Probe-Fed Polygonal Patch UWB Antennas

Abstract

The chapter deals with the design of probe-fed planar antennas to operate at wider bands and techniques to improve peak or boresight gain using reflectors. The phenomenon of frequency excitation in dual-band, that is, C-band and X-band using the technique of partial removal of the ground plane, is well demonstrated here. The impedance bandwidth achieved by the sample antenna is 285 MHz and 380 MHz, respectively. The reduced ground plane technique is further exploited along with modifications in the shape of the ground plane to cover the entire ultra-wideband (UWB) range in a probe-fed hexagonal monopole antenna. Due to the existence of higher modes and especially when fed with a probe, UWB antennas are only capable of providing mediocre gain at higher frequencies. An approach to increase the probe-fed hexagonal UWB antenna’s peak gain involves the utilization of an appropriate reflector. The antenna is given an artificial magnetic conductor (AMC)-based reflector, which increases the peak gain as well as boresight gain across a band ≤ UWB. Peak and boresight gains of 3.74 dB and 5.5 dB, respectively, are observed with AMC. The equivalent circuit model and simulated impedance results of the sample antennas are validated with the measurement results.

1. Introduction

Antennas are essential front-end entities of modern wireless communication systems. Today’s wireless communication systems utilize planar antennas, which are popular over other types of radiators, especially in personal communication devices for wireless access. The reason for the popularity of planar antennas is essentially credited to their being economical, low profile, and easy integration with portable and personal communication devices. The advantages of planar antenna do accompany some drawbacks too, for example narrow bandwidth, poor radiation efficiency, and low power handling capacity. The limitations of patch antennas that need to be addressed in the present communication system are their intrinsic narrow-band behavior and polarization purity [1]. A signal transmitted by any radio base station cannot maintain its polarization state as it transverses toward the mobile terminal device due to channel properties. Thus, the polarization purity of antennas installed in terminal devices cannot be represented as a very strong design constraint [2]. It is difficult to anticipate the polarization state of the signal received on an antenna, even with the use of statistical analysis [3], suggesting that antennas should not be constructed based only on polarization assumptions for the reception. An antenna with a high cross-polarization level is a clear choice for polarization diversity applications and does not negatively affect radio-link performance as in cellular or satellite communications [4]. The necessity to keep the antenna dimensions as small as possible destroys the pretense of meeting greater bandwidth requirements. In the earlier generation of communication systems, the task is usually accomplished by techniques that rely on introducing slots or using reactive loads, but in current and future generation systems, subscriber expectation from service providers is extensive, and thus, novel solutions should be explored.

To guarantee that more services are available on various carrier frequencies, the possibility of a multi-frequency operation is expected in a communication link. Both wide-band and multi-frequency operations rely on the stimulation of two or more resonances, which in the case of wide-band antennas must resonate close together, while in the case of multi-frequency operation, they must resonate widely apart. Polygonal patch forms are an intriguing area for investigation among the patch antenna geometries that exhibit many resonances [5, 6, 7, 8, 9]. For an antenna designer to investigate and excite many resonances to obtain broadband or multi-resonant characteristics for the antenna, the patch size, the number of edges, the slope of the edges, etc. represent acceptable degrees of freedom [10, 11].

Complex electromagnetic wave interactions may be modeled using supercomputing in the frequency and time domains. It’s challenging to create new antenna designs that can carry out demanding duties [12]. Kolundzija et al. [13] proposed an automated meshing of polygonal surfaces to segment a polygonal model into convex quadrilaterals to analyze efficiently as per electromagnetic theory. Sorokosz et al. [14] confirmed that a circular patch can be approximated with an appropriately designed polygon when the model analysis is performed. Many commercial simulation software have emerged during the past two decades, for example, computer simulation technologies (CST), Microwave Studio (MWS), Ansoft HFSS, etc., have supported the rapid advancement of polygonal patch antenna research. They have become fundamental tools in the design and simulation of planar antennas. The excitation and boundary conditions are satisfied via the method of moments (MoM), which makes use of integral equations that are discovered for the fields generated by unidentified currents. Maxwell’s equations are transformed into difference equations via the full wave (FW) approach or the finite-difference time-domain (FDTD) method. The Rayleigh–Ritz variational approach is used by the finite element method (FEM) to solve Maxwell’s equation as the vector wave equation [15]. Yikai et al. [16] reviewed characteristic modes for radiation problems from antenna design to feeding design and found that with the help of many unique and attractive features of control management, physical understandings of the radiating problems can be much clearer, computation burdens in antenna optimization procedure can be greatly alleviated, and designs with favorite features such as compact and low profile can often be obtained. After a real prototype has been built and measured in a lab, the CST MWS Suite enables virtual prototyping of one’s idea, reducing any unpleasant surprises.

Various techniques are available for the fabrication of microstrip patch antenna, but a commonly popular economical fabrication technique such as the wet-etching method will be more suitable in case one of the objectives is technology transfer to the industry shortly. Photolithography technique can be used to transfer the mask image on electroplated copper on a printed circuit board (PCB) using negative photoresist, and then, it is developed in a developer solution. The unexposed unwanted features are etched out in an etching chemical solution.

A polygon with an odd number of edges as in the case of pentagon geometries may be of a symmetrical shape as that of a regular hexagon with an even number of edges or can be asymmetric too. After the substrate thickness and permittivity are chosen, the resonant frequencies of a regular patch rely on the geometry of the conductor. By using the appropriate degrees of freedom, the resonances along the frequency axis may be controlled [11]. Polygonal patch geometries can be triangular or rectangular as per the conventional definition of the word polygon, but in general conception, polygon refers to geometries with edges greater than or equal to five [17]. The text in the chapter will follow this general conception.

The selection of a dielectric substrate for a patch antenna is one of the significant aspects of the antenna design. Many researchers have exploited different dielectric substrates with different permittivities for patch antenna in different applications. Radiofrequency (RF) energy may be provided to microstrip patch antennas using several methods. Contact feed and non-contact feed are two categories into which these approaches may be divided. Microstrip line and coaxial probe feeding are the most often used contact feeding methods, while aperture coupling and proximity coupling feeding are the most widely used non-contact methods. Distinct geometries of patch antenna like a triangular, rectangular, pentagon, hexagon, etc. are well explored by many researchers. By altering the substrate’s dielectric constant, the patch’s sizer and the conductor strip’s metal thickness, any antenna design that is acceptable for operation across a range of impedance bandwidths may be produced. Hexagonal is a popular geometry used to design a stripline-fed monopole antenna [18, 19, 20, 21] and is investigated in detail by Ray et al. [22]. There are dozens of research publications about microstrip patch antennas scattered among traditional periodicals. In a 2012 assessment of patch antenna development strategies, Lee et al. [15] discovered that all the ways that described widening the working bands of patch antennas result in increased volume, negating the low-profile benefit of microstrip patch antennas. Due to its broader band yet higher order modes, the hexagonal structure is favored over other geometries [22, 23]. Further use of the hexagonal shape may be used to produce lower modes and produce broader bands or UWBs.

Ground plane geometry plays a vital role in the design of polygonal patch antenna. For contemporary wireless communication systems, hexagonal monopole antennas fed at the edge and the vertex are extensively investigated at lower frequencies [24]. Because CPW-fed antennas cannot be used for the small overall construction, efficient direct probe feeding becomes the best option. However, employing a coaxial probe or connection to feed a direct-fed UWB monopole antenna presents a problem for antenna researchers. Antenna feed plays a significant role in exciting higher order mode and modification of the feed; such as using a larger diameter probe may permit the antenna to generate a higher order mode [25]. Even with a modified connector feed, the design of a probe-fed UWB planar antenna is still a challenge for the antenna research community. According to [26], adding more ground plane structures may raise the boresight gain of planar antennas; however, the strategy also results in larger antennas. For a stable and reliable radiation pattern, a technique for producing a directed pattern in a hexagonal UWB antenna fed via probe must be understood. The UWB monopole antenna’s peak gain may be increased using a variety of methods, including a reflector with a frequency-selective surface (FSS) base. The gain of the patch antenna at higher frequencies within the operational range of the antenna may be greatly increased by defects in the ground plane, such as the insertion of alternative slot geometries or alteration of the ground plane shape.

The literature survey concludes that although many researchers have explored polygonal geometries through their work, a systematic approach to understanding the effect of polygonal geometry over antenna performance has not been undertaken in the past and still is an interesting subject of research. The main limits of polygonal patch antennas in a present communication system are both the intrinsic narrow-band behavior and the polarization purity. The request to keep the antenna’s overall dimensions small is often made in conjunction to meet these increased bandwidth requirements.

Every novel patch antenna that should be designed, developed, and characterized should achieve some of the common patch antenna features such as compact antenna size, operating band enhancement, gain enhancements, etc. To reduce the size of the antenna by moving the resonance frequency to the lower side, the ground plane defects and fractal geometries should be investigated. A printed circuit board with FR-4 as a dielectric will be an economic approach for designing the polygonal patch antenna. Recent studies point toward the use of coaxial feed as one of the approaches that may yield multiband or broadband antenna characteristics, which may be further exploited to achieve super wide-band characteristics. The literature review reports various attempts to address polygonal patch antenna(s) and to explore it more.

Based on the available literature, the motivation of the chapter is briefed as follows:

• Analyzing a hexagonal geometry, which reveals that antenna performance needs further analysis and still is an interesting subject of research.

• Exploring limits of hexagonal patch antennas such as the intrinsic narrow-band behavior and the polarization purity.

• Keeping the antenna’s overall dimensions small in conjunction with increased bandwidth demands.

• Utilizing an economic printed circuit board with FR-4 as a dielectric for designing the hexagonal patch antenna.

Using a survey of reported literature and preliminary work including hexagram design [27], pentaflake antenna [27], and polygonal patch antenna, it is observed that a probe-fed polygonal patch antenna is not much explored, with coaxial feed as one of the approaches that may yield multiband or broadband antenna characteristics, which may be further exploited to achieve super wide-band characteristics.

2. Low cross-polarization vertex-fed hexagonal antenna

Impedance mismatch affects probe-fed hexagonal patch antennas, particularly when the feed is situated near one of the polygon vertices. High cross-polar levels also affect hexagonal planar antennas. A technique for the low cross-polarization vertex-fed hexagonal antenna is demonstrated. To indicate improvement in impedance values, vertex feeding is illustrated in this section. It has an impedance that is excessive when compared to the probe impedance. The suggested approach may be tuned to match the impedance and obtain excellent return loss. Here, a wide bandwidth (600 MHz) low cross-polarization vertex-fed hexagonal antenna operating at a frequency of 5 GHz is suggested [28]. Therefore, the antenna shown in Figure 1 is a good fit for unlicensed UNII-1 indoor wireless local area network (LAN) applications. Antennas 1–3 (A1, A2, and A3) are similar in structure as shown in Figure 1 but differ in their geometrical features, which are listed in Table 1. These developed antennas will demonstrate the impact of ground plane miniaturization.

Figure 1.

Vertex-fed hexagonal antenna with the reduced ground for (a) A1, (b) A2, (c) and A3. (d) Circuit model of the antenna with its probe feeding network.

Design considerations (mm)	Antenna
	A1	A2	A3
Ground width (wg)	24.44	33.33	39.00
Hexagonal patch circumradius (rh)	12.00	15.00	17.50
Ground reduction factor (Gp)	14.00	19.00	28.00
Effective ground length (lg - Gp)	10.44	14.24	9.00
Feed point radius from O (fr)	10.00	14.00	17.50
Slot radius (rcut)	0.00	2.50	3.00
Substrate length (ls)	32.00	44.44	46.00
Substrate width (ws)	33.50	44.44	46.00

Table 1.

Parameters used for three antenna designs.

The co- and cross-polarization levels are significantly influenced by the substrate dimension [29]. All three antenna designs’ substrate dimensions as presented in Table 1 are set at a value that is optimal to reduce cross-polarization. The antennas may be modeled using a simple RLC resonant equivalent circuit [17, 30] as shown in Figure 1d. According to formulae, lumped elements (RLC) may be derived for all the antennas through Eqs. (1)–(3). Eqs. (1)–(3) can be used to calculate patch capacitance (C_patch), patch inductance (L_n), and patch resistance (R_n) for a given f_n, and they can also be used to calculate Z₁₁ and patch impedance (Z_patch), which are expressed in Eqs. (4) and (5), respectively.

$$C_{\mathit{\text{patch}}}=\left(\frac{{\epsilon }_0{\epsilon }_r}{2h}\right)\left(\frac{3\sqrt{3}{r}_h^2}{2}\right)\left(1-\frac{G_p}{l_g}\right)$$E1

$$L_n=\frac{1}{{\left(2\pi f_n\right)}^2{C}_{\mathit{\text{patch}}}}$$E2

$$R_n=\frac{Q}{\left(2\pi f_n\right)C_{\mathit{\text{patch}}}}$$E3

where f_n is the working band’s center frequency, and h and r_h are the properties of the substrate, respectively. G_p affects the overlapping area of the patch with the ground, resulting in the change of patch capacitance (C_patch). The input impedance (Z₁₁) as shown in Figure 1d with the probe feeding network is given by the following expression.

$$Z_{11}=R_{\mathit{ph}}+j2\mathit{\pi f}{L}_{\mathit{ph}}+\frac{1}{\frac{1}{R_p+\frac{1}{\frac{1}{\frac{1}{\frac{1}{Z_{\mathit{\text{patch}}}}+j2\mathit{\pi f}{C}_{j2}}+j2\mathit{\pi f}{L}_{j1}}+j2\mathit{\pi f}{C}_{j1}}+j2\mathit{\pi f}{L}_0+j2\mathit{\pi f}{L}_p}+j2\mathit{\pi f}{C}_{\mathit{ph}}}$$E4

An equivalent circuit can be modeled along the same lines as in [30] and is presented in Figure 1d. Due to the probe-to-patch junction, the capacitance (C_j1 and C_j2) and inductance (L_j1) are present. When the probe is within the substrate, it displays resistance (R_p) and inductance (L_o + L_p). Resistance (R_ph), inductance (L_ph), and capacitance (C_ph) are introduced depending on how high the probe is above the substrate.

$$Z_{\mathit{\text{patch}}}=\frac{1}{\frac{1}{R_n}+j2\mathit{\pi f}{C}_{\mathit{\text{patch}}}-\frac{j}{j2\mathit{\pi f}{L}_n}}$$E5

then, Eq. (6) may be used to compute the reflection coefficient, S₁₁ (dB).

$$S_{11}\left(\mathit{dB}\right)=20{\mathit{log}}_{10}\left(\frac{Z_{11}-Z_0}{Z_{11}+Z_0}\right)$$E6

where Z₀ is the characteristics impedance of the probe, which is 50 Ω. Eq. (6) may be used to generate the |S₁₁| (in dB) of the resonant equivalent circuit model shown in Figure 1d by simply sweeping the frequency (f) for the desired frequency range. The reflection coefficient generated using the resonant equivalent circuit provides a similar result as obtained using simulation software as shown in Figure 2 for (a) A1, (b) A2, and (c) A3.

Figure 2.

Simulated reflection coefficient, S₁₁ (dB), for (a) A1, (b) A2, and (c) A3.

The value of G_p is varied to analyze its effect on the reflection coefficient of the three-antenna designs used for the analysis and presented in Figure 2a–c, respectively. The following can be concluded by observing the results presented in Figures 2 and 3, that is, simulated and measured, respectively. A ground reduction method is appropriate for matching the impedance of the demonstrated antenna, thereby suppressing any extra resonance. The suggested antenna impedance (53.37-j-5.2) matched at 5 GHz. The Antenna 3 is appropriate for WLAN (UNII-1) applications since it has a 3 dB gain and works at 5 GHz within a 600 MHz bandwidth. Further details regarding low cross-polarization for the vertex-fed hexagonal antenna at the antenna’s boresight may be found in [28], which suggests that antenna 3 ground plane reduction suppresses higher order mode.

Figure 3.

(a) |S₁₁| (in dB), measured return loss (Inset: front and back of the developed antennas). Variation in the antennas’ input impedance: (b) real part, (c) imaginary part.

3. Reduced ground plane probe-fed polygonal patch for C- and X-band applications

This section analyzes and presents the effects of a decreased ground plane on radiation and impedance in a hexagonal antenna that is supplied coaxially. In this study, the measured and simulated impedance findings for an antenna design are compared with the equivalent circuit model. Lower X-band and higher C-band frequencies that are stimulated by the ground plane are reduced. Here, the antenna displayed in Figure 1a and described in an earlier section of the chapter is again used for the analysis. The developed hexagonal antenna makes use of a substrate that measures 32 × 33.5 mm² and a smaller ground plane that is 10.44 (l_g – G_p) × 24.44 (w_g) mm² as shown in Figure 4 [31]. Table 1 for antenna A1 may be referred to for the description and values of all the design variables presented in Figure 4(a). The suggested antenna has an impedance bandwidth in the C-band and X-band of 285 MHz and 380 MHz, respectively. For C-band and X-band applications, the developed antenna with a smaller ground plane performs well.

Figure 4.

(a) Reduced ground plane probe-fed polygonal patch for C and X-band applications. (b) Reflection coefficients (S₁₁) when G_p and f_r = 12.6 mm. (c) Simulated S₁₁ (dB) of the antenna when f_r varies when G_p = 14 mm.

As illustrated in Figure 5, RLC components are employed to mimic the proposed antenna and the corresponding circuit. As mentioned in the third part of the study, the equivalent circuit model is produced for the resonating frequencies of 7 GHz (f₁) and 8.69 GHz (f₂) as observed during experiments on a vector network analyzer (VNA). The values of the lumped component RLC are derived like that used in [32] for an E-patch. For a hexagonal patch antenna, Eqs. (7)–(9) are found by changing the equation provided in [33].

Figure 5.

Circuit model of the antenna with its probe feeding network.

$${\mathrm{C}}^{\text{'}}=C_n=\frac{{\epsilon }_o{\epsilon }_{\epsilon }{{\rm A}}_e}{2\mathrm{h}}$$E7

$$L_n=\frac{1}{\left(2\pi f_n\right)C^{\prime }}$$E8

$$R_n=\frac{Q}{\left(2\pi f_n\right)C^{\prime }}$$E9

where A_e is a patch area over the ground plane, C′ and C_n are calculated using Eq. (7), and n = 1, 2, and so on.

For a complete ground and capacitance of C_n = 4.75 pF (for frequencies f₁ and f₂) as shown in Figure 5, the patch area, A_e, is 374.12 mm². The patch size, A_e = 150.03 mm², and capacitance, C′ = 1.90 pF, are for decreased ground (G_p = 14 mm). The value of the capacitance for the hexagonal patch, which is represented by its series capacitance (ΔC_rg), is decreased as a result of the reduction in the ground. The formula in Eq. (10) may be used to get a hexagonal patch’s extra series capacitance.

$$\frac{1}{C^{\prime }}=\frac{1}{C_n}+\frac{1}{{\mathit{\Delta C}}_{\mathit{rg}}}$$E10

VNA is used to measure the antenna’s reflection coefficient S₁₁ (dB), which is displayed in Figure 6. In Figure 6, simulation results utilizing CST MWS and feed probe data from the RLC model are compared. By observing the measured, simulated, and circuit model bandwidth, it may be concluded that, due to the inductance introduced by the coaxial feed, the VNA bandwidth is lower (SMA connector).

Figure 6.

(a) S₁₁ (in dB), the reflection coefficient of the antenna. (b) Measured real and imaginary impedance (Z₁₁).

To analyze the impedance matching, the real and imaginary impedance parts are measured and compared with simulated results as shown in Figure 6. By using values simulated of real and imaginary impedance, it is shown that the optimal value of input impedance, Z₁₁, at 8.6 GHz is 49.16 - j 27.19 in the operational range for the hexagonal form (Figure 6b). In the operational range of the designed antenna, measurements observed on a VNA reveal that the value of Z₁₁ measured at 8.62 GHz is 50.06 - j 18, which is pretty much like the value described above or observed during simulations.

To attain an X-band lower frequency of 8.69 GHz, the impact of the ground reduction in the hexagonal design is investigated and assessed. By raising G_p from 0 to 18 mm, the ground is reduced. Due to direct probe feeding, inductance is added, reducing the antenna impedance bandwidth. At 7 GHz and 8.69 GHz, the input impedance, Z₁₁, is measured to be 38.6 + j 2 and 50.06 - j 18, respectively. In the operational bandwidth, the radiation patterns are frequency independent. The antenna shown in this section is suitable and affordable for wireless applications since it has a bandwidth of 285 MHz and 340 MHz at frequencies of the C-band and X-band, respectively. The study in this section is limited to impedance analysis. Further analysis such as radiation pattern and gain of the presented antenna is given in [31].

4. Flangeless SMA connector hexagonal UWB antenna fed via probe

This section of the chapter introduces a UWB antenna that is supplied via a flangeless standard SMA connection close to one of the hexagonal patch’s vertices as reflected in Figure 7. Figure 7a uses the same notation as described in Table 1 to describe the design variables. To accomplish UWB with monopole radiation characteristics, the antenna has a ground plane that is half elliptical but truncated and has a rectangular slot. The antenna prototype has a WLAN band rejection of 1.6 GHz from 4.9 GHz to 6.5 GHz and an impedance bandwidth of 8.3 GHz from 2.3 GHz to 10.6 GHz [34]. The removal of flanges transforms a C-band antenna into a UWB antenna, according to antenna tests. The proposed method may be used with a probe-fed antenna to obtain UWB radiation. Measurement results are consistent with what is anticipated based on simulation outcomes.

Figure 7.

UWB hexagonal antenna: (a) Dimensions and layout (c) Simulated |S₁₁| (in dB), when the feed point (f_r) is at 17 mm, and the hexagonal slot radius (r_cut) is 3 mm, for various values of slot width (s_gw) and slot length (s_gl). (d) Simulated scattering parameter, |S₁₁| (in dB) vs. frequency, for various f_r value slot points (f_r) is at 17 mm, and r_cut is 3 mm when slot length (s_gl) is 2 mm and slot width (s_gw) is 10 mm.

It is shown how an antenna presented in this section responds to SMA connection flanges in terms of impedance bandwidth. The suggested antenna displays C-band characteristics when fed via a connector with a flange, but a flangeless connector is a good option to obtain UWB characteristics in a direct-fed antenna. The designed antenna prototype shown in Figure 8 exhibits WLAN band rejection between 4.9 GHz and 6.5 GHz. The designed antenna prototype has a 1.6 GHz WLAN spectrum rejection and is suited for UWB applications between 2.3 GHz and 10.6 GHz.

Figure 8.

Probe-fed hexagonal monopole UWB antenna. (a) Measured |S₁₁| (in dB) and (b) gain (dB).

5. Determination of band edge frequencies of probe-fed printed hexagonal monopole antenna

The calculation of the lowest edge resonance frequency of a printed monopole antenna is not addressed much as done for the resonant frequency of a dipole antenna. It is well known that expressions available for the calculation of the resonant frequency of a dipole antenna cannot be used for the calculation of a lower edge frequency of a printed monopole antenna. Resonant modes in a dipole antenna are generated due to half-wave variation along its horizontal and vertical axis, but printed monopole antennas have negligible patch capacitance. In this chapter, an empirical formula is proposed to calculate the lower and higher edge frequencies of a probe-fed printed monopole antenna as it possesses band-pass impedance characteristics. Three types of printed monopole antennas have been studied and simulated for validation of the empirical formula proposed utilizing full-wave simulation software. It is observed that the probe-fed hexagonal antenna exhibits a wider band, which motivated us to validate the empirical formula through an experiment. Experimental results validated the results obtained from the proposed empirical formula. Percentage error magnitude is also calculated and presented in the section for each case studied in this work.

The empirical formulas for the calculation of the lower edge frequency of the impedance bandwidth (f_L) for a rectangular monopole antenna, a hexagonal monopole antenna, and a circular monopole antenna are given in [22, 35, 36], respectively. A stripline-fed quarter-wave hexagonal monopole antenna is modeled in [22], and the empirical formula to calculate the f_L (in GHz) of a stripline-fed hexagonal monopole antenna is given in [22]. Reference [36] exploits a modified trapezoid-based empirical formula given in [37] to derive the formula for a circular monopole antenna. The expressions given in [22, 35, 36, 37] can be used to calculate the f_L (GHz) of the designed antenna with a stripline feed when fed at the vertex of the printed monopole antenna. As the area of a hexagon is treated as an equivalent circular area, the empirical value of 1.15 is multiplied in the denominator to calculate the f_L of the vertex-fed hexagonal monopole. Also, instead of a quarter wavelength, that is, 0.25 λ, 0.24 λ is used in the expression, which results in a constant of 7.2 in the numerator [22]. Antenna configurations with different patch geometries, that is, rectangle, hexagonal, and circular monopole antenna with dimensions as given in [22, 35, 36], are used to calculate f_L and indicated in Table 2.

Antenna configuration	Measured/simulated fL (GHz)	Calculated fL (GHz) using			Percentage error in fL using
		[35]	[22]	[36, 37]	[35]	[22]	[36, 37]
Rectangle in [35]	1.5	1.35	0.92	1.55	10	38.8	3.3
Hexagon in [22]	1.1	1.06	1.0743	0.8975	3.8	2.336	18.41
Circular in [36]	2.65	3.40	2.54	2.65	28.3	4.2	1.766

Table 2.

Comparison of f_L of various monopole antenna configurations.

The expressions given in [22, 35, 36, 37] are modified by changing the parameters to avoid loss of generality, and f_L can be calculated near practical results. In the case of a printed monopole antenna, the lower edge frequency is a significant parameter rather than the resonant frequency. The lower edge frequency of a printed monopole antenna is given by

$$f_L=\frac{c}{\lambda \sqrt{{\epsilon }_{\mathit{eff}}}}$$E11

where c is the speed of light.

But here, quarter-wave monopole antennas are used and compared. Thus, the length will be L = λ/4, which results in λ = 4L_eff; therefore,

$$f_L=\frac{c}{4L_{\mathit{eff}}\sqrt{{\epsilon }_{\mathit{eff}}}}$$E12

$$f_L=\frac{7.5}{L_{\mathit{eff}}\sqrt{{\epsilon }_{\mathit{eff}}}}$$E13

In the case of a stripline-fed monopole antenna, the effective length will be L_eff = L + L_s, and hence, the lower edge frequency is given by

$$f_L=\frac{7.5}{\left(L+L_s\right)\sqrt{{\epsilon }_{\mathit{eff}}}}$$E14

where effective dielectric constant, ε_eff = (ε_r - 1)/2, ε_r is the permittivity of the substrate material, and L_s is the length of the stripline.

The empirical formula for the calculation of the f_L for circle and hexagonal monopole antenna is modified by considering L = 2 × R and L = 2 × h_r, respectively, where R (in cm) is the circle radius and h_r (in cm) is the circumradius of the hexagon; the final form of the expression is as given in Eq. (15).

$$f_L\left(\mathrm{GHz}\right)=\left\{\begin{array}{c}\frac{7.5}{\left(L+L_s\right)\sqrt{{\epsilon }_{\mathit{eff}}}};\text{for rectangle}\\ \frac{7.5}{\left(2h_r+L_s\right)\sqrt{{\epsilon }_{\mathit{eff}}}};\text{for hexagon}\\ \frac{7.5}{\left(2R+L_s\right)\sqrt{{\epsilon }_{\mathit{eff}}}};\text{for circle}\end{array}\right.$$E15

The empirical formula for f_L calculation of the circular monopole antenna as given in [36, 37] is modified for the hexagonal monopole antenna by considering circumradius W₁ = W₂ = 3 × h_r and L = 2 × h_r, and the final expression for rectangle, hexagon, and circle are given by Eq. (16). Measured and calculated values are displayed in Table 3.

Antenna configuration	Measured/simulated fL (GHz)	Calculated fL (GHz) using the expression		Percentage error in fL for the expression
		(15)	(16)	(15)	(16)
Rectangle in [35]	1.5	1.46	1.55	2.7	3.3
Hexagon in [22]	1.1	1.107	1.11	0.6	0.9
Circular in [36]	2.65	3.51	2.65	32.4	1.766

Table 3.

Comparison of f_L of various monopole antenna configurations using modified formula.

$$f_L\left(\mathrm{GHz}\right)=\left\{\begin{array}{c}\frac{904}{4\mathit{\pi L}+W_1+W_2};\text{for rectangle}\\ \frac{904}{8\pi h_r+6h_r};\text{for hexagon}\\ \frac{904}{10\mathit{\pi R}+120h};\text{for circle}\end{array}\right.$$E16

For the formulation of probe-fed hexagonal monopole antenna, the empirical value, that is, k (dielectric constant), is avoided by assuming it as ‘1’, which is earlier used in stripline-fed hexagonal monopole antennas, due to the fringing extension and the effective dielectric constant (1 < ɛ_eff < ɛ_r [38]). The additional effective h_reff and feed line length are also avoided since a direct probe is used to feed the vertex of the hexagon. Another reason for choosing k = 1 is that due to the negligible capacitance of the patch because of a monopole configuration and purely inductive patch, the effective dielectric constant leads to 1. The hexagonal monopole configuration is conventionally modeled as an equivalent circular monopole antenna. For a vertex-fed hexagonal monopole antenna, the length of the hexagon will be twice the circumradius of the hexagon, that is, L = 2 × h_r; substituting it in Eq. (12) results in Eq. (17).

$$f_L=\frac{c}{4\left(2h_r\right)\sqrt{1}}$$E17

Although expressions for vertex-fed hexagonal monopole have been explored earlier and empirically [22], derived for a stripline-fed antenna, here an empirical formula that is more suited to a probe-fed hexagonal monopole antenna when fed at the vertex of the hexagon is presented:

$$f_L=\frac{7.5}{2h_r}\text{or}\frac{3.75}{h_r}$$E18

where h_r is in cm. The empirical expression can be justified by the fact that the monopole can be modeled as a pure inductance with negligible capacitive effect.

Moreover, the higher edge frequency of the impedance bandwidth (f_H) of the probe-fed hexagonal antenna can also be estimated using the following empirical formula, that is, Eq. (18). A similar technique is used in [21] for the calculation of the f_H of an irregular hexagon. The higher edge frequency empirical formula is because the smallest edge of the patch will contribute to the wavelength; that is, the lowest radiating wavelength will be equal to the edge of the patch with the smallest dimension. But, in a regular hexagon, the edge dimension is the same as the circumradius of the hexagon. The estimation of f_H using Eq. (18) for the probe-fed hexagonal monopole antenna overlooks weakly rejected bands. Although the monopole antenna exhibits high pass impedance characteristics [35], the calculation of f_H is sometimes appreciated while designing UWB monopole antennas.

$$f_H=\frac{c}{h_r\sqrt{{\epsilon }_{\mathit{eff}}}}$$E19

where c is the light speed in free space, h_r is in meters, and ɛ_eff = (ɛ_r + 1)/2.

The effective dielectric constant in Eqs. (18) and (19) is estimated from enormous simulations, experiments, and analyses to achieve an appropriate empirical formula for a probe-fed hexagonal monopole antenna. Eq. (18) is used to calculate the f_L for three planar monopole antennas, that is, square, circle, and hexagon. All three antenna configurations are assumed to have the same circumradius of 16.5 mm. The calculated values of f_L are indicated in Table 4. The values of f_L are further verified through CST MWS simulation results.

Antenna configuration	Simulated		Calculated		Percentage error in
	fL (GHz)	fH (GHz)	fL (GHz) using expression (18)	fH (GHz) using expression (19)	fL	fH
Rectangle	2.3	11.2	2.27	11.2	1.3	0
Circle	2.4	8.9	2.27	11.2	5.41	25.8
Hexagon	2.3	11.6	2.27	11.2	1.3	3.4

Table 4.

Comparison of f_L of proposed probe-fed monopole antenna configurations using proposed formula.

Three different probe-fed monopole antenna configurations, that is, rectangle, circle, and hexagon with feed position at the vertex of the polygon, are designed in CST microwave studio as shown in the inset of Figure 9a and simulated for S₁₁ characteristics of the designed antenna as reflected in Figure 9a. The probe at the vertex of the polygon helps in designing the monopole antenna by avoiding overlapping with the ground. The patch has been modeled as a regular design with the circumradius h_r. The three designed configurations consist of an FR-4 substrate of 46 × 46 mm², a ground plane with dimensions 3 × 40 mm², and a patch with a circumradius of 16.5 mm. The ground dimensions of the antenna configurations are chosen such that the designed probe-fed hexagonal monopole antenna has a minimum size. All three antennas have almost the same lowest edge frequency as may be observed from Figure 9 at −10 dB and as indicated in Table 4.

Figure 9.

(a) Scattering parameter, |S₁₁| (in dB) of different monopole antenna configurations (Inset: pictures of antennas). (b) Variation in f_L with h_r of probe-fed hexagonal monopole antennas.

Eq. (18) is found to be more suitable for a probe-fed hexagonal monopole antenna, especially when fed at the vertex of the hexagon, which yields f_L = 2.27 GHz, which provides an error of 1.3% as indicated in Table 4. As observed from Figure 10, the probe-fed hexagonal monopole antenna possesses wideband characteristics and was further chosen for fabrication to design a probe-fed UWB monopole antenna. The hexagon monopole antenna shows weak rejection at 4.3 GHz as depicted in Figure 10.

Figure 10.

|S₁₁| (in dB) for probe-fed hexagonal monopole antennas.

The value of f_L is calculated for different values of h_r using Eq. (18) and observed using CST software for probe-fed hexagonal monopole antennas. The optimized value of h_r of probe-fed hexagonal monopole antennas demonstrates maximum bandwidth, for a given f_L, and is displayed in Figure 9b. The probe-fed hexagonal monopole antenna, especially when fed at the vertex of the hexagon, demonstrates maximum bandwidth because of the best transition of impedance bandwidth.

f_L is found to be 1.72 GHz when h_r = 1.65 cm using Eq. (14). The dimensions of the hexagon mentioned earlier are chosen to accommodate the entire S-band along with the UWB band. But, after fabrication, the f_L calculated using Eq. (14) provides an error of 25.21%, because probe feeding is used for the excitation of the hexagonal monopole antenna. A more suitable expression for the calculation of f_L for probe-fed hexagonal monopole antenna is presented in Eq. (17), and it provides an error of only 1.3% (Figure 10).

A simple empirical formula has been proposed and presented to accurately calculate the lower edge frequency of probe-fed regular hexagonal monopole antennas. The antenna is fed at the vertex of the hexagon and found that the values obtained for lower edge frequency are quite close to the simulated and measured |S₁₁| results of the designed and developed antennas. Lower edge frequency dependency of the probe feeding on the square, circle, and hexagon monopole antenna has been studied using simulation for maximum bandwidth, and the S₁₁ results have been demonstrated. The lower edge frequency of the probe-fed hexagonal monopole antenna also depends on the hexagon circle radius, and its variation is also presented. The probe-fed antenna designed using the presented expression demonstrates UWB performance, which ranges from 2.3 GHz to 10.6 GHz with a weak rejection between 5 GHz and 6.5 GHz. The calculated lower and higher edge frequencies of the designed antenna are found to be 2.27 GHz and 11.2 GHz, respectively, which provide an error of only 1.3% and 3.4%, respectively, when compared with the measured S₁₁(dB) results.

6. Gain boosting of a probe-fed hexagonal UWB antenna using an AMC reflector

Due to the existence of higher modes, particularly when fed with a probe, UWB antennas are restricted to having weak gain at higher frequencies. In this section, a technique for increasing the peak gain of a hexagonal UWB antenna fed via probe is presented. An artificial magnetic conductor (AMC)-based reflector is added to the antenna shown in Figure 11, enhancing both the peak gain for UWB antennas and the boresight gain to a broader band. Peak and antenna boresight gain improvements on average are 3.74 dB and 5.5 dB [39], respectively. In the presence of an AMC-based reflector, the boresight gain increases, becoming positive for a 1 GHz broader band. The UWB antenna measures 46 by 46 mm², while the AMC reflector increases the antenna’s overall size to 100 by 100 mm². The suggested antenna configuration is suitable for UWB applications and may provide a directed and steady radiation pattern.

Figure 11.

Probe-fed hexagonal UWB antenna using an AMC reflector: (a) Design; (b) |S₁₁| (dB); (c) boresight gain (dB); (d) peak gain (dB).

The presented antenna’s boresight and peak gain are compared and shown in Figure 11c and d, respectively, to help comprehend the gain enhancement phenomena brought on by the AMC reflector. In Figure 11c, it is apparent. In the simulation, the AMC reflector increases the average boresight gain by around 5.46 dB. Without an AMC reflector, the antenna’s positive boresight gain is visible between 2.2 GHz and 4.3 GHz, whereas with an AMC, a broader band between 2 GHz and 5.8 GHz is seen. The observation of a large increase in boresight gain across a broader band emphasizes the need for an AMC reflector. The boresight gain of the antenna is measured and shown in Figure 11 to better understand how AMC affects the augmentation of boresight gain. During testing, the antenna’s boresight gain seems to be positive across broadband that spans from 2 GHz to 6 GHz as opposed to 2.2 GHz to 4.5 GHz when no AMC reflector is used. During testing, it is shown that applying AMC to a hexagonal monopole antenna increased the average boresight gain by a factor of 5.5 dB.

The use of an AMC reflector with a square-shaped loop unit cell to convert a monopole-like radiation pattern into a directional pattern increases the gain of the presented antenna. To increase the peak gain and gain of the UWB antenna, an AMC reflector with a 20 by 20 array of unit cells is built at the rear of the hexagonal radiator. After using an AMC reflector, the antenna’s boresight and peak gain are both greatly improved by around 5.5 dB and 3.74 dB, respectively. The antenna that has been put together with AMC may be used for UWB applications.

7. Conclusions

Polygonal patch antenna is the keystone of modern wireless communication systems and services. In the development of contemporary wireless communication systems, an antenna with a wide radiation bandwidth is demanded to cater to such a demand. These concerns encourage the antenna researcher to design an antenna with a wide radiation bandwidth.

Hexagon is chosen here to fulfill the requirement of modern wireless communication systems and services while maintaining a fundamental mode. Feed is an important part of the antenna; the impedance and the gain will influence the antenna performance. To increase the antenna’s bandwidth, the specified antenna probe feed point is altered. According to the probe feed analysis, a polygonal patch antenna’s wideband performance is optimal when the feed point is maintained closer to the polygon’s vertex.

Hexagonal patch antennas with probes show narrow band behavior. It is shown how a vertex-fed slotted hexagonal antenna with a truncated half elliptical ground plane responds to SMA connection flanges in terms of impedance bandwidth. The suggested antenna displays C-band characteristics when fed via a connection with a flange, but a flangeless connector may be used to obtain UWB characteristics in a direct-fed antenna. A ground plane reduction approach is also employed that changes the dipole configuration to a monopole configuration to obtain UWB using a hexagonal patch. The ground plane slot enabled the antenna’s bandwidth to be increased. Multiple modes in the UWB band are excited using a rectangular slot and a ground plane reduction approach. The antenna has broadband between 2.4 GHz and 10 GHz.

The use of an AMC reflector with a square-shaped loop unit cell to convert a monopole-like radiation pattern into a directional pattern increases the gain of the hexagonal UWB antenna. To increase the peak gain and gain of the UWB antenna, an AMC reflector may be mounted at the rear of a hexagonal radiator. After using an AMC reflector, the presented antenna’s boresight and peak gain are greatly improved by around 5.5 dB and 3.74 dB, respectively. The antenna that has been put together with AMC may be used for UWB applications.

Acknowledgments

This research work was funded by the Department of Science and Technology, New Delhi, India (Reference Number: SR/FST/ETI-346/2013) for equipment.