A method for calculating the radiation resistance of antennas in seawater using cylindrical surface integral

Abstract

The present invention discloses a method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral, which belongs to the field of wireless communication technology. The method calculates the radiation resistance of a loop antenna in seawater by using a cylindrical surface integral model, and provides a new way to accurately calculate the radiation resistance of the loop antenna. The method specifically comprises the following steps: calculating the average value of the power density generated by the outward radiation of the loop antenna in seawater, the Poynting vector S av ; In the loop antenna radius r L is the radius, and the height of the loop antenna is h is the average power density on the high cylindrical surface S av The invention proposes a model for calculating the radiation resistance of a loop antenna in seawater using cylindrical surface integrals. Its technical approach and implementation scheme have been verified by computer simulation and offshore experiments. This method can more accurately calculate the radiation resistance of underwater loop antennas, thereby accurately evaluating and optimizing the performance of antennas and communication systems.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications, and in particular relates to a method for calculating the radiation resistance of an antenna in seawater by utilizing cylindrical surface integral. Background Art

[0002] The ocean is an important strategic space for the sustainable development of mankind and a strategic commanding height that countries around the world are competing for. Underwater vehicles, seabed observation networks, and underwater sensor networks will provide strong support for the acquisition and exchange of ocean information. Information interaction between underwater platforms such as unmanned autonomous underwater vehicles (AUVs) and underwater robots will become more and more frequent. These devices need reliable and efficient underwater communication technology as a guarantee to acquire, process and transmit information in the marine environment.

[0003] At present, information transmission in the marine environment mainly relies on carriers such as cables, sound waves, blue-green lasers and electromagnetic waves. Underwater wired communication technology is mature and has high speed, but it is difficult to lay, has high cost and is easily interfered by the external environment. Underwater wireless communication technology includes underwater acoustic communication, underwater blue-green laser communication and underwater electromagnetic wave communication. Underwater acoustic communication is the most widely used technology. Although it has long-distance transmission capability, it is restricted by problems such as slow propagation speed, large noise interference and limited bandwidth. Underwater blue-green laser communication has high speed and strong concealment, but requires precise alignment and is greatly affected by obstacles. Underwater electromagnetic wave communication is a hot topic in modern research, with fast transmission speed, strong anti-interference ability and little impact from the environment. At the same time, when electromagnetic waves propagate near the near-ocean interface, due to their unique cross-interface propagation characteristics, their effective distance is greatly increased compared to when they propagate directly in seawater.

[0004] Affected by the absorption and attenuation of seawater, the selection of electromagnetic wave carrier frequency is limited by many factors. In the past, only ultra-long wave communication has been put into practical use, but its antenna is large in size, high in energy consumption, and the communication rate is extremely low. In recent years, with the development of digital signal processing technology and antenna technology, underwater high-speed electromagnetic wave communication has become possible. High-performance and small-volume loop antennas are an important research direction for underwater electromagnetic wave communication technology. The radiation resistance of the antenna is one of the most important parameters of the electromagnetic wave communication system. It determines the amount of energy radiated outward by the transmitting system. The radiation resistance of the loop antenna working in seawater will change greatly compared to that in the air. The change in radiation resistance will cause the radiation efficiency and radiation power of the antenna to change accordingly. Therefore, accurate modeling and calculation of the radiation resistance of the underwater loop antenna will be the key to the design and development of the underwater electromagnetic wave communication system.

[0005] The study of the calculation method of antenna radiation resistance has always been a hot topic in the research of underwater electromagnetic wave communication technology. James R. Wait proposed in the 20th century that the loop in the conductive medium is surrounded by a spherical insulating cavity. The integral expression of the field inside the cavity was derived, and the continuity condition was used to determine the influence of the cavity on the coil impedance. Finally, it was concluded that under a given coil current, the power radiated by the coil to the surrounding is roughly inversely proportional to the inverse of the cavity diameter. After considering the geometric shape of the wire and the current distribution, Martin B. Kraichman obtained the expression of the external resistance and reactance of the ring in the conductive medium by performing spherical integral on the current distribution of the ring wire.

[0006] Existing methods for calculating the radiation resistance of underwater loop antennas are not accurate enough to meet the design of antennas and communication systems. Therefore, a method for calculating the radiation resistance of antennas in seawater using cylindrical surface integrals is needed to solve the above problem. Summary of the invention

[0007] The object of the present invention is to provide a method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral, so as to solve the problems raised in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solution: a method for calculating the radiation resistance of an antenna in seawater using cylindrical surface integral, specifically comprising the following steps: calculating the average value of the power density generated by the outward radiation of the loop antenna in seawater, the Poynting vector S av , with the radius of the loop antenna r L is the radius, and the height of the loop antenna is h is the average power density on the high cylindrical surface S av To perform integration:

[0009] (1)

[0010] In the formula, is the angular frequency of the electromagnetic wave, and are the attenuation coefficient and phase shift coefficient, N is the number of turns of the loop antenna, is the current in the loop antenna coil, S is the area of ​​the loop antenna, is the seawater conductivity, is the magnetic permeability of seawater, and are the integral variables in the cylindrical coordinate system, and after integration, the radiation power of the loop antenna in seawater is obtained PThe expression of is derived and it is proved that the sum of the power of the energy radiated from the upper and lower surfaces of the loop antenna is 0, and the energy is only radiated to the side of the antenna.

[0011] Transforming the radiation power expression, the radiation resistance expression of the loop antenna in seawater is obtained as follows:

[0012] (2);

[0013] By comparing with the measured data at sea, the feasibility and accuracy of the method of calculating the radiation resistance of the loop antenna in seawater through the cylindrical surface integral model were verified.

[0014] The present invention mainly analyzes the radiation power and radiation resistance of the loop antenna in seawater, and proposes a new method and idea, which calculates the radiation resistance of the loop antenna in seawater through a cylindrical surface integral model, and provides a new way to accurately calculate the radiation resistance of the loop antenna;

[0015] As a preferred solution, the propagation constant of electromagnetic waves in seawater is derived, and the radiation power density of the loop antenna in seawater under the vertical magnetic dipole model is calculated.

[0016] As a preferred solution, since the loop antenna is only in the spherical coordinate system r The energy is radiated outward in the direction. According to the geometric relationship, the average value of the Poynting vector derived in the spherical coordinate system is S av The orthogonal decomposition is carried out into the cylindrical coordinate system, and then the radiation power expression of the loop antenna in seawater is obtained through cylindrical surface integral.

[0017] As a preferred solution, the selected integral surface can minimize the impact of seawater attenuation on the calculation of antenna radiation power; based on the relationship between current, resistance and power, the radiation power expression of the ring antenna in seawater is transformed accordingly to obtain its radiation resistance.

[0018] As a preferred solution, by combining computer simulation with offshore field experiments, the calculated results are compared to verify the effectiveness and accuracy of the method.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] The cylindrical surface integral model proposed in the present invention can more accurately calculate the radiation resistance of the loop antenna in seawater. The technical approach and implementation plan have been verified by computer simulation and offshore experiments. This method can more accurately calculate the radiation resistance of the underwater loop antenna, thereby accurately evaluating and optimizing the antenna performance and the performance of the communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a model diagram of the underwater loop antenna wrapped by a cylindrical surface of the present invention;

[0022] Figure 2 It is a schematic diagram of a comparison model between cylindrical surface integral and spherical surface integral of the present invention;

[0023] Figure 3 is a graph showing the relationship between the radiation resistance and the operating frequency of the present invention;

[0024] Figure 4 A graph showing the relationship between the radiation resistance and its radius of the present invention;

[0025] Figure 5 This is a comparison diagram between the actual measured data and the simulation of the radiation resistance of the present invention;

[0026] Figure 6 Schematic diagram showing the comparison between the theoretical value of radiation resistance and the measured value of radiation resistance in the present invention. DETAILED DESCRIPTION

[0027] The present invention will be further described below in conjunction with the embodiments.

[0028] The following examples are used to illustrate the present invention, but they cannot be used to limit the scope of protection of the present invention. The conditions in the examples can be further adjusted according to specific conditions. Simple improvements to the method of the present invention under the premise of the concept of the present invention belong to the scope of protection claimed in the present invention.

[0029] See also Figure 1-6 The present invention provides a method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral, which specifically comprises the following steps: calculating the average value of the power density generated by the outward radiation of the loop antenna in seawater, the Poynting vector S av , with the radius of the loop antenna r L is the radius, and the height of the loop antenna is h is the average power density on the high cylindrical surface S av To perform integration:

[0030] (1)

[0031] In the formula, is the angular frequency of the electromagnetic wave, and are the attenuation coefficient and phase shift coefficient, N is the number of turns of the loop antenna, is the current in the loop antenna coil, S is the area of ​​the loop antenna, is the seawater conductivity, is the magnetic permeability of seawater, and are the integral variables in the cylindrical coordinate system, and after integration, the radiation power of the loop antenna in seawater is obtained P The expression of is derived and it is proved that the sum of the power of the energy radiated from the upper and lower surfaces of the loop antenna is 0, and the energy is only radiated to the side of the antenna.

[0032] Transforming the radiation power expression, the radiation resistance expression of the loop antenna in seawater is obtained as follows:

[0033] (2);

[0034] By comparing with the measured data at sea, the feasibility and accuracy of the method of calculating the radiation resistance of the loop antenna in seawater through the cylindrical surface integral model were verified;

[0035] In order to construct and use the cylindrical surface integral model to accurately calculate the radiation resistance of the loop antenna in seawater, the following steps are required for relevant calculations: first, the propagation constant of electromagnetic waves in seawater is derived, then the radiation power density of the loop antenna in seawater under the vertical magnetic dipole model is calculated, and then the radiation power of the loop antenna in seawater is calculated based on the cylindrical surface integral. Finally, the radiation resistance of the loop antenna in seawater is obtained based on the relationship between current, resistance and power.

[0036] The propagation constant of electrical conductivity in seawater is affected by many factors, including the composition and concentration of electrolytes, temperature, and pressure.

[0037] Assuming that seawater is a homogeneous and isotropic medium, and its conductivity parameters remain constant in time and space, the following are the commonly used electromagnetic parameters of seawater medium: Dielectric constant of air , relative dielectric constant of seawater , seawater conductivity , seawater magnetic permeability ;

[0038] Propagation constant in seawater k , which can be expressed as:

[0039] (3) ;

[0040] In the formula, is the angular frequency of electromagnetic waves, and the complex dielectric constant of seawater is , the dielectric constant of seawater Attenuation coefficient and phase shift coefficient It can be expressed as:

[0041] (4)

[0042] (5) ;

[0043] In the formula, the attenuation constant The unit is Np / m, which means the attenuation value of the amplitude per unit distance; the phase shift constant The unit is rad / m, and its physical meaning is the phase lag per unit distance;

[0044] Since the conductivity of seawater is several orders of magnitude greater than that of ordinary freshwater rivers and lakes, and the operating frequency is relatively low, seawater is a good conductor under low-frequency conditions:

[0045] (6);

[0046] At this time, the attenuation coefficient formula (4) and the phase shift coefficient formula (5) can be expressed as:

[0047] (7);

[0048] The attenuation coefficient is an important parameter for studying the propagation law of electromagnetic waves in seawater. It can be seen from formula (7) that the attenuation coefficient increases with the increase of conductivity. Because the electric field of electromagnetic waves excites the conduction current, part of the electromagnetic energy is converted into heat energy, resulting in the loss of electromagnetic wave energy.

[0049] The radiation power density of the underwater loop antenna: When the circumference of the loop antenna is less than one tenth of the wavelength in the air, this loop antenna is called a small loop antenna, and the antenna is equivalent to a magnetic dipole model; when the loop antenna is placed horizontally, the center of the hollow current loop is located at the origin of the spherical coordinates , that is, when it is a vertical magnetic dipole, substitute the parameters of the small loop antenna;

[0050] Assuming that the loop antenna is in an infinite seawater space, the radiated electric field component of the antenna in the seawater is , radiated magnetic field component and as follows:

[0051] (8)

[0052] (9)

[0053] (10) ;

[0054] In the formula, N is the number of turns of the loop antenna; is the current in the energized coil, in units of A ; S is the area of ​​the loop antenna, in m 2; r is the distance between point P in the field and the center of the magnetic dipole, in meters; k is the propagation constant in seawater. To calculate the radiated power of the loop antenna, we first need to calculate the average value of the power density generated by the loop antenna, that is, the average value of the Poynting vector S av , the expression is:

[0055] (11);

[0056] In the formula, × represents cross product and * represents conjugation. Directional for:

[0057] (12);

[0058] Formula (12) indicates Taking the real part as zero, it means and Formed The average value of the Poynting vector in a direction is zero, and energy flows back and forth in that direction and does not radiate outward;

[0059] Substituting equation (9) and equation (10) into the formula r Directional for:

[0060] (13) ;

[0061] Formula (13) indicates and Formed r The average value of the Poynting vector in the direction is not zero, and the energy radiates outward in this direction. The average power density of the loop antenna in seawater is:

[0062] (14);

[0063] The calculation of the radiation power of the underwater loop antenna based on the cylindrical surface integral is as follows: the radiation power of the antenna is solved in free space, generally the average value of the Poynting vector of the electromagnetic field radiated by the antenna S It is obtained by integrating on a spherical surface with a radius tending to infinity. However, the value of the average value integral of the Poynting vector on spherical surfaces with different radii in seawater is different, because the electromagnetic wave radiated from the antenna is attenuated by the seawater before reaching the integral surface. As the radius increases, the attenuation will also increase, resulting in differences in the results of different integral surfaces, especially the result of integration on a spherical surface with a radius tending to infinity is zero;

[0064] Since integration on a spherical surface will always result in a partial loss of energy, it is necessary to redefine an integral surface to minimize the energy loss. Therefore, the integral surface is selected to be a cylindrical surface with the same radius and height as the antenna, so that the influence of seawater attenuation on the calculation of antenna radiation power can be minimized.

[0065] According to the above derivation results, the loop antenna is only in the spherical coordinate system. r The energy radiates outward in the direction. According to the geometric relationship, substituting into equation (14), the average value of the Poynting vector derived in the spherical coordinate system is Orthogonal decomposition into cylindrical coordinates The average value of the Poynting vector in the direction and The average value of the Poynting vector in the direction :

[0066] (15)

[0067] (16) ;

[0068] Spherical coordinate system Convert to cylindrical coordinate system The conversion relationship is:

[0069] (17);

[0070] Convert equations (15) and (16) into cylindrical coordinate components according to equation (17): express:

[0071] (18)

[0072] (19);

[0073] The radius of the loop antenna The average value of the average active power density of the closed cylindrical surface formed by the cylindrical surface S1 with a radius of 200 and the upper and lower bottom surfaces S2 and S3 of the loop antenna , Corresponding to the integrals respectively, we have:

[0074] (20);

[0075] In the formula, is the radius of the antenna, is the height of the antenna. The total power of the energy radiated by the loop antenna to the upper and lower bottom surfaces S2 and S3 is 0. Directional radiation energy, the power of radiation energy is: (twenty one);

[0076] The loop antenna in seawater has a radius of r L Gao Wei h The expression of the radiation power on the cylindrical surface of the seawater is shown in the above formula. It can be seen from the above formula that the radiation power of the loop antenna in seawater is not only related to the structure of the antenna itself, but also to the parameters of the seawater medium. and It is also related that the spherical surface integral space will lose more radiation energy than the cylindrical surface integral;

[0077] The underwater loop antenna radiation resistance: Changing the antenna radiation power formula (21) yields:

[0078] (twenty two);

[0079] In the formula, I e is the effective value of the current in the loop antenna. According to the definition of power, the expression of the radiation resistance of the antenna can be obtained as follows:

[0080] (twenty three)

[0081] Substituting equation (7) into equation (23), the radiation resistance expression of the loop antenna in seawater is obtained as follows:

[0082] (twenty four);

[0083] From equation (24), we can see that the radiation resistance of the loop antenna in seawater is proportional to the antenna radius: r L , antenna height h, number of turns N、 It is related to angular frequency and electromagnetic parameters of seawater;

[0084] The adaptive Gaussian quadrature method and the double recursive Simpson mixed numerical integration method are used to simulate and solve equation (24). The simulation results are as follows: Figure 3 , Figure 4 shown.

[0085] Depend on Figure 3 From the simulation results, we can see that the radiation resistance R sr At different antenna radii, the operating frequency f It rises first and then falls. As the operating frequency of the loop antenna increases, the slope of the radiation resistance increase of antennas with different radii is not much different. The larger the radius of the antenna, the smaller the radiation resistance peak, and the smaller the corresponding operating frequency to reach the radiation resistance peak.

[0086] Depend on Figure 4 From the simulation results, we can see that the radiation resistance Rsr At different frequencies, the antenna radius r L It rises first and then falls, and the higher the frequency, the higher the radiation resistance peak, and the smaller the antenna radius corresponding to the peak. The change at low frequency is slow and stable, while the change at high frequency is more drastic and the peak is obvious.

[0087] The radiation resistance obtained by solving the cylindrical surface integral proposed in the present invention is generally closer to the actual measured data of the antenna radiation resistance than the values ​​solved by several classical spherical surface integrals.

[0088] The working principle and use process of the present invention: Calculate the average value of the power density generated by the outward radiation of the loop antenna in seawater Poynting vector S av , with the radius of the loop antenna r L is the radius, and the height of the loop antenna is h is the average power density on the high cylindrical surface S av To perform integration:

[0089] (1)

[0090] In the formula, is the angular frequency of the electromagnetic wave, and are the attenuation coefficient and phase shift coefficient, N is the number of turns of the loop antenna, is the current in the loop antenna coil, S is the area of ​​the loop antenna, is the seawater conductivity, is the magnetic permeability of seawater, and are the integral variables in the cylindrical coordinate system, and after integration, the radiation power of the loop antenna in seawater is obtained P The expression of is derived and it is proved that the sum of the power of the energy radiated from the upper and lower surfaces of the loop antenna is 0, and the energy is only radiated to the side of the antenna.

[0091] (2);

[0092] By comparing with the measured data at sea, the feasibility and accuracy of the method of calculating the radiation resistance of the loop antenna in seawater through the cylindrical surface integral model were verified.

[0093] Working principle and use process of the present invention: When verifying this method, theoretical simulation and offshore experiments were carried out to verify the conductivity of seawater. , the magnetic permeability is The radiation resistance of underwater loop antennas with different sizes and operating frequencies was simulated and calculated. The results show that when determining the size parameters of the underwater loop antenna, there is a certain relationship between the radiation resistance and the operating frequency, such as Figure 3 When determining the operating frequency, the relationship between the radiation resistance of the underwater loop antenna and its radius is as follows: Figure 4 As shown;

[0094] Sea experiment conditions: The conductivity of seawater is , the temperature is 27.2℃. A loop antenna with a radius of 0.285m and a height of 0.13m was used for the experiment. The loop antenna was placed horizontally in the seawater at a depth of 1 meter, and the radiation resistance of the antenna in the seawater was measured using a loop analyzer;

[0095] 1) The method for calculating the radiation resistance of the underwater loop antenna proposed in the present invention is feasible:

[0096] The method for calculating the radiation resistance of an underwater loop antenna proposed in the present invention integrates the average value of the power density of a cylindrical surface with the same radius and height as the antenna when solving the radiation power of the underwater loop antenna, and then obtains the radiation resistance of the loop antenna through the relationship between the radiation power, current and radiation resistance. Both the calculation method and steps are feasible;

[0097] 2) The accuracy of the underwater loop antenna radiation resistance calculation method proposed in the present invention is improved compared with the existing method:

[0098] The present invention uses cylindrical surface integral to solve the radiation resistance of underwater loop antenna, which is different from the traditional spherical surface integral and avoids the inaccurate calculation of radiation resistance caused by the attenuation loss of electromagnetic wave propagation caused by seawater in the traditional integral. The present invention verifies the correctness and accuracy of the calculation method of underwater loop antenna radiation resistance through modeling simulation and offshore experiments;

[0099] According to the implementation examples, it can be considered that the method proposed in the present invention for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral is feasible and can realize the accurate calculation of the resistance of an underwater loop antenna.

[0100] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the radiation resistance of an antenna in seawater using cylindrical surface integral, characterized in that: The radiation resistance of the loop antenna in seawater is calculated by the cylindrical surface integral model, which provides a new way to accurately calculate the radiation resistance of the loop antenna. The specific steps include: calculating the average power density Poynting vector generated by the outward radiation of the loop antenna in seawater S av , with the radius of the loop antenna r L is the radius, and the height of the loop antenna is h is the average power density on the high cylindrical surface S av To perform integration: (1) In the formula, is the angular frequency of the electromagnetic wave, and are the attenuation coefficient and phase shift coefficient, N is the number of turns of the loop antenna, is the current in the loop antenna coil, S is the area of ​​the loop antenna, is the seawater conductivity, is the magnetic permeability of seawater, and are the integral variables in the cylindrical coordinate system, and after integration, the radiation power of the loop antenna in seawater is obtained P The expression of is derived and it is proved that the sum of the power of the energy radiated from the upper and lower surfaces of the loop antenna is 0, and the energy is only radiated to the side of the antenna. Transforming the radiation power expression, the radiation resistance expression of the loop antenna in seawater is obtained as follows: (2)； By comparing with the measured data at sea, the feasibility and accuracy of the method of calculating the radiation resistance of the loop antenna in seawater through the cylindrical surface integral model were verified.

2. The method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral according to claim 1, characterized in that: The propagation constant of electromagnetic waves in seawater is derived, and the radiation power density of the loop antenna in seawater under the vertical magnetic dipole model is calculated.

3. The method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral according to claim 1, characterized in that: Since the loop antenna is only in the spherical coordinate system r The energy is radiated outward in the direction. According to the geometric relationship, the average value of the Poynting vector derived in the spherical coordinate system is S av The orthogonal decomposition is carried out into the cylindrical coordinate system, and then the radiation power expression of the loop antenna in seawater is obtained through cylindrical surface integral.

4. The method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral according to claim 1, characterized in that: The selected integral surface can minimize the impact of seawater attenuation on the calculation of antenna radiation power; based on the relationship between current, resistance and power, the radiation power expression of the ring antenna in seawater is transformed accordingly, and then its radiation resistance is obtained.

5. The method for calculating the radiation resistance of an antenna in seawater by using cylindrical surface integral according to claim 1, characterized in that: By combining computer simulation with offshore experiments, the calculated results are compared to verify the effectiveness and accuracy of the method.

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