Bioinspired planar switched beam network using Butler matrix on a flexible substrate targeting multifaceted millimeter-wave applications

Abstract

This paper details the design and development of a planar switched beam network using 4 × 4 Butler matrix (BM) over a thin and flexible type biocompatible substrate. Four mils thick liquid crystal polymer (LCP) is used as a substrate here (ϵ_r = 2.92, tanδ = 0.002). The proposed design is centered at 28 GHz, targeting commercial millimeter-wave applications. Floral-shaped antenna with defective ground structures has been implemented as basic radiating elements. The whole structure is based on microstrip line configuration. The architecture occupies an area of 23.85 × 19.20 mm² over the LCP substrate. Individual components of the BM are detailed here, followed by a system analysis of the whole integrated structure. The present work also covers the electrical equivalent circuit modeling of the whole beam-forming network. The fabricated prototype offers better than 18 dB return losses at each input port for the desired frequency band with 6 dBi (max.) peak gain and 500 MHz bandwidth around the center frequency. Port-to-port isolation of better than 15 dB is achieved with this topology. Experimental and simulated results are in good agreement in all aspects. A comparative study is also chalked out to highlight the significance of the current research work with respect to alike earlier reported structures.

Introduction

The last few decades have witnessed the explosive growth of wireless communication. “Antenna” is an indispensable component in the systems used in such wireless communication. Modern day communication needs “smart antenna” in the field of sitcom, navigation, RADAR application, microwave imaging, and even for the 5G network. Switch beam networks find wide application in this gigantic augmentation to realize electronic scanning method. The scanning is accomplished by altering the orientation of the antenna’s radiation pattern. The traditionally employed mechanical scanning system suffers due to the wear and tear problem associated with bulky body parts. On the contrary, electronic means of scanning offer multiple technological advantages, viz lightweight, complete removal of wear and tear problems, easy controlling mechanism, etc. Historically, this scanning system was employed in the wireless communication field to mitigate two prime challenges, named “multipath fading” and “inferences” [1]. Continuous scanning applications require “phased array” antenna structures. However, scanning in a single dimension can be achieved by incorporating the concept of switched beam topology. Various phase distributions of the beam-forming network can produce independent beams with different orientations.

Keeping in view of future wireless communication for multi-gigabit services with high data rates, the millimeter-wave (mmW) frequency spectrum is of utmost importance. The mmW spectrum in the 28–38 GHz band [2–8] has applications in the outdoor 5G cellular system; local multipoint distribution services, cellular backhaul, and intra-cell communication systems [9]. Even this particular band of frequency has immense potential in various biomedical applications, such as MRI systems, imaging, etc.

Practically, there are three main categories of Radio frequency (RF) beam-forming networks that have been developed, such as Blass matrix [10], Rotman lens [11], and Butler matrix (BM) [12]. Blass matrix and Rotman lens mainly suffer due to design-oriented challenges. Traditionally, Blass matrix suffers from excessive losses and larger in size [13]. In Rotman lens architecture, beam angle and beamwidth change dynamically with operating frequency, which becomes main disadvantages while a constant beamwidth is demanded [14]. Additionally, efficiency is also restricted due to dummy ports. On the contrary, BM is preferred in terms of design topology, higher efficiency, and minimum RF loss [15]. This topology can produce uniform amplitude distributions. It has some inherent characteristics, such as orthogonal beam formation, high directivity, very less number of circuit elements, low fabrication cost, etc. Furthermore, it can generate multiple fixed overlapping antenna beams creating wide angular coverage area. Several structures have been reported incorporating circulators [16, 17] and multilayer fabrication strategies [18, 19]. However, these structures invite complexity in terms of fabrication as well as in measurement methods. In comparison to that, the planar version of the same is appreciated for its easier implementation techniques and experimentation. In the modern communication world, while miniaturization plays an important role, multifaceting conformal properties act as an addendum to the planar version of portable devices [20–32].

In the current research work, a planar switched beam network using the BM is presented over a low-loss, thin, flexible substrate named liquid crystal polymer (LCP). It is a biocompatible, radiation-resistant, and high-frequency substrate (even go up to 110 GHz) with very low water absorption capability (<0.04%) [26, 27].

The targeted frequency of operation is chosen as 28 GHz, which falls under the mmW band. Floral-shaped (bioinspired) antenna elements with defective ground structures are employed here. The whole architecture is based upon microstrip geometry, which offers an easy procedure for manufacturing the structure along with ease of testing.

In the subsequent sections, detailed design of BM with electromagnetic wave (EM) simulation results, equivalent circuit modeling, and fabrication of prototypes with measured results have been elaborated.

Elements of beam-forming network

Many pieces of literature are already available on the topic of BM; however, most of the designs focus on the enhancement of the overall bandwidth of the network by implementing multilayer techniques. In this current research work, one of the targets is to make an efficient, low-cost antenna array for biomedical applications that can be easily manufactured. Due to this reason, we have employed a single-layer planar design over a biocompatible and flexible microwave substrate for the BM feed network. Individual building blocks of the beam former are explained in subsections Design of 3-dB directional coupler, wideband crossover, 45° phase shifter, bio inspired antenna and also the building blocks of Butler matrix.

A typical four-beam BM contains four numbers of 3-dB quadrature directional couplers, one 0-dB RF crossover, and two 45° phase shifters. The aim of this network is to feed the neighboring antenna elements with equal amplitude and equally varying phase shifts. Different phase shifts arise while different input ports are exited and that lead the resultant antenna beam to switch in different orientations. Figure 1 depicts such a scheme. Each input or feeding point is responsible for producing different sets of linear phases that are orthogonal in nature. Each individual set is used as an input for the antenna array to form multiple beams in the desired directions.

Figure 1. Schematic design of 4 × 4 Butler matrix.

Considering the linear-phase distribution and exciting the input port, the resultant antenna beam at the output is tilted by the angle given by Equation (1) [1],

(1)\begin{equation}{\theta _{p\,\,}} = si{n^{ - 1}}\left[ {\frac{{\left( {N + 1} \right) - 2p}}{{2N}} \times \frac{\lambda }{d}} \right]\end{equation}

where p varies from 1, 2, … N; λ = free-space wavelength, d = distance between adjacent antenna elements, N = 2ⁿ (here n = 2) no. of radiators.

Design of wideband quadrature 3-dB directional coupler

Traditionally, it is known that a quadrature directional coupler has the ability to provide 90° out-of-phase signals at the output ports with an equal magnitude of power levels [28]. It consists of a primary transmission line, coupled with a secondary transmission line by two-quarter wavelength (λg/4) long sections spaced λg/4 distance apart (Fig. 2). S-parameter of this four-port network can be written as in Equation (2). The coupler design is finalized for the frequency band of 24–30 GHz. It is based upon the use of Rogers ULTRALAM 3850 laminate (LCP), which has a permittivity of 2.92, a loss tangent of 0.0028, and a thickness of 0.1 mm. The coupler is fed by a 50 Ω (Z ₀) microstrip line with the geometrical specifications depicted in Table 1 (Fig. 2). The simulated results demonstrate a phase imbalance of less than ±3°, an amplitude imbalance of less than 0.5 dB, and an isolation of better than 15 dB for the entire desired band (Fig. 3)

(2)\begin{equation}\left[ S \right] = - \frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 0&j&1&0 \\ j&0&0&1 \\ 0&1&j&j \\ 0&1&j&0 \end{array}} \right]\end{equation}

(2.a)\begin{equation}{{\text{S}}_{{\text{21}}}}{\text{ = j}}{{\text{S}}_{{\text{31}}}}\end{equation}

(2.b)\begin{equation}{{\text{S}}_{{\text{24}}}}{\text{ = }}\; - {\text{j}}{{\text{S}}_{{\text{34}}}}.\end{equation}

Figure 2. Wideband quadrature coupler design.

Figure 3. S-parameter of the coupler.

Table 1. Optimized dimension of the coupler and crossover designs

Design of wideband crossover

Planar wideband crossovers based on Lange couplers have been widely reported in literature [20–27]. However, these designs have constraints due to its fabrication intricacies, as multiple electrical connections are essential in a Lange coupler. A comparatively simpler design is adopted in this current research work by cascading two wideband quadrature directional couplers. It alleviates all the associated fabrication issues. Full-wave analysis of the structure results in optimized dimensions, as depicted in Table 1 (Fig. 4). The proposed structure offers an insertion loss of around 1.5 dB (max.), impedance matching of better than 16 dB, and isolation of better than 14 dB for the entire design frequency band of 24–29 GHz (Fig. 5). S-parameter of an ideal four-port RF crossover network can be expressed in terms of Equations (3–9)

Figure 4. Wideband crossover design.

Figure 5. S-parameter of the crossover.

(3)\begin{equation}\left[ S \right] = \left[ {\begin{array}{*{20}{c}} 0&0&1 \\ 0&0&0 \\ 1&0&0 \\ 0&1&0 \end{array}\,\,\,\,\,\,\begin{array}{*{20}{c}} 0 \\ 1 \\ 0 \\ 0 \end{array}} \right].\end{equation}

An ideal crossover is governed by the following S-parameters:

(4)\begin{equation}{S_{11}} = {S_{21}} = {S_{41}} = 0\,;\,\,\,\,\,\,\left| {{S_{31}}} \right| = 1.\end{equation}

Equation (4) depicts that, if one injects some power into port 1, none of it goes to port 2. All the power goes cross coupled into port 3, whereas port 4 is an isolated port. Layout of phase shifter is shown in Fig. 6. Owing to the presence of fully symmetry (even-odd mode) analysis can be invoked in Fig. 7, which results into four eigen admittances

(5)\begin{equation}{Y_{ij}}\left[ {i = \{ o,e\} ,\,\,j = \{ o,e\} } \right].\end{equation}

Figure 6. Layout of the phase shifter.

Figure 7. Black-box diagram of a fully symmetric RF crossover core. XX′ and YY′ are the two axes of symmetry.

These admittances are related to S-parameters as follows [28]

(6)\begin{equation}{S_{11}} = \frac{{{{{\Gamma }}_{ee}} + \,{{{\Gamma }}_{eo}} + \,{{{\Gamma }}_{oe}} + \,{{{\Gamma }}_{oo}}}}{4}\end{equation}

(7)\begin{equation}{S_{21}} = \frac{{{{{\Gamma }}_{ee}} - \,{{{\Gamma }}_{eo}} + \,{{{\Gamma }}_{oe}} - \,{{{\Gamma }}_{oo}}}}{4}\end{equation}

(8)\begin{equation}{S_{31}} = \frac{{{{{\Gamma }}_{ee}} - \,{{{\Gamma }}_{eo}} - \,{{{\Gamma }}_{oe}} + \,{{{\Gamma }}_{oo}}}}{4}\end{equation}

(9)\begin{equation}{S_{41}} = \frac{{{{{\Gamma }}_{ee}} + \,{{{\Gamma }}_{eo}} - \,{{{\Gamma }}_{oe}} - \,{{{\Gamma }}_{oo}}}}{4}\end{equation}

where ${{{\Gamma }}_{ij}} = \frac{{1 - {Z_{0\,}}{Y_{ij}}}}{{1 + {Z_{0\,}}{Y_{ij}}}}$, Z ₀ = port termination impedance.

Design of 45° phase shifter

For the present research work, the BM requires two numbers of 45° phase shifters. It is realized by choosing the suitable length of the 50 Ω transmission line as governed by Equation (10) [29]

(10)\begin{equation}{{\theta }} = {{\beta }}.\ell \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}

where θ is the phase shift required (here it is 45°); β is phase constant $( = {\text{ }}2\pi /{\lambda _g})$; λ_g is guided wavelength, and $\ell $ is the physical length of the transmission line. For our case, $\ell $ is coming around 0.76 mm. Figure 6 demonstrates the structure of the phase shifter with optimized design dimensions (W ₃ = 0.223, L ₅ = 0.56, L ₆ = 0.2, L ₇ = 0.1, and L ₈ = 0.1 mm). S-parameter of the phase shifter can be expressed as Equation (11)

(11)\begin{equation}\left[ S \right] = \left[ {\begin{array}{*{20}{c}} 0&{1 + j} \\ {1 - j}&0 \end{array}} \right].\end{equation}

Design of bioinspired antenna

A printed version of the monopole antenna with bioinspired geometry is proposed for the beam-forming network (Fig. 8). The said antenna looks like a flower with seven petals. Miniaturization and enhancement of directive gain for the individual antenna elements are achieved by this biomimicry method [30–34].The bioinspired geometry of Jasmine-shaped flower increases the perimeter of the antenna compared to a classical patch antenna (microstrip) and consequently the frequency behavior. The electric length of the radiator increases, which helps to attain high gain. From a mathematical point of view, this flower-shaped radiator is a class of fractal, which refers to a set in Euclidean space with specific properties, such as self-similarity or self-affinity. In this fractal shape, polar transformations give rise to a wide class of shapes. This polar transformation can be defined through a vector function

(12)\begin{equation}\bar \nu \left( t \right) = \left[ {\left( {x\left( t \right),\,y\left( t \right)} \right)} \right],\,t \geq 0;\end{equation}

Figure 8. Proposed bioinspired antenna.

that is, for each real value, t is associated with a vector in ${\mathcal{R}^2},$ Equation (13)

(13)\begin{equation}\bar \nu \left( t \right):I \to {\mathcal{R}^n}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}

\begin{equation*}t \to \bar \nu \left( t \right)\end{equation*}

The proposed radiator occupies an area of 5.08 × 4.14 mm² over the LCP substrate [35].

The shape of the petals is governed by the analytic curve following Equation (14). Each of the petals consists of two same types of Chebyshev tapering. It is formed by choosing an independent variable, “L”. Then, each petal is rotated by an angle of “θ”

(14)\begin{equation}y = N \times {({\raise0.7ex\hbox{$t$} \!\mathord{\left/ {\vphantom {t L}}\right.} \!\lower0.7ex\hbox{$L$}})^5} - {({\raise0.7ex\hbox{$t$} \!\mathord{\left/ {\vphantom {t L}}\right.} \!\lower0.7ex\hbox{$L$}})^2}.\end{equation}

Here, t is the variable, with respect to which the equation varies; it varies between 0 and L. The variable L is responsible for length of the petal, whereas N determines its width,

(15)\begin{equation}{\text{where,}}\;\theta = \tan \left( {\frac{{_{\frac{{{W_2}}}{2} - \frac{{{W_f}}}{2}}}}{{_{{L_3}}}}} \right)\end{equation}

Parametric EM simulation refers to the optimized dimension of the antenna as summarized in Table 2. The reflection parameter reveals that the floral-shaped antenna is well matched (>10 dB) for a narrow-band centering at 28 GHz (Fig. 9) with 5.6 dBi directive gain. For the present work, the radiating element faces a loading effect of the BM at the input point. Hence, careful matching of the impedance profile for the desired frequency band (28 ± 0.25 GHz) is mandatory.

Table 2. Optimized dimension of the floral-shaped antenna

Figure 9. Reflection coefficient for the antenna.

Integration of building blocks of BM

Individual building blocks, explained in the previous subsections, are integrated systematically to form the feed network of the beam former (Fig. 10). It acts as a passive microwave network with eight numbers of I/O ports, which offers better than 8 dB return losses for the desired frequency band of the antenna (27.75–28.25 GHz), as shown in Fig. 11 for all different excitation ports. Ports 1–4 are excitation ports, and ports 5–8 are designated as output ports, which are used further to excite the radiating patches. Patches are placed equidistantly (0.65 λg) by adjusting a suitable meandering technique in 50 Ω lines, emanating from all output ports of the feed network (Fig. 12). Table 3 summarizes the overall dimension of the beam-forming network.

Figure 10. Feed network of beam-forming smart antenna.

Figure 11. S₁₁-parameter for all input ports.

Figure 12. Complete architecture of the proposed Butler matrix (left – front view; right – rear view).

Table 3. Optimized dimension of the Butler matrix

The beam-steering property of the whole Butler matrix was computed by feeding the input signals from different input ports. Figure 13 demonstrates the orientation-dependent radiation characteristics in both the E and H planes. Here, characteristics have been shown only for two ports, as the rest of the two ports will be just symmetric ones instead of 180° phase shifts. It is clearly visible that there is a signature of beam-steering for different port excitations. It infers the exhibition of smart antenna engineering, implementing the electronically scanning array technique.

Figure 13. Far-field radiation pattern of the Butler matrix with different port excitations.

Equivalent circuit modeling of Butler network

In the proposed topology, the antenna array, along with the beam-forming network, acts as a transmitter. In this transmission mode, the antenna itself appears as a load on the generator [36, 37–39]. An equivalent circuit representation of the transmitter (Tx) array antenna with beam-former is shown in Fig. 14.

Figure 14. Circuit modelling of Butler network.

where Z _G = equivalent impedance of generator [Z _G = (R _G + jX _G)]

Z _B = R _B + jX _B = equivalent impedance of BM

I _in = current at the antenna’s input terminal

(16)\begin{equation}\left[ {{I_{in}} = \frac{V}{{\left( {{Z_G} + {Z_B} + {Z_A}} \right)}}} \right]\end{equation}

Z _A = equivalent antenna’s impedance at terminals a–b

(17)\begin{equation} = {R_A} + j{X_A} = \left( {{R_L} + {R_{rad}}} \right) + j{X_A}\end{equation}

V _th = induced voltage at antenna while incident wave impinges upon it, this is analogous.

R _A = antenna resistance at terminals a–b

R _L = loss resistance of antenna

R _rad = radiation resistance of antenna

R _G = resistance of generator impedance

X _G = reactance of generator impedance

X _A = antenna reactance at terminals “a–b”

X _B = reactance of BM’s impedance

R _B = resistance of BM’s impedance.

The total power (P _Tot) produced by the generator is the summation of power delivered to the antenna terminals (P _T) and the power lost (P _G) in the generator’s internal resistance R _G.

Thus,

(18)\begin{equation}{P_{Tot}} = {P_T} + {P_G}.\,\,\,\,\,\,\,\,\end{equation}

Again, a portion of P _T is radiated away (P _rad), and the rest amount is dissipated as Ohmic losses, P _Ohm.

Thus,

(19)\begin{equation}{P_T} = {P_{rad}} + {P_{Ohm}}.\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}

Equation (3) can be expressed as,

(20)\begin{equation}{P_T} = \frac{1}{2}{\left| {{I_{in}}} \right|^2}{R_A} = \frac{1}{2}{\left| {{I_{in}}} \right|^2}\left[ {{R_{rad}} + {R_L}} \right].\,\,\,\,\end{equation}

Power delivered to the antenna (array) for radiation,

\begin{equation*}{P_{rad}} = \frac{1}{2}{\left[ {{I_{in}}} \right]^2}{R_{rad}}\end{equation*}

(21)\begin{equation} = \frac{1}{2}{\left[ {{V_g}} \right]^2}\left[ {\frac{{{R_{rad}}}}{{{{\left( {{R_{rad}} + {R_L} + {R_G} + {R_B}} \right)}^2} + {{\left( {{X_A} + {X_G} + {X_B}} \right)}^2}}}} \right].\,\,\,\,\,\end{equation}

Overall antenna efficiency is given by [25]

(22)\begin{equation}{e_0} = {e_r}{e_c}{e_{d\,\,\,\,\,}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}

where e ₀ = total efficiency, e _r = mismatch efficiency,

${e_r} = \left( {1 - {{\left| \tau \right|}^2}} \right),$ e _c = conduction efficiency, e _d = dielectric efficiency, $\tau $ = Voltage standing wave ratio (VSWR) at antenna input terminal.

(23)\begin{equation}\tau = \frac{{{Z_{in}} - {Z_0}}}{{{Z_{in}} + {Z_0}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{equation}

where Z _in = input impedance of the antenna

Z ₀ = characteristic impedance of Tx line.

Usually, e _c and e _d are very difficult to evaluate separately [35]. Hence, traditionally e ₀ is written as

(24)\begin{equation}{e_0} = {e_{cd}}\left( {1 - {{\left| \tau \right|}^2}} \right).\,\,\,\,\,\,\,\end{equation}

This radiation efficiency can be obtained through Wheeler’s cap method [40] and directivity/gain measurement. Equivalent circuit of antenna has a very little to do with it. However, e ₀ can be expressed as follows:

(25)\begin{equation}{e_0} = \frac{{{R_{rad}}}}{{\left( {{R_{rad}} + {R_B} + {R_L}} \right)}}.\,\,\,\,\,\,\,\end{equation}

Fabrication and measurement

The proposed BM has been fabricated on a thin (100 ± 10 μm), flexible, and biocompatible LCP substrate. Standard photolithography and wet-etching chemistry are adopted to realize the geometry. It is very clear that all four input ports are placed in close proximity, which restricts the assembly of standard RF connectors to them for signal launching. Hence, it evokes some measurement-related practical issues. It is solved here with the use of air coplanar probe (ACP)-type RF coplanar probes (ground-signal-ground: GSG) [38] of 150 µm pitch size. The in-house made coplanar waveguide in microstrip patch (CPW-MS) [39–46] transition makes a suitable alternative for RF measurement and launching of signals from probes to microstrip feed lines of Butler networks. De-embedding techniques were adopted to achieve the intended response of the device under test (DUT). Figure 15 depicts the return loss profiles for all of the input ports on the fabricated prototype. Figure 16 shows the front and rear view of fabricated prototype on flexible substrate along with the transition structure. The flexibility of the substrate is also observed from the same. Further, in the compact antenna test facility, the radiation characteristics of the prototype antenna are evaluated. It shows a maximum gain of around 5.8 dBi. The far-field radiation pattern is exhibited in Figs. 17 and 18 for different input ports. The performance metrics of the antenna infer that it is a high-gain and narrow-band candidate, mostly suitable for detecting the tumor cell/malignant tissue at a precise operating frequency in the mmW band. Even so, it can be used for radiotherapy or mmW hyperthermia applications. A comparison table (Table 3) is included here to discuss various performance metrics of the proposed network with respect to recently reported structures. It can be inferred that our work occupies minimum layout area over thin substrate for the same 4 × 4 BM configuration to provide appreciable gain (>5 dBi) with satisfactory port to port isolation than that of (>15 dB) earlier reported results.

Figure 15. Simulated and measured results.

Figure 16. Fabricated prototype: (a) front view, (b) rear view, and (c) CPW-MS transition structure used at the time of measurement.

Figure 17. Simulated and measured far-field pattern in E-plane of the Butler matrix at 28 GHz.

Figure 18. Simulated and measured far-field pattern in H-plane of the Butler matrix at 28 GHz.

A comparison table is provided in (Table 4) that compares the proposed work with recently reported structure. The gain characteristic of the bioinspired antenna is shown in the Fig. 19. It has been shown that maximum gain of the antenna is 5.8–6 at the desired frequency band.

Table 4. Comparison of performance metrics of proposed network amongst recently reported structures

Figure 19. Gain of the bioinspired antenna.

Conclusion

This work reports the design and development of a novel configuration for a planar switched beam network targeting multifaceted mmW applications. The novelty of the current research work comes from the implementation of the bioinspired antenna in the BM configuration along with the usage of flexible and biocompatible LCP substrate. Other reported works [2–5, 22, 24] in this context achieve higher gain and bandwidth, at the cost of a larger layout area. However, the current R&D work exhibits its superiority in all intended performance metrics with its reduced dimension by incorporating the said novelties into the architecture. The proposed design offers a maximum gain of around 5 dBi with 500 MHz bandwidth. Further, it can be enhanced by enlarging the dimension of the BM but at the cost of increased footprint area. The high gain feature with a narrow-band profile makes the current antenna suitable for detecting tumor cells and hyperthermia treatments. Finally, the substrate makes the proposed antenna as a conformal candidate for arbitrary 3D shapes. As per the author’s knowledge to date, such a miniaturized antenna based upon planar configuration never has been reported with all state-of-the-art performance metrics for biomedical applications with the flexible substrate.