1 Introduction

The world has witnessed several fascinating revolutions in the field of telecommunications during the transition from twentieth century to twenty-first century. Among those wireless revolution has provided mobile communication, Global Positioning System, Wireless LAN, WiMax, WiFi, LTE and many other services [1]. These wireless communication techniques support fast data transmission [2–4] rate and novel modulation techniques. In addition to these, the wireless revolution has made the electronic system small and compact. Antenna in such a wireless system is responsible for radiating and receiving electromagnetic waves for communication. Besides these in the modern wireless systems the antenna has to adapt the following functionalities.

  • Needs to handle large amounts of data in short period of time, which means it needs to possess broadband characteristics.

  • An antenna designed for a particular operating frequency exhibits good characteristics for that frequency and may not have fully functional operation at other frequencies. Most of the telecommunication systems operate at separate frequencies to avoid the interference. Hence one may have accommodated dedicated antennas for every operating frequency. To avoid this one antenna capable of operating at all the required frequencies is good practice. For this the antenna need to be multifrequency or frequency independent.

  • Owing to the modern communication devices like mobile radio and handheld communication systems, the antenna has to be conformal with the compactness of the system and environment. This is achieved with miniaturisation of the antenna.

  • Most of the Miniaturised antennas have poor radiation efficiency and directivity. One would be interested in making a small antenna a better radiator for example by using low loss dielectric and stacking patches.

In this paper multiband and miniaturisation characteristics of planar fractal based antennas are studied. The fractals are carved on microstrip patch antennas and are explored to meet the above requirements. The study and analysis is based on the simulation of the geometry and measured data on the fabricated prototypes. The study of multiband characteristics is based on the Sierpinski geometry. The Sierpinski Bowtie (SPKBT) geometry is used for studying the miniaturisation characteristics. The entire investigation on the miniaturisation is subdivided into four cases starting from a square patch in case 1 to a SPKBT of third iteration in case 4. For each geometry analysis basing on the reflection coefficient, radiation pattern, and frequency versus Directivity reports are presented.

1.1 Microstrip Patch Antennas

High frequency structure simulation (HFSS) tool based on finite element method (FEM) numerical technique is used for simulation throughout this work. All the geometries proposed in this work belong to the basic category of microstrip patch antennas (MPA). The Microstrip Antenna (MA) technology is heard for the first time during 1950s as novel feeding techniques to achieve enhanced BW, Gain and for accurate prediction of the numerically analysed results. The choice of MPA is always backed up with its advantages with respect to its structure. An MPA is low profile, low cost, conformal to the device structure, low volume. The electrical characteristics of the MPA are supportive to both dual and circular polarization. The resonant characteristics of the antenna are easily controllable with its dimensions. They are compatible and easy adaptable with every system. On the other side there are some drawbacks with this antenna type. They have a very narrow bandwidth. As a single element antenna it exhibits limited beam steering and has radiation pattern which is hardly controllable.

1.2 Fractal Geometry

The concept of combining the fractal geometry (FG) with electromagnetic is analyzed. The word antenna is often prefixed with the word latest which gives the state of research in the field. In the latest antenna research the fractal geometry plays a vital role. It is a powerful means of describing any geometrical shapes. The shapes of Coast line, leaf, clouds etc. are some complex phenomenon that are described effectively using fractals [1]. This magnificent strategy has drawn the attention of many elites from mathematics, computer science, statistics, image and signal processing and electromagnetic group. Earlier the objects are classified using Euclidean geometry as one, two and three dimensional. The objects in the world are not described using Euclidean geometry. Here comes the application of FG. The fractals have the properties like (a) Self Similarity, (b) Fractional Dimension and (c) Fractal boundaries.

The self similarity property of the FG can be easily explained with the geometry with shape within shape. The fractional dimension property of the FG does the job of space filling. The third property i.e., fractal boundaries can explain in two ways like mass fractals and boundary fractals. Mass fractals have their internal structure a fractal again. Boundary fractal has the boundaries (outer structures) of the regular shape as fractals.

Considering these excellent properties listed above the FG are applied to the antenna field. Much new geometry has been derived from Mandelbrot’s “Concept of New Geometry” [5]. Some of them are very popular in serving as radiating elements. Among those, Sierpinski triangle and Sierpinski carpet are named after Sierpinski (1916), Hilbert curves named after Hilbert.D (1891), Koch curves named after Koch.V.H (1904), Julian structures named after Julia.G (1918) and Contor shapes named after Contor.G (1872) have wide applications in electromagnetic with their vital electrodynamics. Some fractal shapes are presented in the following Fig. 1.

Fig. 1
figure 1

Geometrical shapes of some fractal geometry. a Tree Fractal, b Cesàro fractal, c Barnsley’s fern. d Dragon curve, e H-fractal, f Sierpinski square, g Sierpinski triangle

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2 Multiband Characteristics of Sierpinski

The basic geometry of the Sierpinski (SPK) is as mentioned in the Fig. 1g is considered here. An SPK has various flavors of construction. These variations are observed with respect to the point of view, rotation and scaling. The multiband behavior of the fractal shaped SPK is described by Lizzi et al. [6], Werner and Werner [7], Mushiake [8], Chowdary et al. [9], Vinoy et al. [10], Puente-Baliarda et al. [11], Anagnostou et al. [12], Na and Xiao-wei [13], and further a comparative study between the SPK monopole and dipole is also presented in it. The resultant log periodic behavior of the SPK is due to the self similarity property of it. The dimension of the FG is measured using the following formula.

$$ {\text{D}} = {\text{Log N}}\left( {{\text{number}}\;{\text{of}}\;{\text{new}}\;{\text{pieces}}} \right)/{\text{Log M}}\left( {{\text{Magnification:}}\;{\text{factor}}\;{\text{of}}\;{\text{finer}}\;{\text{resolution}}} \right) $$

For the SPK with respect to the Fig. 1g the dimension is calculated as

$$ {\text{D}} = \log_{2}\left( 3 \right) = 1.584 $$
(1)

where the scaling factor is 2 and the number new pieces formed are 3.

2.1 Effective Area Considerations in SPK

A triangle is the initiator for SPK triangle geometry. In every iteration a scaled down triangle of its previous iteration is tweaked out. For each iteration the circumference and the area varies. If a triangle of unit area is considered then after the first iteration 1/4 of the area is removed. Consequently after the second and third iteration, 3/16 and 9/64 of the area is removed respectively as shown in the Fig. 1. The generalized expression for this phenomenon is given by

$$ A_{N} = 1/3\sum\limits_{i = 1}^{N} {(3/4)^{i} } $$
(2)

where AN refers to the area removed. From the above equation it can be inferred that after infinite iterations A∝ = 1. This means that the resultant gasket has no area but has infinite circumference. The same is depicted in the Fig. 2a–d. The triangle in Fig. 1a is considered to have A0 = 1 area then, the corresponding generations from (b) through (d) will have areas A1, A2, and A3 given as

$$ A_{1} = (3/4){\text{A}}_{0} , $$
(3a)
$$ A_{2} = (3/4)^{2} A_{0} $$
(3b)
$$ A_{3} = (3/4)^{3} A_{0} $$
(3c)

2.2 Formulation of Resonant Frequencies

The analytical estimation of the resonant frequencies of a Sierpinski monopole after n iterations is as mentioned below by [14].

$$ fr = \left\{ {\begin{array}{*{20}l} {(0.15345 + 0.34\rho x)\frac{c}{{h_{e} }}(\xi^{ - 1} )} \hfill & {for\;n = 0} \hfill \\ {0.26\frac{c}{{h_{e} }}\delta^{n} } \hfill & {for\;n > 0} \hfill \\ \end{array} } \right. $$
$$ x = \left\{ {\begin{array}{*{20}l} 0 \hfill & {k = 0} \hfill \\ 1 \hfill & {k > 1} \hfill \\ \end{array} } \right. $$

where \( h_{e} = \frac{{\sqrt {3S_{e} } }}{2},\;S_{e} = S + t(\varepsilon_{r} )^{ - 0.5} \) and δ = scale factor of the geometry, \( \xi = \frac{1}{\delta } \) and ρ = ξ − 0.230735.

Fig. 2
figure 2

Variation in area from a generation 1 and iteration 0 through d generation 4 and iteration 3 in Sierpinski geometry

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2.3 Simulation of SPK5 (5 Iteration SPK)

The geometry of the SPK monopole after five iterations is as shown in the Fig. 3. The height of the monopole is 90 mm and base of the initiator triangle is 102 mm. Five iterations state that it has five bands of operation as shown in the Fig. 4.

Fig. 3
figure 3

Geometry of the SPK after 5th iteration

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Fig. 4
figure 4

Band representation of the SPK5

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The reflection coefficient of the simulated SPK5 geometry is as shown in the Fig. 5a and the corresponding VSWR is presented in Fig. 5b. A study of reflection coefficient characteristics from Fig. 5a, reveals various resonant frequencies at which the computed value takes minima. It can be inferred from the reflection coefficient characteristics that at five different frequencies (i.e., 2.54, 3.56, 5.17, 6.49, 8.84 GHz) there is considerable S11 magnitude of less than −10 dB. Other dips which are above the reference level are ignored.

Fig. 5
figure 5

a Simulated reflection coefficient plot of SPK5. b VSWR plot of SPK5

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To understand the multifrequency characteristics of an antenna a study of the reflection coefficient curves alone is not sufficient it may show a very low reflection coefficient in some modes with exhibiting the desired radiation pattern. To support the same, radiation pattern reports are generated at the resonant frequencies as shown in the Fig. 6a through Fig. 6h. Figure 6a–d represent the distribution of the field for all θ and Ø = 0° and Fig. 6e–h represent the distribution of the field for all θ and Ø = 90°. Similarly VSWR values at the resonating frequencies are considerably good in analogous to reflection coefficient curve.

Fig. 6
figure 6

Radiation patterns of the antenna at .54, 3.56, 5.17, 6.49 GHz resonant frequencies for Ø = 0°

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3 Miniaturisation Characteristics of SPK Bowtie

As discussed earlier in the introduction part, the investigations for miniaturisation of the antenna with FG are carried on SPK Bowtie geometries on microstrip patch antenna. The study is subdivided into four cases. The experiment is carried with a square patch as initiator which is referred as case 1. In case 2 a Bowtie is carved on the Square patch of case 1. A SPK geometry is patterned on Bowtie of case 2 to frame the case 3 experiment. A next iteration is observed on case 3 geometry to form the case 4 geometry. This is depicted in the following Fig. 7. All the geometries are designed using effective CAD tool integrated in HFSS and then simulated and solved using the effective FEM engine. Throughout all the cases the ARLON 320C substrate is considered with copper coating on both sides of the substrate. The patch is patterned on top side of the antenna and bottom side forms the ground plane. The height of the substrate is 1.6 mm.

Fig. 7
figure 7

Transition of geometry from square to SPKBT-2. a Square patch, b Bowtie, c SPKBT-2

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All the antennas and the reports pertaining to the characteristics are presented as follows. For every case, frequency versus reflection coefficient plot, frequency versus VSWR plot, E-field distribution, Radiation Characteristics in 2D polar plot, 3D format and Frequency versus Directivity plots are taken using terminal solution reports menu in HFSS. Every report has a scope for investigation of various characteristics of the antenna with its own significance. The resonating frequency is identified from the reflection coefficient graphs for those dip values which have S11 less than −10 dB. The identified resonating frequency is confirmed if the VSWR value at that frequency from the VSWR report is below two. The radiation characteristics of the proposed geometry are studied from the 2D polar and 3D radiation plots.

These plots are taken at the resonating frequency or frequencies identified from the RC and VSWR plots. As all the antennas belong to a class of patch antennas the polar plot of the radiation pattern should have single major lobe on the upper zone and minor lobe or no lobe on the lower region. This shall be treated as the template pattern diagram for the patch antenna in any form. Hence it should be understood that the identified dip frequency from S11 plot has to be considered as resonating frequency only if it posses the template radiation pattern of the patch [15–19]. The Frequency versus Directivity plot will be useful to study the directivity characteristics of the antenna over every sweep frequency. The resonating frequency should report good directivity with a value greater than one which is the directivity of isotropic antenna. The plot is drawn between frequency and peak directivity in some direction. The works mentioned in [20–22] motivated us to develop this antenna design study.

3.1 CASE 1: Square Patch

The designed square patch antenna geometrical dimensions are as shown in the Fig. 8a. The side dimension is 40 mm. This simulated square patch is used as an initiator for the next generations of the experiment. The feed point is optimized and placed at 1.5 mm along positive Y axis. The Reflection Coefficient (RC) curve over a range of 1–2 GHz and the corresponding VSWR plot are as shown in the Fig. 8b, c. From the RC plot it can be read that the antenna shows a minimum dip at 1.975 GHz. This dip frequency is supported by the minimum value under 2 in the VSWR characteristics. With these 2 reports the resonating frequencies of the square patch antenna can be concluded as 1.975 GHz.

Fig. 8
figure 8

a Square patch geometry. b Reflection coefficient plot. c VSWR plot. d Radiation Pattern polar plot. e 3D radiation pattern

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The radiation characteristics of the patch antenna are as shown in the Fig. 8d and the corresponding 3D plot is Fig. 8e. These two reports are taken at the resonating frequency investigated from the reflection coefficient and the VSWR plots.

3.2 CASE 2: Classic Bowtie

A bowtie antenna is formed by attaching two triangular patches connected at the short edges. The geometry of the simulated classic bowtie is as shown in the Fig. 9a. This geometry is derived from the square patch which is discussed on the case 1 section. The channel describes the current through put along these two triangular arms. In this proposed geometry, the width of the adjoining channel is 3.6 mm. The feed point is located at 1.75 mm from the center towards the +ve Y-axis. The reflection coefficient report obtained for the simulated geometry is presented in the Fig. 9b. The resonating frequency is identified as 1.2650 GHz from the RC plot. The corresponding radiation pattern polar plot is drawn at this operating frequency and is as shown in the Fig. 9c and the corresponding 3D radiation pattern is Fig. 9d. The fabricated prototype photograph is presented in the Fig. 9f. The geometry is etched using chemical wash on the arlon 320c purchased from a local vendor. Agilent 8719ES model network analyzer is used for reflection coefficient and VSWR measurements. Initially the cable losses are nullified in open-cal conditions by calibrating it to 0 dB. The start and stop frequencies are 1 and 2 GHz respectively. The curve displayed on the screen is converted into tabular form file with.csv extension. Then this data is imported into excel and finally a plot is drawn as shown in the Fig. 9g.

Fig. 9
figure 9

a Geometry of Bowtie. b Reflection coefficient curve of BT. c Polar radiation plot. d 3D radiation pattern. e E-field distribution representation on BT. f Fabricated BT prototype. g Measured reflection coefficient of the fabricated prototype

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3.3 Case 3: SPK Bowtie-1 (SPKBT-1)

Figure 10a shows the proposed geometry of the SPKBT-1. This is obtained by taking the triangular geometry on the both the arms of the Bowtie antenna to 1st iteration of SPK. The terminals of the inner triangle are the midpoints of the outer triangle to depict a scaling factor of 2. The resonant frequency from the simulated reflection coefficient curve (Fig. 10b) of the SPKBT-1 is identified as 1.196 GHz. This is well supported by the VSWR plot as shown in the Fig. 10c. The fundamental mode of the operation can be studied from the E-field distribution plot of Fig. 10d. The fabricated prototype of the proposed geometry is as shown in the Fig. 10e. The measured S11 over sweep frequencies of 1–2 GHz are saved to excel file format from the vector Network Analyzer directly. Figure 10g shows the measured S11 (dB) plot. The resonant frequency from this plot is 1.24 GHz. This less than the classic BT antenna investigated in the earlier case.

Fig. 10
figure 10

a SPK Bowtie-1 geometry. b Simulated reflection coefficient plot. c VSWR plot. d E-field distribution. e Fabricated prototype of SPKBT-1. f Measured reflection coefficient of the prototype

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3.4 CASE 4: SPK Bowtie-2 (SPKBT-2)

The geometry of the SPKBT-2 obtained by taking an iteration further over the previous geometry mentioned in the case 3 is as shown in the Fig. 11a. The simulated reflection coefficient curve of the designed SPKBT-2 as shown in Fig. 11b reads the resonating frequency as 1.14 GHz with an S11 value well below the −10 dB reference level. The corresponding radiation patterns in 2D and 3D at resonating frequency obtained from the RC plot are shown in the Fig. 11c, d. The fundamental mode operation and the corresponding field distribution can be observed from the Fig. 11e.

Fig. 11
figure 11figure 11

a Geometry of the SPKBT-2. b Simulated reflection coefficient of the SPKBT-2 geometry. c Radiation pattern. d 3D Radiation pattern. e E-field distribution. f Fabricated prototype of SPKBT-2. g Network analyzer. h Measured S11 of the prototype

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The fabricated prototype of the SPKBT-2 is as shown in the Fig. 11f. Figure 11g is the screen shot of the Vector Network Analyzer screen while the S11 of the prototype is displayed. This data is exported to MS Excel and then plotted to identify the resonant frequency which is 1.17 GHz according to Fig. 11h. The measured resonant frequency is less than the earlier SPKBT-1 geometry keeping the similar trend from square patch to SPKBT-2.

3.5 Concept of Miniaturization in SPK Bowtie

The resonant frequencies obtained from the above four cases are tabulated in Table 1. From the square patch to SPKBT-2 the effective area is diminishing and the corresponding resonant frequencies are also observing a decrease similarly. It is observe that the height of the antenna is made constant with diminishing operating frequency. This is made possible by carefully patterning the SPK geometry on the surface of the antenna. This shift in the operating frequency can also be controlled by the scaling factor of the SPK.

Table 1 Tabulated measured and simulated resonant frequencies of various geometries
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4 Conclusion

The multiband characteristics of Sierpinski Fractal antenna are well explored in terms of several parameters and reports like reflection coefficient, VSWR and radiation pattern plots. Under miniaturisation category a Sierpinski Bowtie is considered and various characteristics are analyzed. Starting from patch to Bowtie and further at each iteration the resonating frequency decreases considerably with diminishing surface area. This clearly manifests miniaturization characteristics with increased directivity. Complexity is always involved with the fabrication of these typical antennas, which can be minimized by proposing modified fractal shapes. A study of the trend of the bandwidth with change in frequency would have a good scope of future work.