Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 9, No. 1, 2024 

 

165 

A	3D	Array	High‐Gain	Vivaldi	Antenna	Design 

Hongyang Xu*, Haisheng Song 

School of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070, China 
*Corresponding author: Hongyang Xu (E-mail: 13259770734@163.com) 

 

Abstract: This article designs a 3D array high-gain Vivaldi antenna suitable for K-band. First, by adding a positive trapezoidal 
dielectric structure to the radiation port of the original Vivaldi antenna unit, the purpose is to increase the gain of the Vivaldi 
antenna unit. The Vivaldi antenna unit was simulated and analyzed through HFSS software to obtain a new Vivaldi antenna unit 
with a frequency band width of 20GHz-26.4GHz and a gain of 10.8dB.Wider bandwidth, improved gain performance and 
enhanced directionality of the Vivaldi antenna unit compared to the original antenna. A 4-cell antenna array with a 3D structure 
is designed in order to be suitable for smaller planar size operating environments, and the antenna structure is further analyzed 
by...In this paper, the power division feed network conforming to this array is designed and the performance of this 2×2 antenna 
array is investigated, and the simulation results show that this array has good bandwidth and radiation performance, strong 
directionality, and almost no offset angle in the E-plane. 

Keywords: 3D array; Vivaldi antenna; Pilot; High gain; Power division feed network; Directionality; Bandwidth. 
 

1. Introduction 
The rapid development of radar technology, the emergence 

of miniaturized, low-cost radar, so that the application of 
radar is more extensive, vehicle collision avoidance radar 
came into being. In the process of automobile driving, 
collision avoidance radar can prejudge whether the 
surrounding vehicles and obstacles will have an impact on the 
automobile driving, and then through the issuance of 
warnings to draw the attention of the driver to the possible 
dangers that may occur, and if the driver is too late to react, it 
can also be a temporary substitute for the driver to make a 
deceleration to avoid or emergency braking and other safety 
operations to avoid accidents. 

Currently, the two frequency bands used internationally for 
on-board radar are 24 GHz and 77 GHz. Of these, 24 GHz is 
used for short-range radar, where the Vivaldi antenna has 
good radiation characteristics and a wide bandwidth. In 1979, 
Gibson first proposed a tapered chipped slot antenna using 
exponentially tapering curves, known as a conventional 
antenna, which belongs to the category of tapering, non-
periodic, end-shooting traveling-wave antennas, in which 
electromagnetic waves are radiated from the narrower gap 
end to the wider open end by means of an exponentially 
tapering slit structure. In order to improve the performance of 
the antenna, loading of metamaterials on top of conventional 
structures, introduction of slit structures, loading of dielectric 
lenses, etc. are usually used. The Vivaldi conventional 
antenna unit proposed in literature has a gain of 6.3 dB at an 
operating frequency of 24 GHz and its operating bandwidth 
is 23-27 GHz. Literature proposes to add an inverted 
trapezoidal guide to the radiating port of the heeled Vivaldi 
antenna, and the gain of the prototype heeled Vivaldi antenna 
is 10 dB at 24 GHz operating frequency, and the gain rises to 
12.8 dB after the addition of the guide, however, literature 
only improves the gain of the heeled Vivaldi antenna, and no 
research has been carried out in the aspect of the conventional 
Vivaldi antenna. Literature proposes to load a rectangular slot 
on a conventional Vivaldi antenna with a bandwidth of 2-4 
GHz operating band and a triangular pilot at the radiating port, 
the antenna has a gain of 6.7 dB at an operating frequency of 

3 GHz, which is a total gain improvement of 1.8 dB compared 
to the conventional Vivaldi antenna. 

In this paper, a new high-gain Vivaldi antenna unit at 24 
GHz is proposed to add a positive trapezoidal structure at the 
radiating port of a conventional Vivaldi antenna with a 
bandwidth of 20 GHz-26.4 GHz, and the maximum gain is 
about 10.8 dB at the operating frequency of 24 GHz. 
Compared to literature there is a great improvement in terms 
of gain and bandwidth. Compared to literature this paper 
applies the idea of a pilot to a conventional Vivaldi antenna 
with appropriate structural changes. Compared to literature 
where this paper improves the gain by 1 dB when only the 
pilot is loaded, literature improves it by only 0.8 dB. And this 
paper proposes a 2×2 3D structure of the array and designs a 
common feed network to match with it, so that its array 
increases 4.2dB compared to the cell gain and the bandwidth 
is 5.9GHz, which meets the design and requirements. 

In this paper, a 3D 4-cell 2×2 array antenna operating at 24 
GHz frequency has been designed by investigating the array, 
feed, etc. As in literature to design a 1 × 4 linear array of 
Vivaldi antenna units, this design compared to its linear array 
1 × 4 array, greatly reducing the size required for the array 
plane, and other performance has been improved for the 
design of Vivaldi antenna arrays to provide a new way of 
thinking. 

2. 24GHz Vivaldi Antenna Unit Design 

2.1. Calculation of the original antenna unit 
and its dimensions 

The schematic of the original Vivaldi antenna structure is 
shown in Figure 1 below. 



 

166 

   
(1) Negative            (2) Backside 

Figure 1. Traditional Vivaldi antenna structure 
 
(1) Slotted line structure 
Vivaldi antenna is a traveling wave antenna with end-

shooting characteristics, according to the radiation principle 
of Vivaldi antenna, it can be known that the antenna starts to 
radiate electromagnetic waves only when the slot line end 
opening is larger than 1/2 wavelength, so when the frequency 
is increased to the width of slot line end opening is larger than 
1/2, the antenna starts to radiate electromagnetic waves 
outward, so the width of the slot line end opening decides the 
low-frequency characteristics of the antenna, and when the 
frequency is continued to increase, the antenna is not able to 
radiate efficiently when the width of the antenna's starting end 
is larger than two times the wavelength, therefore, the width 
of slot line starting end decides the antenna's high-frequency 
characteristics[4]. 

Knowing the width of the openings at the beginning and 
end of the exponential tapering groove line, the exponential 
tapering groove line can be sized using the formula for 
exponential tapering groove lines. 

Vivaldi index gradient groove line formula 
 

y C e C               (1) 
 

C                 (2) 

 

C               (3) 

 
Where, (x1,y1), (x2,y2) are the coordinates of the start 

point and end point, r is the curvature of the slot line, which 
determines the degree of curvature of the slot line, when r is 
larger, the more curved the exponential asymptotic curve is, 
the lower the low frequency cutoff frequency is, and the better 
the antenna's low-frequency characteristics are, and vice 
versa. 

(2) Radial-slot line structure 
Vivaldi antenna by the microstrip line to the slot line feed, 

according to the Vivaldi antenna principle, this form of balun 
disadvantage is narrow bandwidth, so in order to further 
broaden the bandwidth of the balun, the lower end of the 
microstrip line to extend the branch section into a fan-shaped 
short cut-off line structure, so as to make the microstrip line 
in the wider band to maintain an open-circuit state. The 
extended branch section at the lower end of the slotline is 
converted into a circular resonant cavity structure, which 
ensures that the end of the slotline remains short-circuited 
over a wide frequency band[1]. The diameter D of the circular 

resonant cavity is 1/4 of the slotline waveguide wavelength, 
and the radius of the short fan-shaped section is 1/4 of the 
microstrip line waveguide wavelength. 

(3) 1/4 Multi-section impedance matching network 
By the formula of microstrip line and slot line and the 

relationship between microstrip line characteristic impedance 
and slot line characteristic impedance as shown in the 
following equation. 

 
Z N ∗ Z                  (4) 

 
Where, N is a conversion factor of size. 
 

N cos（2πud/λ ） cot（q）sin（2πud/λ ）(5) 
 

q 2πud/λ tan             (6) 
 

U ε λ /λ              (7) 
 

V λ /λ 1             (8) 
 

According to the theory of small reflections, this paper uses 
a multi-section Chebyshev impedance converter with 
reflection coefficients, as in the following equation: Γ（θ）

2e Γ cosNθ Γ cos N 2 θ  . . . . . . Γ cos N
2n θ . . . Ae T secθ cosθ . 

When designing a Chebyshev multinode impedance 
converter, the coefficients of the polynomial (|A|) are first 
determined based on the maximum reflection coefficient (Γm) 
allowed in the passband. 

 
Γ |A|                   (9) 

 
The number of matching sections N is found according to 

the following equation: 
 

θ
（ / ）

            (10) 

 

secθ =cosh*[ cosh
/

]     (11) 

 
In the formula, Z  represents the load impedance, and Z  

represents the input impedance, i.e. 50Ω. 
Find the impedance of each section in turn based on the 

following equation: 
 

Γ ln                  (12) 

 
In this paper, N = 4 is obtained, so the physical dimensions 

of the conventional Vivaldi antenna are shown in Table 1, 
with length in mm. 

Table 1. Vivaldi antenna unit dimensions 
L W R1 R2 H L_c L_1 W_1 

26.017 14.05 1.5 2.39 0.5008 1.5 2.1625 1.152 
W_2 L_3 W_3 L_4 W_4 r W_c L_2 

0.7512 2.2275 0.4 2.25 0.39 0.2 0.2 2.1925 

2.2. High gain 24 GHz Vivaldi antenna unit 
design and simulation 

A forward trapezoidal deflector is added to the radiating 
port of the original Vivaldi antenna unit, as shown in Figure 
2. The addition of the pilot structure is known to enhance the 



 

167 

surface current at the radiating port and increase the gain of 
the Vivaldi antenna unit. In this paper, the addition of a 
positive trapezoidal dielectric plate at the radiating port can 
limit the radiation direction of the surface current at the port 
to the antenna, thus enhancing the gain of the antenna unit. 
Using the parameter optimization function of the HFSS 
software, the size parameter of W_4 was determined to be 
0.39 mm, and its physical dimensions are shown in Table II 
in mm. 

 

 
(1) Top view 

 

 
(2) Main view 

Figure 2. New Vivaldi antenna unit 
 

Table 2. Dimensions of trapezoidal media structures 
θ L_t W_t H_t 

15° 17.16 3.5008 5.6 
 
Using HFSS software, a 50 Ω collector port is added at the 

excitation source, and the surface current simulation analysis 
of the original Vivaldi antenna cell and the new Vivaldi 
antenna cell are carried out respectively, and it can be found 
that the currents of the radiating cell are mainly distributed in 

the vicinity of the tapering slot, which is in accordance with 
the principle. Surface current simulation distribution is 
obtained Figure 3. From Figure 3, it can be found that the 
current strength of the original Vivaldi antenna (b) at the 
radiating port is relatively weak. It can be found that the 
current strength of the new Vivaldi antenna (a) at the radiating 
port is significantly enhanced after the addition of the 
trapezoidal dielectric structure, so it can be concluded that 
after the addition of the trapezoidal dielectric structure, the 
surface currents are concentrated at the radiating port of the 
antenna, which enhances the antenna's radiating 
characteristics and improves the antenna unit's gain. 

 

       
(a) Original Vivaldi Antenn  (b) New Vivaldi Antenna 

Figure 3. Comparison of surface current simulation 
 
Comparing with the S-parameters and gain characteristics 

of the original Vivaldi antenna unit, the S-parameter 
simulation results are obtained as shown in Fig. 4, and it can 
be observed that the return loss of the new Vivaldi antenna is 
less than -10dB in the bandwidth of 20GHz-26.4GHz, and 
even less than -15dB in the bandwidth of 21.5GHz-24.9GHz, 
and reaches -26.2dB in the frequency of 23.3 At 23.3 GHz, it 
reaches -26.2 dB; compared with the original Vivaldi antenna, 
the bandwidth is wider, with a bandwidth of 6.4 GHz, and the 
return loss at 24 GHz is lower. 

 

 
Figure 4. S-parameter simulation results of the novel Vivaldi antenna 

 
The simulation results of the gain direction diagram of the 

new Vivaldi antenna and the original Vivaldi antenna at a 
frequency of 24 GHz are shown in Figure 5. From Figure 5(a), 
it can be seen that after adding the positive trapezoidal 
dielectric structure, the gain of the new Vivaldi antenna 
reaches about 10.8 dB higher than that of the original Vivaldi 
antenna at a frequency of 24 GHz, which is about 1 dB higher 

than that of the original Vivaldi antenna, and it can be clearly 
seen that the sub-flap of the Vivaldi antenna is reduced. And 
through the directional map of the antenna in Figure 5(b), it 
is clearly observed that the beam width of the new antenna 
unit is narrower, indicating that the new Vivaldi antenna unit 
is more directional. 

 



 

168 

 
(a) Gain 

 
(1) Surface E                       (2) Surface H 

(b) Orientation plan 
Figure 5. Gain and Direction Graph 

 

3. Power Divider Feeder Network 
Design and Simulation 

First, according to the designed array and unit, because the 
feeding part of the Vivaldi antenna is fed by microstrip 
feeding and it is a top and bottom structured array, so in this 
paper, the power divider adopts the microstrip-coaxial-
microstrip feeding structure, which utilizes the transmission 
characteristics of coaxial and microstrip lines to realize the 
signal transmission of the array. 

From the point of view of the circuit analysis, firstly the 
characteristic impedance of the feed port of the antenna unit 
is 50 ohms, to realize a feed network with a characteristic 
impedance of 50-50 ohms, and secondly there are four units 
in the array, so it is necessary to make a one-part-two-repeat-
two power divider, whose equivalent circuit diagram is shown 
below in figure 6. 

 

 
Figure 6. Schematic diagram of equivalent circuit 

 
Because Z 50 Ω, according to the Wilkinson power 

divider principle, this gives Z Z 100 Ω. In order to 
realize the impedance matching of the transmission line, 
Z , Z   is processed through the quarter wavelength in 
impedance transformation principle, which makes Z′

Z′ 50 Ω, Consequently, Z Z Z Z 100 Ω. In 
order to realize impedance matching between the power 
divider and the antenna, the principle of quadrature 
wavelength transformation is used in the same way so that 
Z′ Z′ Z′ Z′ 50Ω. 

Considering that the whole array is three-dimensional, it is 
necessary to use coaxial lines to connect the upper and lower 
microstrip power dividers, as shown in Figure 8, and in this 
paper, we consider two structures of microstrip-coaxial 
connection. 

The upper and lower microstrip lines have the same 
characteristic impedance where they are connected to the 
coaxial line. The upper microstrip line has a characteristic 
impedance of 50 Ω, and the lower microstrip line has a 
characteristic impedance of 100 Ω. Impedance matching is 
performed using coaxial lines 

So the two methods were simulated and tested and the 
results are shown in Figure 7 below. 

 



 

169 

 
(1) Same impedance up and down S-parameter 

 
(2) Different S-parameters for upper and lower impedance 

Figure 7. Test results of S-parameters for two cases 
 
From the above figure, we can find that (1) the test results 

are better, (1) the S11 is bigger, indicating that only a weak 
signal is reflected back, (1) the S12 tends to be close to 0, 
indicating that the input is as much as the output, and there is 
basically no loss in the transmission process. The test result 
of (2), on the other hand, indicates that there is some loss of 
signal on the coaxial line.  

Therefore, the microstrip-coaxial structure in this paper 
adopts the way of (1), so the design of the power divider needs 
to fully consider the structure of (1), according to the formula 
of the coaxial line, this paper adopts the coaxial line with an 
inner column radius of 0.05 mm and an outer column radius 
of 0.5925 mm, connecting the microstrip line to the coaxial 
line with the coaxial line with a high height of 14.5 mm, and 
its common denominator feeder network is shown in Figure 
8. 

 
Figure 8. Fractional feeder network 

 
By optimizing some parameters of the microstrip line and 

coaxial line, the simulation results of the return loss profile of 
the final power division feeder network are shown in Fig. 9 
below. 

 

 
Figure 9. Return loss of a power-divided feeder network 
 
The power division feeder network designed in this paper 

is fed in a one-in-four manner, with 1 as the input port and 2, 
3, 4, and 5 as the output ports, and it can be seen that S11 is 
less than -10dB in the frequency band of 20-28GHz, and 
reaches -48dB at 24.6GHz, and below -28dB at 24GHz, 
which indicates that there is only a tiny amount of signal 
reflection, S12, S13, S14, and S15 of this feeder network, are 
all greater than -7dB in the frequency band of 20-28GHz.The 
above simulation results show that in the operating band, the 
power divider, divides the input signal at port 1 nearly 
uniformly among the four output ports 2, 3, 4, and 5, and there 
is basically no signal reflected back. The bandwidth of the 
power division feed network designed in this paper is 
applicable to the new Vivaldi antenna designed in this paper 
and satisfies the design requirements. 

4. Array Design 

4.1. Array structure 
From the design point of view, in order to reduce the plane 

size of the array, so the design of a double-layer 3D 2 × 2 
arrays, but by the mutual coupling between the units, so the 
characteristics of their arrays and units work alone when the 
characteristics of the difference is very large, so the further 
study of the antenna unit and in the performance of the array, 
the simulation study, the structure of the structure as shown in 
Figure 10 (1). 

 

 
(1) 3D array structure 

 
(2) Linear array structure 

Figure 10. Array structure 
 

The structure of the array is that the spacing between the 
upper two cells is 5.77 mm, the spacing between the lower 
two cells is 7.34 mm, and the spacing between the upper and 
lower cells is 13.5 mm, which realizes the 3D array and 



 

170 

occupies a planar area of 42.7 × 34.35. The planar area of a 1 
× 4 linear array is 75 × 31.6, so the structure greatly reduces 
the planar area required by a 4-cell linear antenna array (e.g., 
Figure 10(2)). The structure greatly reduces the plane area 
required for a 4-cell linear antenna array (as in Figure 10(2)). 

4.2. Array Simulation 
Synthesizing the above articles, we obtain the array 

antenna shown in Fig. 11 below, with slight variations in 
performance due to the effects of mutual coupling between 
the units, and losses on each device. 

 

 
Figure 11. Schematic of array antenna 

 
In this paper, the 3D array is composed of 2 × 2 arrays, 

which greatly reduces the plane area required for the 4-unit 
array, and at the center frequency of 24 GHz, Figure 12 shows 
the simulation results of the 3D array without common feed 
network and the linear array, which shows that the gain of the 
3D array with reactive power division feed network is 16 dB, 
and the main flap beamwidth is about 26°, which is basically 
the same as that of the linear array of 1 × 4, and the main flap 
beamwidth is narrower than that of the linear array. It is 
basically the same, and the main flap beamwidth is narrower 
compared to the linear array, which indicates that the 3D array 
is more directional, and the bandwidth of the 3D array is 6.4 
GHz compared to the linear array, which is wider. 

 

 
(1) Gain 

 
(2) S11 

Figure 12. Comparison of simulation results between 3D 
array and linear array of power division free feeder network 

At the center frequency of 24 GHz, Figure 13 shows the 
simulation comparison results of the final 3D array Vivaldi 
antenna designed in this paper, and it can be seen that the gain 
of this 3D array antenna is about -15 dB, and the main flap 
beamwidth is about 23°, compared with the array antenna 
without common feed network, the gain is slightly decreased, 
mainly due to the increase of the power divider circuit, the 
internal loss increase, and some parameters The design is 
slightly flawed, resulting in a weak reflection of the signal in 
the transmission process can not achieve the ideal 
transmission, but the results are basically in line with the 
principle. By comparing the data, it can be seen that its 
directionality is stronger, and reduce the sub-flap, after adding 
the power division feed network, it can be obviously found to 
improve the antenna's E-plane offset angle so that it reaches 
90°, although the bandwidth basically remains unchanged, 
but in the 24GHz operating frequency, the return loss number 
reaches -43dB, to reach the lowest return loss, and to meet the 
design requirements. 

 

 
(1) Gain 

 
(2) S11 

Figure 13. Comparison results of simulation of power-
division-containing feeder networks 

 
Figure 13 (2) shows the simulation comparison results of 

the return loss S11 of the array antenna containing the power-
division feeding network, and the bandwidth of the array 
antenna designed in this paper is less than -10 dB within 21-
26.9 GHz, and it is even less than -15 dB within the bandwidth 
of 22 GHz-26 GHz, and it reaches -43 dB at the frequency of 
24 GHz. 

5. Conclusion 
In this paper, a new ultra-wideband high-gain Vivaldi 

antenna unit with a gain of 10.8 dB at an operating frequency 
of 24 GHz is designed. The antenna is based on the original 
Vivaldi antenna, and a positive trapezoidal dielectric structure 
plate is added to its radiating port to enhance the antenna's 



 

171 

surface currents at the radiating port, which not only reduces 
the sub-flap of the antenna unit, but also strengthens the 
antenna's radiating characteristics and Directionality. The 
return loss of the antenna is less than -10dB in the bandwidth 
of 20GHz-26.4GHz, and it has good characteristic impedance. 
In this paper, on top of the antenna unit, a 4-cell 3D antenna 
array operating at 24 GHz is also designed, and its matched 
common feed network is investigated. The array greatly 
reduces the plane area required for a typical 4-cell linear 
antenna array and has stronger directionality, with a gain of 
15 dB at an operating frequency of 24 GHz, and the return 
loss of the antenna is less than -10 dB in a bandwidth of 21 
GHz-26.9 GHz, and improves the gain peak offset angle of 
the E-plane directional map of the array antenna. 

Acknowledgment 
This work is supported by the National Natural Science 

Foundation of China (11747030) and the Science and 
Technology Program of Gansu Province (20JR10RA080). 

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