A method for calculating the average power capacity of dielectric integrated suspension lines

Abstract

The present invention discloses a method for calculating the average power capacity of a dielectric integrated suspension line. The corresponding relationship between the surface temperature of the SISL and the input power is calculated by heat transfer analysis. The parallel plate thermal model of the SISL is established for internal heat transfer analysis by analogy of the heat flow field with the electrostatic field. The corresponding relationship between the internal maximum temperature and the input power of the SISL under the condition of composite medium heat transfer is calculated by numerical modeling and heat transfer analysis, thereby realizing the rapid calculation of the average power capacity of the SISL transmission line. The present invention provides a method for rapidly calculating the average power capacity of the SISL transmission line. When the SISL transmission line is used for circuit design, the maximum continuous wave power that it can withstand can be rapidly estimated, which has important reference significance when designing high-power circuits using the SISL platform.

Description

Technical Field

[0001] The invention relates to the technical field of dielectric integrated suspension lines, and in particular to a method for calculating the average power capacity of a dielectric integrated suspension line. Background Art

[0002] Transmission lines are the most basic components of microwave and millimeter wave circuits and systems. Commonly used transmission lines are divided into planar structures and non-planar structures. Planar structure transmission lines mainly include microstrip lines, coplanar waveguides and slot lines, etc. The advantage is that it is easy to integrate circuits and devices, but the disadvantage is high loss and low average power capacity. Non-planar structure transmission lines mainly include metal waveguides and coaxial lines. The advantages are high power capacity and high quality factor, but the disadvantage is that they are large in size and difficult to integrate with other circuits and devices.

[0003] Substrate integrated waveguide (SIW) has received extensive attention in recent years. Its electric field is distributed in the dielectric, so the loss is large, which seriously affects the average power capacity. Although the air-filled SIW significantly reduces the dielectric loss, it still has the disadvantage of being unable to be integrated with active devices.

[0004] Many high-performance RF microwave circuits have been implemented on dielectric integrated suspension line (SISL) due to its advantages of low loss, low cost, self-packaging, and easy integration with other transmission lines and devices. In high-power circuit design, in addition to transmission characteristics, temperature characteristics are also a factor that should be considered. When the circuit transmits continuous waves, if the applied continuous wave power exceeds the allowable limit, the temperature increase caused by the loss will cause the substrate material properties to change, affecting the circuit performance. This allowable power limit is the average power capacity of SISL.

[0005] The heat transfer performance of the outer surface of SISL is similar to that of SIW. The outer surface can also be considered isothermal on the cross section in the transmission direction, but there is an obvious temperature gradient inside SISL, which is different from the thermal model of thermal uniformity on the cross section of SIW. In addition, compared with the microstrip line, which is also a dual-conductor transmission line, because SISL is a composite structure composed of dielectric, metal and cavity, the thermal model of microstrip line is also not applicable to SISL transmission line. Because SISL has good performance, it has many excellent applications in high power, but there is no discussion on the analysis of SISL average power capacity. In order to ensure the stable operation of SISL high-power circuits, a method that can analyze and calculate the average power capacity of SISL is urgently needed to guide the power considerations when designing SISL transmission lines. Summary of the invention

[0006] The purpose of the present invention is to provide a method for calculating the average power capacity of a dielectric integrated suspension line in view of the technical defects in the prior art, so as to guide the design of SISL transmission lines based on power considerations.

[0007] The technical solution adopted to achieve the purpose of the present invention is:

[0008] A method for calculating the average power capacity of a dielectric integrated suspension line, comprising:

[0009] S1. Obtain the attenuation constant of the SISL transmission line through simulation and calculate the heat flux Φ generated in the SISL transmission line gen The first expression of Φ: gen =-ΔP, ΔP represents the power variation over the length Δz of the SISL transmission line; where ΔP = -2αPΔz, P = P0e -2αz , α is the attenuation constant of the uniform SISL transmission line obtained by full-wave simulator simulation, P is the power flow function along the transmission direction (z direction) of the lossy transmission line; P0 represents the input power, corresponding to the coordinate z = 0;

[0010] S2. Calculate and SISL the outer surface temperature T of the transmission line s and heat flow Φ gen The relationship between them is used to obtain the heat flow Φ gen The second expression:

[0011]

[0012] where n and m are the number of surface layers associated with the convection and radiation boundaries, respectively, and h c,i is the heat transfer coefficient, A i is the surface layer area associated with convection, A j is the surface layer area related to radiation, and the surface layer area A on the SISL transmission line Δz length i and A j The calculation method is the product of the width or height of the SISL transmission line and Δz, where the area of ​​the upper and lower horizontal surfaces is the product of the width and Δz, the area of ​​the left and right vertical surfaces is the product of the height and Δz, σ is the blackbody radiation constant, ξ is the emissivity of the surface layer related to radiation, T ∞ is the ambient temperature, where and The superscript of is the fourth power;

[0013] S3. Calculate the maximum temperature T inside the SISL transmission line w and heat flow Φ gen The relationship between them is used to obtain the heat flow Φ gen The third expression

[0014]

[0015]

[0016] Among them, Φ cond Indicates that K air is the thermal conductivity of air, W e Δz is the area of ​​heat conduction, W e It means that the SISL transmission line is equivalent to a parallel plate thermal model and is widened by the substrate supporting the signal line. h = b / 2, where b is the total height of the upper and lower cavities. Represents the total radiation heat transfer in the upper and lower cavities; ξ c is the emissivity of the signal line, ξ d is the emissivity of the medium, ξ in is the emissivity of the material on the bottom PCB surface and the top PCB surface, F 12 is the viewing angle factor from the circuit layer to the corresponding cover plate, w air represents the cavity width in the transmission line, w is the signal line width, where and The superscript of is the fourth power;

[0017] S4. Calculate the average power capacity of SISL transmission lines

[0018] Through the heat flow Φ gen The first expression, the second expression and the third expression are combined to obtain two equations about the input power P0 and the outer surface temperature T of the SISL transmission line. s The two equations are combined into a system of equations. By solving the system of equations, the maximum temperature inside the SISL reaches the glass softening temperature T of the medium. g The corresponding input power P0 is the average power capacity of the SISL transmission line.

[0019] The method of the present invention realizes the calculation of the corresponding relationship between the surface temperature of SISL and the input power through heat transfer analysis; by analogy of the heat flow field with the electrostatic field, a parallel plate thermal model of SISL is established for internal heat transfer analysis; through numerical modeling and heat transfer analysis, the calculation of the corresponding relationship between the internal maximum temperature and the input power of SISL under the condition of composite medium heat transfer is realized, and the rapid calculation of the average power capacity of the SISL transmission line can be realized.

[0020] The present invention provides a method for quickly calculating the average power capacity of a SISL transmission line. When a SISL transmission line is used for circuit design, the maximum continuous wave power that it can withstand can be quickly estimated, which has important reference significance when a high-power circuit is designed using a SISL platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a three-dimensional schematic diagram of SISL;

[0022] Figure 2 is a schematic diagram of the SISL cross section;

[0023] Figure 3 It is a schematic diagram of the cross section of the air-filled SISL and its electrostatic field and thermal flow field;

[0024] Figure 4 is a schematic diagram of the equivalent parallel plate thermal model of air-filled SISL;

[0025] Figure 5 It is the S parameter curve of SISL transmission line;

[0026] Figure 6 It is the attenuation constant curve of SISL transmission line;

[0027] Figure 7 This is the temperature cloud diagram of SISL. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0029] like Figure 1 As shown, a method for calculating the average power capacity of a SISL transmission line according to an embodiment of the present invention can quickly calculate the average power capacity of a SISL transmission line. The specific steps are:

[0030] Step 1: Obtain the attenuation constant of the SISL transmission line through simulation and calculate the heat flux generated in the SISL transmission line.

[0031] The attenuation constant α of the uniform SISL transmission line is obtained by full-wave simulator simulation. When the input power is P0, the power drop at the length z of the SISL transmission line is:

[0032] P=P0e -2αz (1)

[0033] The power variation over the length Δz of the SISL transmission line is:

[0034] ΔP=-2αPΔz (2)

[0035] Therefore, the heat flux Φ generated in the SISL transmission line gen for:

[0036] Φ gen =-ΔP (3)

[0037] Step 2: Calculate the outer surface temperature T of the SISL transmission line s and heat flow Φ gen The relationship between them.

[0038] The heat dissipation of SISL transmission lines includes convection and radiation. Due to the presence of copper cladding and a large number of metallized vias, the self-packaging of SISL transmission lines is approximately isothermal.

[0039] The heat transfer coefficient of convection heat transfer h c The calculation formula is as follows:

[0040] 1) Heat transfer coefficient when the hot surface is facing upward

[0041]

[0042] 2) Heat transfer coefficient when the hot surface is facing downward

[0043]

[0044] 3) Heat transfer coefficient when the hot surface is vertical

[0045]

[0046] Among them, T ∞ is the ambient temperature, w box is the width of SISL self-encapsulation, h box is the height of the SISL package. The temperature of the outer surface of the SISL transmission line is T s and heat flow Φ gen The relationship formula is as follows:

[0047]

[0048] where n and m are the number of surface layers associated with the convection and radiation boundaries, respectively, and h c,i is the heat transfer coefficient, A i is the surface layer area associated with convection, A j is the surface layer area related to radiation, and the surface layer area A on the SISL transmission line Δz length i and A j is calculated as the product of the width or height of the SISL transmission line and Δz, where the area of ​​the upper and lower horizontal surfaces is the product of the width and Δz, the area of ​​the left and right vertical surfaces is the product of the height and Δz, σ is the blackbody radiation constant, ξ is the emissivity of the surface layer related to radiation, and T ∞ is the ambient temperature, where T s and T ∞ The superscript is the fourth power;

[0049] Step 3: Calculate the maximum temperature T inside the SISL transmission line w and heat flow Φ gen The relationship between them.

[0050] The loss generated by SISL is mainly located in the signal line and the supporting medium around the signal line. The heat converted from this part of the loss will be transferred to the outer surface through the composite medium composed of the upper and lower cavities and the signal line supporting medium. Usually, the cavity height of SISL is not enough to produce convective heat transfer, and the internal heat transfer method is only conduction and radiation, and the two paths exist in parallel.

[0051] When SISL is filled with air, the thermal flow field can be compared to the electrostatic field. In order to accurately calculate the area of ​​heat conduction from the signal line and the supporting medium around the signal line, SISL is equivalent to a parallel plate thermal model according to the principle that the thermal flow field is analogous to the electrostatic field. The calculation formula for the thermal flow field width is as follows:

[0052]

[0053] Where, h = b / 2, b is the total height of the upper and lower cavities, is the characteristic impedance of the air-filled SISL. When the SISL configuration fits within the stripline range, It can be approximated by the following formula

[0054] 1) When w / (bt)≤0.35, t / b≤0.25, and d″ / d′≤0.11:

[0055]

[0056]

[0057] 2) When w / (bt)≥0.35, t / b≤0.25:

[0058]

[0059]

[0060] Wherein, t is the signal line thickness, d″ is the smaller of w and t, and d′ is the larger of w and t.

[0061] Since the thermal conductivity of the substrate under the signal line is much higher than that of air, the parallel plate thermal model width w calculated with only air filling is e It is widened to both sides, and the specific width is the same as the cavity height h air , cavity width w air , the thermal conductivity K of the substrate supporting the signal line sub, signal line width w and substrate thickness h supporting the signal line sub The present invention proposes to fit the width w of the parallel plate thermal model of the air-filled SISL transmission line by numerical modeling. e The width of the parallel plate model affected by the substrate supporting the signal line is W. e =λ·w e .

[0062] A large amount of data on the relationship between the input power and the maximum internal temperature of SISL is simulated by thermal simulation software as samples, and a mathematical model is used to fit the width w of the parallel plate thermal model of the air-filled SISL transmission line. e The multiple of widening λ, λ and cavity height h air , cavity width w air , the thermal conductivity K of the substrate supporting the signal line sub , signal line width w and substrate thickness h supporting the signal line sub These variables are all correlated.

[0063] The heat transfer heat can be calculated by the following formula:

[0064]

[0065] Where K air is the thermal conductivity of air, W e Δz is the area of ​​heat conduction.

[0066] The total radiation heat transfer in the upper and lower cavities can be approximately calculated by the following formula:

[0067]

[0068] ξ c is the emissivity of the signal line, ξ d is the emissivity of the medium, ξ in is the emissivity of the material on the bottom PCB surface and the top PCB surface, F 12 is the viewing angle factor from the circuit layer to the corresponding cover plate, and the calculation formula is

[0069]

[0070] Finally, according to the law of conservation of energy, we have:

[0071]

[0072] Step 4: Calculate the average power capacity of the SISL.

[0073] Substituting equations (3)-(6) into equation (7), we get an equation for input power and surface temperature:

[0074] Substituting equations (3) and (8)-(15) into equation (16), we get the second equation about input power and surface temperature: The two equations are combined into a system of equations. By solving this system of equations, we can get the maximum temperature inside the SISL that reaches the glass softening temperature of the medium, T g The corresponding input power is the average power capacity of SISL.

[0075] The average power calculation method of the transmission line of the embodiment of the present invention can be realized by a processing model implemented by a computer program. After the corresponding parameters are input into the model, the model outputs the corresponding results. By changing the input power, the change of the transmission temperature is realized. When the maximum temperature inside the SISL reaches the glass softening temperature T of the medium g The corresponding input power is the average power capacity of SISL. In this way, when using SISL transmission line for circuit design, the maximum continuous wave power it can withstand can be quickly estimated, so as to guide the circuit design to ensure that the designed circuit meets the corresponding power requirements, which has important reference significance when using SISL platform to design high-power circuits.

[0076] Below, we take a section of SISL transmission line operating at 3GHz as an example to calculate its maximum transmission power. Its S parameters are as follows Figure 5 The boards that make up the SISL transmission line are all made of FR4, and the relative dielectric constant of the medium is ε r =4.4, tanδ=0.02. The glass softening temperature of ordinary FR4 is 140℃, so the maximum operating temperature of SISL transmission line is 140℃. The thickness of the five-layer board is 0.3mm, 0.6mm, 0.127mm, 0.6mm, 0.3mm, and the copper thickness is 0.035mm. The working environment is room temperature T ∞ =22℃.

[0077] The width w of the SISL transmission line from the package box =20mm, height h box =1.997mm, cavity width w air =10mm, cavity height h air =0.6mm, b=1.397mm, signal line width w=1.75mm, the thermal conductivity of FR4 and copper are 0.294W / (m·℃) and 400W / (m·℃) respectively, and the emissivity are 0.9 and 0.1 respectively.

[0078] Step 1: Obtain the attenuation constant of the SISL transmission line through simulation.

[0079] like Figure 6 As shown, the attenuation constant is 0.186N at 3GHz p / m, and the heat flux generated by the loss in the transmission line is calculated by substituting into equations (2) and (3):

[0080] Φ gen =2αPΔz=2×0.186×P0×Δz (17)

[0081] Step 2: Calculate the outer surface temperature T of the SISL transmission line s and heat flow Φ gen The relationship between them.

[0082] Ambient temperature T ∞ The temperature is 295K (22℃), and equations (4)-(6) and data such as dimensions and materials are substituted into (7) to obtain:

[0083]

[0084] Step 3: Calculate the maximum temperature T inside the SISL transmission line w and heat flow Φ gen The relationship between them.

[0085] Because the size of the SISL in the embodiment conforms to the stripline, the characteristic impedance can be calculated by equations (11) and (12):

[0086]

[0087]

[0088] Therefore, the width of the parallel plate thermal model is

[0089]

[0090] Using a monomial as the model function of λ, an expression for λ fitted by many sets of data on the corresponding relationship between input power and maximum temperature as samples is:

[0091]

[0092] The applicable range of this expression is: signal line width w: 0.1mm-50Ω corresponding line width, cavity height h air :0.3mm-2mm, cavity width w air :max{4w,w+4h air}-30mm, signal line support medium thickness h sub :0.127mm, signal line support medium thermal conductivity K sub :0.2W / (m·℃)-0.3W / (m·℃)

[0093] From this we can calculate W e

[0094]

[0095] The glass softening temperature T g Substitute T w , the heat flux of heat conduction is

[0096]

[0097] The view factor of radiation heat transfer in SISL transmission line can be calculated as

[0098]

[0099] The total radiation heat transfer in the upper and lower cavities is

[0100]

[0101] Finally, substituting equations (23) and (25) into equation (16), we have

[0102]

[0103] Step 4: Calculate the average power capacity of the SISL transmission line.

[0104] Substituting formula (17) into formula (18), we get

[0105]

[0106] Substituting formula (17) into formula (26), we get

[0107]

[0108] By solving the equations composed of equations (27) and (28), we can obtain P0 = 58.96W, T s =76.48°C, 58.96W is the average power capacity of the SISL transmission line in the embodiment.

[0109] In order to verify the accuracy of the calculation results, thermal simulation software is used to verify the calculation results.

[0110] Modeling and simulation were performed in a full-wave simulator and the simulation model and results were imported into thermal simulation software. The heat dissipation boundary conditions were set to convection and radiation, and the convection heat transfer coefficients of the upper and lower surfaces and the side surfaces were calculated using equations (1)-(7) respectively.

[0111] By changing the input power P0, the maximum temperature of SISL is 140℃. The steady-state thermal simulation results are shown in Figure 7As shown, when the maximum temperature of SISL reaches the glass softening temperature, the input power is 64.10W, and the corresponding surface temperature is 77.78℃. The accuracy of loss data transmission and grid division from the full-wave simulator to the thermal simulation software are part of the reasons for the temperature and power deviation. Nevertheless, this is very close to the calculation results in the example, thus proving the accuracy of the calculation method of the present invention.

[0112] The basic principles and main features of the present invention and the advantages of the present invention are shown and described above. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0113] Therefore, no matter from which point of view, the embodiments should be regarded as illustrative and non-restrictive, and the scope of the present invention is limited by the appended claims rather than the above description. Therefore, it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any figure signs in the claims should not be regarded as limiting the claims involved.

[0114] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for calculating the average power capacity of a dielectric integrated suspension line, characterized in that: Includes steps: S1. Obtain the attenuation constant of the SISL transmission line through simulation and calculate the heat flux Φ generated in the SISL transmission line gen The first expression of Φ: gen =-ΔP, ΔP represents the power variation over the length Δz of the SISL transmission line; where ΔP = -2αPΔz, P = P0e -2αz , α is the attenuation constant of the uniform SISL transmission line obtained by full-wave simulator simulation; P is the power flow function along the transmission direction of the lossy transmission line; P0 represents the input power, corresponding to the coordinate z = 0; S2. Calculate the outer surface temperature T of SISL transmission line s and heat flow Φ gen The relationship between them is used to obtain the heat flow Φ gen The second expression: where n and m are the number of surface layers associated with the convection and radiation boundaries, respectively, and h c,i is the heat transfer coefficient, A i is the surface layer area associated with convection, A j is the surface layer area related to radiation, and the surface layer area A on the SISL transmission line Δz length i and A j The calculation method of is the product of the width or height of the SISL transmission line and Δz, where the area of ​​the upper and lower horizontal surfaces is the product of the width and Δz, the area of ​​the left and right vertical surfaces is the product of the height and Δz, σ is the blackbody radiation constant, ξ is the emissivity of the surface layer related to radiation, and T ∞ is the ambient temperature, and The superscript of is the fourth power; S3. Calculate the maximum temperature T inside the SISL transmission line w and heat flow Φ gen The relationship between them is used to obtain the heat flow Φ gen The third expression Among them, Φ cond Indicates that K air is the thermal conductivity of air, W e Δz is the area of ​​heat conduction, W e represents the width of the parallel plate thermal model affected by the substrate supporting the signal line, h = b / 2, b is the total height of the upper and lower cavities, Represents the total radiation heat transfer in the upper and lower cavities; ξ c is the emissivity of the signal line, ξ d is the emissivity of the medium, ξ in is the emissivity of the material on the bottom PCB surface and the bottom PCB surface, F 12 is the viewing angle factor from the circuit layer to the corresponding cover plate, w air represents the cavity width in the transmission line, and w is the signal line width; S4. Calculate the average power capacity of SISL transmission lines Through the heat flow Φ gen The first expression, the second expression and the third expression are combined to obtain two equations about the input power P0 and the outer surface temperature T of the SISL transmission line. s The two equations are combined into a system of equations. By solving the system of equations, the maximum temperature inside the SISL reaches the glass softening temperature T of the medium. g The corresponding input power P0 is the average power capacity of the SISL transmission line.

2. The method for calculating the average power capacity of a dielectric integrated suspension line according to claim 1, characterized in that: h c,i The heat transfer coefficient includes the heat transfer coefficient when the hot surface is facing upward. Heat transfer coefficient when the hot surface is facing downward Heat transfer coefficient when the hot surface is vertical The calculation formulas are as follows: Among them, w box h is the width of the SISL transmission line self-package, box is the height of the SISL transmission line from the package.

3. The method for calculating the average power capacity of a dielectric integrated suspension line according to claim 1, characterized in that: The width W of the parallel plate thermal model affected by the substrate supporting the signal line e , is to calculate the width w of the air-filled SISL parallel plate thermal model by equating the air-filled SISL transmission line to a parallel plate thermal model e Finally, the width w of the air-filled SISL parallel plate thermal model was fitted by numerical modeling. e The signal line is widened by a factor of λ due to the substrate supporting it, and then e =λ·w e Calculated.

4. The method for calculating the average power capacity of a dielectric integrated suspension line according to claim 3, characterized in that: The air-filled SISL parallel plate thermal model width w e The calculation formula is as follows: Where h = b / 2, b is the total height of the upper and lower cavities in the SISL transmission line, is the characteristic impedance of the air-filled SISL transmission line. When the SISL transmission line configuration conforms to the stripline range, It is found by the following formula: When w / (bt)≤0.35, t / b≤0.25: d0 is an intermediate variable and can be calculated by the following formula: When w / (bt)≥0.35, t / b≤0.25: C f is the edge capacitance, which can be calculated by the following formula: Wherein, t is the signal line thickness, d″ is the smaller value between w and t, and d′ is the larger value between w and t.

5. The method for calculating the average power capacity of dielectric integrated suspension lines according to claim 3, characterized in that: Air-filled SISL parallel plate thermal model width w e The multiple λ of the widening affected by the substrate supporting the signal line is obtained by using a thermal simulation software to simulate a large number of data on the corresponding relationship between the input power and the internal maximum temperature of the SISL transmission line as samples, and fitting it using a mathematical model.

6. The method for calculating the average power capacity of a dielectric integrated suspension line according to claim 3, characterized in that: Air-filled SISL parallel plate thermal model width w e The widening factor λ and the cavity height h affected by the substrate supporting the signal line air , cavity width w air , the thermal conductivity K of the substrate supporting the signal line sub , signal line width w and substrate thickness h supporting the signal line sub Related.

7. The method for calculating the average power capacity of dielectric integrated suspension lines according to claim 1, characterized in that: View factor F from the circuit layer to the corresponding cover 12 The calculation formula is as follows: Among them, h air Represents the height of the cavity in the transmission line.

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