1 Introduction

Right from the advent of MPAs at around the earlier part of the 1970s, extensive researches were performed with the intention of improvement in the bandwidth. This can be augmented using familiar techniques, for instance enhancing substrate height (Mishra et al. 2015) or with the help of a lowly contrasted dielectric substrate (Radavaram and Pour 2019). Increment in bandwidth can also be done by locating parasitic patches either in a non-identical (Lee et al. 1987) or in the same layer (Chen et al. 1993), that produces stacked or coplanar configurations, individually. However, stacked configuration does not satisfy a few of the key features of these antennas, for instance low profile and the simple nature in fabrication (Gaharwar et al. 2021), while the coplanar configuration enhances the dimensions of the antenna. Detailed researches have been done to amplify the impedance bandwidth of the antennas which consists of a single-layer and various other studies were carried out that were solely based on wireless sensor communications (Ashraf 2020; Ashraf et al. 2020). Apart from this, research studies were concentrated on ascertaining the varied properties of these U-slot patch antennas (Lee et al. 2010; Weigand et al. 2003; Khan and Chatterjee 2016; Radavaram and Pour 2019; Naz et al. 2020; Deshmukh et al. 2021). Other than the U-slot design, other configurations were also proposed, for instance half U-slot antennas (Mak et al. 2003), C-shaped (Nguyen et al. 2021), E-shaped (Yang et al. 2001) and \(\psi \)-shaped (Sharma and Shafai 2009).

Slot-loaded antennas are extensively useful in the field of wireless communications, as they are inexpensive in comparison to other antennas, and in addition to this, their low-profile nature (Saini and Kumar 2021) makes them invaluable. In general, patch antennas have lesser weights and are significantly in demand owing to the fact that their fabrication process is of simple-nature (Gopi et al. 2021) and on top of that their manufacturing is less tedious. These MPAs are fabricated on a PCB (Printed Circuit Board) using photolithographic techniques (Jung et al. 2020; Yunas et al. 2020; AL-Amoudi 2021). It primarily consists of a flat rectangular metallic sheet, that basically is the “patch” which we know about. It is then placed on top of a dielectric medium, which is the substrate, and beneath this layer there is an additional metal layer, which behaves like the ground plane. The entire radiation procedure happens as a result of the phenomenon of fringing where the virtual length of the patch seems larger than its actual physical length (Balanis 2016). A suitable antenna utilises a patch which is half of an ideal antenna wavelength. Usually, patches are abundant in a variety of sizes and figures. These can be elliptical in nature (Alani et al. 2020; Kaur and Malik 2021), even rectangular in shape (Ata et al. 2020; Bansal and Gupta 2020), or at times, circular (Ou et al. 2020; Prakasam et al. 2020). In addition to all these varieties, a variety of different shape modifications are in abundance. Furthermore, it is possible to create a patch antenna by creation of an arbitrary constant shape (Goudos et al. 2017), but keeping in mind that radiation must occur in an appropriate manner from the patch itself. Usually, ground planes that are virtually large in terms of electrical length (Balanis 2016), create pretty sound radiation patterns and are also responsible in enhancing the overall size of the antenna. Normally, it is quite a common occurrence where the ground plane measurement is slightly larger than patch measurement (Baudha et al. 2020). Assuming that the measurement of ground plane is nearly as close as possible to the dimensions of radiator (Dhara et al. 2021), a situation can arise where coupling can occur, thus producing current at the plane boundaries that can radiate as well. An antenna pattern is established, as a dual set of radiating metal elements combines together to create such an event (He and Li 2020). The process of radiation could be imagined as, that takes place as a result of certain slots that radiate from the topmost and the underlying layer, or at times even simultaneously as a result of current flowing through patch and ground layers.

Applications for the S-band (2–4 GHz) (Prajapati and Rawat 2020; Ghaffar et al. 2021) spectrum have recently attracted a lot of attention. These applications include satellites for communication, radars for precise weather prediction, radars used on ship surfaces, wireless local area network (WLAN), and also for its usage in multimedia, such as mobile TV and radio for satellites, etc. A variety of magnetically electrical dipole antenna designs with higher gain and bandwidth were examined thoroughly (Cai et al. 2020; Sun et al. 2019; Gao et al. 2019).

Upon careful evaluation of the state-of-the- literature, the authors have come to a conclusion that, enhancing the bandwidth of a patch antenna can make it far more effective for wideband applications and make it vastly useful for various wireless communication purposes. Keeping this in mind, a patch antenna is proposed, and its wideband performance is analysed. For this, we have prepared the proposed antenna design, which can generate a good wideband performance, contrary to a normal patch antenna, and in our efforts, we have included several number of iterations building up to the final model, via alterations in the patch measurements. In this endeavour, we have analysed the various performance parameters of our proposed structure like return loss, impedance bandwidth and radiation pattern, along with those iterations as well. Along with these, the plots of gain and VSWR were also studied which are important performance metrics for any patch antenna. Our main goal is to establish that, the proposed design could prove to be a good fit when compared to a conventional patch antenna with regards to its wideband performance and better radiation patterns. And for this reason, we have analysed the performance of our proposed antenna after implementing its design by checking the different performance metrics as mentioned above. The same was done with the help of a software named, Ansoft HFSS (Cendes 2016) which is mainly a simulation software based on antenna design.

2 Theory and formulae

An MPA (Microstrip Patch Antenna) can be easily established by carving slots (Guo et al. 1998) in favourable locations on the patch surface, which can be operated on a relatively smaller dielectric constant and a much broader substrate. The patch length measurement is always a vital factor as the procedure of fringing has an influence on the outcome of this parameter.

2.1 Patch length of proposed antenna

$$ L_{P} \approx \frac{1}{{2f_{res} \sqrt {\varepsilon_{0} \varepsilon_{c} u_{0} } }} $$
(1)

The patch length is denoted as LP, \(\mu_{0}\) signifies free space permeability, and \({\upvarepsilon }_{0}\) signifies free space permittivity, while \({\upvarepsilon }_{\mathrm{C}}\) represents permittivity of Rogers RT/duroid 5880 substrate. fres denotes patch antenna resonant frequency, which will be discussed shortly.

(\({\upvarepsilon }_{0}\) = \(8.85\times 10\)−12 Fm−1 and \(\mu_{0}\) = 1.257 × 10–6 Hm-1)

2.2 Effective length of proposed patch

$$ L_{ef} = \, L_{P} + {2}\Delta L_{P} $$
(2)

The patch antenna effective length is represented as Lef. This is of utmost importance as the effect of fringing (Balanis 2016) makes the patch a touch larger than its actual length virtually, when compared to its tangible dimensions. \(\Delta \)LP is the add-on length of patch antenna.

2.3 Length extension of proposed patch

Like mentioned earlier, the fringing phenomenon makes the antenna enhance its length of the patch.

$$ \Delta L_{P} = \, t\left( {0.{412}} \right)\frac{{\left( {\varepsilon_{ref} + 0.3} \right)}}{{\left( {\varepsilon_{ref} - 0.258} \right)}}\left( {\frac{{\frac{wd}{t} + 0.264}}{{\frac{wd}{t} + 0.8}}} \right) $$
(3)

\(\Delta \)LP symbolizes a slight amendment in patch length that occurs as a result of the fringing process (Balanis 2016). The width of patch and substrate thickness are symbolised by wd and t separately, in the preceding equation.

2.4 Calculation of resonant frequency

$$ f_{res} \approx \frac{c}{{2L_{P} \sqrt {\varepsilon_{c} } }} $$
(4)

In the preceding equation, fres denotes resonant frequency and \({\upvarepsilon }_{\mathrm{c}}\) as mentioned earlier denotes permittivity of Rogers RT/duroid 5880 substrate, having value 2.2.

2.5 Effective permittivity

$$ \varepsilon_{ref} = \frac{{\varepsilon_{c} + 1}}{2} + \frac{{\varepsilon_{c} - 1}}{2}\left[ {1 + 12\left( \frac{t}{wd} \right)} \right]^{{ - {1}/{2}}} $$
(5)

The effective permittivity of the antenna afterwards, when the fringing process has been finally completed (Balanis 2016) at the end, ends up being \(\upvarepsilon \)ref like shown in the preceding equation.

2.6 Bandwidth calculation for the antenna

In general, narrow bandwidth is a major problem when we consider the case of any normal patch antenna. In our case, we have been able to generate a fairly broader bandwidth % after performing several iterations by altering the antenna dimensions like length and width of patch, height of the substrate and several other factors as well, which we will discuss in detail in Sect. 3.1 (ref. Fig. 3a)

$$ BW\% = \frac{{f_{H} - f_{L} }}{{f_{C} }} $$
(6)

where, BW% = Bandwidth %, fH = peak frequency at − 10 dB return loss point, fL = starting frequency at − 10 dB return loss point, fC = center frequency of the patch antenna.

2.7 Inductance for coaxial cable

The inductance for coaxial cable is not just dependant on the material’s dielectric constant encompassed by the pair of conductors, and is related to the logarithmic value of ratio between the conductor couple.

$$ I = 0.459log_{10 } \left( {\frac{Do}{{di}}} \right) $$
(7)

where, I = Coaxial cable Inductance in µH.m−1, Do = Diameter of external conductor, di = Diameter of internal conductor.

2.8 Impedance for coaxial cable

The impedance for coaxial cable is primarily obtained from the internal and external conductor diameters. Aside from this, the dielectric constant is responsible in ascertaining the characteristic impedance.

$$ Z_{ch} = \, \left( {138 \, log_{10} \left( {Do/di} \right)} \right)/\sqrt {\varepsilon_{c} } $$
(8)

where, Zch = characteristic impedance of coaxial cable in ohms.

2.9 Velocity of signal through coax cable

With regards to movement in free space, the signal velocity when passing through a medium (Vm) changes in an inverse manner with respect to square root of \({\upvarepsilon }_{\mathrm{c}}\).

$$ V_{m} = \frac{1}{{\sqrt {\varepsilon_{c} } }} $$
(9)

2.10 Evaluation of antenna radiation pattern

In order to compute the approximate strength of electric field in far field region of the antenna, an equivalent magnetic current line source is assigned at an arbitrary point (Kanda 1990) on the periphery of the patch (\({\overrightarrow{p}}_{l}\)).

$$ \vec{p}_{l} = t\widehat{no}x\vec{F}|_{b} $$
(10)

where, the electric field inside the microstrip cavity (when cavity model is considered) (Palanisamy and Garg 1986) is symbolised as \(\overrightarrow{F}\), \(\widehat{no}\) is the normal which is assumed from patch boundary in the plane of the patch, pointing to the outward direction and x represents the axis on which the normal is taken. The patch boundary, that is represented by b, is present in z = 0 plane, where t represents substrate thickness.

Electric vector potential \(\overrightarrow{V}\) in region of far-field is computed with the help of the following equation (Sarkar et al. 2019).

$$ \begin{gathered} \vec{V}\left( {r,\theta ,\Phi } \right) = \frac{{ - 2{\text{e}}^{{ - jk_{0} r}} }}{4\pi r} \int\limits_{ - \infty }^{\infty } {\iint {\vec{k} \left( {x,y,z} \right)}} \hfill \\ e^{{jk_{0} \left( {x\cos \phi \sin \theta + y\sin \phi \sin \theta + z\cos \theta } \right)}} dxdydz \hfill \\ \end{gathered} $$
(11)

where k0 denotes free-space wave number and r, θ, Φ denote the spherical polar coordinates, where r is the distance from the origin, θ is the angle from the polar direction and Φ is azimuthal angle. The three axes of the cartesian coordinate system are represented by x, y and z. The components of the electric field are accomplished as follows (Werner 2018),

$$ F_{\theta } = k_{0} \left( { - V_{x} \sin {\Phi } + V_{y} \cos {\Phi }} \right) $$
(12)
$$ F_{\Phi } = - k_{0} \left( { - V_{x} \cos {\Phi } + V_{y} \sin {\Phi }} \right)\cos \theta $$
(13)

A decent antenna radiation pattern is a key performance parameter in determining how well an antenna performs. A symmetric pattern of radiation would mean that the antenna radiates well uniformly across all directions. This factor is in addition to the fact, that a patch antenna generates a wideband performance because of change in the antenna height and substrate thickness. The E-field and H-field radiation patterns for the proposed antenna can be seen in Fig. 6a and b, respectively.

3 Design and simulated results of the antenna

In order to propagate the impedance bandwidth, the desired patch antenna is designed by placing symmetrically a couple of opposite-faced U-slots, located equidistantly from the center as given in Fig. 1. The antenna has a size of (l × w = 38 mm × 35 mm) and it is placed upon a substrate that comprises of Rogers RT/duroid 5880 material. It possesses a height of 3.14 mm. The lower part of the substrate is coated with perfect electric conductor (PEC), which behaves like a ground plane. The size of the substrate is l × w × h = 95 mm × 95 mm × 3.14 mm. It is made to feed coaxially with the help of a couple of 50-Ω probes that have the same magnitudes. In order to maintain the symmetry of radiation patterns, the couple of probes should be located at equal distances from the patch centre as demonstrated in Figs. 1 and 2. It must be noted that the asymmetric placement of probes severely affects impedance bandwidth.

Fig. 1
figure 1

Top view of patch antenna design

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Fig. 2
figure 2

Side view of patch antenna design

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The notable characteristic of the proposed antenna, is that it creates a decent range of bandwidth around a particular resonant frequency, interestingly whose value matches exactly with the patch antenna centre frequency i.e., 3 GHz along with having a fairly good impedance match. In addition to this, the patterns of radiation that are acquired, are perfectly symmetrical which indicates that an ideal balance is retained between coaxial probe-pair, and are equi-distant from patch centre.

3.1 Influence on bandwidth through change in antenna parameters

In general, we know that the amendment in length of patch produces shifting in resonant frequency at the output end. A several number of iterations were considered to validate this point. Additionally, certain iterations were also taken care of, where the patch width was modified and thickness of substrate was changed, but the material of the substrate was kept unchanged. A comparative analysis was done for all the parameters with respect to the proposed parameters and a final comparison was done altogether in a graph in order to keep a close eye on where exactly these changes are taking place.

In this case, we are dealing with 3 dB bandwidth, where comparisons were done for the various values for separate iterations with respect to the proposed parameters. As the name indicates, bandwidth of the frequencies for all the iterations were evaluated over a range of 3 dB where the starting and ending values of that range were examined for the desirable resonant frequency. Upon examining the various iterations in Fig. 3b with the modified parameters, a gradual variation is visible in the position of each and every resonant frequency as they move nearer to 3 GHz, which is the design centre frequency.

Fig. 3
figure 3

a Impedance bandwidth of the antenna. b 3 dB Bandwidth analysis of antenna via amendment of specific antenna dimensions

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From the readings, it can be observed that position of resonant frequency for the proposed antenna in Fig. 1, matches exactly with the antenna centre frequency at 3 GHz. This antenna design has minimal losses as it is clear from the reflection coefficient value in the graphical analysis, after comparison with each and every iteration. This even suggests that the impedance match for the antenna proposed is nearly perfect and this explains the decent value of bandwidth. Furthermore, from the graph it can be seen that − 10 dB impedance bandwidth range of the proposed antenna, starts from 2.54 GHz and ends at 3.91 GHz, and its value in % turns out to be 45.67 (ref. Eq. 6) as seen from Fig. 3a.

3.2 Influence on impedance in Smith chart

The amendment in the antenna dimensions too has a say on the impact of impedance on Smith chart. It contributes importantly to the impedance match of an antenna. It is not that hard to determine that the name, Smith chart, originates from the name of its inventor, Phillip Smith, who had founded it around the 1940s. It’s a renowned mechanism for measuring the input impedance and is very widely used for this purpose. Even though, its application is a little less now, after different simulation softwares have come into existence, but despite that, it is significant in its own way as we can see from Fig. 4a and b, for the determination of input impedance.

Fig. 4
figure 4

a Input impedance in Smith chart for the antenna b Analyzing input impedance via amendment of specific dimensions of the antenna

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3.3 Influence on electric field distribution of patch

The distribution of electric field also varies based on the adjustments done to the parameters as visible in Fig. 5a–d. An interesting thing to note is, as we slowly move further from the patch centre towards the slot boundaries, the value of electric field keeps escalating further. Although, the reading at mid-point of the patch is nearly zero and additionally, the subsequent area adjacent to the slots also have no magnitude. Thus, it can be said that changes in the electric field only occurs within the area adjacent to the slots and does not take place anywhere else. Figure 5e shows field distribution of proposed antenna.

Fig. 5
figure 5

a Analysis of electric field distribution of antenna having dimensions l = 40 mm, w = 35 mm, h = 3.14 mm; b Analysis of Electric field distribution of Antenna having dimensions l = 39 mm, w = 38 mm, h = 3.14 mm; c Analysis of Electric field distribution of Antenna having dimensions l = 41 mm, w = 34 mm, h = 3.14 mm; d Analysis of Electric field distribution of Antenna having dimensions l = 41 mm, w = 36 mm, h = 1.57 mm; e Electric field distribution of the Patch Antenna with proposed dimensions (l = 38 mm, w = 35 mm, h = 3.14 mm)

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3.4 Influence on radiation pattern of antenna

The amendment of the patch parameters also brings about variations in the field radiation patterns. From Fig. 6c, it is seen that different E-field radiation patterns of several iterations are analysed. It is seen that; these field patterns slowly move nearer towards the field pattern of the antenna with the proposed dimensions. Determining an antenna radiation pattern is key in analysing the measure of performance of an antenna and more symmetric the pattern, the better will be its radiation. A peak radiation intensity value of 14 dB is achieved for 0o as seen in Fig. 6c apart from it being purely symmetric. Figure 6a and b show E and H field radiation patterns and its importance in judging the antenna bandwidth is discussed in Sect. 2.10.

Fig. 6
figure 6

a E-field antenna radiation pattern; b H-field antenna radiation pattern c Analysis of E-field antenna radiation pattern having specified antenna dimensions

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3.5 Gain and VSWR plot

The gain and VSWR plots with respect to frequency are observed from Figs. 7 and 8 respectively. While noticing Fig. 7, we see a gain of close to 6 dB is achieved for our desired structure for the center frequency of 3 GHz. It’s an acceptable value with regards to Bluetooth and also WLAN networks. Referring to the VSWR graph in Fig. 8, it is seen that a value of 1.03 is achieved which is quite close to an ideal VSWR value. Generally, its value must be below 2, only then we can say that the antenna has a good impedance match. Precisely, it should lie as near as possible to 1. So, its value should lie in between 1 and 2 for an almost perfect match, whereas if VSWR exceeds 2, then it would suggest improper matching of the input and output terminals of the antenna.

Fig. 7
figure 7

Gain vs freq for proposed antenna with value at center frequency = 3 GHz

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Fig. 8
figure 8

VSWR graph of the antenna proposed (value can be seen very near to 1)

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3.6 Comparative study of antenna parameters

Figure 9 shows the Bar graph comparison of the different 3 dB bandwidths with respect to the bandwidth of the proposed resonant frequency. The readings are correlated alongside the measurements of our desired patch antenna in order to check the measure of bandwidth improvement occurring for each resonant frequency. While referring to Fig. 3b, it is seen that the alteration in the parameters causes the resonant frequency for each of the iterations to move closer to the patch antenna center frequency. The most enhanced bandwidth of all the iterations (other than proposed value) that we obtain is 70 MHz for 2.52 GHz of resonant frequency, while the least value that we obtain is 37.5 MHz for a resonant frequency having value 2.69 GHz. The value of bandwidth for proposed dimensions of the antenna at 3 GHz is 100 MHz. It is to be noted that, the improvement in the bandwidth for the 3 GHz centre frequency is zero in the mentioned figure. This is because, the bandwidth at 3 GHz frequency matches identically with the bandwidth at the antenna center frequency, which is 3 GHz as well. Therefore, as both bandwidths are identical at that same frequency of 3 GHz, the improvement in bandwidth for that particular frequency is zero as seen in Fig. 9. The impedance match of the proposed antenna is decent when we consider 1.03 as VSWR value. In ideal cases, 1 signifies perfect matching of an antenna. And normally, decent impedance matching would mean that VSWR value must be below 2. Furthermore, a gain close to 6 dB was achieved for our desired structure at 3 GHz of center frequency. Thus, it can be said that our proposed antenna has a good wideband performance within the range of S-band (2–4 GHz) and is ideally suited to that frequency range.

Fig. 9
figure 9

Bar graph analysis of 3 dB antenna bandwidth

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A detailed analysis was done on the various parameters on patch antenna in Table 1 and these were compared with recent relevant studies to check their variations of different parameters like VSWR, radiation intensity and radiation pattern symmetry. While referring to Table 1, it will be seen that the greatest value of radiation intensity achieved is 14 dB at 0° for our desired structure with the least VSWR value of 1.03 along with symmetric radiation pattern.

Table 1 Comparative study of Antenna Parameters between proposed work and various published articles
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4 Fabricated antenna design

The patch antenna fabricated model is seen in Fig. 10 that has identical dimensions like the one used for simulation. It was initially modelled with the help of Ansoft HFSS and that was followed by printing the design on the surface of a glossy paper. After that, this part of the design was extracted and put on top of a Rogers-RT/duroid 5880 substrate having proposed measurements. Chemical etching procedure was then applied for eliminating the surplus metal surrounding the substrate in such a manner that only the design portion is left intact.

Fig. 10
figure 10

Fabricated prototype of proposed structure

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Some variations are noticeable when simulated and measured results are compared as observed in Figs. 11 and 12. These probably take place as a result of the consequences of the soldering process in the fabricated structure.

Fig. 11
figure 11

Comparison between the results of the values of measurement and simulation for the reflection coefficient of the proposed model

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Fig. 12
figure 12

Comparison between the Results of the values of measurement and simulation for the VSWR of the proposed model

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As it can be seen from Fig. 11, the simulated value of the reflection coefficient for the proposed antenna is − 38.48 dB. Whereas when observe the measured value graph, the value of reflection coefficient is then − 31.05 dB. Likewise in Fig. 12, the difference in values of measurement and simulation is visible from the VSWR plot. From the simulated result, we can see that graph of VSWR is almost 1 at 3 GHz frequency, where the value 1 indicates a perfect match. But in this case, as it can be seen, the measured value is almost at a close proximity to the simulated one for 3 GHz.

5 Conclusion

It is well known that narrow bandwidth is quite an area of concern with regards to patch antennas that hinders their long-term performances. For our case, increment in bandwidth was done for a particular resonant frequency, incidentally that resembles the antenna center frequency of 3 GHz besides having a formidable impedance match. The same was obtained via inclusion of a slot-couple on the patch in addition to having a couple of probes and besides that, a few mathematical iterations were performed on the measurements of the patch. This process was continued and eventually our proposed model was designed, and for a certain resonant frequency of 3 GHz, an impedance bandwidth of 45.67% was achieved, which is more than what a conventional patch antenna would generate at this frequency range of 2–4 GHz (S-band). In addition to this, purely symmetric field radiation pattern of antenna was achieved with a formidable radiation intensity having 14 dB as its value at 0° with a VSWR of 1.03. A potentially high gain of 5.92 dB was achieved with regards to the above-mentioned range of frequency, and all of these factors combined make our antenna a really good candidate for wideband generation within that frequency range. Also simulated results are in good compatibility with the measured values.