1 Introduction

Micro-strip patch antennas are extensively used in missiles, radar, aircraft, remote sensing, satellite communications, biomedical telemetry and other wireless communication systems, but the micro-strip antenna designer often encounters the problem of designing a suitable radiating patch for different applications. The design of a radiating patch or ground plane is rather intuitive and is the choice of the designer. Radiating patch as well as ground plane design, its size, slots, notches and their size and geometry determine the antenna parameters like resonant frequency, impedance bandwidth, gain, radiation pattern and efficiency; therefore, these physical parameters become important for an antenna designer. The literature is full of micro-strip antennas with different geometrical shapes and numeral- and alphabet-shaped radiating patches. At present, micro-strip antenna designs are oriented towards designing multiband antennas [1,2,−3] with a shape which occupies a lesser patch area and volume. Such antennas are advantageous due to volume and area reduction and are good candidates to be embedded in small devices and MMICs.

Modern-day global mobile communication systems (GSM) require antenna bandwidth about 7.6%, around 9.5% for digital communication systems (DCS), 12.2% for universal mobile telecommunication systems (UTMS) and 7.5% for personal communication systems (PCS) [4]. The designers are trying to meet out these bandwidth requirements in addition to improving antenna gain and radiation efficiency. However, the narrow bandwidth, low gain and poor radiation efficiency restrict the applications of micro-strip patch antenna [5]. The researchers are trying to improve the bandwidth of the patch antenna by employing different shapes and sizes of the radiating patch, loading slots and notches of different sizes and shapes. Loading different shapes and sizes of slots and notches in the ground plane or on the patch not only leads to the reduction in the planar area of patch and shift in resonant frequency but also increases the current length and thus enables the antenna to operate at dual or multi-bands [2, 6,7,−8].

However, other bandwidth enhancement techniques are also available, but the technique of loading slots or notches is simple and improves the bandwidth without increasing the volume of the structure. Recently a dual-band patch antenna using slots is reported [7] with an improved bandwidth of 14.08/13.3% at lower/higher resonant frequencies. This dual-band antenna was modified to a wide-band patch antenna, and further an improved bandwidth of 25.87% is reported [7].

A short description and review of the alphabet-shaped micro-strip antenna are presented in Table 1. It is inferred from the perusal of Table 1 that the D-, I-, J-, L-, Q-, V- and Z-shaped antennas are exhibiting single resonant frequency, whereas B-, C-, E-, F-, G-, H-, K-, M-, N-, O-, P-, R-, S-, T-, W- and Y-shaped antennas are resonating at dual frequencies. A-, M-, U- and X-shaped antennas are resonating at three different frequencies. Lower resonating frequencies (Lfr) of B-, F-, G-, H-, O-, P-, T-, U-, V-shaped antennas lie within the 2.4–2.7 GHz frequency band. However, D- and I-shaped antennas are single resonant frequency antennas (both resonating at 2.4 GHz) and the M-shaped antenna is resonating at both dual and triple frequencies (2.44/5.77 and 2.4/3.5/5.8 GHz). The antennas operating either at a standalone frequency (D-shape), dual or multiple frequencies, or at the frequency band of 2.4–2.7 GHz are useful for WLAN applications. 2.4 GHz center frequency is allocated to ISM band applications as per the Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT) and approved in 2016 [9].

Table 1 Description of alphabet-shaped micro-strip patch antenna
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Higher resonating frequencies (Hfr) of B-, F-, G-, H-, K-, M-, O-, P-, T-, U- and W-shaped antennas lie between 5.0 and 5.8 GHz frequency band. However, Z-shaped antenna is resonating at a single resonant frequency of 5.25 GHz, whereas the K-shaped antenna possesses peculiar resonating frequencies of 5.2/5.8 GHz which is within 5.0–5.8 GHz band of frequency. This frequency band (5.0–5.8 GHz) is allocated to Industrial, Scientific and Medical (ISM) band [9] which includes WiFi (802.11ac, 802.11n), cordless phones, radio-frequency identification devices (RFID). This band is also useful for WiMAX/WLAN applications. Higher resonating frequencies (Hfr) of A-, C-, E- and J-shaped antennas lie between 6.0 and 10.0 GHz frequency bands which are useful for C-band applications and satellite communications.

Lower resonating frequency of C (4.14 GHz)- and W (4.17 GHz)-shaped antenna lies in C-band, and they find use in WiMAX applications, whereas E (3.1 GHz)-shaped and one middle band of M- and U-shaped antenna as well as lower resonating frequency of Y-shape (3.5 GHz) lies in S-band and are used for broadband wireless access systems. The J-shaped antenna is operating in the X-band frequency range which is utilized in military requirements for land, airborne and naval radars.

L- and Q-shaped antennas are operating at single resonant frequencies of 1.6 GHz and 1.93 GHz. L-shaped antenna finds applications in global positioning systems (GPS) and voice and data communications, whereas Q-shaped antenna finds use in applications such as mobile communication services on board aircraft (MCA) and mobile communication services on board vessels (MCV). The lower resonating frequency (1.48 GHz) of the N-shaped antenna is useful for mobile/fixed communication networks (MFCN) and terrestrial equipment for digital audio broadcasting (T-DAB). The higher resonating frequency (4.9 GHz) of N-shaped antenna is used in military systems and radio astronomy.

Lower/higher resonating frequencies (0.225/0.450 GHz) of R-shaped antenna find the applications in terrestrial broadcasting and onsite paging including wide area paging in a tuning range of frequency. The lower/higher resonating frequency (0.9/2.0 GHz) of S-shaped antenna is utilized for GSM mobile applications and for mobile satellites service including handheld earth stations.

Resonant frequencies of X-shaped antenna (15.3/17.6/18.9 GHz) are useful for K- and Ku-band applications. The lower frequency (15.3 GHz) finds applications in passive sensors of the satellite systems and military radiolocation, whereas the higher frequencies (17.6/18.9 GHz) are used in earth stations on mobile platforms (ESOMPs) in the frequency bands available for use by uncoordinated fixed-satellite service (FSS) earth stations within the ranges of 17.3–20.2 GHz.

The higher resonating frequency (4.63 GHz) of Y-shaped antenna is useful for military applications and fixed-satellite services. Among the single resonating antennas of Table 1, we observe maximum impedance bandwidth (45.71%—simulated, 23%—measured) for I- and L-shaped antennas, respectively. The minimum impedance bandwidth (3.2%—measured) is reported for V-shaped antenna among single-band antennas. A maximum measured impedance bandwidth of 87.7% (6.66 GHz—C-shape) and minimum impedance bandwidth of 0.57% (2.44 GHz—M-shape) are reported among the antennas resonating at dual frequencies.

Considering the antennas operating at three different resonant frequencies, the X-shaped antenna exhibits the minimum impedance bandwidth (3.27%—simulated), whereas maximum impedance bandwidth (47.42%—measured) is observed for U-shaped antenna. As the X-shaped antenna is operating at a higher frequency range (15.3–18.9 GHz), its low impedance bandwidth is predictable. In case of triple resonating antennas (except X-shape) operating between 2.4 and 6.58 GHz, a maximum impedance bandwidth of 47.42% (U-shape) and minimum impedance bandwidth of 3.9% (M-shape) are observed.

We observe a maximum impedance bandwidth of 50% (N-shape, 1.48 GHz) and minimum impedance bandwidth of 3.35% (R-shape, 0.450 GHz) for the resonating frequencies between 220 and 2000 MHz. Similarly, antennas operating between 2.1 and 3.1 GHz show a maximum impedance bandwidth of 45.7% (I-shape, 2.4 GHz) and a minimum impedance bandwidth (0.57%) for M-shape at 2.44 GHz.

The antennas operating between 3.2 and 4.9 GHz show a maximum/minimum impedance bandwidth of 65.2% /3.9% for C-shape and M-shape, respectively. We observe a maximum impedance bandwidth of 87.7% for C-shaped (6.66 GHz) and minimum impedance bandwidth 2.77% (theoretical) for W-shaped (5.78 GHz) antenna operating between the frequency ranges of 5.0–7.2 GHz.

Two antennas (J-shape and X-shape) are operating between the frequency ranges of 8.0–19.0 GHz) wherein we observe a maximum impedance bandwidth of 10.54% (J-shape) and a minimum impedance bandwidth of 3.27% (X-shape).

Table 1 shows that the X-shaped antenna occupies the minimum area (75.62 mm2). X-shaped antenna due to the minimum area is exhibiting higher resonating frequencies (15.3–18.9 GHz). L- and Q-shaped antennas have the maximum area (4900 mm2 and 4680 mm2), and both the antennas are operating at a single band with impedance bandwidths around 20% and with gains of 2.45 and 7.9 dBi. The large impedance bandwidth and gain are obtained at the expense of a large area. The C-shaped antenna (dual band) with an area of 625 mm2 has the highest impedance bandwidth (65.2/87.7%) at the resonating frequencies of 4.14/6.66 GHz. However, the gain of 3.5dBi is achieved which is expected because it is difficult to achieve a large bandwidth and high gain simultaneously.

The antennas operating at triple band are designed and fabricated with a maximum area of 3968 mm2 (M-shape) and a minimum area of 75.62 mm2 (X-shape). However, the small area also reduces the impedance bandwidth (3–4.5%).

Maximum simulated/theoretical gain is observed in W-shaped antenna (9.06 dBi at 4.18 GHz), and minimum simulated/theoretical gain is observed in O-shaped antenna (1.26 dBi at 2.47 GHz). Maximum measured gain (5.7 dBi at 6.58 GHz) is observed in A-shaped antenna, and minimum measured gain is observed (1.5 dBi at 2.42 GHz) for G-shaped antenna.

2 H-shaped Antennas

We have come across a sufficient number of H-shaped patch antenna designs which is the basis for proposing a new H-shaped (alphabet-shaped) patch antenna and for comparative study. A brief survey of reported H-shaped antennas in terms of shape, size, substrate material, simulated tools used along with the applications of the patch antenna is presented in Table 2.

Table 2 H-shaped antennas with tabulated parameters
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The H-shaped patch antennas as reported in the literature (Table 2) are not based on gap coupling, and also parasitic patches have not been used in the reported antenna designs. The H-shaped antenna proposed in this work is different from other reported antennas as the parasitic patches (three parasitic patches) are gap-coupled to the fed patch, whereas the other reported antennas are not designed using the concept of gap coupling.

Table 2 shows reported H-shaped antennas along with its parameters for comparison. Formation of H-shape in each case as shown in Table 2 is conceptually different, but visually all of them appear to be H-shaped antenna. The patch area of the proposed antenna (1024 mm2) is less approximately by the factors of 1.7, 1.13, 1.56 and 2.34 than that of antennas referred to in references [10,11,12,−13], whereas it is large approximately by the factors of 1.4, 1.2 and 1.1 as compared to the antennas reported in references [14,15,−16]. The antennas presented in Table 2 have been simulated by means of commercially available tools like CST Microwave Studio, IE3D, AWR and HFSS and through the programming of FDTD and MOM codes. However, it is true that the conditions and specifications for each antenna are different, different simulation environments have been used, and no exact comparison can be drawn between two antennas, but still it is fair enough to draw comparison on the basis of its visual shape, i.e., H-shape, their applications and the range of frequency in which these antennas are operating. In the foregoing section of results and discussion, an investigative study of various antennas of Table 2 has been made.

3 Design and Analysis of Gap-coupled H-shaped Antenna

The present design is unique in the sense that it uses the concept of gap coupling to create H-shape, whereas the other reported H-shaped antennas (given in Table 2) are not gap-coupled antennas. This unique feature leads to the improvement in bandwidth and reduction in overall patch area and volume.

Design and simulation of the proposed antenna structure are carried out by means of two electromagnetic tools, viz. High Frequency Structure Simulator (HFSS) and Microwave Office of Applied Wave Research (AWR). The proposed antenna is a sequential development of three antennas (antenna 1, 2 and 3), and its return loss versus frequency analysis has been performed to finalize the proposed structure. The proposed antenna (antenna-4) is fabricated on FR4 epoxy substrate (\( \epsilon_{r}\) = 4.4). Antenna parameters like return loss, VSWR, radiation pattern, gain, frequency ratio and surface current distribution and group delay determine the performance of the antenna. VSWR, return loss and group delay are experimentally measured by vector network analyzer E5071C.

The geometry of the proposed antenna is shown in Fig. 1 and its prototype is fabricated for the experiment. Two vertical slots of dimension \( ({{L}}_{{{n}}} \times {{W}}_{{{n}}} ), \) along the y-axis, and one horizontal slot of dimension \( \left( {{{L}}_{s}\times { W}_{{{s}}} } \right)\) have been cut on a circular patch of diameter ‘D’ to obtain H-shaped geometry. A patch placed closed to the fed or driven patch gets energized through the suitable coupling between the two patches, and such patche is termed as parasitic patch. H-shaped cut on the circular patch creates four small patches which are electromagnetically coupled by the proper adjustment of the space (\( {\varvec{W}}_{{\varvec{s}}} \user2{ }\) = \( \user2{ W}_{{\varvec{n}}} = {\varvec{W}}\)) between parasitic and fed patch. The gap between the fed and parasitic patch is normally represented by an equivalent T or π-circuit, and gap coupling provides improved bandwidth [17, 18]. The patch is excited via coaxial feed with 1 mm diameter and 50 Ω characteristics impedance.

The side view and the top view geometries of the proposed patch antenna are shown in Fig. 1a, b, and the related design parameters are presented in Table 3. Figure 1c, d shows the photograph of front and back views of the fabricated antenna.

Fig. 1
figure 1

Geometrical configuration and fabricated photograph of gap-coupled H-shaped antenna: a side view, b top view, c top view of fabricated antenna and d rear view of fabricated antenna

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Table 3 Specifications of the proposed antenna with dimensions
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4 Results and Discussion

The proposed dual-wideband antenna has been successfully designed, fabricated and tested for its desired performance. The results are obtained by using the finite element method-based simulator, HFSS [19], and method of moments-based simulator, AWR [20], and the return loss, VSWR and group delay are experimentally verified by vector network analyzer E5071C.

Simulated return loss versus frequency analysis is presented in Fig. 2 for antennas 1–4. The analysis has been performed to optimize the antenna configuration, and on the basis of analysis, antenna 4 has been chosen as the proposed antenna. A perusal of Fig. 2 clearly shows that the return loss of antennas 1 and 2 is not sufficient (below − 10 dB emission point) for any practical use, whereas a single operating band is observed for antenna 3. We observe dual band in antenna structure 4 and maximum return loss (above − 10 dB emission point) at both the operating frequencies. To obtain a symmetrical pattern along radiating patch, identical parasitic patches are gap-coupled to both the radiating edges of the main fed patch so that the phase delay for both the parasitic patches remains the same and the overall pattern of three patches is superposition of the individual pattern and tends to remain symmetrical [13]. The dimension of the fed patch is large as compared to parasitic patch in case of antennas 1 and 2, and also there is no parasitic patch on the other side of the radiating patch. This geometrical configuration of the antennas 1 and 2 is responsible for the absence of dualband and return loss below − 10 dB emission point. Antenna 3 because of the symmetrical parasitic patches on both sides of the radiating patch produces a single band around 3.7 GHz with a return loss of − 24 dB, but it still fails to produce dual band. The dimension of the parasitic patch is less as compared to the main fed patch, and it fails to provide the sufficient electrical coupling to create a dual band.

Fig. 2
figure 2

Simulated (HFSS) return losses |S11| versus frequency for different radiating patches (antenna 1–4)

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By cutting a horizontal slot in mid of the x-axis in antenna 3, a parasitic patch of the same dimension as that of the fed patch is created which results in the configuration of antenna 4. The newly created parasitic patch is also coupled through the slot with the parasitic patches situated on either side of the radiating patch. The geometrical configuration of antenna 4 reveals H-shaped slot which couples the radiating and parasitic patches both. The symmetry of parasitic patches and gap coupling in antenna 4 provides dual band with sufficient return loss.

The current distributions of the proposed antenna (antenna 4) at resonant frequencies (3.8 GHz and 4.7 GHz) are shown in Fig. 3a, b. From Fig. 3, it is observed that the maximum current strength is obtained in the left parasitic patch at 3.8 GHz and in the upper parasitic patch at 4.7 GHz of the proposed antenna. Current distribution on the radiating patch reveals that the current is flowing along the x-axis at 3.8 GHz and along the y-axis at 4.7 GHz and are responsible for the generation of TM10 and TM01 excited modes, respectively.

Fig. 3
figure 3

Current distribution of gap-coupled H-shaped antenna at a 3.8 GHz and b 4.7 GHz

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The variation of return loss with frequency for different substrate thicknesses ‘h’ in case of the proposed antenna is shown in Fig. 4. From Fig. 4, it is observed that as the value of h increases from 0.6 to 2.6 mm, lower resonant (\( Lf_r \)) and higher resonant (\( Hf_r \)) frequencies are shifted toward the lower scale of the frequency axis. The impedance loci tend to become more inductive as the thickness of the substrate increases. An inductive shift is primarily caused by a thick substrate, and it is one of the primary reasons for a shift in resonating frequencies [21].

Fig. 4
figure 4

Return loss (|S11|) as a function of frequency for different substrate thicknesses ‘h’

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In Fig. 5, the plot of |S11| as a function of frequency is shown, which demonstrates the variation of gap length (\( {\text{W}}_{{\text{s}}}\) = \( {\text{W}}_{{\text{n}}}\)) between the parasitic patch and fed patch. We observe from Fig. 5 that the gap length of 2 mm and 1.5 mm produces only single resonant frequency between 4.6 and 4.8 GHz, whereas the gap length of 1 mm produces dual resonant frequency between 3.8 and 4.7 GHz and therefore has been chosen as optimum gap length for fabrication and testing.

Fig. 5
figure 5

|S11| as a function of frequency for different gaps (Ws) between radiating and parasitic patches

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The lower resonant frequencies as observed from Fig. 6 are 3.8 GHz (HFSS), 3.84 GHz (AWR) and 3.77 GHz (experimental). The higher resonant frequencies (cf. Fig. 6) are 4.7 GHz (HFSS), 4.6 GHz (AWR) and 4.65 GHz (experimental).

Fig. 6
figure 6

Simulated (HFSS and AWR) and experimental |S11| versus frequency of proposed antenna

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The calculated bandwidths of the antenna at lower resonant frequencies are 4.0% (HFSS), 4.2% (AWR) and 3.7% (experimental), whereas at upper resonant frequencies are 7.6% (HFSS), 2.6% (AWR) and 9.4% (experimental) as observed from the perusal of Figs. 7 and 8. We observe maximum return loss of − 14.56 dB (AWR), − 16 dB (experimental) and − 17 dB (HFSS) at lower resonating frequencies of 3.84 GHz, 3.80 (HFSS) and 3.77 GHz, respectively. Numerical values of maximum return loss at higher resonating frequencies are − 18.2 dB (AWR), − 36.75 dB (HFSS) and − 40 dB (experimental) observed (cf. Fig. 8) at resonating frequencies of 4.6 GHz, 4.7 GHz and 4.65 GHz, respectively.

Fig. 7
figure 7

Simulated (HFSS and AWR) and experimental impedance bandwidth at |S11|

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Fig. 8
figure 8

Simulated (HFSS and AWR) and experimental impedance bandwidth (-10 dB) and |S11| at different resonating frequencies

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A negligible difference is observed between simulated (AWR and HFSS) and experimental results at the lower resonant frequency. In AWR simulation tool shape of the feed is solid rectangular, and in HFSS a cylindrical-shaped coaxial feed is used. The area of the rectangular feed has been taken the same as that of the area of cylindrical feed (AWR), which is a kind of mathematical approximation, and the effect of feed shape is more predominant at the higher resonant frequency as compared to the lower resonant frequency which results in lowering of return loss values and impedance bandwidth. Simulating the frequency in very small step size of below 0.1 GHz for this structure is not possible in AWR, whereas the structure was simulated by taking step size of 0.01 GHz in HFSS which leads to the difference in simulated and measured results and the effect of step size is more pronounced at higher frequencies. Further, the differences in simulated (AWR and HFSS) return loss, impedance bandwidth and resonating frequencies are attributed to the fact that AWR utilizes the method of moments, whereas HFSS is based on finite element method.

A perusal of Table 2 reveals that the simulated impedance bandwidths (3.66%, 1%) of patch antenna referred to in references [11, 15] at lower resonating frequencies (Lfr) (3.35, 2.75 GHz) are less than those of the proposed antenna with simulated impedance bandwidths of 4% (3.8 GHz-HFSS) and 4.2% (3.84 GHz-AWR). The antenna reported in [11] is fabricated using foam as a substrate with substrate height of 6 mm with a patch area of 1158 mm2. The total volume (6948 mm3) of the antenna given in [11] is larger by a factor of 4.24 as compared to the volume (1638 mm3) of the proposed antenna. The antenna reported in [15] shows a bandwidth of only 1% at 2.75 GHz despite the fact it is designed on duroid substrate. In references [10, 14, 16] a higher bandwidth (9.4%, 4.8%—simulated, 4.69%—calculated) at Lfr is reported which is high in the first case and marginally high in the latter two cases. As shown in Table 2, the patch area of antenna referred to in reference [10] is 1.7 times larger than that of the patch area of the proposed antenna, whereas the total volume of the antenna given in [14] is 2944 mm3 which is 1.8 times larger than total volume (1638 mm3) of the antenna proposed in this work, and the total volume of the antenna reported in [16] is 1444 mm3 which is fractionally (1.1 times) lower than the proposed antenna. The theoretical impedance bandwidth (4.69%) obtained in reference [16] is marginally high, but the same has been obtained at the resonating frequency of 0.72 GHz which is much lower than the lower resonating frequency (3.8 GHz) of the proposed antenna. Antennas [10, 16] utilize the same substrate, but higher bandwidth obtained is at the expense of large volume of the antenna, whereas in [16] the lower resonating frequency cannot be utilized for WiMAX or WLAN applications.

The measured bandwidth (3.7%) of the proposed antenna at Lfr is almost same (3.66%) as reported in reference [11], but larger than that reported (1%) in reference [15]. However, in references [10, 14, 16] only simulated/calculated bandwidths have been reported; thus, a comparison with measured results cannot be drawn readily. The bandwidths reported in references [10, 14, 16] at higher resonating frequencies (5.31, 4.76, 1.4, 5.0, 5.05, 2.34 and 4.65 GHz) are 3.7%, 10.25%, 0.43%, 3.8%, 1.5%, 2.18% and 1.5%, respectively.

The percentage bandwidth except in one case (10.25%) [11] is less than the simulated (HFSS) and measured bandwidths of the proposed antenna. Further, in two cases [12, 16] the antennas are not designed for WiMAX /WLAN applications. The bandwidth of 10.25% observed in [11], is larger by a factor of 1.09 (9.4%) and 1.34 (7.6%) as compared to the measured and simulated bandwidths of the proposed antenna. However, this marginal enhancement in impedance bandwidth is achieved because of the substrate (foam) and at the cost of increasing the volume of the antenna by 4.24 times than that of the proposed antenna in this work.

A comparative plot of return loss versus frequency of the proposed antenna and the antennas mentioned in references [10, 14, 16] is shown in Fig. 9. Figure 9 is used for calculating the return loss, impedance bandwidths and resonating frequencies which are mentioned in Table 2. The maximum return loss at lower bands in [10, 14, 16] are found to be − 16, − 15.9, − 19.08, − 22.9, − 32.9, − 12.9, − 12.8, − 19.7 dB, and at higher band the maximum return loss at higher bands are − 40, − 23.4, − 21.8, − 22.5, − 35, − 47.5, − 11.1, − 21.8 dB. Return loss values are indicative of good reception capability of the antenna, and in the present case the proposed antenna with a return loss value of − 40 dB (at the higher band) is observed which is maximum except than that of antenna reported in [14]. The marginally better return loss value in [14] is due to the use of different substrates (foam) and due to the thicker substrate which increases the overall volume of the antenna in [14] by a factor of 1.8.

Fig. 9
figure 9

Return loss (|S11|) versus frequency plot of various H-shaped antennas of Table 2

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The return loss values at lower bands are comparable with the other antennas. The return loss value for the proposed antenna at the lower band is better than the antenna reported in [10, 15, 16]. The better return loss values are achieved by antennas [11,12,13, 16] at lower bands, but the impedance bandwidth of antennas in [11, 13] is less than the proposed antenna.

The electric field and magnetic field radiation patterns at lower and upper resonating frequencies are shown in Figs. 10 and 11, respectively. It is evident that the maximum power is radiated in the broadside direction within the operating band. Figure 12 shows the gain as a function of the frequency of the proposed antenna. The gain of the proposed antenna at lower and higher resonating frequencies (3.8 and 4.7 GHz—HFSS) is 1.61 dB and 1.80 dB, respectively. A maximum gain of 2.52 dB (4.63 GHz) and 1.97 dB (3.71 GHz) is obtained which is well within the lower and higher bands of resonating frequencies.

Fig. 10
figure 10

E-field and H-field radiated power versus angle of the proposed antenna at 3.8 GHz

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Fig. 11
figure 11

E-field and H-field radiated power versus angle of the proposed antenna at 4.7 GHz

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Fig. 12
figure 12

Simulated antenna gain as a function of frequency

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VSWR as a function of frequency is shown in Fig. 13. VSWR < 2 is observed at both lower and higher resonant frequencies. At lower resonant frequencies, we observe VSWR as 1.34 (HFSS), 1.39 (AWR) and 1.59 (measured). VSWR of 1.06 (HFSS), 1.86 (AWR) and 1.19 (measured) is observed at the higher resonant frequency. As observed from the values of VSWR in each case, the proposed antenna has a good matching condition. The deviation in the case of simulated and measured VSWR is in consonance with the deviations observed in Fig. 6. However, the nature of the curves in all the cases remains more or less same which is indicative of the fact the deviations do not affect the impedance bandwidth, gain and radiation pattern of the proposed antenna.

Fig. 13
figure 13

Experimental and simulated VSWR as a function of frequency

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In the present work, the main parasitic patch is symmetrical to the radiating patch and also the parasitic patches on the sides of the radiating and main parasitic patch are symmetrical; therefore, a good group delay response is expected as reported by [7, 22]. Group delay also depends on the location of the feed point and shows the degree of distortion in transmitted/received pulses. A group delay less than 0.5 ns is desirable [23], and recently, a group delay of 0.4 ns has been reported in case of a multilayer antenna [7].

Figure 14 illustrates the group delay of the proposed dual-band H-shaped antenna, and it is observed that the simulated (HFSS, AWR) and measured group delay for the proposed antenna is less than 0.4 ns in the entire frequency range except for the AWR group delay values ( < 0.8 ns) at higher resonant frequency. A higher group delay is seen in the case of AWR simulation at higher resonating frequency which is expected because of the rectangular feed shape and step size.

Fig. 14
figure 14

Experimental and simulated group delay as a function of frequency

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Figure 15 shows the gain versus elevation angle plot of the proposed antenna and beamwidth at both resonating frequencies (3.8 and 4.7 GHz). The calculated (cf. Figure 15) E- and H-field beamwidths (3-dB) are 130° and 111°, respectively, at 3.8 GHz. Similarly at 4.7 GHz, E- and H-field beamwidths (3-dB) are 109° and 106°, respectively. E- and H-field beamwidth values suggest that the antenna radiates most of the power at these specified beamwidths for the resonating frequencies. E- and H-field beamwidth values are also corroborated from the perusal of the radiation patterns (cf. Figs. 10 and 11) of the proposed antenna.

Fig. 15
figure 15

Gain versus θ (theta elevation angle) at 3.8 and 4.7 GHz for dual-band antenna

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5 Conclusions

The proposed H-shaped antenna is operating at two frequencies 3.8/4.7 GHz, and the separation of two resonant frequencies is controllable with the change in gap length and the number of vertical and horizontal cuts on the circular patch and by changing the thickness of the substrate. The variation between simulated impedance bandwidth (HFSS and AWR) at lower resonant frequencies is 2.5% and at higher resonant frequencies is 2.1%. The variation between a measured value and simulated value (AWR) at the lower resonant frequency is 2.5%. The lower resonant frequency obtained by HFSS is same as obtained experimentally. Variation between measured and simulated values (AWR and HFSS) at higher resonating frequencies is 0.5% and 2.0%, respectively.

A measured impedance bandwidth (9.4% at \( Hf_r \)—4.59 GHz) is observed for the proposed antenna which is the highest measured impedance bandwidth among the H-shaped antennas.