CN105489993A - Dimension design method for double-layer dielectric substrate integrated coaxial line - Google Patents

Abstract

The invention discloses a dimension design method for a double-layer dielectric substrate integrated coaxial line. The double-layer dielectric substrate integrated coaxial line consists of two layers of dielectric substrates with same thickness and different dielectric constants, two rows of metal through holes, a center conductor, an upper grounding plate and a lower grounding plate. According to the design method, on the basis of the transmission line capacitance per unit length, by using an equivalent capacitance principle, namely dividing a transmission unit of the substrate integrated coaxial line and integrating the transmission line capacitance per unit length in the transmission unit, the substrate integrated coaxial line is equivalent to be a rectangle coaxial line, and the relational expression between the equivalent width of the equivalent rectangle coaxial line and the dimension of the substrate integrated coaxial line is obtained. Consequently, an equivalent dimension formula of the double-layer dielectric substrate integrated coaxial line can be obtained. According to the method provided by the invention, the relational expression between the equivalent width of the equivalent rectangle coaxial line and the dimension of the substrate integrated coaxial line can be obtained, and the design flows of microwave and millimeter wave devices based on SICL are effectively simplified.

Description

A kind of sizing method of substrate integrated coaxial line of two-layered medium

Technical field

The present invention relates to the sizing method of a kind of application prospect substrate integrated coaxial line widely, by the SICL of two-layered medium equivalence is become conventional transmission line, and then draw the size of SICL of two-layered medium, belong to microwave and millimeter wave technical field.

Background technology

Since the twentieth century later stage, along with the development of new material technology and integrated circuit technology, the realization of the active solid-state circuit of microwave and millimeter wave frequency range has been made to become possibility.But in this frequency range, the shortcoming of microstrip circuit is as large in loss, quality factor are low, radiation and leakage serious etc., what become is more and more obvious, and the volume that conventional metals waveguide component and device brings is large, processing difficulties, expensive and be difficult to the problem such as mutually integrated with planar circuit and also constrain its application in high-frequency circuit designs.In this case, substrate integration wave-guide (SubstrateIntegratedWaveguide, SIW) and substrate integrated coaxial line (SubstrateIntegratedCoaxialLine, SICL) technology are arisen at the historic moment.

SICL is a kind of novel guided wave structure formed, structurally very similar to traditional rectangular coaxial line based on multilayer dielectricity substrate process, is jointly made up of central inner conductor and outer field shielded conductor shell.The same with coaxial line, it is guided wave structure formed that substrate integrated coaxial line also belongs to on-dispersive, and its transmission holotype is transverse electro-magnetic wave (TransverseElectromagneticMode, TEM), operating frequency is uncorrelated with sectional dimension, and characteristic impedance is only relevant to the ratio of the size of internal and external conductor.

Owing to adopting standard printed circuit board (PrintCircuitBoard, PCB) processes, the planar set that therefore SICL has generic coaxial line incomparable becomes second nature, and can be integrated in planar circuit system easily.Compared with microstrip line, owing to having relatively complete closed housing, the radiation loss of substrate integrated coaxial line is lower, is not easy to form mutual interference with other circuit.Filled by dielectric substrate completely due to it simultaneously, have higher effective dielectric constant, less circuit area can be realized.These significant advantages make substrate integrated coaxial line be well suited for being applied to modern microwave millimetre-wave circuit, especially compared with the microwave frequency band of low frequency and broadband application, at utmost can play its miniaturized integrated and non-dispersive advantage.Meanwhile, traditional planar transmission line as strip line and microstrip line, and the method for designing of coaxial line function element can Rapid transplant to SICL technology.But the design of the existing microwave device based on SICL mostly adopts and SICL is similar to strip line, namely first uses stripline design, replaced with SICL again, finally utilize full-wave simulation software to carry out simulation optimization parameter, step is comparatively loaded down with trivial details, and design efficiency is lower.

Summary of the invention

Goal of the invention: for problems of the prior art with not enough, the invention provides a kind of sizing method of substrate integrated coaxial line of two-layered medium, design the equivalents between a kind of SICL of two-layered medium and conventional transmission line, simplify the design cycle based on the microwave and millimeter wave device of SICL, promote design efficiency.

Technical scheme: a kind of sizing method of substrate integrated coaxial line of two-layered medium, described two-layered medium is the two-layered medium of differing dielectric constant, based on the transmission characteristic that the SICL of the two-layered medium of differing dielectric constant is similar to rectangular coaxial line, by the SICL of equivalent two-layered medium and the capacitance per unit length of rectangular coaxial line, and according to double-deck rectangular coaxial line and strip line Electric Field Distribution, calculate the approximate expression of the capacitance per unit length of double-deck rectangular coaxial line and strip line respectively, and then draw the size of this two-layered medium of specific dimensions SICL.

Concrete steps are:

1) double-deck substrate integrated coaxial line equivalence is become the cascade of many same units;

2) similar to the magnetic distribution that rectangular coaxial line transmits according to double-layer substrate integration waveguide characteristic, is equivalent to the cascade of strip line and rectangular coaxial line by transmission line unit;

3) electric capacity of two-layered medium substrate integrated coaxial line unit length and the electric capacity expression formula of rectangular coaxial line unit length is calculated respectively;

4) double-deck substrate integrated coaxial line is equivalent to the rectangular coaxial line with same units length electric capacity, thus draws the expression formula of this equivalent rectangular coaxial line width.

Described substrate integrated coaxial line two layer medium dielectric constant of reaching the standard grade is different, and thickness is identical.The center signal line width of its center conductor width same substrate integrated coaxial line is identical, and thickness trends towards zero, and its outer conductor height is identical with the height of former substrate integrated coaxial line.

Beneficial effect: compared with prior art, the sizing method of the substrate integrated coaxial line of two-layered medium provided by the invention, becomes conventional transmission line by the SICL of two-layered medium equivalence, effectively simplifies the design cycle of the microwave and millimeter wave device based on SICL.

Accompanying drawing explanation

Fig. 1 is the schematic three dimensional views of the SICL structure of two-layered medium in the present invention;

Fig. 2 is the schematic diagram of the SICL transmission line unit of two-layered medium in the present invention;

Fig. 3 is the circuit with lumped element model of one section of infinitely small length Δ x transmission line;

Fig. 4 is the distribution map of the electric field of the longitudinal tangent plane of rectangular coaxial line;

Fig. 5 is the model schematic of the precision being detected equivalent formulation in the present invention by simulation means;

Fig. 6 is the return loss comparison diagram of two formula under one group of parameter combinations;

Fig. 7 is the return loss comparison diagram of two formula under another group parameter combinations.

Embodiment

Below in conjunction with specific embodiment, illustrate the present invention further, these embodiments should be understood only be not used in for illustration of the present invention and limit the scope of the invention, after having read the present invention, the amendment of those skilled in the art to the various equivalent form of value of the present invention has all fallen within the application's claims limited range.

Fig. 1 is the schematic three dimensional views of SICL structure.As seen from the figure, its structure by the metallic vias 1 of arranged on both sides, upper and lower double layer of metal floor 4, the metallic conductor holding wire 3 at center, and the two layer medium substrate 2 being distributed in dielectric constant between metal ground different forms.Height between upper and lower metal floor 4 is h, and the thickness of two layer medium substrate 2 is h/2.Can find out, SICL transmission line presents periodic structure, therefore analysis its capacitance per unit length be that a unit that can repeat with its cycle carrys out equivalent analysis.SICL and rectangular coaxial line have similar transmission characteristic, all transmit TEM mould and longitudinal cross-section Electric Field Distribution is similar, therefore by the SICL of two-layered medium being equivalent to the rectangular coaxial line of specific dimensions, the design cycle of the microwave and millimeter wave device based on SICL can be simplified thus.

Fig. 2 is the generalized section of bowing of SICL transmission unit.Inner wire width is w _in, in the cylindrical hole of both sides metallic vias 1, horizontal spacing is w in the heart _out, the longitudinal pitch between adjacent metal cylindrical hole is that (distance namely between two cylindrical hole centers of circle is p) to p, and the diameter of cylindrical hole is D.As shown in the figure, the center of the through hole of a selected metal cylinder is initial point O, this center refers to SICL two and arranges metal throuth hole cross section (cross section here refers to the cross section at center conductor place, the i.e. center of metal throuth hole) center of circle, take longitudinal direction as x-axis, parameter x refers to the distance of distance center O point as shown in Figure 2 here.Distance between inner wire and metal cylinder through hole is set to function g (x) of x.From the periodic characteristic of SICL, can separately at a unit, i.e. in the region of 0 < x≤p, its characteristic is analyzed.In SICL, intercept x value is arbitrary cross section in 0 < x≤p, if x≤D/2 or x > p-D/2, then this cross section is a square-section, and its shape is similar to traditional rectangular coaxial line.If its D/2 < x≤p-D/2, then this cross section is similar to traditional strip line.

If segmented in the x direction by SICL transmission line unit, then it can regard the cascade of the infinitesimal transmission line of multistage as.Fig. 3 is the circuit with lumped element model of transmission line.Wherein R, L, G, C are the amount of unit length, are defined as follows:

R represents the series resistance of two conductor unit length;

L represents the series inductance of two conductor unit length;

The shunt conductance of G representation unit length;

The shunt capacitance of C representation unit length.

In a lot of actual conditions, the loss of transmission line is very little, therefore can make R=G=0, is the model only comprising series inductance and shunt capacitance by this model simplification.Can be obtained by transmission line theory, the total equivalent parallel electric capacity of this SICL transmission line unit in 0≤x < p be namely equivalent to its segment in the x direction after electric capacity sum on every section, even strip line electric capacity sum in rectangular coaxial line electric capacity and D/2 < x≤p-D/2 in x≤D/2 or x > p-D/2.

The distribution map of the electric field of the longitudinal tangent plane of rectangular coaxial line of Fig. 4 two-layered medium.Its electric capacity is divided into three parts:

4. the electric capacity C between center conductor and rectangular coaxial line horizontal conductor wall in parallel ₁, C ₂;

5. the edge capacitance C that produces of rectangular coaxial line outer conductor vertical wall ₃;

6. the stray capacitance C that produces with outer conductor horizontal wall of central inner conductor edge ₄, C ₅.

Because central inner conductor thickness is approximately zero, therefore the stray capacitance C that Part III is produced with outer conductor horizontal wall by central inner conductor edge ₄, C ₅negligible.Electric capacity C between center conductor and rectangular coaxial line horizontal conductor wall in parallel ₁, C ₂can be provided by following formula:

$C_1=\frac{2{\mathrm{\&epsiv;}}_1{w}_{in}}{h}$ (formula 1)

$C_2=\frac{2{\mathrm{\&epsiv;}}_2{w}_{in}}{h}$ (formula 2)

$C_3\left(x\right)=\frac{2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)}{\mathrm{\&pi;}}log(1+\coth \frac{\mathrm{\&pi;}g\left(x\right)}{h})$ (formula 3)

Therefore the electric capacity of rectangular coaxial line can be expressed as

C _rCL=C ₁+ C ₂+ 2C ₃(x) (formula 4)

Inner wire thickness is that the electric capacity of the two-layered medium strip line of 0 can be provided by following formula:

$C_{sripline}=2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)(\frac{w_{in}}{h}+\frac{2}{\mathrm{\&pi;}}ln2)$ (formula 5)

Wherein ε ₁and ε ₂be respectively the dielectric constant of upper and lower two layer medium.

Can obtain thus, the total capacitance of SICL transmission line unit in unit is:

$C_{SICL}P=C_{stripline}\left(P-D\right)+\underset{-D/2}{\overset{D/2}{\&Integral;}}\left(C_1+C_2+2C_3\left(\frac{w_{out}-w_{in}}{2}-\sqrt{x\left(D-x\right)}\right)\right)dx$ (formula 6)

Due to the transmission characteristic that SICL is similar to rectangular coaxial line, therefore SICL can be equivalent to outer conductor height and the inner wire width rectangular coaxial line identical with it, and calculate the outer conductor width of the rectangular coaxial line of equivalence by the mode of equivalence capacitance per unit length between the two.If the outer conductor width of rectangular coaxial line to be solved is w _eff, following equation solution can be had:

C _sICLp=C _rCL(w _eff) P (formula 7)

Then w _effcan be provided by following formula:

$w_{eff}=w_{in}+\frac{2h}{\mathrm{\&pi;}}{\coth }^{-1}\left(\exp \right(\frac{\frac{C_{SICL}}{P}-{\mathrm{\&delta;}}_1}{{\mathrm{\&delta;}}_2})-1)$ (formula 8)

${\mathrm{\&delta;}}_1=\frac{2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)w_{in}}{h}$ (formula 9)

${\mathrm{\&delta;}}_2=\frac{4({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)}{\mathrm{\&pi;}}$ (formula 10)

Thus, SICL transmission line can be equivalent to rectangular coaxial line by the line capacitance of equivalence.The accuracy of this equivalent method can be provided, as Fig. 5 by return wave loss parameter SICL transmission line and rectangular coaxial line cascade obtained.Traditional SICL equivalent method is all the substrate integrated coaxial lines based on uniform dielectric, i.e. single-layer medium substrate.And the method is extended to the situation of two-layered medium substrate by the present invention.Fig. 5 gives the mode by " rectangular coaxial line-SICL-rectangular coaxial line " cascade, and as shown in Figure 5, one section of SICL structure two ends are namely in series with rectangular coaxial line cascade system respectively.Emulation mode is utilized to compare the method for the equivalent formulation described in patent of the present invention with traditional equivalent formulation precision.As shown in the figure, the two ends level of SICL transmission line is associated with two sections of rectangular coaxial lines.After the size of fixing SICL, the computing formula provided respectively by this invention draw with the outer conductor width w of the rectangular coaxial line of its cascade _eff, and the outer conductor width w of the equivalent rectangular coaxial line drawn is optimized by CST ^*.The size of the dielectric constant of the two-layered medium substrate of SICL and height, inner wire holding wire is identical with the relevant parameter of rectangular coaxial line.Two-port is respectively Port1 and Port2.

Fig. 6 gives at parameter combinations w _in=1mm, w _out=2mm, h=1mm, P=0.6mm, D=0.4mm, ε ₁=2.2, ε ₂the return loss being respectively 3.55,6.15 and 9.9 compares.Wherein in Fig. 6 parameter list, two lines of the first row represent two layer medium substrate dielectric constant when being respectively 2.2 and 3.55 respectively, provide by patent of the present invention the equivalent rectangular coaxial line width w that formulae discovery draws _eff=1.80mm and optimized the equivalent rectangular coaxial line width w drawn by electromagnetic simulation software CST ^*the return loss plot of=1.74mm.Other two suites lines represent that two layer medium substrate dielectric constant is respectively 2.2,6.15 and 2.2 respectively, provide by patent of the present invention the equivalent rectangular coaxial line width w that formulae discovery draws under 9.9 two kind of combined situation _effwith optimized the equivalent rectangular coaxial line width w drawn by electromagnetic simulation software CST ^*return loss plot.Fig. 7 gives at parameter combinations w _in=0.75mm, w _out=2mm, h=1.5mm, P=0.6mm, D=0.4mm ε ₁=2.2, ε ₂the return loss being respectively 3.55,6.15 and 9.9 compares.As shown in the figure, being compared with optimizing by electromagnetic simulation software CST the return loss characteristic drawn by the equivalent formulation return loss characteristic that patent of the present invention is provided, fully showing the accuracy of the equivalent formulation that patent of the present invention provides.Under the parameter combinations condition that other are optional, also show similar characteristic, just do not add at this and repeat.The accuracy of the equivalent formulation that simulation results show patent of the present invention provides.

Claims (5)

1. the sizing method of the substrate integrated coaxial line of a two-layered medium, it is characterized in that: described two-layered medium is the two-layered medium of differing dielectric constant, based on the transmission characteristic that the SICL of the two-layered medium of differing dielectric constant is similar to rectangular coaxial line, by the SICL of equivalent two-layered medium and the capacitance per unit length of rectangular coaxial line, and according to double-deck rectangular coaxial line and strip line Electric Field Distribution, calculate the approximate expression of the capacitance per unit length of double-deck rectangular coaxial line and strip line respectively, and then draw the size of this two-layered medium of specific dimensions SICL;

Concrete steps are:

1) double-deck substrate integrated coaxial line equivalence is become the cascade of many same units;

2) similar to the magnetic distribution that rectangular coaxial line transmits according to double-layer substrate integration waveguide characteristic, is equivalent to the cascade of strip line and rectangular coaxial line by transmission line unit;

3) electric capacity of two-layered medium substrate integrated coaxial line unit length and the electric capacity expression formula of rectangular coaxial line unit length is calculated respectively;

4) double-deck substrate integrated coaxial line is equivalent to the rectangular coaxial line with same units length electric capacity, thus draws the expression formula of this equivalent rectangular coaxial line width.

2. the sizing method of the substrate integrated coaxial line of two-layered medium as claimed in claim 1, it is characterized in that: its structure of substrate integrated coaxial line of described two-layered medium is by the metallic vias of arranged on both sides, upper and lower double layer of metal floor, the metallic conductor holding wire at center, and be distributed in the different two layer medium substrate composition of dielectric constant between metal floor; Height between upper and lower metal floor 4 is h, and the thickness of two layer medium substrate is h/2; SICL transmission line presents periodic structure, therefore analysis its capacitance per unit length be that a unit that can repeat with its cycle carrys out equivalent analysis.

3. the sizing method of the substrate integrated coaxial line of two-layered medium as claimed in claim 2, is characterized in that: inner wire width is w _in, in the cylindrical hole of both sides metallic vias, horizontal spacing is w in the heart _out, the longitudinal pitch between adjacent metal cylindrical hole is p, and the diameter of cylindrical hole is D; The center of the through hole of a selected metal cylinder is initial point O, take longitudinal direction as x-axis, distance between inner wire and metal cylinder through hole is set to function g (x) of x, in SICL, intercept x value is arbitrary cross section in 0 < x≤p, if x≤D/2 or x > p-D/2, then this cross section is a square-section, and its shape is similar to rectangular coaxial line; If its D/2 < x≤p-D/2, then this cross section is similar to strip line.

4. the sizing method of the substrate integrated coaxial line of two-layered medium as claimed in claim 3, is characterized in that: if segmented in the x direction by SICL transmission line unit, then it can regard the cascade of the infinitesimal transmission line of multistage as; The loss of transmission line is very little, therefore can make R=G=0; Can be obtained by transmission line theory, the total equivalent parallel electric capacity of this SICL transmission line unit in 0≤x < p be namely equivalent to its segment in the x direction after electric capacity sum on every section, even strip line electric capacity sum in rectangular coaxial line electric capacity and D/2 < x≤p-D/2 in x≤D/2 or x > p-D/2.

5. the sizing method of the substrate integrated coaxial line of two-layered medium as claimed in claim 4, is characterized in that: the longitudinal tangent plane electric capacity of rectangular coaxial line of two-layered medium is divided into three parts:

1. the electric capacity C between center conductor and rectangular coaxial line horizontal conductor wall in parallel ₁, C ₂;

2. the edge capacitance C that produces of rectangular coaxial line outer conductor vertical wall ₃;

3. the stray capacitance C that produces with outer conductor horizontal wall of central inner conductor edge ₄, C ₅.

Because central inner conductor thickness is approximately zero, therefore the stray capacitance C that Part III is produced with outer conductor horizontal wall by central inner conductor edge ₄, C ₅negligible; Electric capacity C between center conductor and rectangular coaxial line horizontal conductor wall in parallel ₁, C ₂can be provided by following formula:

$C_1=\frac{2{\mathrm{\&epsiv;}}_1{w}_{in}}{h}$ (formula 1)

$C_2=\frac{2{\mathrm{\&epsiv;}}_2{w}_{in}}{h}$ (formula 2)

$C_3\left(x\right)=\frac{2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)}{\mathrm{\&pi;}}log(1+\coth \frac{\mathrm{\&pi;}g\left(x\right)}{h})$ (formula 3)

Therefore the electric capacity of rectangular coaxial line can be expressed as

C _rCL=C ₁+ C ₂+ 2C ₃(x) (formula 4)

Inner wire thickness is that the electric capacity of the two-layered medium strip line of 0 can be provided by following formula:

$C_{sripline}=2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)(\frac{w_{in}}{h}+\frac{2}{\mathrm{\&pi;}}ln2)$ (formula 5)

Wherein ε ₁and ε ₂be respectively the dielectric constant of upper and lower two layer medium;

Can obtain thus, the total capacitance of SICL transmission line unit in unit is:

$C_{SICL}P=C_{stripline}(P-D)+\underset{-D/2}{\overset{D/2}{\&Integral;}}(C_1+C_2+2C_3(\frac{w_{out}-w_{in}}{2}-\sqrt{x(D-x)}\left)\right)dx$ (formula 6)

Due to the transmission characteristic that SICL is similar to rectangular coaxial line, therefore SICL can be equivalent to outer conductor height and the inner wire width rectangular coaxial line identical with it, and calculate the outer conductor width of the rectangular coaxial line of equivalence by the mode of equivalence capacitance per unit length between the two; If the outer conductor width of rectangular coaxial line to be solved is w _eff, then w _effcan be provided by following formula:

$w_{eff}=w_{in}+\frac{2h}{\mathrm{\&pi;}}{\coth }^{-1}\left(\exp \right(\frac{\frac{C_{SICL}}{P}-{\mathrm{\&delta;}}_1}{{\mathrm{\&delta;}}_2})-1)$ (formula 7)

${\mathrm{\&delta;}}_1=\frac{2({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)w_{in}}{h}$ (formula 8)

${\mathrm{\&delta;}}_2=\frac{4({\mathrm{\&epsiv;}}_1+{\mathrm{\&epsiv;}}_2)}{\mathrm{\&pi;}}$ (formula 9)

Thus, SICL transmission line can be equivalent to rectangular coaxial line by the line capacitance of equivalence.