Design of a Novel Ultra-Wideband Antipodal Vivaldi Antenna Based on Klopfenstein Curve

Abstract

We propose a new ultra-wideband antipodal Vivaldi antenna design based on the Klopfenstein curve, incorporating exponential slots, horns, and apertures to improve the antenna’s return loss and increase its gain in high-frequency bands. The antenna achieves high gain and wide bandwidth characteristics, with measured −10 dB bandwidth ranging from 2 GHz to 20 GHz, maximum gain of 14 dBi, and gain exceeding 10 dBi from 3.5 GHz to 14 GHz.

1. Introduction

With the continuous development of technology, radar systems have increasingly high requirements for imaging accuracy, detection range, and target quantity. Both the signal transmission and reception processes require antennas with higher bandwidth, gain, and more stable directivity characteristics, and research on ultrawideband antennas is increasing rapidly. As a traveling-wave antenna, the Vivaldi antenna has characteristics such as ultrawide bandwidth, high gain, and ease of processing, which have been extensively studied and applied in this field [1]. The Vivaldi antenna operates in resonance mode at low frequencies and in traveling-wave mode at high frequencies. The lowest resonance frequency is determined by the aperture width [2]. After P. J. Gibson proposed the coplanar slotted Vivaldi antenna, several researchers, including Ehud Gazit and J. D. S. Langley, proposed an improved Vivaldi antenna structure called the antipodal Vivaldi antenna (AVA), as well as a further improved balanced antipodal Vivaldi antenna (BAVA) [3,4]. Compared to the three-layer structure of the balanced antipodal Vivaldi antenna, the one-layer double-sided structure of the antipodal Vivaldi antenna is simpler and easier to manufacture, making it more applicable.

Many scholars have conducted extensive research on how to improve the performance of antipodal Vivaldi antennas, such as using split-ring resonator structures, multi-layer planar dielectric lenses, and metamaterial lens structures to focus the radiation beam and improve impedance matching performance [5,6,7], and using Chebyshev curves, cubic curves, and fern fractal leaf curves to extend matching bandwidth [8,9,10]. They have all proposed impressive curving structures, which vastly improved the impedance matching performance and directivity.

We found that the Klopfenstein curve has not yet been used in ultra-wideband complementary Vivaldi antennas [11]. The Klopfenstein curve is derived from the step Chebyshev transformer with an infinite number of sections, which theoretically achieves optimal impedance matching performance. The Klopfenstein curve is relatively flat at the front end and the end of the tapered slotline, which is conducive to low-frequency impedance matching and maintaining beamwidth, making it a high-performance tapered curve structure.

We propose a novel ultra-wideband antipodal Vivaldi antenna utilizing the Klopfenstein curve, which significantly enhances impedance matching across the operating frequency range. The design also reduces sidelobes and boosts gain at high frequencies through innovative slotting, director loading, and perforation techniques. Simulations using Ansys HFSS were followed by fabrication and measurement in a Near-field Spherical Anechoic Chamber. The measured results closely align with the simulation, demonstrating the antenna’s excellent performance.

The proposed antenna structure is compact, small, easy to process, and has wider bandwidth and higher gain characteristics over the ultra-wide bandwidth. It can be used in radar detection, electronic reconnaissance, ultra-wideband communication, and many other fields.

2. Design and Performance Analysis of Proposed Antenna Structure

The newly designed ultra-wideband antipodal Vivaldi antenna model based on the Klopfenstein curve is shown in Figure 1, with a size of 180 mm × 82 mm, using a 1 mm-thick Rogers RO4003C substrate (Suzhou, China) with a thickness of 3.55 and a thickness of 0.0027, and the radiation plate is bilaterally printed on both sides of the substrate. Newly designed internal and external curves, slotting, loading director, and perforating enhance the proposed antenna’s bandwidth and gain, achieving excellent sidelobe suppression.

2.1. Improved Impedance Matching with Klopfenstein Inner Curve Design

The internal curve is improved based on the Klopfenstein curve, which theoretically has the best impedance matching effect to extend impedance matching bandwidth and optimize in-band impedance matching performance. The curve is defined by the following equation [11]:

$$\ln Z\left(x\right)={\displaystyle \frac{1}{2}}\ln \left(Z_1{Z}_2\right)+{\displaystyle \frac{{\mathsf{\Gamma }}_0}{\cosh \left(A\right)}}{A}^2\varphi \left({\displaystyle \frac{2x}{L}}-1,A\right)$$

(1)

The ${\mathsf{\Gamma }}_0$ is calculated by the following equation:

$${\mathsf{\Gamma }}_0={\displaystyle \frac{Z_2-Z_1}{Z_2+Z_1}}$$

(2)

The function $\varphi \left(x,A\right)$ is determined by the equation below:

$$\varphi \left(x,A\right)=-\varphi \left(-x,A\right)={\displaystyle \underset{0}{\overset{x}{\int }}\frac{I_1\left[A\sqrt{1-y^2}\right]}{A\sqrt{1-y^2}}}dy$$

(3)

$I_1$ is the first-kind modified Bessel function, which requires a simplified calculation method [12]:

$$\varphi \left(x,A\right)={\displaystyle \underset{0}{\overset{x}{\int }}\frac{1}{2}{\displaystyle \sum _{k=0}^{\infty }\frac{{\left(\frac{A^2}{4}\right)}^k{\left(1-y^2\right)}^k}{k!\left(k+1\right)!}}}dy$$

(4)

By setting the opening width and A value, the final shape of the curve can be determined. According to the design principle of the Vivaldi antenna, the antenna aperture width is selected as 75 mm, and the optimized A value is chosen as 5. The outer curve is selected in the form of an exponential curve as follows, and $\alpha =0.23$:

$$y=c_1{e}^{\alpha x}+c_2$$

(5)

To match the 50 Ω antenna terminal, the impedance equation of the Vivaldi antenna is used as follows [13]:

$$Z_0=\left\{\begin{array}{l}{\displaystyle \frac{60}{\sqrt{{\epsilon }_e}}}\cdot \ln \left({\displaystyle \frac{8d}{w}}+{\displaystyle \frac{w}{4d}}\right),{\displaystyle \frac{w}{d}}\le 1\\ {\displaystyle \frac{120\pi }{\sqrt{{\epsilon }_e}\left[\frac{w}{d}+1.393+0.667\ln \left(\frac{w}{d}+1.444\right)\right]}},{\displaystyle \frac{w}{d}}\ge 1\end{array}\right.$$

(6)

The calculated feed width is 2.24 mm, and the inner and outer curves of the antenna are connected to form the Klopfenstein curve Antipodal Vivaldi Antenna (KAVA), as shown in the Klopfenstein curve part in Figure 1. The Klopfenstein curve was first calculated with the equations above in Maple, then all the point data were imported into Ansys HFSS to obtain the correct shape of the antenna inner curve. The flowchart of the Klopfenstein curve is shown in Figure 2.

To further demonstrate the advantage of the Klopfenstein curve over the original exponential curve, the structure comparison between the Klopfenstein curve antipodal Vivaldi antenna and the original exponential antipodal Vivaldi antenna is shown in Figure 3, and the S11 comparison between the two is shown in Figure 4.

It can be seen from the S11 comparison in Figure 4 that using the Klopfenstein curve can significantly improve the impedance matching characteristics of the antenna over the entire frequency range, and the ultra-wideband impedance matching characteristics are stable. The flat characteristic of the Klopfenstein curve at the end of the slot line is beneficial for maintaining the beamwidth of the antenna. As shown in Figure 5, the main lobe beamwidth using the Klopfenstein curve is smaller than that of the traditional antipodal Vivaldi antenna, and the sidelobe level can be optimized and improved through surface slotting and other methods.

2.2. Sidelobe Suppression with Slotting Design

To improve the sidelobe and front-to-back ratio of KAVA, we proposed the Slotted Klopfenstein curve Antipodal Vivaldi Antenna (SKAVA) structure with quarter-wavelength long slots. The slots use the quarter-wavelength open-circuit principle, which can effectively suppress edge currents on the surface and reduce the radiation caused by edge currents. The slotted structure extends the current path, which can improve impedance matching performance.

The starting length of the slot is designed to be 3 mm, and the terminating length is 22 mm. At lower frequencies, narrower slots cannot maintain good edge current suppression over a wide bandwidth. Therefore, we used a variable-width slotting structure, with a wide slot width of 2 mm at lower frequencies and a narrow slot width of 1 mm at higher frequencies, so that the effective edge current suppression effect can cover the required frequency range from 2 GHz to 20 GHz.

The slotting structure length variation adopted an exponential curve, as shown in Figure 6. The SKAVA antenna with a slotted structure significantly improves both the sidelobe and front-to-back ratio compared to the traditional antipodal Vivaldi antenna, as shown in the comparison of directivity patterns in Figure 7.

The comparison of surface current and S11 curve between SKAVA and KAVA is shown in Figure 8 and Figure 9. As can be seen from Figure 6, the edge currents on the surface are significantly reduced after slotting, and the current at the main lobe radiation direction becomes more concentrated while the sidelobe is significantly smaller.

It can be seen from Figure 7 that better impedance matching performance is achieved from 5 GHz to 15 GHz after slotting.

2.3. Gain Enhancement by Adding the Director

The gain characteristic of SKAVA decreases from 11 GHz to 16 GHz. This is due to the decreased coupling coefficient between the radiating plates at high frequencies, causing discontinuity in the radiation electric field at the aperture of the antenna. To solve this problem, we load a metal director in the shape of a water drop at the aperture of the antenna, which forms the Slotted Klopfenstein curve Antipodal Vivaldi Antenna with Director (DSKAVA), as shown in the director part in Figure 1.

The director is located inside the antenna, which does not increase the size of the antenna. It can improve the coupling coefficient between the radiating plates, concentrate the radiation beam, and increase the gain characteristic of the antenna. As can be seen from Figure 10, after loading the director, the gain characteristic is significantly improved, with a gain of more than 15 dBi from 8 GHz to 10 GHz, and up to 7 dB improvement compared to SKAVA from 11 GHz to 16 GHz.

Figure 11 shows the comparison of the S11 between DSKAVA and SKAVA. As can be seen, the impedance matching does not deteriorate after loading the director. The size-optimized drip-shaped director improves the impedance matching performance from 15 GHz to 20 GHz, meeting the bandwidth requirement of 2–20 GHz.

The director significantly improves the gain performance of the antenna without increasing the size of the antenna or affecting other performance.

2.4. Further Sidelobe Suppression with Perforating Design

After loading the director, the sidelobe and front-to-back ratio were slightly degraded due to signal reflection. To solve this problem, two holes of different sizes were trepanned at the tail of the antenna, which form the Perforating Slotted Klopfenstein curve Antenna with Director (TDSKAVA), as shown in the perforating part in Figure 1. Perforating can further suppress surface currents at the rear end, improve the antenna’s sidelobe and back lobe suppression performance, reducing the sidelobe level and improving the front-to-back ratio. The directivity simulation results of the antenna between TDSKAVA and DSKAVA are shown in Figure 12.

As can be seen from Figure 12, the sidelobe level is reduced after perforating, indicating that perforating has a significant optimizing effect on the antenna’s sidelobe performance.

As can be seen from Figure 13, the overall impedance match of the antenna does not deteriorate after perforating, and it meets the bandwidth requirements of 2–20 GHz.

Figure 14 shows the comparison of the front-to-back ratio of the four improved antenna structures, which demonstrates that measures such as slotting, loading director, and perforating can significantly improve the front-to-back ratio performance of the antenna. Compared to the original Klopfenstein curve Antipodal Vivaldi Antenna, the front-to-back ratio can be improved by more than 10 dB on average, and the front-to-back ratio of the antenna can reach 40 dB at 8.8 GHz, with an average front-to-back ratio of over 15 dB.

Figure 15 shows the gain comparison of four improved antenna structures, which demonstrates that the loading director can greatly increase the gain characteristic, with the highest gain exceeding 15 dBi from 8 GHz to 10 GHz and an increase of up to 7 dB compared to not loading the director from 11 GHz to 16 GHz.

Finally, we propose a new type of ultra-wideband antipodal Vivaldi antenna based on the Klopfenstein curve (TDSKAVA) by changing the internal curve shape of the antenna through the Klopfenstein curve, using a quarter-wavelength slot line with width variation and length index variation, loading a droplet-shaped director within the antenna radiation aperture, and perforating at the tail of the antenna. The simulation results of antenna gain are greater than 5 dBi over the entire frequency range, and greater than 10 dBi from 3.5 GHz to 16 GHz, with a maximum gain of over 15 dBi and −10 dB bandwidth of 2–20 GHz, meeting the requirements for ultra-wideband and high-gain applications.

Figure 16 shows the schematic of the overall parameters of the new ultra-wideband antipodal Vivaldi antenna based on the Klopfenstein curve (TDSKAVA), and

Table 1. Specific structure parameters of TDSKAVA.

Parameter	Value	Parameter	Value
L	180 mm	x3	0
W	82 mm	y3	−1.12 mm
W1	75.22 mm	a1	0.23
h	1 mm	a2	0.02
d	2.24 mm	x5	41 mm
x1	40 mm	y5	−19 mm
y1	41 mm	y6	−38 mm
x13	100 mm	y13	11 mm
x14	160 mm	y14	11 mm
x15	42 mm	y15	4 mm
x16	34 mm	a	20 mm
b	11 mm	cr	6 mm
mr	2.5 mm

provides the list of the antenna design parameters.

3. Antenna Measurement

To further verify the feasibility of the proposed new ultra-wideband antipodal Vivaldi antenna design, we have conducted the fabrication and measurement of the design. We used Rogers RO4003C substrate, and metal plates were printed on the upper and lower surfaces of the substrate. The feeding connector is an SMP terminal, and the frequency range of the terminal is DC—40 GHz. The SMP terminal is welded together with the antenna, and Figure 17 shows the front and back views of the overall structure of the antenna. The anaerobic chamber is a Near-Field Spherical Anechoic Chamber with a KEYSIGHT PNA-X N5242B VNA (Santa Rosa, CA, USA) with a bandwidth of 10 MHz to 26.5 GHz. The Near-Field Spherical Anechoic Chamber has conducted S11 parameter testing and directivity and gain testing from 2 GHz to 20 GHz. The connection and impedance matching of the cable to the antenna connector were conducted by engineers at the University of Electronic Science and Technology, and all tests have been run multiple times to obtain precise results with automated measurement support. The feed transition design is a coaxial-to-microstrip transition.

Figure 18 shows the comparison between simulated and measured S11 parameters of the new ultra-wideband antipodal Vivaldi antenna based on the Klopfenstein curve. The impedance bandwidth is basically consistent, with better performance in the low- to mid-frequency range than in simulation results, and slightly weaker in the mid- to high-frequency range. The −10 dB bandwidth is slightly wider than the simulation result, which may be due to processing and testing differences.

Figure 19 shows the comparison between the simulated and measured gain of the antenna. The maximum gain measured exceeds 14 dBi, and the trend is consistent with the simulation. The difference between measurement and simulation is less than 1 dB below 10 GHz and about 2 dB beyond 14 GHz, and the overall gain characteristic matches well. The antenna can still achieve a gain of more than 10 dBi within the frequency range of 3.5–14 GHz, and the difference caused by factors such as processing, welding, and the terminal is within a reasonable range. Figure 20 and Figure 21 show the comparison of simulated and measured radiation patterns of the antenna. Due to the influence of the manufacturing and testing environment, the measured sidelobe of the antenna above 10 GHz increases compared to the simulation, with less than a 2 dB difference. However, the overall main-to-side-lobe ratio is still at a relatively good level, and the main lobe is consistent with the simulation. This verifies the feasibility and high performance of the design of our newly designed ultra-wideband antipodal Vivaldi antenna based on the Klopfenstein curve.

Table 2. Comparison between TDSKAVA and other ultra-wideband antipodal Vivaldi antennas.

	Bandwidth (GHz)	Size (mm)	Electric Size (λ)	Gain/Lowest Point (dBi/GHz)	Gain/Highest Point (dBi/GHz)
This passage	2–20	180 × 82	1.81 × 0.82	5.62/2	14.3/8
Reference [7]	3.1–14	130 × 76	2.75 × 1.61	5.8/3.1	7.26/10
Reference [14]	1–28	260 × 120	1.3 × 0.6	4.9/1	14.4/18
Reference [15]	1.35–17	93.5 × 90	0.69 × 0.66	3.5	9.3
Reference [16]	3.7–18	42 × 36	1.09 × 0.93	1.8	6.9
Reference [17]	3.01–10.6	34 × 16	0.73 × 0.34	3.27/3.01	6.23/10.6
Reference [18]	1.65–18	202 × 120	2.04 × 1.21	6.7/1.65	10.3/3
Reference [19]	6–18	68 × 52	1.7 × 2.2	10.7/6	12.7/12
Reference [20]	1.13–12	130 × 80	-	2.27	14
Reference [21]	2.5–57	186 × 77	-	4/2.7	15/29.8
Reference [22]	0.72–17	158 × 125	0.3 × 0.38	1	12.5

compares the newly designed ultra-wideband antipodal Vivaldi antenna based on the Klopfenstein curve with other ultra-wideband antipodal Vivaldi antennas from relevant references. Compared with other ultra-wideband antipodal Vivaldi antennas, our design integrates multiple methods such as the Klopfenstein curve, slotting, loading director, and perforating, achieving smaller physical size and electrical size, wider relative bandwidth, and higher and smoother gain across the entire frequency range. According to all the references, our work has achieved the most stable −10 dB bandwidth and maintains high gain through a large operating range. Compared with other similar antennas, our work outperforms others with the highest gain through the whole operating range while maintaining a bandwidth of 2–20 GHz and keeping a relatively small form factor.

4. Conclusions

We proposed a novel ultra-wideband high-gain antipodal Vivaldi antenna based on the Klopfenstein curve with dimensions of 180 mm × 82 mm × 1 mm, a −10 dB bandwidth from 2 GHz to 20 GHz, and a relative bandwidth of 163%. The antenna is characterized by excellent directivity characteristics and high gain throughout the operating frequency range, with a measured gain exceeding 5 dBi across the entire frequency range, exceeding 10 dBi from 3.5 GHz to 14 GHz, and reaching a maximum gain of over 14 dBi. The measurement results of the antenna match well with simulation results, verifying the feasibility and high performance of our design. Our design has reference value for the research of ultra-wideband antennas and is suitable for multiple fields such as radar detection, electronic reconnaissance, and ultra-wideband communications.