. As expected, the antenna is asymmetrical in the E plane. For a better visualization of this effect, 3D patterns, at the same frequency, are presented in Figure 12.

Figure 11: Normalized radiation pattern of the HB antenna.

(a) Copolarization

(b) Cross-polarization

(c) Total field

Figure 12: 3D pattern for the HB antenna.

As intended, the design process produced a uniform radiation pattern, with balanced 3 dB angles: circa 75.63o in the E plane and 78.50o in the H plane. In addition, the antenna shows 7.9 dB directivity, 78.6% radiation efficiency, and 1.02% relative frequency bandwidth, all calculated at 2.45 GHz.

As noticed from Figure 12(b), no cross field exists in the broadside direction or along the E and H planes. Rather, it is more intense close to the antenna ground plane and on the planes that bisect the quadrants formed by planes (xy) and (xz). Consequently, its most significant effect consists of “beefing up” the total field pattern in the neighborhood of the ground plane, thus lowering the antenna directivity (to circa 7.9 dB) relative to the copolarization (Dcop), calculated as 8.6 dB, in this case.

The asymmetrical radiation pattern in the E plane is now analyzed. Since the E plane of a hybrid antenna, as shown in Figure 1, coincides with the xz plane of the adopted coordinate system, its far electric field is given by making in (15). Thus, the following expression for the normalized Eθ component results, given Eϕ is zero on this plane [28],

which can be rewritten as

where

From (13), mode {1, 0} and mode {1, 2} characteristics are seen to be opposite from the primary mode; that is, at the operating frequency, e₁₁ is imaginary, whereas e₁₀ and e₁₂ are real. In the case of the HB antenna at the operating frequency, they are e₁₁ = i0.00696845, e₁₀ = i0.000253281, and e₁₂ = i0.000123797. Thus, in the first quadrant, where θ ranges from 0 to 90 degrees, the terms sin[(k₀acosθ/2)] and cos[(k₀acosθ/2)] are positive, so their subtraction lowers the amplitude of eθ relative to the primary mode amplitude e₁₁cos[(k₀acosθ)/2]. In the second quadrant, on the other hand, where θ ranges from 90 to 180 degrees, a negative cosθ changes the sign of the term sin[(k₀acosθ)/2]; consequently, the amplitude of eθ is now larger than the primary mode one e₁₁cos[(k₀acosθ)/2], resulting in an asymmetrical radiation pattern in the E plane. In addition, analysis of (19), (20), and (21) shows that e₁₀ is not dependent on zc, but e₁₁ and e₁₂ are. This fact is directly related to the resonant mode field distribution along the plane yc = b/2. In fact,

Therefore, the excitation of mode {1, 0} does not depend on the feeder position zc (along the yc = b/2 plane), but zc substantially affects the level of {1, 1} and {1, 2} modes, thus becoming one of the causes of the E plane radiation pattern asymmetry of hybrid microstrip antennas. Normalized E plane radiation patterns for the HB antenna are shown in Figure 13 for different feeder positions at 2.45 GHz. They clearly show that pattern asymmetry increases with zc. That is, the lower the antenna input impedance is, the more asymmetrical the E plane pattern is. This fact is noticeable from (18), since the larger zc is, the smaller the contribution from the e₁₁ term, whereas the larger that from e₁₂ will be for a fixed e₁₀.

Figure 13: Normalized E plane radiation pattern of the HB antenna: zc = 5 mm—blue curve; zc = 10 mm—red curve; zc = 15 mm—orange curve; and zc = 20 mm—green curve.

5. HFSS Comparison

In order to validate the analysis and design procedures set forth, simulations were run in HFSS. The initial predesigned dimensions of the HB antenna, adjusted according to Hammerstad [30], are presented in Table 5. For the HFSS simulations, the antenna was centered on a ground plane of dimensions Wz × Wy, where the subscripts indicate the ground plane sides parallel to the coordinate axes z and y. It is noticed from Table 5 that the predesigned dimensions are very close to the ones simulated via HFSS, besides being obtained in a significantly reduced processing time.

Table 5: HB antenna dimensions (; ).

Dimension
Hammerstad
HFSS

aa (mm)
48.45
48.28

ba (mm)
59.59
59.59

ya (mm)
29.80
29.80

za (mm)
18.27
18.18

Results for the antenna input impedance are shown in Figure 14, whereas the comparisons between the predesigned results and those obtained via HFSS are presented in Table 6.

Figure 14: Input impedance of the HB antenna.

Table 6: Input impedance at 2.45 GHz.

HB

Zin (Ω)—equivalent cavity
50.30 + i13.99

Zin (Ω)—HFSS
50.02 + i10.36

The good agreement between these results confirms the effectiveness of the equivalent resonant cavity for predesigning hybrid antennas. Nevertheless, for ℓp = 1.3 mm, the predesigned impedance turns out to be more inductive than the HFSS simulation result. One way to reduce the input inductive reactance consists of increasing the effective width of the current strip feeder. The effect of different values of ℓp is also plotted in Figure 14, showing the optimal ℓp value is somewhere between 1.6 and 2.8 mm. Curves for Zin calculated for ℓp = 2.3 mm are presented in Figure 15.

Figure 15: Input impedance of the HB antenna: ℓp = 2.3 mm.

Last, radiation patterns in the E (xz plane—in blue) and H (xy plane—in red) planes are shown in Figure 16. The HFSS patterns were simulated for an infinite ground plane. The excellent agreement confirms once again the effectiveness of the equivalent resonant cavity model for predesigning hybrid antennas.

Figure 16: Normalized radiation pattern in the E and H planes of the HB antenna: solid line—Mathematica; dotted line—HFSS.

It is worth mentioning that the HB antenna, although electrically thin at 2.45 GHz, shows an inductive input impedance, Zin = 50.26 + i11.78 Ω (ℓp = 2.3 mm), which shifted up the best matching frequency, causing a significant reduction of its symmetrical operating bandwidth. In the following section, the HB antenna will be optimized at the operating frequency in terms of impedance matching to its SMA connector feeder.

6. Project Optimization for Null Reactance

A very effective way to match the antenna to the 50 Ω characteristic impedance of its SMA connector feeder, without any external resource, consists of adjusting the antenna design for the null reactance condition [31]. With that, the following dimensions were obtained for the equivalent cavity: , , and yc = b/2 e zc = 18.95 mm. The resulting input impedance and reflection coefficient module are shown in Figure 17.

Figure 17: Input impedance and reflection coefficient module.

After its redesign for null reactance, the antenna is much better matched to its feeding SMA connector, with Zin = 50.19 − i0.15 Ω at 2.45 GHz. It is also noticed the 26 MHz (circa 1.06%) bandwidth is now symmetrical around the design frequency. Other electrical characteristics remain very close to the previous HB design.

The antenna dimensions after adjusting per Hammerstad are shown in Table 7, whereas the results for the input impedance and the reflection coefficient module are superimposed in Figure 17. Once again, the excellent agreement between predesigned and HFSS results confirms the effectiveness of the equivalent resonant cavity model for predesigning hybrid antennas.

Table 7: Antenna dimensions for null reactance design. (; ).

Dimension
Hammerstad
HFSS

aa (mm)
48.51
48.31

ba (mm)
59.75
59.75

ya (mm)
29.88
29.88

za (mm)
18.17
18.05

7. SIW Prototype

To validate further the proposed design approach, a prototype antenna was built and tested, as described in this section. Given the implementation of vertical electric walls through the substrate in microstrip structures is not an easy task, an effective alternative approach is the use of SIW technology. In the present case, the vertical metallic walls are implemented with a sequence of cylindrical pins, as illustrated in Figure 18, in which Δp is their center-to-center spacing. The SIW antenna dimensions were determined from the values presented in Table 7.

Figure 18: SIW antenna geometry: top view.

First, the b dimension was determined in order to make beff equal to 59.75 mm, based on the following relationship,

set up in [32] for the propagation of the TM₀₁ mode in SIW guiding structures, where d denotes the pin diameter. After further optimization in HFSS, the following dimensions were obtained: aa = 47.63 mm, ba = 60.52 mm, ya = 29.875 mm, and za = 17.64 mm, with d = 0.508 mm and Δp = 4.266 mm. Based on those, radiation patterns in the E (xz plane—in blue) and H (xy plane—in red) planes, simulated in HFSS, are presented in Figure 19.

Figure 19: Normalized radiation pattern of the SIW antenna.

Results for the input impedance and the reflection coefficient module are presented in Figure 20. Other electrical characteristics of the SIW antenna are the following: 49.99 − i0.79 Ω input impedance, 80.5% radiation efficiency, 8.02 dB directivity, and balanced 3 dB angles in the E and H planes: circa 76° on the E plane and 78° on the H plane, consistently with the predesigned values.

Figure 20: Input impedance and reflection coefficient module of the SIW antenna, designed under the null reactance condition.

With those dimensions established in HFSS, a prototype antenna was manufactured, as shown in Figure 21, and tested. Experimental results for the input impedance and reflection coefficient module are shown in Figure 20, overlaid to the simulation results. As noted, the prototype resonant frequency was 16 MHz below requirement (2.45 GHz). Confidence in the simulation results and in the manufacturing process led us to believe this effect could be caused by a printed circuit board (PCB) permittivity shift from its nominal value, specified as εr = 2.55 ± 0.04. To check this hypothesis, a conventional, linearly polarized rectangular microstrip antenna, fed by a 50 Ω SMA connector, was designed to operate at 2.45 GHz and manufactured from the same PCB lot (Figure 22).

Figure 21: SIW antenna prototype.

Figure 22: Conventional microstrip antenna prototype.

This design option was based on ease of construction and numerous previous successful implementations. From HFSS simulation, the following dimensions resulted the following: , , and . Simulated and experimental results for the input impedance and the reflection coefficient module of the conventional antenna are presented in Figures 23 and 24.

Figure 23: Input impedance of the conventional microstrip antenna.

Figure 24: Reflection coefficient module of the conventional microstrip antenna.

As noticed in this simple case, the resonant frequency of the prototype antenna is still 16 MHz below the expected HFSS simulation, thus confirming the hypothesis on permittivity variation. Since the resonant frequency shifted down, the actual permittivity of the laminate is greater than 2.55. Further HFSS simulation for a range of values closed on 2.583, as pictured in Figures 23 and 24.

Having confirmed the cause of the shift, the SIW antenna was simulated again, but now for εr = 2.583. Results for the input impedance and the reflection coefficient module are presented in Figures 25 and 26. This time, an excellent match between the simulated and experimental results is observed.

Figure 25: Input impedance of the SIW antenna.

Figure 26: Reflection coefficient module of the SIW antenna.

Radiation patterns in the E and H planes at 2.434 GHz are presented in Figures 27 and 28. As noticed, experimental and HFSS co-pol patterns on the E and H planes show a good match. Simulated cross-pol patterns are not plotted since they are below −40 dB. The higher level of the measured cross-polarization patterns relative to their simulation can be traced to the lack of a balun for the antenna under test. Results are good regardless, as expected for hybrid antennas.

Figure 27: Normalized E plane radiation pattern.

Figure 28: Normalized H plane radiation pattern.

8. Final Comments

An efficient procedure based on the equivalent resonant cavity model for fast and accurate predesign of probe-fed hybrid microstrip antennas is proposed in this article. This procedure, implemented in Mathematica in a straightforward way, has provided a comprehensive understanding of the effect of the electrical and geometrical parameters involved in the antenna analysis and synthesis, thus becoming a powerful tool for educational purposes. The proposed design criteria were focused on establishing an operation equivalent to the conventional antenna, but now with uniform radiation patterns in all planes, that is, balanced 3 dB angles. Besides, as the antenna is fed by a 50 Ω SMA connector, the zero input null reactance condition was used for proper impedance matching, resulting in a symmetrical bandwidth around the design frequency. Moreover, according to the rectangular coordinate system adopted, the Eθ component directly defines the copolarization of the hybrid antenna, whereas the cross-polarization is given by Eϕ, thus facilitating their analysis in 3D patterns. Additionally, the asymmetry of the E plane radiation pattern was addressed, indicating that the lower the antenna input impedance is, the more asymmetrical the E plane pattern will be. Finally, it is important to notice that, differently from their conventional counterparts, hybrid microstrip antennas fed by coaxial probes exhibit low cross-polarization level in the H plane.

Predesign results obtained with the proposed model for the hybrid radiator closely matched HFSS simulations, as well as actual measurements in a prototype that was built and tested. The excellent agreement validates the use of the cavity model for predesigning hybrid microstrip antennas in a simple, accurate, and time- and cost-effective way.

Since the practical implementation of vertical electric walls in microstrip structures is not an easy task, the SIW technique was used in the manufacturing of the prototype antenna, showing very good results.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors are grateful to FAPESP and CNPq for sponsoring Projects 2012/22913-5 and 402017/2013-7, respectively, and to IFI-DCTA for providing the anechoic chamber.

References

CST, “Product overview,” http://www.cst.com.

HFSS, “Product overview,” https://www.ansys.com/products/electronics/ansys-hfss.

G. A. Deschamps, “Microstrip microwave antennas,” in The Third USAR Symposium on Antennas Research and Development Program, vol. 1, pp. 189–195, University of Illinois, Monticello, IL, USA, 1953.

“Special Issue on Microstrip Antennas,” IEEE Transactions on Antennas and Propagation, vol. 29, 1981.

S. Bhardwaj and Y. Rahmat-Samii, “Revisiting the generation of cross-polarization in rectangular patch antennas: a near field approach,” IEEE Antennas and Propagation Magazine, vol. 56, no. 1, pp. 14–38, 2014.

P. Bhartia, K. V. S. Rao, and R. S. Tomar, Millimeter-Wave Microstrip and Printed Circuit Antennas, Artech House, Norwood, MA, USA, 1991.

R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook, Artech House, Norwood, MA, USA, 2001.

J. L. Volakis, Ed., Antenna Engineering Handbook, McGraw-Hill, New York, NY, USA, 4th edition, 2007.

D. C. Nascimento, P. C. Ribeiro Filho, A. F. Tinoco-S, and J. C. S. Lacava, “Analysis and design of cavity-backed probe-fed hybrid microstrip antennas on FR4 substrate,” International Journal of Antennas and Propagation, vol. 2015, Article ID 206967, 12 pages, 2015.

H. Pues and A. Van de Capelle, “Accurate transmission-line model for the rectangular microstrip antenna,” IEE Proceedings H - Microwaves, Optics and Antennas, vol. 131, no. 6, pp. 334–340, 1984.

W. F. Richards and Y. T. Lo, “An improved theory for microstrip antennas and applications,” in Antennas and Propagation Society International Symposium, 1979, vol. 29, no. 1, pp. 38–46, Seattle, WA, USA, Jan. 1979.

P. Perlmutter, S. Strikman, and D. Treves, “Electric surface current model for the analysis of microstrip antennas with application to rectangular elements,” IEEE Transactions on Antennas and Propagation, vol. 33, no. 3, pp. 301–311, 1985.

A. F. Tinoco-S, M. V. T. Heckler, R. Schildberg, and J. C. S. Lacava, “Cylindrical: an effective CAD package for designing probe-fed rectangular microstrip antennas conformed onto cylindrical structures,” IEEE Antennas and Propagation Magazine, vol. 50, no. 1, pp. 164–169, 2008.

D. B. Ferreira and J. C. S. Lacava, “An efficient approach to the analysis and synthesis of spherical-circular thin microstrip antennas,” in 2010 IEEE Antennas and Propagation Society International Symposium, pp. 1–4, Toronto, ON, Canada, July 2010.

A. F. Tinoco-S, D. C. Nascimento, R. Schildberg, and J. C. S. Lacava, “Analysis and design of rectangular microstrip antennas for educational purposes,” IEEE Antennas and Propagation Magazine, vol. 53, no. 1, pp. 151–155, 2011.

P. C. Ribeiro Filho, D. C. Nascimento, A. F. Tinoco-S, and J. C. S. Lacava, “Design of flush-mounted hybrid microstrip antennas,” in 2013 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC), pp. 1–5, Rio de Janeiro, Brazil, Aug. 2013.

D. C. Nascimento and J. C. S. Lacava, “Cavity-backed hybrid microstrip antenna on FR4 substrate,” in 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI), pp. 166-167, Orlando, FL, USA, 2013.

D. Ghosh, S. K. Ghosh, S. Chattopadhyay et al., “Physical and quantitative analysis of compact rectangular microstrip antenna with shorted non-radiating edges for reduced cross-polarization radiation using modified cavity model,” IEEE Antennas and Propagation Magazine, vol. 56, no. 4, pp. 61–72, 2014.

Y. Luo and J. Bornemann, “Circularly polarized substrate integrated waveguide antenna with wide axial-ratio beamwidth,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 266–269, 2017.

F. Ren, W. Hong, and K. Wu, “W-band series-connected patches antenna for multibeam applications based on SIW Butler matrix,” in 2017 11th European Conference on Antennas and Propagation (EUCAP), pp. 198–201, Paris, France, 19–24 Mar. 2017.

Z. C. Hao, K. K. Fan, and H. Wang, “A planar polarization-reconfigurable antenna,” IEEE Transactions on Antennas and Propagation, vol. 65, no. 4, pp. 1624–1632, 2017.

D. C. Nascimento, Microstrip Antenna Arrays on Thick Substrates with Control of Main Beam Direction, Side Lobe Level, and Directivity, [Ph.D. Thesis], Technological Institute of Aeronautics, Brazil, 2013.

E. Penard and J. P. Daniel, “Open and hybrid microstrip antenna,” IEE Proceedings H Microwaves, Optics and Antennas, vol. 131, no. 1, pp. 38–44, 1984.

M. H. A. Hassan, Design and Analysis of Substrate-Integrated Cavity-Backed Antenna Arrays for Ku-Band Applications, [Ph.D. Thesis], University of Tennessee, Knoxville, TN, USA, 2011.

P. C. Ribeiro Filho, A. F. Tinoco-S, D. C. Nascimento, and J. C. S. Lacava, “Probe-fed hybrid-patch cylindrical SIW antenna,” in 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI), pp. 1714-1715, Memphis, TN, USA, July 2014.

P. C. Ribeiro Filho, A. F. Tinoco-S, D. C. Nascimento, and J. C. S. Lacava, “Circumferential array of cylindrical hybrid antennas,” in 2015 9th European Conference on Antennas and Propagation (EuCAP), Lisbon, Portugal, April 2015.

Y. T. Lo, D. Solomon, and W. F. Richards, “Theory and experiment of microstrip antennas,” IEEE Transactions on Antennas and Propagation, vol. 27, no. 2, pp. 137–145, 1979.

N. R. Rabelo, Spectral Fields in Multilayer Structures Excited by Embedded Sources, [Ph.D. Thesis], Technological Institute of Aeronautics, Brazil, 2015.

Mathematica, “Wolfram research product overview,” http://www.wolfram.com/.

E. O. Hammerstad, “Equations for microstrip circuit design,” in 1975 5th European Microwave Conference, pp. 268–272, Hamburg, Germany, September 1975.

D. C. Nascimento and J. C. S. Lacava, “Design of low-cost probe-fed microstrip antennas,” in Microstrip Antennas, N. Nasimuddin, Ed., Chapter 01, InTech, 2011.

Y. J. Cheng, Substrate Integrated Antennas and Arrays, CRC Press, Boca Raton, FL, USA, 2015.