Method for obtaining electro-thermal coupling passive intermodulation under oxidative corrosion conditions

Abstract

This invention discloses a method for obtaining passive intermodulation interference induced by electrothermal coupling under oxidation and corrosion conditions. First, by calculating the oxidation and corrosion area, the change process of the effective conductive area of ​​the microstrip line decreasing over time is quantitatively described, and the equivalent resistance of the metal microstrip conductor under oxidation and corrosion conditions is further determined. Then, the electrothermal coupling effect is introduced, and the temperature coefficient of metal resistance is used to represent the modulation effect of temperature rise on conductor resistance. Thus, under multi-carrier excitation conditions, the intermodulation frequency components are extracted, and combined with the characteristic impedance of the output port of the microstrip antenna structure, the electrothermal coupling passive intermodulation interference at the output port is calculated, thereby realizing an accurate assessment of passive intermodulation interference induced by oxidation and corrosion during the application of base station antennas.

Description

Technical Field

[0001] This invention belongs to the field of base station antenna maintenance technology, and more specifically, relates to a method for obtaining electrothermal coupling passive intermodulation interference under oxidative corrosion conditions. Background Technology

[0002] As a crucial radio frequency component for wireless signal transmission and reception, base station antennas need to operate for extended periods in complex and variable outdoor environments, requiring high-power excitation to improve electromagnetic radiation signal coverage. However, under the combined influence of diverse outdoor environmental factors and strong electromagnetic excitation, the microstructure of the base station antenna's metallic radiating structure undergoes physical and chemical changes, leading to nonlinear characteristics and inducing passive intermodulation (PIM) interference. When the generated PIM products fall into the base station antenna's receiving frequency band, they interfere with the received signal, thereby reducing the antenna's receiving sensitivity and degrading the overall performance of the wireless communication system.

[0003] PIM interference caused by oxidation and corrosion of base station antennas mainly originates from two aspects: metal connection components and electromagnetic radiation components. Existing research has made some progress in interference modeling and quantitative prediction targeting these two sources. In research on metal connection components, such as coaxial connectors, the focus is mainly on the effects of corrosion damage and ambient temperature. For example, the Chinese invention patent "CN111460697B", authorized on February 28, 2023, entitled "A Method for Predicting Passive Intermodulation of Coaxial Connectors with Different Corrosion Degrees", establishes a polynomial prediction model that can quantitatively describe the relationship between the connector corrosion process and third-order passive intermodulation (PIM3) power by accelerating corrosion tests and using contact resistance at different corrosion stages as a metric. The Chinese invention patent application published on March 26, 2024, with publication number "CN117764017A" and titled "A Method for Predicting Passive Intermodulation of Connectors under Temperature Cycling Conditions," establishes a nonlinear relationship model between ambient temperature and connector PIM3, achieving quantitative prediction of the PIM3 variation law of connectors under temperature cycling conditions. In summary, existing research on PIM induced by oxidation and corrosion of metal connector components mainly focuses on modeling and predicting external influencing factors such as the degree of oxidation and corrosion and ambient temperature, achieving a quantitative description of the PIM variation law of connectors.

[0004] In research related to electromagnetic radiation components (such as microstrip lines), for example, the invention patent application published on October 31, 2025, with publication number "CN120880576A" and titled "A Method for Obtaining Passive Intermodulation Interference Caused by Oxidation and Corrosion of Base Station Antennas," addresses the oxidation and corrosion problem of microstrip line surfaces. It constructs mathematical expressions from microscopic physical parameters to macroscopic PIM3 voltage, achieving a quantitative assessment of the antenna's nonlinear interference level under corrosive conditions. However, this research mainly relies on microscopic tunneling effects for nonlinear modeling and has not further considered the local high resistance of the oxide film formed after microstrip line oxidation and corrosion, nor the electrothermal coupling nonlinear mechanism caused by Joule heat accumulation under strong electromagnetic excitation. Therefore, there is an urgent need to propose a method for obtaining electrothermal coupling passive intermodulation interference under oxidation and corrosion conditions to comprehensively evaluate the passive intermodulation interference problem under these conditions. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for obtaining electrothermal coupling passive intermodulation interference under oxidative corrosion conditions, so as to achieve accurate assessment of passive intermodulation interference induced by oxidative corrosion in base station antennas during application.

[0006] To achieve the above-mentioned objective, the present invention provides a method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions, characterized by comprising the following steps:

[0007] (1) Establish the descriptive expression for the oxidation and corrosion of the microstrip antenna structure:

[0008]

[0009] in, For the area of ​​oxidation corrosion, This represents the initial effective conductive area of ​​the metallic microstrip conductor. Indicates the oxidation and corrosion time. The value of is the oxidation corrosion rate constant, which is obtained by conducting environmental accelerated aging tests or field measurements on the metal microstrip conductor under test, and by curve fitting of the data on the change of corrosion area over time.

[0010] The remaining effective metallic conductive area on the surface of the metallic microstrip conductor for:

[0011]

[0012] (2) Calculate the equivalent resistance of the metal microstrip conductor under oxidation and corrosion conditions.

[0013] Under the action of oxidation and corrosion, the remaining effective metal conductive area Determined equivalent resistance for:

[0014]

[0015] in, This represents the equivalent resistance of the metallic microstrip conductor in its initial state. The equivalent resistance of a metallic microstrip conductor in a fully oxidized state;

[0016] (3) The electrothermal coupling passive intermodulation interference at the output port was calculated. :

[0017]

[0018] in, Let α be the characteristic impedance of the output port of the microstrip antenna structure, and α be the temperature coefficient of resistance of the metallic microstrip conductor. , The first , The current amplitude of the circuit excitation signal, For the oxidation corrosion zone in the first , Equivalent thermal resistance under the road excitation signal.

[0019] The objective of this invention is achieved as follows:

[0020] This invention provides a passive intermodulation analysis method for electrothermal coupling under oxidation and corrosion conditions. First, it quantitatively describes the decrease in the effective conductive area of ​​a microstrip line over time by calculating the oxidation and corrosion area. Then, it determines the equivalent resistance of the metal microstrip conductor under oxidation and corrosion conditions. Subsequently, it introduces the electrothermal coupling effect, using the temperature coefficient of metal resistance to represent the modulation effect of temperature rise on the conductor resistance. Based on this, under multi-carrier excitation conditions, it extracts the intermodulation frequency components and, combined with the characteristic impedance of the microstrip antenna structure's output port, calculates the passive intermodulation interference of electrothermal coupling at the output port. This enables accurate assessment of passive intermodulation interference induced by oxidation and corrosion in base station antennas during application. Attached Figure Description

[0021] Figure 1 This is a flowchart of a specific implementation of the method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions according to the present invention;

[0022] Figure 2 This is a schematic diagram of the equivalent circuit of the oxidized and corroded region. Detailed Implementation

[0023] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0024] Figure 1 This is a flowchart of a specific implementation of the method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions according to the present invention.

[0025] In this embodiment, as Figure 1 As shown, the method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions of the present invention includes the following steps:

[0026] Step S1: Establish the descriptive expression for the oxidation and corrosion of the microstrip antenna structure.

[0027] Metallic microstrip conductors are electromagnetic radiators in base station antennas. During outdoor operation, microstrip conductors are susceptible to oxidation and corrosion under environmental conditions. In this invention, the initial physical parameters of the metallic microstrip conductor in the microstrip antenna structure to be evaluated are first obtained, including the initial surface area S0 of the microstrip conductor. In practical applications, the initial surface area S0 can be calculated from microstrip line design drawings and structural dimensional parameters. To address the oxidation and corrosion problem of metallic microstrip conductors in outdoor environments, a kinetic expression describing the increase of the oxidation and corrosion area over time is established, which describes the change in the oxidation and corrosion area on the conductor over time. The expression is as follows:

[0028] (1)

[0029] in, For the area of ​​oxidation corrosion, The initial effective conductive area is represented. Indicates the oxidation and corrosion time. The oxidation corrosion rate constant is used to represent the corrosion rate of a metal microstrip conductor under outdoor environmental conditions. Its value is obtained by conducting environmental accelerated aging tests (such as constant temperature and humidity tests, salt spray corrosion tests, or temperature cycling tests) or field measurements (such as obtaining data from long-term field operation) on the metal microstrip conductor under test, and by combining the data on the change of corrosion area over time with curve fitting, thus obtaining an oxidation corrosion rate constant applicable to the current environmental conditions.

[0030] Based on the above-mentioned pattern of oxidation corrosion area changing over time, the remaining effective metal conductive area on the surface of the metal microstrip conductor can be further calculated. Specifically, the remaining effective conductive area This can be expressed as the difference between the initial effective conductive area and the area that has undergone oxidation and corrosion, i.e., the remaining effective metallic conductive area on the surface of the metallic microstrip conductor. for:

[0031] (2)

[0032] Step S2: Calculate the equivalent resistance of the metallic microstrip conductor under oxidation and corrosion conditions.

[0033] As the oxidation and corrosion zone gradually expands, the effective conductive area of ​​the metal microstrip conductor surface that is not oxidized... It continues to decrease. Let the equivalent resistance of the metallic microstrip conductor in its initial state be... Under the action of oxidation and corrosion, the remaining effective metal conductive area Impact, resistance of the unoxidized portion of the metal microstrip conductor It can be represented as:

[0034] (3)

[0035] When the resistance of the metal microstrip conductor in the fully oxidized state is At that time, the resistance of the oxidized part The calculation is as follows:

[0036] (4)

[0037] like Figure 2 As shown, the unoxidized portion of the metal With oxidation part Because it is a parallel structure, under the action of oxidation and corrosion, the remaining effective metal conductive area will be used to conduct electricity. Determined equivalent resistance for:

[0038] (5)

[0039]

[0040] Step S3: Calculate the electrothermal coupling passive intermodulation interference at the output port.

[0041] Let the radio frequency excitation current flowing through the microstrip conductor be... Due to oxidation and corrosion, the conductive area of ​​the metal decreases, resulting in a significant increase in the equivalent resistance of this region. According to Joule's law, when radio frequency current flows through this region, a significant Joule heating effect will occur, with its transient heating power... can be The calculation shows that:

[0042] (6)

[0043] Based on the electrothermal coupling relationship, the effective transient temperature rise of the oxidation and corrosion region can be expressed as:

[0044] (7)

[0045] in, This represents the equivalent thermal resistance of the oxidized and corroded region, and its magnitude is determined by the thermal resistance of that region. With heat capacity The calculation expression is jointly determined as follows:

[0046] (8)

[0047] in, ω is the angular frequency of the excitation signal.

[0048] When oxidation and corrosion increase the conductor's resistance, additional Joule heat is generated under the influence of radio frequency current, leading to a localized temperature rise. This temperature rise further alters the resistive characteristics of the metallic conductor, creating an electrothermal coupling feedback mechanism. This leads to the introduction of the temperature coefficient of resistance in the metal. The dynamic resistance of the microstrip line under operating conditions is then... It can be represented as:

[0049] (9)

[0050] Substituting equation (9) into the voltage expression across the metal microstrip conductor From this, we can obtain:

[0051] (10)

[0052] To analyze the nonlinear response characteristics of the oxidation and corrosion region, an application was applied at the input end of the metal microstrip conductor. An excitation signal. At this time, the current flowing through the microstrip conductor... This can be represented as a linear superposition of multiple cosine signals:

[0053] (11)

[0054] In the formula, and The first The current amplitude and angular frequency of the circuit excitation signal.

[0055] Will Substituting into the nonlinear voltage expression By performing a polynomial expansion on the PIM3 voltage component, the voltage component of PIM3 can be further derived. for:

[0056] (12)

[0057] in, , The first , The current amplitude of the circuit excitation signal, , The first , The angular frequency of the excitation signal. For the oxidation corrosion zone in the first , Equivalent thermal resistance under path excitation signal:

[0058] (13)

[0059] in, , These represent the thermal resistance and heat capacity of the oxidized and corroded region, respectively. .

[0060] The characteristic impedance at the output port of the microstrip antenna structure is Under these conditions, based on the average power calculation formula, the expression for PIM3 power at the output port can be derived:

[0061] (14)

[0062] Example

[0063] To better understand this invention, a two-tone signal will be used as the excitation source for further explanation and description below.

[0064] When a two-tone signal is used as the input excitation, the total current across the microstrip conductor can be expressed as:

[0065] (15)

[0066] in, and These are the current amplitudes of the two excitation signals, and... These represent the corresponding carrier frequencies.

[0067] Substituting equation (14) into the nonlinear voltage response model equation (12) and performing a polynomial expansion of the voltage expression, the PIM3 component generated by the system can be obtained. From this, the frequency located at... and The PIM3 component at the location. In this embodiment, the frequency is... Taking the intermodulation component as an example, the corresponding PIM3 voltage expression is as follows:

[0068] (16)

[0069] Furthermore, at the output port of the microstrip antenna structure... Under these conditions, based on the average power calculation relationship, the corresponding PIM3 power expression can be obtained as follows:

[0070] (17)

[0071] This embodiment establishes a dynamic prediction method considering the electrothermal coupling effect, and combines the evolution law of oxidation corrosion with numerical calculations to achieve quantitative prediction of the PIM3 power change with operating time. This method can effectively reveal the mechanism by which the electrothermal coupling nonlinearity in the oxidation corrosion region of the microstrip conductor affects the passive intermodulation performance, providing a technical basis for the reliability assessment, anti-aging design optimization, and operation and maintenance strategy formulation of microstrip conductor structures.

[0072] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions, characterized in that, Includes the following steps: (1) Establish the descriptive expression for the oxidation and corrosion of the microstrip antenna structure: ， in, For the area of ​​oxidation corrosion, This represents the initial effective conductive area of ​​the metallic microstrip conductor. Indicates the oxidation and corrosion time. The value of is the oxidation corrosion rate constant, which is obtained by conducting environmental accelerated aging tests or field measurements on the metal microstrip conductor under test, and by curve fitting of the data on the change of corrosion area over time. The remaining effective metallic conductive area on the surface of the metallic microstrip conductor for: ， (2) Calculate the equivalent resistance of the metal microstrip conductor under oxidation and corrosion conditions. Under the action of oxidation and corrosion, the remaining effective metal conductive area Determined equivalent resistance for: ， in, This represents the equivalent resistance of the metallic microstrip conductor in its initial state. The equivalent resistance of a metallic microstrip conductor in a fully oxidized state; (3) The electrothermal coupling passive intermodulation interference at the output port was calculated. : ， in, Let α be the characteristic impedance of the output port of the microstrip antenna structure, and α be the temperature coefficient of resistance of the metallic microstrip conductor. , The first , The current amplitude of the circuit excitation signal, For the oxidation corrosion zone in the first , Equivalent thermal resistance under the road excitation signal.

2. The method for obtaining passive intermodulation interference of electrothermal coupling under oxidative corrosion conditions according to claim 1, characterized in that, The oxidation corrosion region is in the first , Equivalent thermal resistance under path excitation signal for: ， in, , These represent the thermal resistance and heat capacity of the oxidation and corrosion region, respectively. , The first , The angular frequency of the excitation signal.

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