A method for constructing an equivalent thermal circuit model of a plasmonic transmission line

Abstract

The application provides a kind of equivalent thermal circuit model construction method of artificial surface plasmon transmission line, comprising: the metal conductor band of artificial surface plasmon transmission line is divided into main line and branch two parts, and the thermal resistance of each part is extracted respectively;Extract the vertical thermal resistance of the dielectric region below the metal conductor band of artificial surface plasmon transmission line;Extract the horizontal thermal resistance of the dielectric region around the metal conductor band of artificial surface plasmon transmission line;The upper surface and the lower surface of artificial surface plasmon transmission line are regarded as convection boundary, 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 source;The equivalent thermal circuit model corresponding to the conductor loss and dielectric loss of artificial surface plasmon transmission line is constructed respectively.The application first establishes the equivalent thermal circuit model of artificial surface plasmon transmission line, which provides guidance for efficient analysis and design of artificial surface plasmon transmission line.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microwave transmission technology, in particular to an equivalent thermal circuit model construction method of an artificial surface plasmonic transmission line. BACKGROUND

[0002] The metal strip of the artificial surface plasmonic transmission line presents a periodic sawtooth-shaped corrugated structure, and its transmission loss is lower than that of a planar transmission line represented by a microstrip line. By adjusting the geometric size of the unit structure, the propagation constant, cutoff frequency and other parameters can be flexibly adjusted, thereby providing great flexibility for circuit design. At present, the artificial surface plasmonic transmission line has been widely used in the design of filters, resonators, power dividers and antennas.

[0003] However, when the artificial surface plasmonic transmission line works at a high power, the temperature will rise significantly. When the temperature exceeds a certain threshold, the self-heating effect of the material may cause the transmission performance to deteriorate. At present, there is still a lack of an electro-thermal model for the artificial surface plasmonic transmission line, which limits its application in high-power scenarios. Therefore, it is urgent to establish an equivalent thermal circuit model of the artificial surface plasmonic transmission line to predict its maximum temperature under a certain power input. SUMMARY

[0004] The present application aims to provide an equivalent thermal circuit model construction method of an artificial surface plasmonic transmission line, which can efficiently and accurately predict the maximum temperature of the artificial surface plasmonic transmission line under a certain power input.

[0005] To solve the above problems, the technical scheme of the present application is as follows:

[0006] An equivalent thermal circuit model construction method of an artificial surface plasmonic transmission line, comprising the following steps:

[0007] Divide the metal strip of the artificial surface plasmonic transmission line into a main line and a branch, and extract the thermal resistance of each part respectively;

[0008] Extract the vertical thermal resistance of the dielectric region below the metal strip of the artificial surface plasmonic transmission line;

[0009] Extract the horizontal thermal resistance of the dielectric region around the metal strip of the artificial surface plasmonic transmission line;

[0010] Treat the upper surface and the lower surface of the artificial surface plasmonic transmission line as convection boundaries, and extract the corresponding convection thermal resistance;

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

[0012] An equivalent thermal circuit model of the artificial surface plasmonic transmission line is constructed.

[0013] Preferably, in the step of dividing the metal strip of the artificial surface plasmonic transmission line into a main line and branches, and extracting the thermal resistance of each part, the width of the metal strip of the artificial surface plasmonic transmission line is w, and the thickness is d s ; the metal strip is periodically distributed with rectangular grooves with a width of a and a depth of h, and the period is p; the metal strip of the artificial surface plasmonic transmission line is divided into two parts, i.e. a main line and a plurality of branches on the main line; for a main line with a length of p / 2, the thermal resistance is: where κ metal is the thermal conductivity of the metal; for a branch, the thermal resistance is:

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

[0015] Preferably, in the step of extracting the horizontal thermal resistance of the dielectric region around the metal strip of the artificial surface plasmonic transmission line, heat flows from the metal strip to the edge of the dielectric substrate, and heat is transferred through conduction in the substrate, and heat is dissipated to the external environment in the form of convective heat transfer on the surface of the substrate. By establishing a differential equation, the thermal resistance of this part of the dielectric region is: 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 external air, respectively.

[0016] Preferably, in the step of regarding the upper and lower surfaces of the artificial surface plasmonic transmission line as convective boundaries and extracting the corresponding convective thermal resistance, the surface of the metal strip and the surface of the dielectric region below the metal strip will dissipate heat to the external environment through convective heat transfer. The convective thermal resistance is represented as:

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

[0018] Preferably, in the step of constructing an equivalent thermal circuit model of the conductor loss and dielectric loss of the artificial surface plasmonic transmission line, the heat source of the equivalent thermal 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 conductor losses are considered, the temperature rise at the bottom of the groove and the end of the branch is calculated based on the equivalent thermal circuit model as follows:

[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 calculated based on the equivalent thermal circuit model as follows:

[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 application first establishes an equivalent thermal circuit model of the artificial surface plasmonic transmission line, reveals the physical mechanism of its electro-thermal effect, and provides guidance for efficient analysis and design of the artificial surface plasmonic transmission line.

[0034] 2. The present application uses an analytical method for electro-thermal analysis, avoiding time-consuming numerical simulation, and is suitable for rapid calculation of the temperature rise of the artificial surface plasmonic transmission line. BRIEF DESCRIPTION OF DRAWINGS

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

[0036] Figure 1 A flow chart of the method for constructing the equivalent thermal circuit model of the artificial surface plasmonic transmission line of the present application is shown.

[0037] Figure 2 A top view of the artificial surface plasmonic transmission line is shown.

[0038] Figure 3 A schematic diagram of the unit structure type of the artificial surface plasmonic transmission line is shown.

[0039] Figure 4 An equivalent thermal circuit diagram in the horizontal plane considering conductor loss is shown.

[0040] Figure 5 An equivalent thermal circuit diagram in the vertical plane considering conductor loss is shown.

[0041] Figure 6 An equivalent thermal circuit diagram in the horizontal plane considering dielectric loss is shown.

[0042] Figure 7 An equivalent thermal circuit diagram in the vertical plane considering dielectric loss is shown.

[0043] Figure 8 A schematic diagram of the artificial surface plasmonic transmission line structure in one specific embodiment of the present application is shown.

[0044] Figure 9 A comparison diagram of the temperature rise results obtained by the equivalent thermal circuit model, software simulation and experimental measurement in one specific embodiment of the present application is shown. DETAILED DESCRIPTION

[0045] The present application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present application. These all belong to the protection scope of the present application.

[0046] Specifically, the present application provides an equivalent thermal circuit model construction method of an artificial surface plasmonic transmission line, as shown in the accompanying drawings, the method comprises the following steps: Figure 1

[0047] S1: dividing the metal strip of the artificial surface plasmonic transmission line into two parts of a main line and branches, and extracting the thermal resistance of each part;

[0048] Specifically, the width of the metal strip of the artificial surface plasmonic transmission line is w, and the thickness is d s ; The metal strip is periodically distributed with rectangular grooves with a width of a and a depth of h, and the period is p, so the metal strip presents an irregular corrugated structure. In order to facilitate analysis, the metal strip of the artificial surface plasmonic transmission line is divided into two parts, i.e. a main line with a width of w-h, and a plurality of branches on the main line, as shown in the accompanying drawings. For a main line with a length of p / 2, its thermal resistance is: Figure 2

[0049]

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

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

[0052]

[0053] S2: extracting the vertical thermal resistance of the dielectric region below the metal strip of the artificial surface plasmonic transmission line;

[0054] Specifically, since the thermal conductivity of the dielectric is much smaller than that of the metal, the horizontal thermal resistance of the dielectric region below the metal strip is much larger than that of the metal strip, and can be approximated as an open circuit. Therefore, when analyzing this part of the dielectric region, only the vertical thermal resistance needs to be considered, i.e.

[0055]

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

[0057] S3: extracting the horizontal thermal resistance of the dielectric region around the metal strip of the artificial surface plasmonic transmission line;

[0058] Specifically, heat flows from the metal strip to the edge of the dielectric substrate, and is transferred by heat conduction in the interior of the substrate, and is dissipated to the outside environment in the form of convective heat exchange on the surface of the substrate. If a thin layer with a thickness of Δy is taken at y=y1, then the difference between the heat flow Q on both sides of the thin layer is equal to the heat dissipated by convective heat exchange, i.e.

[0059] ​​Q(y1) = Q(y1 + Ay) + (h conv_u +h conv_l )pAy[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 ambient air, T amb is the ambient

[0061] The above equation can be rearranged as:

[0062]

[0063] Meanwhile, according to the Fourier heat conduction law, the heat flow Q and temperature T in the y direction satisfy

[0064]

[0065] According to equations (5) and (6), the temperature in the y direction satisfies the following second-order differential equation

[0066]

[0067] Let the coordinate of the edge of the conduction band be y0, and the heat flow from this point to the outside medium be Q0, then the boundary condition is

[0068]

[0069] Combining the boundary conditions, the solution of the differential equation (7) is:

[0070]

[0071] Therefore, the thermal resistance of the medium region from the edge of the metal conduction band to the edge of the substrate is:

[0072]

[0073] S4: The upper and lower surfaces of the artificial surface plasmon transmission line are regarded as convective boundaries, and the corresponding convective thermal resistance is extracted;

[0074] Specifically, the surface of the metal conduction band and the surface of the medium region below the metal conduction band will dissipate heat to the outside world through convective heat transfer, so it is necessary to add a convective thermal resistance to describe this process, i.e.:

[0075]

[0076] S5: Under the condition of external power input, the artificial surface plasmon transmission line conductor loss and dielectric loss are extracted as equivalent heat sources;

[0077] Specifically, since the metal conduction band of the artificial surface plasmonic transmission line is an irregular corrugated structure, the loss distribution is not uniform. According to the conductor and dielectric loss distributions obtained by full-wave simulation, the conductor loss is mainly distributed at the bottom of the groove, and 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 the loss power is q c ; the dielectric loss heat source is concentrated at the end of the branch, and the loss power is q d .

[0078] S6: Construct the equivalent thermal circuit model corresponding to the conductor loss and dielectric loss of the artificial surface plasmonic transmission line, respectively.

[0079] Specifically, the unit structure of the artificial surface plasmonic transmission line is divided into two types, as shown in Figure 3 . When only considering the conductor loss, the first type of unit is analyzed, and the equivalent thermal circuit of the unit structure in the horizontal plane is as shown in Figure 4 , and the equivalent thermal circuit in the vertical plane is as shown in 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:

[0080]

[0081]

[0082] wherein

[0083] R total_c = R conv_u ||(R sub + R conv_l )||(R line / 2+ R c1 ) (14)

[0084] R c1 = (R edge + R stub )|| R edge (15)

[0085] When only considering the dielectric loss, the second type of unit is analyzed, and the equivalent thermal circuit of the unit structure in the horizontal plane is as shown in Figure 6 , and the equivalent thermal circuit in the vertical plane is as shown in 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:

[0086]

[0087]

[0088] wherein

[0089] R total_d =R edge ||(R stub +R d2 (18)

[0090] R d1 =(R sub +R conv_l )||R conv_u (19)

[0091] R d2 =(R d1 +R line / 2)||R edge (20)

[0092] The total temperature rise is the sum 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 stub; therefore, the hot spot temperature rise should be the larger of the two, i.e.

[0093]

[0094] Based on the above-described method for constructing the equivalent thermal path model of artificial surface plasmon transmission lines, a specific embodiment is analyzed.

[0095] This embodiment is an artificial surface plasmon transmission line based on PCB technology, such as... Figure 8 As shown. The metallic conductor is copper (conductivity σ = 5.8 × 10⁻⁶). 7 S / m, thermal conductivity κ metal = 400W / (m·℃), thickness d s =0.035mm), the dielectric substrate is Rogers RO4003 (relative permittivity 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.

[0096] When the input power is P in At 10W, the equivalent thermal path model of this invention was used to analyze the maximum temperature rise of the plasmon transport line on the artificial surface. The ambient temperature was 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• C). As a verification, the temperature distribution and the highest temperature of the artificial surface plasmon transmission line are obtained by means of finite element software simulation and infrared thermal imager measurement. When the working frequency changes in the range of 3-6 GHz, the temperature rise results obtained by the equivalent thermal circuit model, software simulation and experimental measurement are compared as shown in Figure 9 It can be seen that the three are highly consistent, verifying the accuracy of the model of the application.

[0097] The specific embodiments of the application are described above. It should be understood that the application is not limited to the specific embodiments described above, and various changes or modifications can be made by those skilled in the art within the scope of the claims, which does not affect the essential content of the application. The embodiments of the present application and the features in the embodiments can be arbitrarily combined with each other without conflict.

Claims

1. A method for constructing an equivalent thermal circuit model of an artificial surface plasmon polariton transmission line, characterized in that, The method comprises the following steps: The metal conductor of the artificial surface plasmon transmission line is divided into a main line and a branch, and the thermal resistance of each part is extracted respectively; The vertical direction thermal resistance of the dielectric region under the metal conductor of the artificial surface plasmon transmission line is extracted; The horizontal direction thermal resistance of the dielectric region around the metal conductor of the artificial surface plasmon transmission line is extracted; The upper surface and the lower surface 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 the artificial surface plasmon transmission line are extracted as equivalent heat sources, the conductor loss power of the artificial surface plasmon transmission line is q c ; and the dielectric loss power is q d ; The equivalent thermal circuit models corresponding to the conductor loss and dielectric loss of the artificial surface plasmonic transmission line are respectively constructed, wherein the thermal resistance includes R line , R stub , R sub , R edge , R conv_u , R conv_l , T gap is the temperature of the groove bottom, T end is the temperature of the branch end, T amb is the ambient temperature; R line is the thermal resistance in the main line direction, R stub is the single branch thermal resistance, R sub is the vertical thermal resistance of the dielectric area, R edge is the side edge diffusion thermal resistance of the dielectric area, R conv_u is the convective thermal resistance above the structure, and R conv_l is the convective thermal resistance below the structure; When only considering conductor loss, the temperature rise at the bottom of the groove is obtained according to the equivalent thermal circuit model as follows: Wherein R total_c = R conv_u + R sub + R conv_l + R line + R c1 ​ At the same time, the temperature rise at the end of the branch is obtained according to the equivalent thermal circuit model as follows: Wherein R c1 = (R edge + R stub ) || R edge ; When only considering dielectric loss, the temperature rise at the end of the branch is obtained according to the equivalent thermal circuit model as follows: Wherein R total_d = R edge || (R stub + R d2 ) At the same time, the temperature rise at the bottom of the groove is obtained according to the equivalent thermal circuit model as follows: Wherein R d1 = (R sub + R conv_l ) || R conv_u R d2 = (R d1 + R line / 2) || R edge .

2. The method of claim 1, wherein, In the step of dividing the metal strip of the artificial surface plasmon transmission line into a main line and branches, the width of the metal strip of the artificial surface plasmon transmission line is w, and the thickness is d s ; the rectangular grooves with a width of a and a depth of h are periodically distributed on the metal strip, and the period is p; the metal strip of the artificial surface plasmon transmission line is divided into two parts, i.e., a main line and a plurality of branches on the main line; for a main line with a length of p / 2, the thermal resistance is: wherein κ metal is the thermal conductivity of the metal; for a branch, the thermal resistance is:

3. The method according to claim 2, wherein, In the step of extracting the vertical direction thermal resistance of the dielectric region under the metal strip of the artificial surface plasmon transmission line, the vertical direction thermal resistance of the dielectric region under the metal strip is: wherein κ sub is the thermal conductivity of the dielectric, and d is the thickness of the dielectric substrate.

4. The method according to claim 3, wherein, In the step of extracting the horizontal thermal resistance of the medium area around the metal strip of the artificial surface plasmon transmission line, heat flows from the metal strip to the edge of the medium substrate, is transferred by heat conduction in the interior of the substrate, and is radiated to the outside environment in the form of convective heat exchange on the surface of the substrate, and by establishing a differential equation, the thermal resistance of the medium area is obtained as: Where h conv_u And h conv_l are the convective heat exchange coefficients between the upper and lower surfaces of the medium substrate and the outside air, respectively.

5. The method of claim 4, wherein, In the step of regarding the upper surface and the lower surface of the artificial surface plasmon transmission line as a convection boundary and extracting a corresponding convection thermal resistance, the surface of the metal conductor and the surface of the dielectric region below the metal conductor both dissipate heat to the outside world in the form of convection heat exchange, and the convection thermal resistance is represented as:

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