The standard FASA design

The sinuous antenna is created with N arms consisting of $P$ cells scaled in dimensions with respect to each other. The $P$th cell can vary from the biggest, first, and outermost cell to the smallest and innermost cell $P$, where $R_p$ represents the outer radius of the $P$th cell. The sinuous curve generated for the $P$th cell is defined in polar coordinates $(r,\phi)$ by the equation:

(1)\begin{equation} \phi = \left({-1} \right)^p \alpha _p \sin \bigg[\frac{180ln \left(r/R_p \right) }{ln \left(\tau_p\right)}\bigg] \pm \delta, \end{equation}

where $ R_{p+1} \leq r \geq R_p $ defines the inner and outer radius of the curve. In (1), $\alpha_p$ represents the angular width of the $P$th cell, $\tau_p$ is the growth rate or the ratio of the inner and outer radius of cell $P$, i.e., $ R_{p+1} = \tau R_p$. The sinuous curve is considered log-periodic if $\tau$ and $\alpha$ are constant and as quasi-log periodic if $\tau_p$ and $\alpha_p$ are depend on the cell number. Figure 1(a) shows the design parameters required to generate a single sinuous curve. Constructing the sinuous arm from the curve requires the addition of a new parameter $\delta$, and a single arm can be generated by rotating the curve $\pm \delta$ as shown in Fig. 1(b). Setting $\delta = 22.5^\circ$ produces a self-complimentary geometry, an important property for the input impedance to have a real and frequency independent characteristic [Reference Huffman and Cencich23].

Figure 1.

Geometry and design parameters of the standard FASA: (a) the sinuous curve, (b) single sinuous arm and (c) standard FASA geometry.

The additional arms of the antenna are created by rotating the initial arm by $90^\circ$, $180^\circ$, and $270^\circ$, resulting in four arms. Opposite pairs of arms are excited, forming a two-port geometry. The final configuration of the standard FASA is shown in Fig. 1(c), where $D_{out}$ represents the outer diameter and $D_{in}$ represents the inner diameter of the opposite arms. The lower operating frequency of the antenna can be reduced by increasing the outer diameter, while the upper operating frequency can be increased by decreasing the inner diameter, and vice versa.

The input impedance equation for the N-arm sinuous antenna is given by:

(2)\begin{equation} Z = \frac{60 \pi}{sin \big( \frac{180}{N}\big)}. \end{equation}

For an infinite four-arm self-complimentary antenna ( $\delta = 22.5^\circ$) with appropriate excitation, the average input resistance over the desired band is approximately 267 $\Omega$s. However, when the antenna is fabricated on a substrate, the input impedance is lower because of the dielectric properties of the substrate. In [Reference Salem24], an investigation of various substrates with different dielectric properties and thicknesses was carried out. It was found that a 0.254 mm Duriod substrate caused minimal performance deterioration. However, Rogers 0.81 mm (R04003C) with a relative permittivity of $\varepsilon_{r} = 3.38$ is used in this study. To evaluate the effect of the substrate on input impedance, the four arms were placed on the substrate, and the optimal average input impedance was determined by adjusting the port impedance from 267 $\Omega$ to lower values. Full-wave electromagnetic simulations were conducted in free space using the time-domain solver in CST Microwave Studio [25]. The $S_{11}$ simulation results revealed that an input impedance of 185 $\Omega$ is ideal, as it allows for the practical design of a feeding line for the balun.

Sharp-edges modification

The resonance of a sinuous antenna arises from two sources: the log-periodic structure of the arms and the sharp edges formed by the truncation of the outer diameters of the arms. Studies on the resonance caused by these sharp edges and their impact have been discussed in [Reference Crocker and Scott8, Reference Kang and Kim26–Reference Kang and Kim28]. This sharp-edge resonance degrades the antenna’s performance, affecting its input impedance, radiation patterns, co-polarized gain, and reflection coefficients, particularly at lower frequencies. In [Reference Kang and Kim28], a modification method was proposed that involves the removal of half of the sharp ends on each arm. This paper presents a similar approach; however, instead of using a straight-line truncation, a circular-shaped curve is employed (see Fig. 2). This modification replaces the sharp tips with curved ends, aligning them with the natural bends of the arms and minimizing disruption to the antenna’s self-complementary properties. As these modifications are applied to the outer portions of the arms, they primarily affect the antenna’s lower frequency range. The $S_{11}$ parameter results, shown in Fig. 3, demonstrates improved impedance matching at lower frequencies when the sharp edges are replaced with curved ends.

Figure 2.

The standard FASA with modified sharp-edges.

Figure 3.

Return loss of the standard FASA with and without sharp edges modification.

Feed-point modification

A critical consideration in designing the FASA is the connection between the arms and the feeding network. Modifications to the feed region of each arm are necessary, but these must be made carefully to preserve antenna symmetry. Various feed-point modification strategies have been proposed in [Reference Jafargholi and Kamyab16–Reference Gonnet, Sharaiha, Terret and Skrivervik18]. However, it is important to note that such modifications can result in asymmetry between the opposite arms, which may negatively impact the antenna’s performance, particularly at higher frequencies. This is because the inner diameter of the geometry, where modifications are applied, plays a crucial role in high-frequency performance. However, the fundamental properties of the antenna can be preserved with optimized modifications. The feed-point modification strategy used in this paper is shown in Fig. 4. All four arms are placed on the upper side of the substrate, with the opposite arms designated as conductors or ground for excitation. To ensure a seamless connection with the feeding network, the two positive arms are modified to have feed points on the same side, and the two ground arms are adjusted similarly. To connect the four arms to the underside of the substrate, 0.5 mm diameter pins are inserted through the substrate. The optimized values for the feed-point modifications, which provide the best antenna performance and are compatible with the feed network, are detailed in Fig. 4. These values were determined by minimizing the distance between opposite arms while maintaining a strong coupling between the ports.

Figure 4.

Geometry and modified feeding point values.

Design of the feed network

A feeding network is essential for effectively exciting the radiating elements of a planar antenna. The design of this network depends on the required polarization and bandwidth. For the sinuous antenna, exciting only two opposite arms is sufficient to achieve single linear polarization. However, utilizing all four arms is necessary to realize DLP. Since the sinuous antenna is a wideband design with a frequency-independent input impedance, it is crucial to develop a broadband balun that maintains these characteristics while seamlessly integrating with the modified feed points of the antenna.

The FASA has a balanced configuration but needs to be fed using an unbalanced 50 $\Omega$ coaxial line. Initially, the antenna input impedance without a substrate is 267 $\Omega$, which decreases to 185 $\Omega$ when a substrate is added. Therefore, it is essential to design a balun to transform the unbalanced 50 $\Omega$ input impedance into a balanced 185 $\Omega$ impedance. To achieve this, an exponentially tapered microstrip balun is designed, a widely used type of balun with broadband characteristics. In such a balun, the transition from an unbalanced to a balanced line is achieved through a gradual change in the line’s cross-section, following an exponential function [Reference Kobayashi and Sawada29]. At the input (unbalanced) side, the cross-section resembles a microstrip, with the ground plane significantly larger than the width of the positive line. At the balanced output, the line transitions into a double-strip configuration, where the widths of the positive and ground strips are equal, forming a paired-strip cross-section. The width of the microstrip line at the input can be calculated using a simple formula or a microstrip line calculator. For the balanced port, the widths of the paired strips can be approximated using image theory, which suggests that the impedance of the paired strip line is twice that of the microstrip line when the strip widths are equal. Using half the distance between the two strips, the desired input impedance can be approximated. The equation of the exponential curve used to design the baluns is $y(x) = ae^{bx}$ where $a = w_1/2,$, $b = ln(w_2/w_1)/L$ for the positive line, $a = w_0/2$, $ b = ln(w_2/w_0)/L$ for the ground side, and $L$ is the length of the balun. Since there are two ports to be excited, two baluns are designed, one for each port on an FR4 substrate with $\varepsilon_{r} = 3.38$, and a thickness of 1.6 mm.

The final design of the two-port exponentially tapered microstrip balun is shown in Fig. 5(a) and (b). The outputs of both baluns are tailored to match the feed-point modifications, ensuring that they are symmetric and equal in length. This symmetry helps preserve the balanced behavior of the antenna. The dimensions of the finalized geometry are provided in Table 1. To evaluate the performance of the feeding network, the balun outputs were terminated with 185 lumped elements $\Omega$, while a 50 $\Omega$ SMA connector was attached to the balun inputs and excited using a waveguide port to compute the scattering parameters. The simulation results showed a return loss of up to $-$15 dB and isolation better than $-$30 dB across the desired frequency band. For comparison, [Reference Aghdam, Faraji-Dana and Rashed-Mohassel17] reported a return loss of $-$12 dB with a 200 $\Omega$ output termination.

Figure 5.

Balun geometry and design parameters: (a) ground side and (b) positive side.

Table 1.

Balun dimensions

The designed four-arm cavity-backed sinuous antenna (FACBSA) configuration

Adding a cavity-backed metallic reflector to the rear side of the antenna, as shown in Fig. 6(a), transforms its radiation pattern from bidirectional to unidirectional, which is preferred in most applications [Reference Abbak, Cayoren and Akduman30, Reference Bhattacharjee, Bhawal, Karmakar, Saha and Bhattacharya31]. To further enhance performance, the cavity is typically filled with an absorbing material to suppress back-side radiation. In this design, the cavity is filled with a preloaded ECOSORB LS-24 absorber, as depicted in Fig. 6(b). As noted in [Reference Yan and Cao32], the depth of the cavity also significantly affects the antenna’s resonance (see Fig. 6(c). The cavity depth $H$ and diameter $D$ were optimized to achieve better performance while minimizing the antenna’s overall size. The final dimensions of the cavity-backed FASA are provided in Table 2.

Figure 6.

The designed FACBSA: (a) antenna without absorber, (b) antenna with absorber and (c) cavity-depth and diameter parameters.

Table 2.

Dimensions of the FACBSA

For analysis purposes, the set of standard cuts taken at the elevation angles $\phi = 0^\circ$ and $\phi = 90^\circ$ will be used to represent the two-dimensional radiation patterns. The standard cuts $\phi = 0^\circ$ and $\phi = 90^\circ$ from port 1 and port 2 indicate unidirectional radiation patterns due to the reduction of back radiation over the 2–5 GHz frequency band (see Figs. 7 and 8).

Figure 7.

Radiation patterns of the FACBSA at $\phi = 90^\circ$ and $\phi = 0^\circ$ from Port 1: (a) 2 GHz, (b) 3.05 GHz, (c) 4.1 GHz and (d) 5 GHz.

Figure 8.

Radiation pattern of the FACBSA at $\phi = 90^\circ$ and $\phi = 0^\circ$ from Port 2: (a) 2 GHz, (b) 3.05 GHz, (c) 4.1 GHz and (d) 5 GHz.

Dual linear polarization measurement

A measurement setup, shown in Fig. 11, was arranged inside an anechoic chamber to evaluate the DLP property of the designed FACBSA. The setup includes the fabricated antenna and a standard linearly polarized double-ridged broadband horn antenna (BBHA 9120 A, 0.8–5 GHz) [33]. The antennas were positioned 2 meters apart, satisfying the far-field condition. Prior to measurements, the antennas were oriented such that port 1 of the sinuous antenna corresponds to the vertically oriented arm (along the $y$-axis) and port 2 corresponds to the horizontally oriented arm (along the $x$-axis), as depicted in Fig. 11. Similarly, the horn antenna was oriented vertically or horizontally, depending on the measured port. The radiation direction for the vertically and horizontally oriented arms is along the $z$-axis, directed toward the horn antenna. Since the electric field is perpendicular to the radiation direction, the co-polarized electric fields $E_\theta$ and $E_\phi $ correspond to the $x$-axis and $y$-axis for the vertically and horizontally oriented arms, respectively. The orientation of the electric field of the horn antenna is provided in [33].

Figure 11.

Dual linear polarization measurement setup.

After calibrating both the sinuous and horn antennas, port 1 of the sinuous antenna was connected to port 1 of the network analyzer, while port 2 of the analyzer was connected to the horn antenna. Measurements were performed by orienting the horn antenna in two positions: first vertically, and then horizontally. Once the measurements for port 1 of the sinuous antenna were completed, port 1 of the network analyzer was connected to port 2 of the sinuous antenna. Similarly, two measurements were performed with the horn antenna oriented vertically and horizontally. The results of the measured parameter $S_{21}$ for port 1 and port 2 of the FACBSA are shown in Fig. 12(a) and 12(b), respectively. The results indicate that port 1 of the antenna, corresponding to the vertically oriented arms, is co-polarized with the horn antenna in the vertical position and cross-polarized when the horn antenna is in the horizontal position. Conversely, port 2 of the antenna, corresponding to the horizontally oriented arms, is co-polarized with the horn antenna in the horizontal position and cross-polarized when the horn antenna is in the vertical position. These measurements clearly confirm the DLP capability of the designed FACBSA.

Figure 12.

Measured co- and cross-polarized $S_{21}$ results: (a) $S_{21}$ from port 1 and (b) $S_{21}$ from port 2.

Using the calibrated horn antenna as a reference and maintaining the same measurement setup, the co-polarized parameters $S_{21}$ were used to calculate the maximum gain in boresight. The maximum simulated and measured gain at boresight for port 1 and port 2 are presented in Fig. 13(a) and 13(b), respectively. The results show a good agreement between the simulated and measured maximum gain values.

Figure 13.

Maximum gain at boresight vs frequency: (a) maximum gain at port 1 and (b) maximum gain at port 2.