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 Dimensional Design Method of Substrate Integrated Coaxial Cable

technical field

The invention relates to a size design method of a substrate integrated coaxial cable with wide application prospects, and belongs to the technical field of substrate integrated coaxial cables.

Background technique

Since the late 20th century, with the development of new material technology and integrated circuit technology, it has become possible to realize active solid-state circuits in the microwave and millimeter wave bands. However, in this frequency band, the disadvantages of microstrip circuits, such as large loss, low quality factor, serious radiation and leakage, etc., have become more and more obvious, while traditional metal waveguide components have large volume, difficult processing, and expensive And the difficulty of integrating with planar circuits also restricts its application in high-frequency circuit design. In this case, Substrate Integrated Waveguide (SIW) and Substrate Integrated Coaxial Line (SICL) technologies came into being.

SICL is a new type of waveguide structure based on multi-layer dielectric substrate technology. It is very similar to the traditional rectangular coaxial line in structure. It is composed of a central inner conductor and an outer shielded conductor shell. Like the coaxial cable, the substrate integrated coaxial cable also belongs to the non-dispersive guided wave structure, and its main mode of transmission is the transverse electromagnetic wave (Transverse Electromagnetic Mode, TEM). The working frequency is not related to the cross-sectional size, and the characteristic impedance is only related to the inner and outer conductors The size ratio is related.

Due to the standard printed circuit board (Print Circuit Board, PCB) process, SICL has a planar integration that cannot be compared with ordinary coaxial cables, and can be easily integrated into planar circuit systems. Compared with the microstrip line, due to the relatively complete enclosure, the radiation loss of the substrate integrated coaxial line is lower, and it is not easy to form mutual interference with other circuits. At the same time, because it is completely filled by a dielectric substrate, it has a higher equivalent dielectric constant and can achieve a smaller circuit area. These significant advantages make the substrate integrated coaxial line very suitable for application in modern microwave and millimeter wave circuits, especially in the lower frequency microwave band and broadband applications, which can maximize its advantages of miniaturization, integration and no dispersion. At the same time, the design methods of traditional planar transmission lines such as stripline and microstrip, and coaxial functional devices can be quickly transplanted to SICL technology. However, most of the existing SICL-based microwave device designs use SICL to approximate the stripline, that is, first use the stripline design, then replace it with SICL, and finally use the full-wave simulation software to simulate and optimize the parameters. It is cumbersome and the design efficiency is low.

Contents of the invention

Purpose of the invention: Aiming at the problems existing in the prior art, the present invention proposes a dimension design method of substrate integrated coaxial lines, finds out the equivalent form between SICL and traditional transmission lines, and simplifies the design of microwave and millimeter wave devices based on SICL. Design process, improve design efficiency.

Technical solution: a dimension design method of a substrate integrated coaxial cable, based on the capacitance per unit length of the transmission line, the relationship between the characteristic impedance and the geometric size of the substrate coaxial cable is obtained. By dividing the transmission unit of the substrate-integrated coaxial line, and integrating the capacitance per unit length of the transmission line in the transmission unit, it is equivalent to the unit in the same longitudinal length of the rectangular coaxial line with similar transmission characteristics length capacitance.

Beneficial effects: The size design method of the substrate integrated coaxial cable proposed by the present invention is based on the similar transmission characteristics of SICL and rectangular coaxial cable, and obtains the specific size of SICL through the equivalent unit length capacitance of SICL and rectangular coaxial cable. The size effectively simplifies the design process of SICL-based microwave and millimeter wave devices.

Description of drawings

Fig. 1 is the three-dimensional schematic diagram of SICL structure among the present invention;

Fig. 2 is the schematic diagram of SICL transmission line unit among the present invention;

Fig. 3 is a lumped element circuit model of a section of infinitesimal length Δx transmission line;

Fig. 4 is a schematic diagram of a model for detecting the accuracy of an equivalent formula by means of simulation in the present invention.

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

Figure 1 is a three-dimensional schematic diagram of a SICL structure. It can be seen from the figure that its structure is composed of metal vias 1 arranged on both sides, upper and lower metal base plates 4 , metal conductor signal line 3 in the center, and double-layer dielectric material 2 distributed between the two metal base plates 4 . The height between the upper and lower metal bottom plates 4 is h. It can be seen that the SICL transmission line presents a periodic structure, so when analyzing its capacitance per unit length, it can be equivalently analyzed with a unit whose cycle repeats. Both SICL and rectangular coaxial lines transmit TEM modes and have similar transmission characteristics. Therefore, the design process of SICL-based microwave and millimeter wave devices can be simplified by equating SICL to a rectangular coaxial line of a specific size.

FIG. 2 is a schematic top sectional view of a SICL transmission unit. The width of the inner conductor is w ₁ , the lateral distance between the metal cylindrical through holes on both sides is w ₂ , the longitudinal distance between the metal cylindrical through holes is p, and the radius of the cylindrical through holes is r. As shown in the figure, select the center of the through-hole of a metal cylinder as the origin O, take the longitudinal direction as the x-axis, and set the distance between the inner conductor and the through-hole of the metal cylinder as the function g(x) of x, the following formula can be used express

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

It can be seen from the periodic characteristics of SICL that its characteristics can be analyzed in a single unit, that is, in the region of 0<x≤p. In SICL, intercept any cross-section where the value of x is 0<x≤p. If x≤r or x>p-r, the cross-section is a rectangular cross-section, and its shape is similar to the traditional rectangular coaxial line. If its r<x≤p-r, the section is similar to a conventional stripline.

If the SICL transmission line unit is subdivided in the x direction, it can be regarded as a cascade of multiple infinitesimal transmission lines. Figure 3 is a lumped element circuit model of a transmission line. Among them, R, L, G, and C are the quantities of unit length Δx, which are defined as follows:

R represents the series resistance of the unit length of the two conductors;

L represents the series inductance of the unit length of the two conductors;

G represents the parallel conductance per unit length;

C represents the parallel capacitance per unit length.

In many practical situations, the loss of the transmission line is very small, so R=G=0 can be used to simplify the model to a model that only includes series inductors and parallel capacitors. It can be obtained from the transmission line theory that the total equivalent parallel capacitance of the SICL transmission line unit within 0≤x<p is equivalent to the sum of its capacitance on each segment after subdivision in the x direction, that is, the unit capacitance is 0≤x<p Points within <p.

The inner conductor of SICL is a flat layer of metal with a thickness of approximately zero. The capacitance per unit length of a rectangular coaxial line with an inner conductor thickness of 0 varies with the distance g(x) between the inner conductor and the outer conductor, that is, the metal cylindrical through hole, and can be given by the 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)

where ε is the permittivity of free space. The capacitance per unit length of a stripline with an inner conductor thickness of 0 can be given by:

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

From this, it can be obtained that the total capacitance of the SICL transmission line unit in the unit is:

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

in

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

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

Since SICL has similar transmission characteristics to rectangular coaxial lines, SICL can be equivalent to a rectangular coaxial line with the same outer conductor height and inner conductor width, and can be calculated by equivalent unit length capacitance between the two Equivalent outer conductor width of a rectangular coaxial cable. Suppose the outer conductor width of the rectangular coaxial line to be solved is w ₃ , then w ₃ can be given by the 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 a SICL transmission line can be given by:

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

Among them, c represents the speed of light in vacuum, and ε _r is the relative permittivity of the dielectric material in the SICL transmission line.

Therefore, the SICL transmission line can be equivalent to a rectangular coaxial line through an equivalent line capacitance. This equivalent accuracy can be given by the return loss parameter obtained by cascading the SICL transmission line with the rectangular coaxial line. The traditional SICL equivalent method is to use the characteristic that the first high-order mode of SICL is the same as the cut-off frequency of the main mode of SIW, and directly apply the equivalent formula that the spacing between two rows of through holes in SIW is equivalent to the width of a rectangular waveguide to the SICL equivalent For the rectangular coaxial line. Figure 4 shows the method of comparing the accuracy of the equivalent formula described in the patent of the present invention with the traditional equivalent formula by means of the cascading method of "rectangular coaxial line-SICL-rectangular coaxial line". As shown in the figure, two rectangular coaxial lines 5 are cascaded at both ends of the SICL transmission line 6 . After fixing the size of SICL, the outer conductor width w ₃ of the rectangular coaxial line cascaded with it obtained by the calculation formula given by the invention, and the rectangular coaxial line cascaded with it obtained by the calculation formula of the traditional equivalent method The outer conductor width w ₄ . The dielectric constant and height of the dielectric material of SICL, and the size of the inner conductor signal line are the same as the corresponding parameters of the rectangular coaxial line. The two ports are Port 1 and Port 2 respectively.

The attached figure shows the return loss comparison when the parameter combination w ₁ =1 mm, w ₂ =2 mm, h=1 mm, p=0.6 mm, r=0.2 mm. Among them, the solid line represents the equivalent rectangular coaxial line width w ₃ = 1.8 mm calculated by the formula given by the patent of the present invention, and the dotted line represents the equivalent rectangular coaxial line calculated by the traditional formula of the cascaded two sides. The axis width w ₄ =1.7 mm, and the dotted line represents the equivalent rectangular coaxial line width w _equal =1.78 mm optimized by the electromagnetic simulation software CST. The attached figure shows the return loss comparison when the parameter combination w ₁ =0.75mm, w ₂ =2mm, h=1.5mm, p=0.6mm, r=0.2mm. Among them, the solid line represents the equivalent rectangular coaxial line width w ₃ = 1.9mm calculated by the formula given by the patent of the present invention, and the dotted line represents the equivalent rectangular coaxial line calculated by the traditional formula of the cascaded two sides. The axis width w ₄ =1.7 mm, and the dotted line represents the equivalent rectangular coaxial line width w _equal =1.75 mm optimized by the electromagnetic simulation software CST. As shown in the figure, the equivalent formula given by the patent of the present invention brings lower return loss characteristics, which is closer to the return loss result obtained by the simulation software optimization. Similar characteristics are also shown under other optional parameter combination conditions, which will not be repeated here. The simulation results verify the superiority of the equivalent formula given by the patent of the present invention over the traditional equivalent formula.

Claims (5)

1. A dimension design method of a substrate integrated coaxial cable, characterized in that: based on the capacitance per unit length of the transmission line, the relational expression between the characteristic impedance of the substrate coaxial cable and the geometric dimension is obtained; The transmission unit of the line is divided, and the capacitance per unit length of the transmission line in the transmission unit is integrated, and it is equivalent to the capacitance per unit length of the transmission line with similar transmission characteristics in the same longitudinal length. 2. The dimension design method of substrate integrated coaxial cable as claimed in claim 1, characterized in that: (1) The substrate-integrated coaxial cable is equivalent to a cascade of multiple identical transmission line units, and the transmission line unit is modeled as a lumped parameter circuit; (2) According to the similar characteristics of the electromagnetic field transmitted by the substrate integrated coaxial line and the rectangular coaxial line, the different sections in the transmission line unit are equivalent to the cascade of the rectangular coaxial line or the strip line, and the calculated substrate coaxial line The relationship between the average unit length capacitance of the line and the geometric size; (3) The unit of the substrate-integrated coaxial cable is equivalent to a rectangular coaxial cable having the same unit length capacitance as the unit, and an equivalent rectangular coaxial cable is obtained; (4) Calculate the capacitance per unit length of the equivalent rectangular coaxial line, and substitute into the relationship between the average capacitance per unit length of the coaxial line of the substrate and the geometric dimension, and obtain the geometrical dimension of the coaxial line of the substrate. 3. The dimensional design method of the substrate integrated coaxial cable according to claim 2, characterized in that: the width of the central signal line of the equivalent rectangular coaxial cable is the same as that of the central signal line of the substrate integrated coaxial cable , the height of the outer conductor is the same as that of the original substrate integrated coaxial line. 4. The dimensional design method of the substrate-integrated coaxial cable as claimed in claim 1, characterized in that: the width of the inner conductor of the substrate-integrated coaxial cable is w ₁ , and the lateral distance between the metal cylindrical through-holes on both sides is w ₂ , the longitudinal distance between the metal cylindrical through holes is p, the radius of the cylindrical through holes is r; the center of a metal cylindrical through hole is selected as the origin O, and the vertical direction is the x axis, and the distance between the inner conductor and the metal cylindrical through hole is The distance between is set to the function g(x) of x; from the periodic characteristics of SICL, its characteristics can be analyzed in a single unit, that is, in the area of 0<x≤p; the value of x is intercepted in SICL to be 0 Any cross section in <x≤p, if x≤r or x>pr, then the section is a rectangular section, its shape is similar to the traditional rectangular coaxial line; if r<x≤pr, then the section is similar over conventional stripline. 5. The dimensional design method of substrate integrated coaxial line as claimed in claim 4, characterized in that: if the SICL transmission line unit is subdivided in the x direction, it can be regarded as a cascade of multi-section infinitesimal transmission lines; The total equivalent parallel capacitance of the SICL transmission line unit within 0≤x<p is equivalent to the sum of its capacitance on each segment after subdivision in the x direction, that is, the integral of the unit capacitance within 0≤x<p; The inner conductor of SICL is a flat layer of metal, and its thickness is approximately 0; the unit length capacitance of a rectangular coaxial line with an inner conductor thickness of 0 varies with the distance g(x) between the inner conductor and the outer conductor, that is, the metal cylindrical through hole changes, and can be given by: $C\left(x\right)=\frac{4\mathrm{\&epsiv;}{\mathrm{\&omega;}}_1}{h}+4\mathrm{\&epsiv;}\left[\frac{2}{\mathrm{\&pi;}}(1+\coth \frac{\mathrm{\&pi;g}\left(x\right)}{h})\right]$ (Formula 1) where ε is the permittivity of free space; the capacitance per unit length of a stripline with an inner conductor thickness of 0 can be given by: $C_1=4\mathrm{\&epsiv;}[\frac{w_1}{h}+0.44127]$ (Formula 2) From this, it can be obtained that the total capacitance of the SICL transmission line unit in the unit is: $C=2\underset{0}{\overset{r}{\&Integral;}}({\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2\&CenterDot;\ln (1+\coth \left(\frac{\mathrm{\&pi;}(\frac{w_2}{2}-\frac{w_1}{2}-\sqrt{2\mathrm{r\; x}-x^2})}{h}\right)))\mathrm{dx}+4\mathrm{\&epsiv;}(\frac{w_1}{h}+0.44127)(p-2r)$ (Formula 3) in ${\mathrm{\&delta;}}_1=\frac{4\mathrm{\&epsiv;}{w}_1}{h}$ (Formula 4) ${\mathrm{\&delta;}}_2=\frac{8\mathrm{\&epsiv;}}{\mathrm{\&pi;}}$ (Formula 5) Since SICL has similar transmission characteristics to rectangular coaxial lines, SICL can be equivalent to a rectangular coaxial line with the same outer conductor height and inner conductor width, and can be calculated by equivalent unit length capacitance between the two The width of the outer conductor of the equivalent rectangular coaxial line; if the width of the outer conductor of the rectangular coaxial line to be solved is w ₃ , then w ₃ can be given by the 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 a SICL transmission line can be given by: $Z_0=\frac{1}{C}\frac{{\mathrm{\&epsiv;}}_r}{c}$ (Formula 7) Among them, c represents the speed of light in vacuum, and ε _r is the relative permittivity of the dielectric material in the SICL transmission line.