CN117870769A - Extraction method of effective dielectric constant of substrate and roughness of conductor - Google Patents
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Abstract
The invention provides an extraction method of the effective dielectric constant of a substrate and the roughness of a conductor, which directly obtains the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation or software simulation by utilizing the characteristics of an odd mode and an even mode of a coupling microstrip line model. The method can obtain the effective dielectric constant of the substrate without measuring the roughness of the conductor, and avoids the adverse effect of inaccuracy in roughness measurement on the measurement of the effective dielectric constant of the substrate; and because the roughness is measured without adopting a traditional measuring method, such as slicing or profilometer, the measuring time is greatly shortened, and the production efficiency is improved. Meanwhile, the extraction method of the effective dielectric constant and the roughness of the conductor can also solve the problem of multiple solutions of the single-ended transmission line method in the parameter extraction process.
Description
Technical Field
The invention relates to the field of integrated circuits, in particular to a method for extracting the effective dielectric constant of a substrate and the roughness of a conductor.
Background
Measuring the effective dielectric constant of the substrate material is critical to package design, integrated circuit design, and PCB design. The effective dielectric constant can affect the impedance matching of the signal lines and determine the propagation speed and phase delay of the signal.
The transmission line method is one of the methods for obtaining the effective dielectric constant of the substrate material at present. The transmission line method can obtain the effective dielectric constant of the substrate material by measuring the phase delay value of the radio frequency signal transmitted in the microstrip line. Specifically, as shown in fig. 1A, which is a schematic diagram of a microstrip line (microstrip line) model, a microstrip line 10 with a length L is disposed on an upper surface of a substrate 11, a lower surface of the substrate 11 is grounded, a radio frequency signal is input from one end of the microstrip line 10 and output from the other end of the microstrip line 10, and an effective dielectric constant of the substrate 11 can be obtained by measuring a phase delay value of the radio frequency signal transmitted in the microstrip line 10.
However, the roughness of the surface of the microstrip line 10 contacting the substrate 11 has a large influence on the effective dielectric constant, as shown in fig. 1B, which is a schematic diagram of the relationship between the Root Mean Square (RMS) of the surface roughness of the microstrip line 10 contacting the substrate 11 and the effective dielectric constant of the substrate 11, wherein the abscissa is the frequency of the radio frequency signal, the ordinate is the effective dielectric constant of the substrate, and the line A, B, C, D is the root mean square of the surface roughness of the microstrip line 10 contacting the substrate 11, which is the relationship between the frequency of the radio frequency signal and the effective dielectric constant of the substrate corresponding to the 0.5 micron, 0.7 micron, 1.5 micron and 3.0 microns, in which the parameters of the microstrip line 10 and the substrate 11 are not changed, and only the roughness of the surface of the microstrip line 10 contacting the substrate 11 is changed, and as can be seen from fig. 1B, the larger the roughness of the surface of the microstrip line 10 contacting the substrate 11 is the larger the effective dielectric constant of the substrate 11. Therefore, in order to accurately extract the effective dielectric constant of the substrate 11, it is necessary to accurately measure the roughness of the surface of the microstrip line 10 in contact with the substrate 11, and thus, in the conventional transmission line method, the roughness value of the copper foil is obtained first, and then the effective dielectric constant can be accurately extracted, but inaccuracy in the roughness measurement may adversely affect the measurement of the effective dielectric constant of the substrate.
Therefore, how to accurately extract the effective dielectric constant of the substrate and the roughness of the surface of the microstrip line in contact with the substrate are one of the important points of current research.
Disclosure of Invention
The invention aims to solve the technical problem of accurately extracting the effective dielectric constant of a substrate and the roughness of the surface of a microstrip line contacted with the substrate.
In order to solve the above problems, the present invention provides a method for extracting an effective dielectric constant of a substrate and roughness of a conductor, comprising: setting a coupling microstrip line model, wherein the coupling microstrip line model comprises a substrate and symmetrical coupling microstrip lines arranged on the surface of the substrate; and directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation or software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupling microstrip line model.
In one embodiment, the method for directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor by numerical calculation by utilizing the odd mode characteristic and the even mode characteristic of the coupled microstrip line model comprises the following steps: the method comprises the steps of carrying out a first treatment on the surface of the Obtaining a first equation of the coupling microstrip line model in an even mode, wherein the unknown number of the first equation is the phase shift of the coupling microstrip line model in the even mode, the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor; obtaining a second equation of the coupling microstrip line model in an odd mode, wherein the unknown number of the second equation is the phase shift of the coupling microstrip line model in the odd mode, the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor; measuring and obtaining the phase shift of the coupling microstrip line model in an even mode, and substituting the phase shift into the first equation to form a third equation with the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor as unknowns; measuring and obtaining the phase shift of the coupling microstrip line model in an odd mode, and substituting the phase shift into the second equation to form a fourth equation with the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor as unknowns; and obtaining the effective dielectric constant of the substrate of the coupling microstrip line model and the roughness of the conductor according to the third equation and the fourth equation.
In an embodiment, the method for obtaining the first equation of the coupled microstrip line model in the even mode comprises: obtaining a relation of relative effective dielectric constants of the substrate of the coupled microstrip line model in an even mode without considering roughness of the conductor:
wherein ε ee For the relative effective dielectric constant epsilon of the substrate in the even mode of the coupled microstrip line model without regard to the roughness of the conductor r Is the effective dielectric constant of the substrate, F e (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
wherein w is the width of one microstrip line in the symmetrical coupling microstrip line, h is the height of the substrate, and s is the distance between two microstrip lines in the symmetrical coupling microstrip line;
obtaining u and g according to the coupling microstrip line model, and substituting the u and g into the relational expression to obtain a relational expression between the relative effective dielectric constant of the substrate and the effective dielectric constant of the substrate when the coupling microstrip line model does not consider the roughness of the conductor in an even mode;
providing a relation between the relative effective dielectric constant of the substrate when the roughness of the conductor is not considered in the coupling microstrip line model in the even mode and the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the coupling microstrip line model in the even mode:
Wherein ε ee_rough For the relative effective dielectric constant of the substrate when considering the roughness of the conductor in the even mode of the coupled microstrip line model, R is the roughness of the conductor;
providing a relation between a phase shift of the coupled microstrip line model in an even mode and a relative effective dielectric constant when considering roughness of the conductor:
wherein phi is ee The phase shift of the coupling microstrip line model in the even mode is that c is the speed of light, f is the frequency of a radio frequency signal input into the coupling microstrip line model, and L is the length of the symmetrical coupling microstrip line;
the first equation is obtained according to the above relation.
The method for obtaining the second equation of the coupled microstrip line model in the odd mode comprises the following steps:
obtaining a relation of relative effective dielectric constants of the substrate of the coupled microstrip line model in an odd mode without considering roughness of the conductor:
wherein ε eo For the relative effective dielectric constant of the substrate, epsilon, of the coupled microstrip line model in odd mode without regard to the roughness of the conductor r Is the effective dielectric constant of the substrate, F o (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
p(g)＝exp(-0.745g 0.295 )/cosh(g 0.68 )
q(g)＝exp(-1.366-g)
wherein w is the width of one microstrip line in the symmetrical coupling microstrip line, h is the height of the substrate, and s is the distance between two microstrip lines in the symmetrical coupling microstrip line;
Obtaining u and g according to the coupling microstrip line model, and substituting the u and g into the relational expression to obtain a relational expression between the relative effective dielectric constant of the substrate and the effective dielectric constant of the substrate when the roughness of the conductor is not considered in the odd mode of the coupling microstrip line model;
providing a relation between the relative effective dielectric constant of the substrate when the roughness of the conductor is not considered in the odd mode of the coupling microstrip line model and the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the odd mode of the coupling microstrip line model:
wherein ε eo_rough For the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the odd mode of the coupling microstrip line model, R is the roughness of the conductor;
providing a relationship between the phase shift of the coupled microstrip line model in odd mode and the relative effective dielectric constant of the coupled microstrip line model when considering the roughness of the conductor:
wherein phi is eo The phase shift of the coupling microstrip line model in the odd mode is that c is the speed of light, f is the frequency of a radio frequency signal input into the coupling microstrip line model, and L is the length of the symmetrical coupling microstrip line;
the second equation is obtained according to the above relation.
In an embodiment, the step of measuring the phase shift of the coupled microstrip line model in the even mode comprises: and obtaining the phase shift of the coupling microstrip line model in the even mode by measuring the scattering parameter of the coupling microstrip line model in the even mode.
In an embodiment, the step of measuring the phase shift of the coupled microstrip line model in the odd mode comprises: and obtaining the phase shift of the coupling microstrip line model in the odd mode by measuring the scattering parameter of the coupling microstrip line model in the odd mode.
In an embodiment, the method for directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor by software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupled microstrip line model comprises the following steps: setting simulation parameters, wherein the simulation parameters comprise an effective dielectric constant of a substrate, a scanning range of the effective dielectric constant, a scanning step of the effective dielectric constant, a roughness of a conductor, a scanning range of the roughness and a scanning step of the roughness; simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an even mode to obtain a phase shift parameter set of the coupling microstrip line model in the even mode; simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a phase shift parameter set of the coupling microstrip line model in the odd mode; testing the real object of the coupling microstrip line model in an even mode and an odd mode to obtain the actual measurement phase shift of the real object of the coupling microstrip line model in the even mode and the odd mode; in a phase shift parameter set of the coupling microstrip line model in an even mode, obtaining a phase shift equal to or different from an actual measurement phase shift in the even mode by a set value, and extracting an effective dielectric constant and roughness corresponding to the phase shift as a first set; in the phase shift parameter set of the coupling microstrip line model in the odd mode, obtaining a phase shift equal to or different from the actually measured phase shift in the odd mode by a set value, and extracting an effective dielectric constant and roughness corresponding to the phase shift as a second set; and performing an intersection operation on the first set and the second set to obtain the effective dielectric constant of the substrate and the roughness of the conductor of the coupled microstrip line model. Roughness of roughness
In an embodiment, in the even mode, the step of simulating the coupled microstrip line model with the effective dielectric constant and the roughness as variables according to the simulation parameters to obtain a phase shift parameter set of the coupled microstrip line model in the even mode specifically includes: simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an even mode to obtain a scattering parameter set of the coupling microstrip line model in the even mode, and obtaining a phase shift parameter set according to the scattering parameter set; the step of simulating the coupled microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a phase shift parameter set of the coupled microstrip line model in the odd mode specifically comprises the following steps: and simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a scattering parameter set of the coupling microstrip line model in the odd mode, and obtaining a phase shift parameter set according to the scattering parameter set.
In one embodiment, the set value ranges from [ -1 °,1 ° ].
In an embodiment, the symmetrically coupled microstrip line is a side-coupled symmetrically coupled microstrip line.
The method for obtaining the effective dielectric constant of the substrate and the roughness of the conductor provided by the embodiment of the invention directly obtains the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation or software simulation by utilizing the characteristics of the odd mode and the even mode of the coupled microstrip line model. The method can obtain the effective dielectric constant of the substrate without measuring the roughness of the conductor, and avoids the adverse effect of inaccuracy in roughness measurement on the measurement of the effective dielectric constant of the substrate; and because the roughness is measured without adopting a traditional measuring method, such as slicing or profilometer, the measuring time is greatly shortened, and the production efficiency is improved. Meanwhile, the extraction method of the effective dielectric constant and the roughness of the conductor can also solve the problem of multiple solutions of the single-ended transmission line method in the parameter extraction process.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings that are required to be used in the description of the embodiments will be briefly described below. It is evident that the drawings in the following description are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1A is a schematic diagram of a microstrip line model;
FIG. 1B is a graph showing the relationship between the root mean square of the surface roughness of the surface of the microstrip line in contact with the substrate and the effective dielectric constant of the substrate;
FIG. 2 is a schematic diagram showing steps of a method for extracting effective dielectric constant and roughness of a conductor of a substrate according to an embodiment of the present invention;
fig. 3 is a schematic perspective view of a coupled microstrip line model provided by the present invention;
FIG. 4 is a schematic diagram of the electric field lines and magnetic field lines of the coupled microstrip line model of the present invention in an even mode;
FIG. 5 is a schematic diagram of the electric field lines and magnetic field lines of the coupled microstrip line model of the present invention in odd mode;
FIG. 6 is a schematic representation of the invention for measuring scattering parameters by a vector network analyzer;
fig. 7 is a schematic diagram illustrating a method for extracting effective dielectric constant and roughness of a conductor according to another embodiment of the present invention.
Detailed Description
The following describes in detail an embodiment of a method for extracting an effective dielectric constant of a substrate and a roughness of a conductor according to the present invention with reference to the accompanying drawings.
The method for extracting the effective dielectric constant of the substrate and the roughness of the conductor provided by the embodiment of the invention comprises the following steps: setting a coupling microstrip line model, wherein the coupling microstrip line model comprises a substrate and symmetrical coupling microstrip lines arranged on the surface of the substrate; and directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation or software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupling microstrip line model.
The method can obtain the effective dielectric constant of the substrate without measuring the roughness of the conductor, and avoids the adverse effect of inaccuracy in roughness measurement on the measurement of the effective dielectric constant of the substrate; and because the roughness is measured without adopting a traditional measuring method, such as slicing or profilometer, the measuring time is greatly shortened, and the production efficiency is improved. Meanwhile, the method for extracting the effective dielectric constant and the roughness of the conductor can also solve the problem of multiple solutions of the single-ended transmission line method in the parameter extraction process.
As an example, an embodiment of the present invention provides a method for directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation by using the odd mode characteristic and the even mode characteristic of the coupled microstrip line model.
Fig. 2 is a schematic step diagram of a method for extracting an effective dielectric constant and a roughness of a conductor of a substrate according to an embodiment of the invention, referring to fig. 2, the method includes:
in step S20, a coupling microstrip line model 300 is provided, where the coupling microstrip line model 300 includes a substrate 301 and symmetrical coupling microstrip lines provided on the surface of the substrate 301.
Please refer to fig. 3, which is a schematic perspective view of a coupled microstrip model 300, wherein a symmetrical coupled microstrip (coupled microstrp line) is disposed on a surface of a substrate 301. One surface of the substrate 301 facing away from the symmetrically coupled microstrip line is grounded, and the height of the substrate 301 is h. The symmetrical coupling microstrip line comprises a first microstrip line 302 and a second microstrip line 303 which are arranged on the surface of the substrate 301 in parallel, the widths of the first microstrip line 302 and the second microstrip line 303 are the same as w, the lengths of the first microstrip line 302 and the second microstrip line 303 are the same as L, and the distance between the first microstrip line 302 and the second microstrip line 303 is s.
In this embodiment, the symmetrical coupling microstrip line is a side coupling symmetrical coupling microstrip line, and the dimensions of the first microstrip line 302 and the second microstrip line 303 are identical.
The base 301 includes a substrate, a substrate material, and the like, and can be provided with a structure for coupling microstrip lines.
Step S21, obtaining a first equation of the coupled microstrip line model 300 in the even mode, where the unknown number of the first equation is the phase shift of the coupled microstrip line model 300 in the even mode, the effective dielectric constant of the substrate 301 of the coupled microstrip line model 300, and the roughness of the conductor.
The Even Mode (Even-Mode) refers to the driving current excitation that has the same size and the same direction on the first microstrip line 302 and the second microstrip line 303. Specifically, a radio frequency signal is applied to the coupled microstrip line pattern 300, and the radio frequency signal generates driving current excitation with the same magnitude and the same direction on the first microstrip line 302 and the second microstrip line 303. Please refer to fig. 4, which is a schematic diagram of the electric field lines (ELECTRIC FIELD LINES) and the magnetic field lines (MAGNETIC FIELD LINES) of the coupled microstrip line model 300 in the even mode.
In an embodiment, the method for obtaining the first equation of the coupled microstrip line model 300 in the even mode includes:
Obtaining the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in even mode without regard to the roughness of the conductor ee Relation (1):
wherein ε ee For the relative effective dielectric constant, ε of the substrate 301 when the coupled microstrip line model 300 is in even mode without regard to the roughness of the conductor r F is the effective dielectric constant of the substrate 301 e (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
wherein w is the width of one microstrip line in the symmetrically coupled microstrip lines, and in this embodiment, the dimensions of the first microstrip line 302 and the second microstrip line 303 are the same, and w is the width of the first microstrip line 302 or the second microstrip line 303 in the symmetrically coupled microstrip lines; h is the height of the substrate 301; s is the distance between two microstrip lines of the symmetrically coupled microstrip lines, i.e. the distance between the first microstrip line 302 and the second microstrip line 303.
Obtaining u and g from the coupled microstrip line model 300 and substituting the above-mentioned relations (1) - (5) to obtain the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in the even mode without considering the roughness of the conductor ee Effective dielectric constant ε with substrate 301 r The relation between:
providing the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in even mode irrespective of the roughness of the conductor ee Relative effective dielectric constant epsilon of substrate 301 in consideration of roughness of conductor in even mode with the coupled microstrip line model 300 ee_rough Relation (6):
wherein ε ee_rough For the relative effective dielectric constant of the substrate 301 of the coupled microstrip line model 300 in the even mode, where the roughness of the conductor is considered, R is the roughness of the conductor;
providing a phase shift phi of the coupled microstrip line model 300 in an even mode ee And the relative effective dielectric constant epsilon when considering the roughness of the conductor ee_rough Relationship (7) between:
wherein phi is ee Is the phase shift of the coupled microstrip line model 300 in the even mode, c is the speed of light, f is the frequency of the radio frequency signal input into the coupled microstrip line model 300, and L is the length of the symmetrically coupled microstrip line;
the first equation is obtained according to the above-described relational expressions (1) to (7):
in this embodiment, the first equation is the phase shift φ of the coupled microstrip line model 300 in the even mode ee The effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 r A function of the roughness R of the conductor.
Phase shift phi of the coupled microstrip line model 300 in even mode ee And the relative effective dielectric constant epsilon when considering the roughness of the conductor ee_rough The derivation of the relation (7) between them is as follows:
wherein T is the transmission delay time of the radio frequency signal in the coupled microstrip line model 300, T is the period of the radio frequency signal, v p Is the phase velocity of the radio frequency signal within the coupled microstrip line model 300.
From relation (8), relation (7) can be derived.
With continued reference to fig. 2, step S22 is performed to obtain a second equation of the coupled microstrip line model 300 in the odd mode, where the unknown number of the second equation is the phase shift of the coupled microstrip line model 300 in the odd mode, the effective dielectric constant of the substrate 301 of the coupled microstrip line model 300, and the roughness of the conductor.
The Odd Mode (Odd-Mode) refers to the driving current excitation with the same magnitude and opposite direction on the first microstrip line 302 and the second microstrip line 303. Specifically, a radio frequency signal is applied to the coupled microstrip line pattern 300, and the radio frequency signal generates driving current excitation with the same magnitude and opposite directions on the first microstrip line 302 and the second microstrip line 303. Please refer to fig. 5, which is a schematic diagram of the electric field lines (ELECTRIC FIELD LINES) and the magnetic field lines (MAGNETIC FIELD LINES) of the coupled microstrip line model 300 in the odd mode.
In an embodiment, the method for obtaining the second equation of the coupled microstrip line model 300 in the odd mode includes:
obtaining the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in odd mode without regard to the roughness of the conductor eo Relation (9):
wherein ε eo For the relative effective dielectric constant, ε of the substrate 301 when the coupled microstrip line model 300 is in odd mode irrespective of the roughness of the conductor r F is the effective dielectric constant of the substrate 301 o (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
p(g)＝exp(-0.745g 0.295 )/cosh(g 0.68 ) (14)
q(g)＝exp(-1.366-g) (15)
wherein w is the width of one microstrip line in the symmetrically coupled microstrip lines, and in this embodiment, the dimensions of the first microstrip line 302 and the second microstrip line 303 are the same, and w is the width of the first microstrip line 302 or the second microstrip line 303 in the symmetrically coupled microstrip lines; h is the height of the substrate 301; s is the distance between two microstrip lines of the symmetrically coupled microstrip lines, i.e. the distance between the first microstrip line 302 and the second microstrip line 303.
Obtaining u and g from the coupled microstrip line model 300 and substituting the above-mentioned relations (9) to (18) to obtain the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in the odd mode without considering the roughness of the conductor eo Effective dielectric constant ε with substrate 301 r A relation between them;
providing the relative effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 in odd mode irrespective of the roughness of the conductor eo Coupled with the microstrip lineThe relative effective dielectric constant epsilon of the substrate 301 when the roughness of the conductor is considered by the model 300 in odd mode eo_rough Relation (19):
wherein ε eo_rough For the relative effective dielectric constant of the substrate 301 of the coupled microstrip line model 300 in the odd mode, where the roughness of the conductor is considered, R is the roughness of the conductor;
providing a phase shift phi of the coupled microstrip line model 300 in odd mode and a relative effective dielectric constant epsilon taking into account the roughness of the conductor eo_rough Relationship (20) between:
wherein phi is eo Is the phase shift of the coupled microstrip line model 300 in the odd mode, c is the speed of light, f is the frequency of the radio frequency signal input to the coupled microstrip line model 300, and L is the length of the symmetrically coupled microstrip line;
the second equation is obtained according to the above-described relational expressions (9) to (20).
In this embodiment, the second equation is the phase shift φ of the coupled microstrip line model 300 in the odd mode eo The effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 r A function of the roughness R of the conductor.
Phase shift phi of the coupled microstrip line model 300 in odd mode eo And the relative effective dielectric constant epsilon when considering the roughness of the conductor eo_rough The derivation of the relation (20) between them is as follows:
wherein t is the radio frequency signal in the coupled microstrip line model 300The transmission delay time in the radio frequency signal, T is the period of the radio frequency signal, v p Is the phase velocity of the radio frequency signal within the coupled microstrip line model 300.
From the relation (21), the relation (20) can be derived.
With continued reference to fig. 2, in step S23, the phase shift of the coupled microstrip line model 300 in the even mode is measured and obtained, and substituted into the first equation to form a third equation with the effective dielectric constant of the substrate 301 of the coupled microstrip line model 300 and the roughness of the conductor as unknowns.
In this step, the phase shift phi of the coupled microstrip line model 300 in the even mode ee Can be obtained by measuring the coupled microstrip line model 300, and the phase shift phi of the obtained coupled microstrip line model 300 in the even mode ee Substituting the first equation, the effective dielectric constant ε of the substrate 301 of the coupled microstrip line model 300 can be obtained r And the roughness R of the conductor is the third equation of the unknown number.
In one embodiment, the phase shift phi of the coupled microstrip line model 300 in the even mode can be obtained by measuring the scattering parameter (i.e., S-parameter) of the coupled microstrip line model 300 in the even mode by a vector network analyzer (Vector Network Analyzer, VNA) ee . Specifically, as shown in fig. 6, which is a schematic diagram of measuring scattering parameters by a vector network analyzer, the vector network analyzer is used to measure scattering parameters S21, S23, S41, S43 of four ports 1 to 4 of the coupled microstrip line model 300, scc21=0.5× (s21+s23+s41+s43), Φ ee =phase (Scc 21), and thus phi can be obtained ee Is a value of (2).
With continued reference to fig. 2, in step S24, the phase shift of the coupled microstrip line model 300 in the odd mode is measured and obtained, and substituted into the second equation to form a fourth equation with the effective dielectric constant of the substrate 301 of the coupled microstrip line model 300 and the roughness of the conductor as unknowns.
In this step, the phase shift phi of the coupled microstrip line model 300 in the odd mode eo Can be obtained by measuring the coupled microstrip line model 300The obtained phase shift phi of the coupled microstrip line model 300 in the odd mode eo Substituting the second equation, the effective dielectric constant ε of the substrate 301 of the coupled microstrip line model 300 can be obtained r And the roughness R of the conductor is a fourth equation of unknown number.
In one embodiment, the phase shift phi of the coupled microstrip line model 300 in the odd mode can be obtained by measuring the scattering parameter (S parameter) of the coupled microstrip line model 300 in the odd mode by a vector network analyzer eo . Specifically, as shown in fig. 6, the scattering parameters S21, S23, S41, S43, sdd21=0.5 (s21—s23—s41+s43), Φ of the four ports 1 to 4 of the coupled microstrip line model 300 are measured by a vector network analyzer eo ＝phase(S dd 21 And then can obtain phi eo Is a value of (2).
With continued reference to fig. 2, step S25 is performed to obtain the effective dielectric constant and the roughness of the conductor of the substrate 301 of the coupled microstrip line model 300 according to the third equation and the fourth equation.
In this step, the effective dielectric constant ε of the substrate 301 of the coupled microstrip line model 300 is obtained r Solving a third equation with the roughness R of the conductor as an unknown number and a third party Cheng Lianli to obtain the effective dielectric constant epsilon of the substrate 301 r And the roughness R of the conductor. In the present embodiment, the roughness R of the conductor of the surface of the microstrip line in contact with the substrate 301 is ten-point average roughness R of the conductor. In other embodiments, other roughness parameters may also be used to characterize the roughness of the conductor of the surface of the microstrip line in contact with the substrate 301.
As an example, when u=w/h=2, g=s/h=1, the above-described relational expressions (1) to (6) are substituted, resulting in:
measuring and obtaining the phase shift phi of the coupled microstrip line model 300 in the even mode ee And further obtaining the coupling microstrip line model 300 in the even mode according to the relation (7)The relative effective dielectric constant epsilon in the mode when considering the roughness of the conductor ee_rough Will epsilon ee_rough Substitution of the values of (2) into the relation (22) enables the effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 to be obtained r And the roughness R of the conductor is the third equation of the unknown number.
As an example, when u=w/h=2, g=s/h=1, the above-described relational expressions (9) to (18) are substituted, resulting in:
measuring and obtaining the phase shift phi of the coupled microstrip line model 300 in the odd mode eo Further, the relative effective dielectric constant epsilon of the coupled microstrip line model 300 under the odd mode considering the roughness of the conductor can be obtained according to the relation (20) eo_rough Will epsilon eo_rough Substitution of the values of (2) into relation (23) enables the effective dielectric constant epsilon of the substrate 301 of the coupled microstrip line model 300 to be obtained r And the roughness R of the conductor is a fourth equation of unknown number.
Third equation and simultaneous solution of the third equation to obtain the effective dielectric constant ε of the substrate 301 r And the roughness R of the conductor.
The above embodiment obtains the effective dielectric constant ε of the substrate 301 by numerical calculation r And the roughness R of the conductor.
As an example, in another embodiment, the invention also provides that the effective dielectric constant epsilon of the substrate 301 is directly obtained by software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupled microstrip line model r And the roughness R of the conductor.
Fig. 7 is a schematic step diagram of a method for extracting effective dielectric constant and roughness of a conductor of a substrate according to another embodiment of the present invention, referring to fig. 7, the method includes:
in step S70, a coupled microstrip line model 300 is provided, where the coupled microstrip line model 300 includes a substrate 301 and a symmetrical coupled microstrip line provided on a surface of the substrate 301. In this step, the coupled microstrip line model 300 is set by simulation software.
Step S71, setting simulation parameters including the effective dielectric constant ε of the substrate 301 r Said effective dielectric constant epsilon r A scanning step of the effective dielectric constant, a roughness R of the conductor, a scanning range of the roughness R, and a scanning step of the roughness.
In this step, the simulation parameters are set in the simulation software. Wherein the effective dielectric constant ε r And the roughness R may be set based on empirical values or manufacturer-provided reference values, e.g., in one embodiment, manufacturer-provided reference values are used as the effective dielectric constant ε r And the roughness R. The effective dielectric constant ε r The scanning range of the effective dielectric constant and the scanning step of the effective dielectric constant can be set according to practical requirements. For example, the effective dielectric constant ε provided by the manufacturer r Is 3.3, the effective dielectric constant epsilon r Extends the scan range of 3.3, e.g. the effective dielectric constant epsilon r The scanning range of the dielectric constant is 3.2-3.8, and the scanning step of the effective dielectric constant is set to be 0.1; the reference value of the provided roughness R provided by the manufacturer is 3.5, and the scanning range of the roughness R is extended on the basis of 3.5, for example, the scanning range of the roughness R is 2.5-5, and the scanning step of the roughness is 0.5. In some embodiments, when the roughness R is a ten-point average roughness, the roughness R may also be obtained by a snowball Model (Hall-Huray Model, copper foil roughness Model).
And step S72, simulating the coupling microstrip line model by taking the effective dielectric constant and the roughness as variables according to the simulation parameters in an even mode to obtain a phase shift parameter set of the coupling microstrip line model in the even mode.
In this step, the coupled microstrip line model is scanned with the effective dielectric constant and the roughness as variables, so that the coupled microstrip line model can be obtainedPhase shift parameter set in even mode. For example, the effective dielectric constant ε r The scanning range of the coupling microstrip line model is 3.2-3.8, the scanning step of the effective dielectric constant is set to be 0.1, 7 groups of phase shift data can be obtained, the scanning range of the roughness R is 2.5-5, the scanning step of the roughness is 0.5, 6 groups of phase shift data can be obtained, and 42 groups of phase shift data can be obtained in the step, and the phase shift data form a phase shift parameter set of the coupling microstrip line model in an even mode. And step S73, simulating the coupled microstrip line model by taking the effective dielectric constant and the roughness as variables according to the simulation parameters in an odd mode to obtain a phase shift parameter set of the coupled microstrip line model in the odd mode. The number of phase shift data obtained in this step is the same as that of step S72, and will not be described again.
And step S74, testing the real object of the coupling microstrip line model in an even mode and an odd mode to obtain the actual measured phase shift of the real object of the coupling microstrip line model in the even mode and the odd mode.
In this step, the real object of the coupled microstrip line model is manufactured according to the parameters of the coupled microstrip line model in step S70, and the real object of the coupled microstrip line model is tested in the even mode and in the odd mode by an analysis instrument, so as to obtain the actually measured phase shift of the real object of the coupled microstrip line model in the even mode and in the odd mode. In one embodiment, the scattering parameters (i.e., S-parameters) of the coupled microstrip line model 300 in the even mode and in the odd mode may be measured by a vector network analyzer (Vector Network Analyzer, VNA) to obtain the measured phase shifts of the coupled microstrip line model 300 in the even mode and in the odd mode.
Step S75, in the phase shift parameter set of the coupled microstrip line model in the even mode, a phase shift equal to or different from the actually measured phase shift in the even mode by a set value is obtained, and the effective dielectric constant and roughness corresponding to the phase shift are extracted as the first set.
In this step, when one data or N data in the phase shift parameter set of the coupled microstrip line model in the even mode is equal to or different from the actually measured phase shift of the coupled microstrip line model in the even mode by a set value, the effective dielectric constant and roughness corresponding to the one data or N data are extracted as the first set.
In some embodiments, the set value ranges from [ -1 °,1 ° ].
Step S76, in the phase shift parameter set of the coupling microstrip line model in the odd mode, the phase shift equal to or different from the actually measured phase shift in the odd mode by a set value is obtained, and the effective dielectric constant and roughness corresponding to the phase shift are extracted as the second set.
In this step, when one data or M data in the phase shift parameter set of the coupled microstrip line model in the odd mode is equal to or different from the actually measured phase shift of the coupled microstrip line model in the odd mode by a set value, the effective dielectric constant and roughness corresponding to the one data or M data are extracted as the second set.
In some embodiments, the set value ranges from [ -1 °,1 ° ].
Step S77, performing an intersection operation on the first set and the second set to obtain an effective dielectric constant of the substrate of the coupled microstrip line model and roughness of the conductor. In this step, the solution of the effective dielectric constant and the roughness of the conductor of the substrate 301 existing in the coupled microstrip line model 300 in the even mode and in the odd mode is the effective dielectric constant and the roughness of the conductor of the substrate 301 to be obtained in the present invention. The effective dielectric constant of the substrate 301 and the roughness of the conductor can be narrowed by the cross operation in this step, so that the accurate effective dielectric constant of the substrate 301 and the roughness of the conductor can be obtained.
In some embodiments, the emulation software is transmission line port (HFSS, high Frequency Structure Simulator) emulation software.
The method for extracting the effective dielectric constant of the substrate and the roughness of the conductor can obtain the effective dielectric constant of the substrate and the roughness of the conductor under a single radio frequency, and if the effective dielectric constant of the substrate and the roughness of the conductor under a plurality of radio frequencies are required to be obtained, the method is required to be executed for a plurality of times.
The method for extracting the effective dielectric constant and the roughness of the conductor of the substrate 301 provided by the embodiment of the invention directly obtains the effective dielectric constant and the roughness of the conductor of the substrate 301 by utilizing the characteristics of the odd mode and the even mode of the coupled microstrip line model 300 through numerical calculation or software simulation. The method can obtain the effective dielectric constant of the substrate 301 without measuring the roughness of the conductor, and avoids the adverse effect of inaccuracy in roughness measurement on the measurement of the effective dielectric constant of the substrate 301; and because the roughness is measured without adopting a traditional measuring method, such as slicing or profilometer, the measuring time is greatly shortened, and the production efficiency is improved. Meanwhile, the extraction method of the effective dielectric constant and the roughness of the conductor can also solve the problem of multiple solutions of the single-ended transmission line method in the parameter extraction process.
It should be noted that the terms "comprising" and "having" and their variants are referred to in the document of the present invention and are intended to cover non-exclusive inclusion. The terms "first," "second," and the like are used to distinguish similar objects and not necessarily to describe a particular order or sequence unless otherwise indicated by context, it should be understood that the data so used may be interchanged where appropriate. The term "one or more" depends at least in part on the context and may be used to describe a feature, structure, or characteristic in a singular sense or may be used to describe a feature, structure, or combination of features in a plural sense. The term "based on" may be understood as not necessarily intended to express an exclusive set of factors, but may instead, also depend at least in part on the context, allow for other factors to be present that are not necessarily explicitly described. In addition, the embodiments of the present invention and the features in the embodiments may be combined with each other without collision. In addition, in the above description, descriptions of well-known components and techniques are omitted so as to not unnecessarily obscure the present invention. In the foregoing embodiments, each embodiment is mainly described for differences from other embodiments, and the same/similar parts between the embodiments are referred to each other.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (10)
1. A method for extracting an effective dielectric constant of a substrate and a roughness of a conductor, comprising: setting a coupling microstrip line model, wherein the coupling microstrip line model comprises a substrate and symmetrical coupling microstrip lines arranged on the surface of the substrate; and directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor through numerical calculation or software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupling microstrip line model.
2. The method according to claim 1, wherein the method for directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor by numerical calculation using the odd mode characteristics and the even mode characteristics of the coupled microstrip line model comprises: obtaining a first equation of the coupling microstrip line model in an even mode, wherein the unknown number of the first equation is the phase shift of the coupling microstrip line model in the even mode, the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor; obtaining a second equation of the coupling microstrip line model in an odd mode, wherein the unknown number of the second equation is the phase shift of the coupling microstrip line model in the odd mode, the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor;
Measuring and obtaining the phase shift of the coupling microstrip line model in an even mode, and substituting the phase shift into the first equation to form a third equation with the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor as unknowns;
measuring and obtaining the phase shift of the coupling microstrip line model in an odd mode, and substituting the phase shift into the second equation to form a fourth equation with the effective dielectric constant of a substrate of the coupling microstrip line model and the roughness of a conductor as unknowns;
and obtaining the effective dielectric constant of the substrate of the coupling microstrip line model and the roughness of the conductor according to the third equation and the fourth equation.
3. The method of claim 2, wherein the method of obtaining the first equation of the coupled microstrip line model in the even mode comprises:
obtaining a relation of relative effective dielectric constants of the substrate of the coupled microstrip line model in an even mode without considering roughness of the conductor:
wherein ε ee For the relative effective dielectric constant epsilon of the substrate in the even mode of the coupled microstrip line model without regard to the roughness of the conductor r Is the effective dielectric constant of the substrate, F e (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
wherein w is the width of one microstrip line in the symmetrical coupling microstrip line, h is the height of the substrate, and s is the distance between two microstrip lines in the symmetrical coupling microstrip line;
obtaining u and g according to the coupling microstrip line model, and substituting the u and g into the relational expression to obtain a relational expression between the relative effective dielectric constant of the substrate and the effective dielectric constant of the substrate when the coupling microstrip line model does not consider the roughness of the conductor in an even mode;
providing a relation between the relative effective dielectric constant of the substrate when the roughness of the conductor is not considered in the coupling microstrip line model in the even mode and the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the coupling microstrip line model in the even mode:
wherein ε ee_rough For the relative effective dielectric constant of the substrate when considering the roughness of the conductor in the even mode of the coupled microstrip line model, R is the roughness of the conductor;
providing a relation between a phase shift of the coupled microstrip line model in an even mode and a relative effective dielectric constant when considering roughness of the conductor:
wherein phi is ee The phase shift of the coupling microstrip line model in the even mode is that c is the speed of light, f is the frequency of a radio frequency signal input into the coupling microstrip line model, and L is the length of the symmetrical coupling microstrip line;
The first equation is obtained according to the above relation.
4. The method of claim 2, wherein the method of obtaining the second equation of the coupled microstrip line model in odd mode comprises:
obtaining a relation of relative effective dielectric constants of the substrate of the coupled microstrip line model in an odd mode without considering roughness of the conductor:
wherein ε eo For the relative effective dielectric constant of the substrate, epsilon, of the coupled microstrip line model in odd mode without regard to the roughness of the conductor r Is the effective dielectric constant of the substrate, F o (u,g,ε r ) U, g, ε r Is a function of (2);
when u=w/h, g=s/h,
p(g)＝exp(-0.745g 0.295 )/cosh(g 0.68 )
q(g)＝exp(-1.366-g)
wherein w is the width of one microstrip line in the symmetrical coupling microstrip line, h is the height of the substrate, and s is the distance between two microstrip lines in the symmetrical coupling microstrip line;
obtaining u and g according to the coupling microstrip line model, and substituting the u and g into the relational expression to obtain a relational expression between the relative effective dielectric constant of the substrate and the effective dielectric constant of the substrate when the roughness of the conductor is not considered in the odd mode of the coupling microstrip line model;
providing a relation between the relative effective dielectric constant of the substrate when the roughness of the conductor is not considered in the odd mode of the coupling microstrip line model and the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the odd mode of the coupling microstrip line model:
Wherein ε eo_rough For the relative effective dielectric constant of the substrate when the roughness of the conductor is considered in the odd mode of the coupling microstrip line model, R is the roughness of the conductor;
providing a relationship between the phase shift of the coupled microstrip line model in odd mode and the relative effective dielectric constant of the coupled microstrip line model when considering the roughness of the conductor:
wherein phi is eo Is the phase shift of the coupling microstrip line model in the odd mode, c is the speed of light, f is the input of the coupling microstripThe frequency of the radio frequency signal of the line model, L is the length of the symmetrical coupling microstrip line;
the second equation is obtained according to the above relation.
5. The method according to claim 2, wherein the step of measuring the phase shift of the coupled microstrip line model in the even mode comprises: and obtaining the phase shift of the coupling microstrip line model in the even mode by measuring the scattering parameter of the coupling microstrip line model in the even mode.
6. The method of claim 2, wherein the step of measuring the phase shift of the coupled microstrip line model in odd mode comprises: and obtaining the phase shift of the coupling microstrip line model in the odd mode by measuring the scattering parameter of the coupling microstrip line model in the odd mode.
7. The method according to claim 1, wherein the method for directly obtaining the effective dielectric constant of the substrate and the roughness of the conductor by software simulation by utilizing the odd mode characteristic and the even mode characteristic of the coupled microstrip line model comprises the following steps:
setting simulation parameters, wherein the simulation parameters comprise an effective dielectric constant of a substrate, a scanning range of the effective dielectric constant, a scanning step of the effective dielectric constant, a roughness of a conductor, a scanning range of the roughness and a scanning step of the roughness;
simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an even mode to obtain a phase shift parameter set of the coupling microstrip line model in the even mode;
simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a phase shift parameter set of the coupling microstrip line model in the odd mode;
testing the real object of the coupling microstrip line model in an even mode and an odd mode to obtain the actual measurement phase shift of the real object of the coupling microstrip line model in the even mode and the odd mode;
In a phase shift parameter set of the coupling microstrip line model in an even mode, obtaining a phase shift equal to or different from an actual measurement phase shift in the even mode by a set value, and extracting an effective dielectric constant and roughness corresponding to the phase shift as a first set;
in the phase shift parameter set of the coupling microstrip line model in the odd mode, obtaining a phase shift equal to or different from the actually measured phase shift in the odd mode by a set value, and extracting an effective dielectric constant and roughness corresponding to the phase shift as a second set;
and performing an intersection operation on the first set and the second set to obtain the effective dielectric constant of the substrate and the roughness of the conductor of the coupled microstrip line model.
8. The method according to claim 7, wherein the step of simulating the coupled microstrip line model in the even mode with the effective dielectric constant and the roughness as variables according to the simulation parameters, and obtaining the set of phase shift parameters of the coupled microstrip line model in the even mode specifically comprises: simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an even mode to obtain a scattering parameter set of the coupling microstrip line model in the even mode, and obtaining a phase shift parameter set according to the scattering parameter set;
The step of simulating the coupled microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a phase shift parameter set of the coupled microstrip line model in the odd mode specifically comprises the following steps: and simulating the coupling microstrip line model according to the simulation parameters by taking the effective dielectric constant and the roughness as variables in an odd mode to obtain a scattering parameter set of the coupling microstrip line model in the odd mode, and obtaining a phase shift parameter set according to the scattering parameter set.
9. The method of claim 7, wherein the set value ranges from [ -1 °,1 ° ].
10. The method of claim 1, wherein the symmetrically coupled microstrip line is a side-coupled symmetrically coupled microstrip line.
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