CN104538717A - Dimension design method for substrate integrated coaxial line - Google Patents

Abstract

The invention discloses a dimension design method for a substrate integrated coaxial line. According to the design method, on the basis of the transmission line capacitance per unit length, the relational expression between the characteristic impedance and the physical dimension of the substrate coaxial line is obtained. A transmission unit of the substrate integrated coaxial line is divided, the transmission line capacitance per unit length in the transmission unit is subjected to integration, and the transmission line capacitance per unit length is equivalent to be the capacitance per unit length of a rectangle coaxial line with the transmission characteristic being similar to that of the substrate coaxial line within the same longitudinal length. Consequently, an equivalent dimension formula of the substrate integrated coaxial line can be obtained. By the adoption of the method, the physical dimension of the substrate coaxial line can be obtained directly according to the needed characteristic impedance.

Description

A kind of sizing method of substrate integrated coaxial line

Technical field

The present invention relates to the sizing method of a kind of application prospect substrate integrated coaxial line widely, belong to substrate integrated coaxial line technology 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 (Substrate Integrated Waveguide, SIW) and substrate integrated coaxial line (Substrate Integrated Coaxial Line, 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, its transmission holotype is transverse electro-magnetic wave (Transverse Electromagnetic Mode, 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 (Print Circuit Board, 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, the present invention proposes a kind of sizing method of substrate integrated coaxial line, find out the equivalents between SICL and conventional transmission line, simplify the design cycle of the microwave and millimeter wave device based on SICL, promote design efficiency.

Technical scheme: a kind of sizing method of substrate integrated coaxial line, based on transmission line capacitance per unit length, obtains the relational expression between the characteristic impedance of substrate coaxial line and physical dimension.By dividing the transmission unit of substrate integrated coaxial line, and integration is carried out to the transmission line capacitance per unit length in transmission unit, and be equivalent to the capacitance per unit length in identical longitudinal length of the rectangular coaxial line similar with its transmission characteristic.

Beneficial effect: the sizing method of the substrate integrated coaxial line that the present invention proposes, based on the transmission characteristic that SICL is similar to rectangular coaxial line, by the capacitance per unit length of equivalent SICL and rectangular coaxial line, draw the size of specific dimensions SICL, effectively simplify 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 SICL structure in the present invention;

Fig. 2 is the schematic diagram of SICL transmission line unit 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 model schematic of the precision being detected equivalent formulation in the present invention by simulation means.

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 base plate 4, the metallic conductor holding wire 3 at center, and the two-layered medium material 2 be distributed between double layer of metal base plate 4 forms.Height between upper and lower double layer of metal base plate 4 is h.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.All transmitting TEM mould in SICL and rectangular coaxial line, there is similar transmission characteristic, therefore by SICL 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 ₁, between the metal cylinder through hole of both sides, horizontal spacing is w ₂, the longitudinal pitch between metal cylinder through hole is p, and the radius of cylindrical hole is r.As shown in the figure, the center of the through hole of a selected metal cylinder is initial point O, take longitudinal direction as x-axis, the distance between inner wire and metal cylinder through hole is set to function g (x) of x, can be represented by the formula

$g\left(x\right)=\frac{w_2}{2}-\frac{w_1}{2}-\sqrt{2\mathrm{rx}-x^2}$ (formula 8)

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≤r or x > p-r, then this cross section is a square-section, and its shape is similar to traditional rectangular coaxial line.If its r < x≤p-r, 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 Δ x, 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, i.e. the integration of specific capacitance in 0≤x < p.

The inner wire of SICL is the metal that one deck is flat, and its thickness is approximately 0.Inner wire thickness is that the capacitance per unit length of the rectangular coaxial line of 0 changes with the distance g (x) between inner wire and outer conductor and metal cylinder through hole, and can be provided by following formula:

$C\left(x\right)=\frac{4\mathrm{\&epsiv;}{\mathrm{\&omega;}}_1}{h}+4\mathrm{\&epsiv;}\left[\frac{2}{\mathrm{\&pi;}}\ln (1+\coth \frac{\mathrm{\&pi;g}\left(x\right)}{h})\right]$ (formula 1)

Wherein ε is the dielectric constant of free space.Inner wire thickness is that the capacitance per unit length of the strip line of 0 can be provided by following formula:

$C_1=4\mathrm{\&epsiv;}[\frac{w_1}{h}+0.44127]$ (formula 2)

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

$C=2\underset{0}{\overset{r}{\&Integral;}}({\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2\&CenterDot;\ln (1+\coth \left(\frac{\mathrm{\&pi;}(\frac{w_2}{2}-\frac{w_1}{2}-\sqrt{2\mathrm{rx}-x^2})}{h}\right)))\mathrm{dx}+4\mathrm{\&epsiv;}(\frac{w_1}{h}+0.44127)(p-2r)$ (formula 3)

Wherein

${\mathrm{\&delta;}}_1=\frac{4\mathrm{\&epsiv;}{w}_1}{h}$ (formula 4)

${\mathrm{\&delta;}}_2=\frac{8\mathrm{\&epsiv;}}{\mathrm{\&pi;}}$ (formula 5)

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 ₃, then w ₃can be provided by following formula:

$w_3=w_1+\frac{2h}{\mathrm{\&pi;}}{\coth }^{-1}(\exp \left(\frac{\frac{C}{p}-{\mathrm{\&delta;}}_1}{{\mathrm{\&delta;}}_2}\right)-1)$ (formula 6)

The characteristic impedance value of SICL transmission line can be provided by following formula:

$Z_0=\frac{1}{C}\frac{{\mathrm{\&epsiv;}}_r}{c}$ (formula 7)

Wherein, c represents the light velocity in vacuum, ε _rfor the relative dielectric constant of SICL transmission line medium material.

Thus, SICL transmission line can be equivalent to rectangular coaxial line by the line capacitance of equivalence.The accuracy of this equivalence can be provided by return wave loss parameter SICL transmission line and rectangular coaxial line cascade obtained.Traditional SICL equivalent method is the characteristic utilizing first of SICL higher mode identical with the cut-off frequency of the main mould of SIW, and equivalent formulation SIW two exhausting hole spacing being equivalent to rectangular waveguide width is applied directly to SICL and is equivalent to rectangular coaxial line.Fig. 4 gives the mode by " rectangular coaxial line-SICL-rectangular coaxial line " cascade, utilizes emulation mode 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 6 is associated with two sections of rectangular coaxial lines 5.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 ₃, and traditional equivalent method computing formula draws the outer conductor width w with the rectangular coaxial line of its cascade ₄.The size of the dielectric constant of the dielectric material of SICL and height, inner wire holding wire is identical with the relevant parameter of rectangular coaxial line.Two-port is respectively Port 1 and Port 2.

Drawings illustrate at parameter combinations w ₁=1mm, w ₂return loss when=2mm, h=1mm, p=0.6mm, r=0.2mm compares.What wherein solid line represented both sides cascade provides by patent of the present invention the equivalent rectangular coaxial line width w that formulae discovery draws ₃=1.8mm, the equivalent rectangular coaxial line width w calculated by traditional formula of represented by dotted arrows both sides cascade ₄=1.7mm, dotted lines representative optimizes by electromagnetic simulation software CST the equivalent rectangular coaxial line width w drawn _equal=1.78mm.Drawings illustrate at parameter combinations w ₁=0.75mm, w ₂return loss when=2mm, h=1.5mm, p=0.6mm, r=0.2mm compares.What wherein solid line represented both sides cascade provides by patent of the present invention the equivalent rectangular coaxial line width w that formulae discovery draws ₃=1.9mm, the equivalent rectangular coaxial line width w calculated by traditional formula of represented by dotted arrows both sides cascade ₄=1.7mm, dotted lines representative optimizes by electromagnetic simulation software CST the equivalent rectangular coaxial line width w drawn _equal=1.75mm.As shown in the figure, the equivalent formulation that patent of the present invention provides brings lower return loss characteristic, more close to the return loss result drawn by simulation software optimization.Under the parameter combinations condition that other are optional, also show similar characteristic, just do not add at this and repeat.The equivalent formulation that simulation results show patent of the present invention provides is relative to the superiority of traditional equivalent formulation.

Claims (5)

1. a sizing method for substrate integrated coaxial line, is characterized in that: based on transmission line capacitance per unit length, obtains the relational expression between the characteristic impedance of substrate coaxial line and physical dimension; By dividing the transmission unit of substrate integrated coaxial line, and integration is carried out to the transmission line capacitance per unit length in transmission unit, and be equivalent to the capacitance per unit length in identical longitudinal length of the transmission line line similar with its transmission characteristic.

2. the sizing method of substrate integrated coaxial line as claimed in claim 1, is characterized in that:

(1) equivalence of substrate integrated coaxial line is become the cascade of multiple same transmission line unit, transmission line Modelon Modeling becomes lumped circuit;

(2) according to substrate integrated coaxial line and rectangular coaxial line transmit the similar characteristic of electromagnetic field, different cross section in transmission line unit is equivalent to the cascade of rectangular coaxial line or strip line, calculates the relational expression between the mean unit length electric capacity of substrate coaxial line and physical dimension;

(3) unit of substrate integrated coaxial line is equivalent to the rectangular coaxial line with this unit with equal unit length electric capacity, obtains equivalent rectangular coaxial line;

(4) calculate the capacitance per unit length of equivalent rectangular coaxial line, and substitute into the relational expression between substrate coaxial line mean unit length electric capacity and physical dimension, draw the physical dimension of substrate coaxial line.

3. the sizing method of substrate integrated coaxial line as claimed in claim 2, it is characterized in that: described equivalent rectangular coaxial line, the center signal line width of its center holding wire same substrate integrated coaxial line is identical, and its outer conductor height is identical with the height of former substrate integrated coaxial line.

4. as right wants the sizing method of the substrate integrated coaxial line as described in 1, it is characterized in that: make substrate integrated coaxial line inner wire width be w ₁, between the metal cylinder through hole of both sides, horizontal spacing is w ₂, the longitudinal pitch between metal cylinder through hole is p, and the radius of cylindrical hole is r; The center of the through hole of a selected metal cylinder is initial point O, take longitudinal direction as x-axis, the 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≤r or x > p-r, then this cross section is a square-section, and its shape is similar to traditional rectangular coaxial line; If its r < x≤p-r, then this cross section is similar to traditional strip line.

5. the sizing method of substrate integrated coaxial line as claimed in claim 4, 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 total equivalent parallel electric capacity of 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, i.e. the integration of specific capacitance in 0≤x < p;

The inner wire of SICL is the metal that one deck is flat, and its thickness is approximately 0; Inner wire thickness is that the capacitance per unit length of the rectangular coaxial line of 0 changes with the distance g (x) between inner wire and outer conductor and metal cylinder through hole, and can be provided by following formula:

$C\left(x\right)=\frac{4\mathrm{\&epsiv;}{\mathrm{\&omega;}}_1}{h}+4\mathrm{\&epsiv;}\left[\frac{2}{\mathrm{\&pi;}}(1+\coth \frac{\mathrm{\&pi;g}\left(x\right)}{h})\right]$ (formula 1)

Wherein ε is the dielectric constant of free space; Inner wire thickness is that the capacitance per unit length of the strip line of 0 can be provided by following formula:

$C_1=4\mathrm{\&epsiv;}[\frac{w_1}{h}+0.44127]$ (formula 2)

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

$C=2\underset{0}{\overset{r}{\&Integral;}}({\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2\&CenterDot;\ln (1+\coth \left(\frac{\mathrm{\&pi;}(\frac{w_2}{2}-\frac{w_1}{2}-\sqrt{2\mathrm{rx}-x^2})}{h}\right)))\mathrm{dx}+4\mathrm{\&epsiv;}(\frac{w_1}{h}+0.44127)(p-2r)$ (formula 3)

Wherein

${\mathrm{\&delta;}}_1=\frac{4\mathrm{\&epsiv;}{w}_1}{h}$ (formula 4)

${\mathrm{\&delta;}}_2=\frac{8\mathrm{\&epsiv;}}{\mathrm{\&pi;}}$ (formula 5)

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 ₃, then w ₃can be provided by following formula:

$w_3=w_1+\frac{2h}{\mathrm{\&pi;}}{\coth }^{-1}(\exp \left(\frac{\frac{C}{p}-{\mathrm{\&delta;}}_1}{{\mathrm{\&delta;}}_2}\right)-1)$ (formula 6)

The characteristic impedance value of SICL transmission line can be provided by following formula:

$Z_0=\frac{1}{C}\frac{{\mathrm{\&epsiv;}}_r}{c}$ (formula 7)

Wherein, c represents the light velocity in vacuum, ε _rfor the relative dielectric constant of SICL transmission line medium material.