Method for constructing equivalent thermal circuit model of artificial surface plasmon transmission line

Abstract

The invention provides a method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line, which comprises the following steps of: dividing a metal conduction band of the artificial surface plasmon transmission line into a main line and a branch knot, and respectively extracting thermal resistance of each part; extracting thermal resistance in the vertical direction of a medium area below a metal conduction band of the artificial surface plasmon transmission line; extracting the thermal resistance in the horizontal direction of a medium area around a metal conduction band of the artificial surface plasmon transmission line; taking the upper surface and the lower surface of the artificial surface plasmon transmission line as convection boundaries, and extracting corresponding convection thermal resistance; under an external power input condition, extracting conductor loss and dielectric loss of the artificial surface plasmon transmission line as an equivalent heat source; and respectively constructing equivalent thermal circuit models corresponding to the conductor loss and the dielectric loss of the artificial surface plasmon transmission line. The equivalent thermal circuit model of the artificial surface plasmon transmission line is established for the first time, and guidance is provided for efficient analysis and design of the artificial surface plasmon transmission line.

Description

Technical Field

[0001] The present invention relates to the field of microwave transmission technology, and in particular to a method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line. Background Art

[0002] The metal conduction band of the artificial surface plasmon transmission line presents a periodic sawtooth fold structure, and its transmission loss is lower than that of the planar transmission line represented by the microstrip line. By adjusting the geometric dimensions of the unit structure, the parameters such as the propagation constant and the cutoff frequency can be flexibly adjusted, thus providing great flexibility for circuit design. At present, artificial surface plasmon transmission lines have been widely used in the design of devices such as filters, resonators, power dividers and antennas.

[0003] However, when artificial surface plasmon transmission lines operate at higher power, the temperature rises significantly. When the temperature exceeds a certain threshold, the self-heating effect of the material may cause the transmission performance to deteriorate. There is currently a lack of electrothermal models for artificial surface plasmon transmission lines, which limits their application in high-power scenarios. Therefore, it is urgent to establish an equivalent thermal circuit model for artificial surface plasmon transmission lines to predict their maximum temperature under a specific power input. Summary of the invention

[0004] The object of the present invention is to provide a method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line, which is used to efficiently and accurately predict its maximum temperature under a certain power input condition.

[0005] To solve the above problems, the technical solution of the present invention is:

[0006] A method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line comprises the following steps:

[0007] The metal conduction band of the artificial surface plasmon transmission line is divided into two parts: the main line and the branch, and the thermal resistance of each part is extracted respectively.

[0008] Extract the vertical thermal resistance of the dielectric region below the metal conduction band of the artificial surface plasmon transmission line;

[0009] Extract the horizontal thermal resistance of the dielectric region around the metal conduction band of the artificial surface plasmon transmission line;

[0010] The upper and lower surfaces of the artificial surface plasmon transmission line are regarded as convection boundaries, and the corresponding convection thermal resistance is extracted;

[0011] Under the condition of external power input, the conductor loss and dielectric loss of artificial surface plasmon transmission line are extracted as equivalent heat sources;

[0012] The equivalent thermal circuit models corresponding to the conductor loss and dielectric loss of artificial surface plasmon transmission lines are constructed respectively.

[0013] Preferably, in the step of dividing the metal conduction band of the artificial surface plasmon transmission line into a main line and a branch, and extracting the thermal resistance of each part respectively, the width of the metal conduction band of the artificial surface plasmon transmission line is w, and the thickness is d s ; Rectangular grooves with a width of a and a depth of h are periodically distributed on the conduction band, and the period is p. The metal conduction band of the artificial surface plasmon transmission line is divided into two parts, namely the main line and multiple branches on the main line. For a main line with a length of p / 2, its thermal resistance is: where κ metal is the thermal conductivity of the metal; for a branch, its thermal resistance is:

[0014] Preferably, in the step of extracting the vertical thermal resistance of the dielectric region below the metal conduction band of the artificial surface plasmon transmission line, the vertical thermal resistance of the dielectric region below the metal conduction band is: where κ sub is the thermal conductivity of the medium, and d is the thickness of the medium substrate.

[0015] Preferably, in the step of extracting the horizontal thermal resistance of the dielectric area around the metal conduction band of the artificial surface plasmon transmission line, heat flows from the metal conduction band to the edge of the dielectric substrate, is transferred inside the substrate by heat conduction, and is dissipated to the external environment by convection heat transfer on the substrate surface. By establishing a differential equation, the thermal resistance of this part of the dielectric area is obtained as: where h conv_u and h conv_l are the convective heat transfer coefficients between the upper and lower surfaces of the dielectric substrate and the outside air, respectively.

[0016] Preferably, in the step of regarding the upper and lower surfaces of the artificial surface plasmon transmission line as convection boundaries and extracting the corresponding convection thermal resistance, the surface of the metal conduction band and the surface of the dielectric region below the metal conduction band will both dissipate heat to the outside through convection heat transfer, and the convection thermal resistance is expressed as:

[0017] Preferably, in the step of extracting the conductor loss and dielectric loss of the artificial surface plasmon transmission line as equivalent heat sources under the external power input condition, the conductor loss power of the artificial surface plasmon transmission line is q c ; The dielectric loss power is q d .

[0018] Preferably, in the step of respectively constructing equivalent heat circuit models corresponding to the conductor loss and dielectric loss of the artificial surface plasmon transmission line, the heat source of the equivalent heat circuit is qc or q d , thermal resistance includes R line , R stub , R sub , R edge , R conv_u and R conv_l .

[0019] Preferably, when only the conductor loss is considered, the temperature rise at the bottom of the groove and the end of the branch is obtained according to the equivalent thermal circuit model:

[0020]

[0021]

[0022] in

[0023] R total_c =R conv_u ||(R sub +R conv_l )||(R line / 2+R c1 )

[0024] R c1 =(R edge +R stub )||R edge .

[0025] Preferably, when only dielectric loss is considered, the temperature rise at the end of the branch and the bottom of the groove is obtained according to the equivalent thermal circuit model:

[0026]

[0027]

[0028] in

[0029] R total_d =R edge ||(R stub +R d2 )

[0030] R d1 =(R sub +R conv_l )||R conv_u

[0031] R d2 =(R d1 +R line / 2)||R edge .

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The method of the present invention establishes the equivalent thermal circuit model of artificial surface plasmon transmission lines for the first time, reveals the physical mechanism of its electrothermal effect, and provides guidance for the efficient analysis and design of artificial surface plasmon transmission lines;

[0034] 2. The present invention uses an analytical method for electrothermal analysis, avoiding time-consuming numerical simulation, and is suitable for rapid calculation of temperature rise of artificial surface plasmon transmission lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0036] Figure 1 A flowchart of a method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line of the present invention;

[0037] Figure 2 It is a top view of the artificial surface plasmon transmission line;

[0038] Figure 3 Schematic diagram of the unit structure type of artificial surface plasmon transmission line;

[0039] Figure 4 This is the equivalent thermal circuit diagram in the horizontal plane when the conductor loss is considered;

[0040] Figure 5 This is the equivalent thermal circuit diagram in the vertical plane when considering conductor loss;

[0041] Figure 6 This is the equivalent thermal path diagram in the horizontal plane when dielectric loss is considered;

[0042] Figure 7 This is the equivalent thermal path diagram in the vertical plane when dielectric loss is considered;

[0043] Figure 8 It is a schematic diagram of the structure of an artificial surface plasmon transmission line in a specific embodiment of the present invention;

[0044] Fig. 9 It is a comparison chart of the temperature rise results obtained by the equivalent thermal circuit model, software simulation and experimental measurement in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0045] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0046] Specifically, the present invention provides a method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line, such as Figure 1 As shown, the method comprises the following steps:

[0047] S1: Divide the metal conduction band of the artificial surface plasmon transmission line into two parts: the main line and the branch, and extract the thermal resistance of each part respectively;

[0048] Specifically, the width of the metal conduction band of the artificial surface plasmon transmission line is w, and the thickness is d. s ; Rectangular grooves with a width of a and a depth of h are periodically distributed on the conduction band, and the period is p, so the metal conduction band presents an irregular fold structure. For the convenience of analysis, the metal conduction band of the artificial surface plasmon transmission line is divided into two parts, namely the main line with a width of wh, and multiple branches on the main line, such as Figure 2 As shown. For a main line with a length of p / 2, its thermal resistance is:

[0049]

[0050] where κ metal is the thermal conductivity of the metal.

[0051] For a branch, the thermal resistance is:

[0052]

[0053] S2: Extract the vertical thermal resistance of the dielectric region below the metal conduction band of the artificial surface plasmon transmission line;

[0054] Specifically, since the thermal conductivity of the medium is much smaller than that of the metal, the horizontal thermal resistance of the medium area below the metal conduction band is much larger than that of the metal conduction band, and can be approximately regarded as an open circuit. Therefore, when analyzing this part of the medium area, only the vertical thermal resistance needs to be considered, that is:

[0055]

[0056] where κ sub is the thermal conductivity of the medium, and d is the thickness of the medium substrate.

[0057] S3: Extract the horizontal thermal resistance of the dielectric region around the metal conduction band of the artificial surface plasmon transmission line;

[0058] Specifically, heat flows from the metal conduction band to the edge of the dielectric substrate, and is transferred by heat conduction inside the substrate, and dissipated to the external environment by convection on the surface of the substrate. If a thin layer with a thickness of Δy is taken at y=y1, the difference in heat flow Q on both sides of the thin layer is equal to the heat lost by convection, that is:

[0059] Q(y1)=Q(y1+Δy)+(h conv_u +h conv_l )pΔy[T(y1)-T amb ] (4)

[0060] where h conv_u and h conv_l are the convective heat transfer coefficients between the upper and lower surfaces and the outside air, T amb is the ambient temperature.

[0062] The above formula can be rearranged to get:

[0063]

[0064] At the same time, according to Fourier's law of heat conduction, the heat flux Q in the y direction and the temperature T satisfy

[0065]

[0066] According to equations (5) and (6), the temperature in the y direction satisfies the following second-order differential equation:

[0067]

[0068] Assume that the coordinate of the side edge of the conduction band is y0, and the heat flux from here to the outer medium is Q0, then there is a boundary condition

[0069]

[0070] Combined with the boundary conditions, the solution of differential equation (7) is:

[0071]

[0072] Therefore, the thermal resistance of the dielectric region from the edge of the metal conduction band to the edge of the substrate is:

[0073]

[0074] S4: The upper and lower surfaces of the artificial surface plasmon transmission line are regarded as convection boundaries, and the corresponding convection thermal resistance is extracted;

[0075] Specifically, the surface of the metal conduction belt and the surface of the dielectric area below the metal conduction belt will dissipate heat to the outside world through convection heat transfer, so it is necessary to add convection thermal resistance to describe this process, that is:

[0076]

[0077] S5: Under external power input conditions, the conductor loss and dielectric loss of the artificial surface plasmon transmission line are extracted as equivalent heat sources;

[0078] Specifically, since the metal conduction band of the artificial surface plasmon transmission line is an irregular fold structure, its loss distribution is not uniform. According to the conductor and dielectric loss distribution obtained by full-wave simulation, the conductor loss is mainly distributed at the bottom of the groove, while the dielectric loss is mainly distributed at the end of the branch. Therefore, it is approximately considered that the conductor loss heat source is concentrated at the bottom of the groove, and its loss power is q c ; The dielectric loss heat source is concentrated at the end of the branch, and its loss power is q d .

[0079] S6: Construct equivalent thermal circuit models corresponding to the conductor loss and dielectric loss of artificial surface plasmon transmission lines respectively.

[0080] Specifically, the unit structure of artificial surface plasmon transmission lines is divided into two types, such as Figure 3 When only the conductor loss is considered, the first unit type is used for analysis. At this time, the equivalent thermal path of the unit structure in the horizontal plane is as follows: Figure 4 As shown, the equivalent thermal path in the vertical plane is as follows Figure 5 According to the equivalent thermal circuit model, the temperature rise at the bottom of the groove and the end of the branch is:

[0081]

[0082]

[0083] in

[0084] R total_c =R conv_u ||(R sub +R conv_l )||(R line / 2+R c1 ) (14)

[0085] R c1 =(R edge +R stub )||R edge (15)

[0086] When only dielectric loss is considered, the second unit type analysis is adopted. At this time, the equivalent thermal path of the unit structure in the horizontal plane is as follows: Figure 6 As shown, the equivalent thermal path in the vertical plane is as follows Figure 7 According to the equivalent thermal circuit model, the temperature rise at the end of the branch and the bottom of the groove is:

[0087]

[0088]

[0089] in

[0090] R total_d =R edge ||(R stub +R d2 ) (18)

[0091] R d1 =(R sub +R conv_l )||R conv_u (19)

[0092] R d2 =(R d1 +R line / 2)||R edge (20)

[0093] The total temperature rise is the superposition of the conductor loss temperature rise and the dielectric loss temperature rise. According to the equivalent thermal circuit model, the hot spot of the artificial surface plasmon is located at the bottom of the groove or the end of the branch. Therefore, the hot spot temperature rise should be the larger of the two, that is,

[0094]

[0095] According to the above-mentioned method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line, a specific embodiment is analyzed.

[0096] This embodiment is an artificial surface plasmon transmission line based on PCB technology, such as Figure 8 As shown. Among them, the metal conductor is copper (conductivity σ=5.8×10 7 S / m, thermal conductivity κ metal =400W / (m·℃), thickness d s =0.035mm), the dielectric substrate is Rogers RO4003 (relative dielectric constant ε r =3.55, loss tangent tanδ = 0.0027, thermal conductivity κ sub =0.71W / (m·℃), thickness d=0.5mm); the dimensions of the artificial surface plasmon unit structure are a=1.5mm, p=4mm, h=7mm, w=8mm, and the entire transmission line contains 20 units in total.

[0097] When the input power is P in = 10W, the equivalent thermal circuit model of the present invention is used to analyze the maximum temperature rise of the artificial surface plasmon transmission line. Where the ambient temperature is T amb =25℃, the upper and lower surfaces of the transmission line are natural convection boundaries, and the convection coefficient is h conv_u =h conv_l =5W / (m 2·℃). As a verification, the temperature distribution and maximum temperature of the artificial surface plasmon transmission line were obtained by finite element software simulation and infrared thermal imager measurement. When the operating frequency changes in the range of 3 to 6 GHz, the temperature rise results obtained by the equivalent thermal circuit model, software simulation and experimental measurement are compared. Fig. 9 As shown, it can be seen that the three are highly consistent, verifying the accuracy of the model of the present invention.

[0098] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line, characterized in that: The method comprises the following steps: The metal conduction band of the artificial surface plasmon transmission line is divided into two parts: the main line and the branch, and the thermal resistance of each part is extracted respectively; Extract the vertical thermal resistance of the dielectric region below the metal conduction band of the artificial surface plasmon transmission line; Extract the horizontal thermal resistance of the dielectric region around the metal conduction band of the artificial surface plasmon transmission line; The upper and lower surfaces of the artificial surface plasmon transmission line are regarded as convection boundaries, and the corresponding convection thermal resistance is extracted; Under the condition of external power input, the conductor loss and dielectric loss of artificial surface plasmon transmission line are extracted as equivalent heat sources; The equivalent thermal circuit models corresponding to the conductor loss and dielectric loss of artificial surface plasmon transmission lines are constructed respectively.

2. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 1, characterized in that: In the step of dividing the metal conduction band of the artificial surface plasmon transmission line into two parts, a main line and a branch, and extracting the thermal resistance of each part respectively, the width of the metal conduction band of the artificial surface plasmon transmission line is w, and the thickness is d. s ; Rectangular grooves with a width of a and a depth of h are periodically distributed on the conduction band, and the period is p. The metal conduction band of the artificial surface plasmon transmission line is divided into two parts, namely the main line and multiple branches on the main line. For a main line with a length of p / 2, its thermal resistance is: where κ metal is the thermal conductivity of the metal; for a branch, its thermal resistance is:

3. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 1, characterized in that: In the step of extracting the vertical thermal resistance of the dielectric region below the metal conduction band of the artificial surface plasmon transmission line, the vertical thermal resistance of the dielectric region below the metal conduction band is: where κ sub is the thermal conductivity of the medium, and d is the thickness of the medium substrate.

4. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 1, characterized in that: In the step of extracting the horizontal thermal resistance of the dielectric area around the metal conduction band of the artificial surface plasmon transmission line, heat flows from the metal conduction band to the edge of the dielectric substrate, and is transferred inside the substrate by heat conduction. On the surface of the substrate, heat is dissipated to the external environment in the form of convection heat transfer. By establishing a differential equation, the thermal resistance of this part of the dielectric area is obtained as follows: where h conv_u and h conv_l are the convective heat transfer coefficients between the upper and lower surfaces of the dielectric substrate and the outside air, respectively.

5. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 1, characterized in that: In the step of considering the upper and lower surfaces of the artificial surface plasmon transmission line as convection boundaries and extracting the corresponding convection thermal resistance, the surface of the metal conduction band and the surface of the dielectric region below the metal conduction band will dissipate heat to the outside through convection heat transfer. The convection thermal resistance is expressed as:

6. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 1, characterized in that: In the step of extracting the conductor loss and dielectric loss of the artificial surface plasmon transmission line as equivalent heat sources under the external power input condition, the conductor loss power of the artificial surface plasmon transmission line is q c ; The dielectric loss power is q d .

7. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 6, characterized in that: In the steps of respectively constructing equivalent heat circuit models corresponding to the conductor loss and dielectric loss of the artificial surface plasmon transmission line, the heat source of the equivalent heat circuit is q c or q d , thermal resistance includes R line , R stub , R sub , R edge , R conv_u and R conv_l .

8. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 7, characterized in that: When only the conductor loss is considered, the temperature rise at the bottom of the groove and the end of the branch is obtained according to the equivalent thermal circuit model: in R total_c =R conv_u ||(R sub +R conv_l )||(R line / 2+R c1 ) R c1 =(R edge +R stub )||R edge 。 9. The method for constructing an equivalent thermal circuit model of an artificial surface plasmon transmission line according to claim 7, characterized in that: When only dielectric loss is considered, the temperature rise at the end of the branch and the bottom of the groove is obtained according to the equivalent thermal circuit model: in R total_d =R edge ||(R stub +R d2 ) R d1 =(R sub +R conv_l )||R conv_u R d2 =(R d1 +R line / 2)||R edge 。

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