Act as a heavily experienced Scientist
---

It is my scientific article
---

Computer Simulation of Ultrawideband Vivaldi Active Phased Array Antenna
Yurii Palianytsia ?,†, Vasyl Dunets ?,†, Grygorij Khymych †, and Mykola Khvostivskyi†
Ternopil Ivan Pului National Technical University, Rus'ka St, 56, Ternopil


Abstract
The utilization of computer simulation in technology development, exemplified by the ultrawideband Vivaldi active phased array antenna instead of omnidirectional antennas for ecological monitoring and drone video broadcasting, offers a multitude of advantages. These include substantial cost savings, enhanced environmental sustainability, and an improved ability to control experimental conditions. By adopting computer simulation, we can minimize health risks and environmental impacts, making it a safer and more efficient approach for societal well-being and a greener future.
Keywords 
computer simulation, ultrawideband Vivaldi antenna, active phased array antenna, ecological monitoring, drone, video broadcasting   
Introduction
Ecological monitoring has become increasingly important due to the growing environmental concerns, such as climate change, deforestation, pollution, and wildlife conservation. Traditional methods of ecological monitoring have limitations, including high costs, time constraints, safety risks, and accessibility issues. In recent years, unmanned aerial vehicles (UAVs), also known as drones, have emerged as powerful tools for ecological monitoring owing to their versatility, speed, accuracy, and cost-effectiveness. Drones have emerged as a powerful tool for ecological monitoring, offering unprecedented flexibility, detail, and accessibility. The state-of-the-art in this field continues to advance rapidly, driven by technological innovations and a growing recognition of the potential benefits to conservation efforts. By leveraging the unique capabilities of drones and combining them with advanced data analysis techniques, scientists can gain valuable insights into ecosystem dynamics and inform effective conservation strategies [1].
In the context of drone video broadcasting, the frequency bands of 0.8, 1.2, 2.4, and 5.8 GHz are commonly utilized. These bands are chosen for their ability to offer higher available bandwidths, which is critical for transmitting video images with minimal interference. The 2.4 GHz and 5.8 GHz bands, in particular, are widely used due to their compatibility with many commercial drones. A study on Real-Time Video Transmission and Communication System via Drones over long distances found that frequencies around 2.2 and 2.3 GHz provided the best video-reception time, which is less than 100 seconds [2]. This suggests that the lower end of the 2.4 GHz band is optimal for real-time video transmission. The chapter Drone Technology: Types, Payloads, Applications, Frequency Spectrum Issues and Future Developments discusses the importance of frequency spectrum for drone communication. It mentions that two popular license-free bands used for drones for command and control and payload communications are the 2.4000-2.4835 MHz and 5.470-5.725 MHz bands, which align with the 2.4 GHz and 5.8 GHz bands commonly used in commercial drones [3]. 
Latest findings
The field of ultrawideband (UWB) Vivaldi active phased array antennas is a rapidly evolving area of research, particularly pertinent to applications in ecological monitoring and drone video broadcasting. The integration of UWB technology in Vivaldi antennas has been instrumental in enhancing the performance of communication systems by providing high directivity and gain across a wide range of frequencies.
One notable approach in this domain is presented by Jiwan Ghimire et al., who developed a compact, wideband, high-gain six-slot Vivaldi antenna array on a single substrate layer. Their design utilizes a unique combination of power splitters based on binary T-junction power splitter topology, frequency-independent phase shifter, and a T-branch, resulting in highly directive radiation patterns and optimal return losses (S-parameters) across the UWB frequency band [4].
Another significant contribution is from Ahmad Hatami, Afsaneh Saee Arezomand, and Ferdows B. Zarrabi, who reviewed various models of Vivaldi antennas to achieve a linear or constant phase center. They emphasized the importance of controlling the field distribution around the antenna for phase control, which is crucial for radar applications and microwave sensing [5].
Furthermore, the work on balanced antipodal Vivaldi antennas for wide bandwidth phased arrays has shown promising results. These antennas are known for their good performance over a wide bandwidth, which is essential for the reliable transmission of high-quality video images from drones [6].
The advancements in UWB Vivaldi active phased array antennas are poised to significantly impact ecological monitoring by providing enhanced resolution and sensitivity for environmental data collection. As the technology continues to mature, we can expect further innovations that will solidify its role in modern communication systems.
The integration of computer simulation in the development of technologies like the ultrawideband Vivaldi active phased array antenna presents numerous benefits over traditional in vitro and in vivo experiments. These range from substantial economic savings and improved environmental sustainability to enhanced precision and control over experimental conditions. By reducing health risks and minimizing the environmental footprint, computer simulation stands as a superior alternative, fostering both scientific innovation and societal well-being.
Advanced mathematical aspects of PCB Vivaldi active phased array antennas
The understanding of mathematical aspects of Printed Circuit Board (PCB) Vivaldi antennas is a complex task that involves various aspects of electromagnetic theory and signal processing [7-11]. Vivaldi antennas, known for their wide bandwidth and end-fire radiation patterns, are a type of continuous transverse stub (CTS) antennas [12]. Their design is based on the exponential tapering of a slot line which results in a traveling wave antenna with a flared aperture. 
Geometrical design and parameters of single antenna element
The fundamental geometry of a Vivaldi antenna can be described by an exponentially tapered slot on a dielectric substrate. The taper rate, which determines the opening of the slot, is a critical parameter that affects the antenna’s impedance bandwidth and gain. The taper rate K_a can be expressed mathematically as: 
K_a=1/L_taper  (log W_taper/s),	(1)
where L_taper is the length of the taper,
W_taperis the width of the aperture,
s is the slot line width.
Impedance Matching
For optimal performance, the antenna must be impedance matched to the transmission line. This is often achieved using a microstrip line with a specific characteristic impedance. The impedance  Z(x) along the tapered slot line can be modeled as a function of the position x, which varies from the feed point to the aperture. 
The impedance transformation can be represented as: 
Z(x)=Z_0 e^(K_a x),	(2)
where Z_0 is the characteristic impedance at the feed point.
Radiation pattern and gain
The radiation pattern of a Vivaldi antenna is determined by the distribution of the electric field along the aperture. The far-field radiation pattern E(?,?) in spherical coordinates can be approximated using the aperture field distribution and the taper profile. The gain G of the antenna can be calculated by integrating the radiation intensity over the entire radiation sphere: 
Z(x)=Z_0 e^(K_a x),	(3)
where P_rad is the total radiated power.
Signal propagation and dispersion
The signal propagation along the tapered slot line is subject to dispersion, which can be modeled using the telegrapher’s equations. The phase velocity v_p and group velocity v_g are crucial for understanding the broadband characteristics of the antenna:
v_p=1/v(L^' C^' ),
v_g=d?/dk,	(4)
where L' and C' are the per-unit-length inductance and capacitance,
? is the angular frequency,
k is the wave number. 
Electromagnetic wave propagation
The performance of a Vivaldi antenna is heavily influenced by the propagation of electromagnetic waves along the tapered slot. The propagation can be described by Maxwell’s equations, which in the case of a Vivaldi antenna, are often simplified to the transverse electromagnetic (TEM) mode due to the planar structure of the antenna. The electric E and magnetic H fields in the TEM mode can be expressed as: 
¦(E(x,y,z)&=-??(x,y) e^(-j?z)@H(x,y,z)&=1/? z ????(x,y) e^(-j?z) ),	(5)
where ?(x,y) is the electric potential,
? is the propagation constant,
? is the intrinsic impedance of the medium.
Antenna aperture
The aperture of the Vivaldi antenna, which is the open end of the tapered slot, acts as the radiating element. The field distribution across the aperture can be modeled using the aperture field method, which assumes that the fields in the aperture are equivalent to those on an imaginary surface in the near-field region. The aperture fields E_ap (x,y) are related to the far-field pattern F(?,?) by the Fourier transform: 




F(?,?)=?_aperture-?E_ap (x,y) e^(-j(k_x x+k_y y) ) dxdy?,	(6)
where k_x and k_y are the wave vector components in the x and y directions, respectively.
Dispersion Analysis
The dispersion characteristics of the Vivaldi antenna are crucial for its wideband performance. The dispersion relation, which links the frequency f to the propagation constant ? can be derived from the transmission line model of the tapered slot. For a non-dispersive line, the relation is linear; however, for a Vivaldi antenna, the relation is more complex due to the varying geometry: 
?(f)=2?f/(v_p (f) ),	(7)

where v_p (f) is the frequency-dependent phase velocity.
Numerical methods for simulation
To accurately simulate the performance of a Vivaldi antenna, numerical methods such as the Finite-Difference Time-Domain (FDTD) method or the Transmission-Line Matrix (TLM) method are employed in Matlab Antenna and RF Toolboxes. These methods discretize the antenna structure into a grid and solve Maxwell’s equations iteratively over time or frequency. The simulation provides detailed information about the antenna’s impedance, radiation pattern, and gain across its operating bandwidth.
Optimization techniques
Mathematical optimization build-in techniques of Matlab Antenna, RF and Phased Array System Toolboxes are used to fine-tune the design of Vivaldi antennas and arrays by default. Techniques such as genetic algorithms (GAs) or particle swarm optimization (PSO) are applied to maximize the antenna’s performance metrics, such as gain or bandwidth, by adjusting design parameters like the taper rate or substrate material properties.
Array configuration and element spacing
The geometry of the phased array is defined by the placement of the individual antenna elements. For a 2x5 array, we have two rows and five columns of elements. The spacing between the elements, both inter-row and inter-column, is a critical factor that influences the array’s performance. The element spacing d is a fraction of the wavelength ? to avoid grating lobes d??/2.
Beamforming and steering
Beamforming is achieved by adjusting the phase of the signal at each antenna element. For a desired beam direction ?_0 and ?_0 , the phase shift ??_mn for the element at row m and column n is given by: 
??_mn=2?/? (md_y sin(?_0 )sin(?_0 )+nd_x cos(?_0 )),	(8)

where d_x and d_y are the inter-element spacings in the x and y directions, respectively.
Impedance matching and mutual coupling
Each element in the array must be impedance matched to ensure maximum power transfer. Additionally, mutual coupling between elements must be considered, as it affects the input impedance of each element. The input impedance Z_(in,mn) of the element at position m,n can be modeled as:
Z_(in,mn)=Z_0+jX_mn+?_¦(p,q@(p,q)?(m,n) )^-Z_(coup,pq) ,
(9)
where Z_0 is the characteristic impedance,
X_mn is the reactance due to the element’s own structure,
Z_(coup,pq) represents the mutual coupling impedance from the element at position p,q.
Radiation Pattern and Gain
The radiation pattern of the array is the result of the superposition of the patterns from each element. The total electric field E_total in the far-field can be expressed as: 
E_total (?,?)=?_(m=1)^M-?_(n=1)^N-E_mn  (?,?) e^(-j??_mn ),	(10)

where E_mn (?,?) is the radiation pattern of the individual element at position m,n, 
M and N are the number of rows and columns, respectively.
Understanding of PCB Vivaldi Antenna Arrays mathematical aspects encompasses a comprehensive analysis of their element spacing, beamforming, impedance matching, and mutual coupling, signal propagation, and dispersion. Numerical simulations play a vital role in predicting the antenna’s performance and guiding the optimization process to achieve the desired wideband characteristics. Using standard-de-facto Matlab tools ensures that Vivaldi antennas can meet the stringent requirements of modern communication systems, including those used for ecological monitoring and drone video broadcasting.
Design and computer simulation results
Single PCB ultrawideband Vivaldi antenna element
Based on the technical requirements, our single PCB ultrawideband Vivaldi antenna element [7] is designed to cover video transmission bands of 0.8, 1.2, 2.4, and 5.8 GHz. The design of the antenna element (Figure. 1a) is executed in the form of a PCB stack (Figure. 1b), where the top side features a cooper layer on FR4 laminate, creating the board shape for the antenna. On the bottom side of the stack, within the lower copper layer, a radial stub matching circuit (commonly referred to as a "bowtie") is constructed to extract electromagnetic energy from the Vivaldi antenna element. 
 
(a)	 
(b)
Figure 1: Geometric dimensions of single Vivaldi antenna element of the active phased array antenna
Leveraging the Matlab Integrated Development Environment , the 3D directivity pattern of the Vivaldi antenna element has been constructed in three-dimensional coordinates for 
0.8, 1.2 GHz bands and for 2.4, 5.8 GHz bands, as depicted in Figure 2 and Figure 3 respectively. This graphical representation provides an insightful visualization of the antenna's radiation pattern, crucial for the precise calibration and optimization of its performance in targeted applications. 
 
(a)	 
(b)
Figure 2: Directivity diagram plot of Vivaldi antenna element pattern in 3-dimensional coordinates for 1.2, 2.4 GHz bands

 
(a)	 
(b)
Figure 3: Directivity diagram plot of Vivaldi antenna element pattern in 3-dimensional coordinates for 5.4, 5.8 GHz bands 
The directivity diagrams of the Vivaldi antenna element have been calculated for video broadcasting frequency ranges of 0.8 (a), 1.2 (b), 2.4 (c), and 5.8 GHz (d), as illustrated in Figure 4. It is observed that the directivity diagrams exhibit asymmetry, which is a characteristic inherent to Vivaldi antennas. The asymmetrical pattern of the Vivaldi antenna element will be neutralized when integrated into an antenna array, which is advantageous for targeted video broadcasting. This ensures precise transmission and reception within the designated frequency bands, optimizing the antenna's performance for specific communication needs. 
  (a)	  (b)
  (с)	  (d)
Figure 3: Azimuth (a) and elevation (b) cut of directivity at 0, 30 45, 60 and 90 degrees elevation/azimuth
It is observed that the directivity diagrams exhibit asymmetry, which is a characteristic inherent to Vivaldi antennas. The asymmetrical pattern of the Vivaldi antenna element will be neutralized when integrated into an antenna array, which is advantageous for targeted video broadcasting. This ensures precise transmission and reception within the designated frequency bands, optimizing the antenna's performance for specific communication needs.
Ultrawideband Vivaldi active phased array antenna











Using the Matlab RF Toolbox, we computed the input impedance of a single Vivaldi antenna element and plotted the resistance and reactance across the specified frequencies of 0.8 GHz, 1.2 GHz, 2.4 GHz, and 5.8 GHz, respectively (Figure 5a). This analysis showed the variation in impedance with frequency, which is crucial for achieving proper impedance matching and minimizing signal reflection.
Moreover, we calculated the S-parameters for the single Vivaldi antenna element, focusing on the S11 parameter, which represents the input reflection coefficient. The S11 parameter, also known as the return loss, indicates how much power is reflected back towards the source (Figure 5b). An S11 value of 0 dB implies that all the power is reflected and none is radiated, which is undesirable. To achieve efficient radiation, the S11 value must be minimized.
 
(a)	 
(b)
Figure 5: Geometric dimensions of single Vivaldi antenna element of the active phased array antenna
The design incorporates impedance matching and mutual coupling mitigation techniques to ensure optimal performance and efficiency. Each Vivaldi element is individually matched to the characteristic impedance of the feed network, and the effects of mutual coupling between adjacent elements are minimized through careful array optimization.


















### Ultrawideband Vivaldi active phased array antenna



We have constructed an active phased array antenna comprising a 2x5 configuration (2 rows horizontally by 5 columns vertically) of Vivaldi antenna elements. This arrangement enables a narrow beam pattern in the horizontal plane (azimuth), which is advantageous for our application. In our case, a high degree of resolution in the vertical plane (elevation) is not a critical requirement.

The design leverages the individual Vivaldi antenna elements discussed earlier, with their optimized performance across the desired frequency bands for video broadcasting (0.8, 1.2, 2.4, and 5.8 GHz). By arranging these elements in a phased array configuration, we can achieve beamforming capabilities, allowing us to steer the radiation pattern in the desired direction electronically.

The inter-element spacing within the array is a crucial parameter that must be carefully chosen to avoid the formation of grating lobes and to ensure optimal radiation characteristics. In our design, the spacing between adjacent elements in both the horizontal and vertical directions is set to be less than half the wavelength (d < λ/2) at the central operating frequency of 2.4 GHz. This spacing ensures that the array radiates a single main beam without the presence of significant grating side lobes.

To achieve beamforming and beam steering, the signals fed to each antenna element are phase-shifted according to the desired beam direction. The phase shift required for an element located at the $$m$$-th row and $$n$$-th column ($$m, n$$) is given by the following equation:

$$Φ_mn = 2π/λ (md_y sin(θ_0) sin(φ_0) + nd_x cos(θ_0))$$

Where:
- $$d_x$$ and $$d_y$$ are the inter-element spacings in the $$x$$ (horizontal) and $$y$$ (vertical) directions, respectively.
- $$θ_0$$ and $$φ_0$$ are the desired elevation and azimuth angles, respectively, for the main beam direction.
- $$λ$$ is the wavelength corresponding to the operating frequency.

By adjusting the phase shifts applied to each element, we can steer the main beam in the desired direction, enabling electronic beam scanning capabilities for the array.

The design incorporates impedance matching and mutual coupling mitigation techniques to ensure optimal performance and efficiency. Each Vivaldi element is individually matched to the characteristic impedance of the feed network, and the effects of mutual coupling between adjacent elements are minimized through careful array optimization.

The resulting ultrawideband Vivaldi active phased array antenna provides a highly directive radiation pattern that can be steered electronically, making it well-suited for applications such as ecological monitoring and drone video broadcasting. The narrow azimuthal beamwidth allows for precise directional transmission and reception, while the wideband frequency coverage accommodates the required video transmission bands.











---
Continue my article in english, keeping in mind it text:


Також ми project the radiation pattern of the ultrawideband Vivaldi active phased array antenna onto the terrain surface for 0.8 (Figure 5a), 1.2 (Figure 5b), 2.4 (Figure 5c), and 5.8 GHz  (Figure 5d) respectively.