JPWO2006090550A1 - Method for measuring dielectric constant of transmission line material and method for measuring electrical characteristics of electronic component using this dielectric constant measuring method - Google Patents

Abstract

A dielectric constant measurement method for a material capable of measuring the dielectric constant of a dielectric material at a high frequency in the form of a transmission line actually used, and capable of obtaining the dielectric constant and tan δ including frequency characteristics with high accuracy. I will provide a. A measuring jig having an unknown electrical characteristic per unit length, in which a transmission path composed of a signal conductor and a ground conductor is formed on a dielectric substrate, is prepared, and at least in the length direction of the transmission path. At four positions, the signal conductor 3 and the ground conductor 4 are short-circuited, and the reflection coefficient S11 is measured. Calculate the characteristics of the transmission line (transmittance α and phase constant β) from the measured values in the short-circuit state, and further calculate the dielectric constant and tan δ of the transmission line material from the characteristics of the transmission line and the physical dimensions of the transmission line. . [Selection] Figure 1

Description

The present invention relates to a method for measuring a dielectric constant and tan δ (dielectric loss tangent) of a dielectric material used for a transmission line substrate and the like, and a method for measuring electrical characteristics such as an impedance value and a Q value of an electronic component.

Conventionally, as a method for measuring the dielectric constant and tan δ of a dielectric material used for a transmission line substrate or the like, as shown in Non-Patent Documents 1 and 2, a capacitance method using an LCR meter is used at low frequencies, A waveguide method using a network analyzer, a resonance method, a free space method, and the like are known.

The capacitance method has a problem that only a low frequency dielectric constant of 30 MHz or less can be measured, and a high frequency dielectric constant exceeding 1 GHz cannot be measured.
The waveguide method is a method in which a dielectric is inserted into a waveguide or a coaxial tube to measure the reflection characteristics and transmission characteristics, and the dielectric constant is measured. The sample is processed according to the dimensions of the waveguide. There is a problem that high machining accuracy is required because the gap is a large error factor.
In the resonance method, since the complex dielectric constant corresponding to the resonance frequency is measured, only a limited frequency measurement is possible, and the frequency characteristics of the dielectric constant of the material cannot be considered.
The free space method is not a simple measurement method because it requires large-scale equipment such as a transmission / reception antenna and a radio wave absorber so as not to be affected by unnecessary radio waves.
In addition, none of the conventional methods measure the material characteristics in the state of being processed into the most important plane as an actual application of the dielectric, and cannot take into account the influence during processing.
Furthermore, a user who has purchased a dielectric substrate processed into a planar shape cannot easily know the characteristics of the substrate material.
Furthermore, the catalog value of the dielectric constant of the dielectric material provided by the material manufacturer of the dielectric substrate is generally a value of about 1 MHz, and there are only two significant figures. Further, frequency characteristics (1 GHz to 20 GHz) are not described in detail.

The problems of dielectric constant data obtained from the conventional dielectric constant measurement method are summarized as follows.
(1) In the conventional dielectric constant measurement method, a dielectric material must be processed in accordance with each measurement method, and cannot be measured in the form of a transmission line that is actually used.
(2) In the conventional dielectric constant measurement method, the relative dielectric constant of the material is obtained, which is different from the dielectric constant in the actual use state.
(3) The effective number of relative permittivity is only about two digits, and the accuracy is remarkably low as compared with the dimensional accuracy, so the characteristic impedance cannot be obtained accurately.
(4) The frequency characteristic of dielectric constant cannot be measured by the resonance method.
(5) The dielectric constant of a purchased material lot or a material processed into a flat shape cannot be grasped.

As described above, since the dielectric constant and tan δ including the frequency characteristics of the lot of the dielectric material to be used could not be accurately grasped, the following problems have occurred.
(1) In high-frequency impedance measurement of electronic components using a network analyzer, calibration methods such as the TRL calibration method that eliminates error factors in the measurement system calibrate the error factors in the measurement system in order to obtain the impedance of the electronic component. It is necessary to multiply the Z parameter calculated from the scattering coefficient (S parameter) obtained in this way by the characteristic impedance of the transmission line used for the measurement. However, since the accuracy of the dielectric constant is poor, the accuracy of the characteristic impedance is poor. There was a problem that the accuracy of impedance characteristics could not be obtained.
(2) The high frequency circuit design has a problem that the design accuracy is poor because the actual dielectric constant is not accurately known. In high-frequency circuit design, the dielectric constant is a parameter that affects the signal delay time, and is an increasingly important parameter for high-precision design as the frequency increases. Tan δ is also an important parameter during the recent development of portable battery-powered devices.
Agilent Technology Application Note 1287-9 “Fixture Measurement Using a Vector Network Analyzer” Osamu Hashimoto, “Method for Measuring Material Constants in the High Frequency Region” Morikita Publishing (2003)

Accordingly, an object of a preferred embodiment of the present invention is to measure the dielectric constant of a dielectric material at a high frequency in the form of a transmission line that is actually used, and to obtain the dielectric constant including the frequency characteristics, tan δ with high accuracy. An object of the present invention is to provide a method for measuring a dielectric constant of a material.
Another object of the present invention is to provide a method for accurately measuring electrical characteristics of electronic parts using this dielectric constant measurement method.

In order to achieve the above object, in a preferred embodiment of the present invention, a measurement jig having a transmission line having an electric characteristic per unit length is prepared on a dielectric substrate, which includes a signal conductor and a ground conductor. Calculating the characteristics of the transmission line from the measured value in the short circuit state, the step of measuring the electrical characteristics by short-circuiting the signal conductor and the ground conductor at at least four locations in the length direction of the transmission line And a step of calculating at least one of the dielectric constant and tan δ of the transmission line material from the characteristics of the transmission line.

In the preferred embodiment of the present invention, since at least one of the dielectric constant and tan δ is obtained from the reflection characteristic of the transmission line, the reflection characteristic (scattering coefficient) must be accurately measured. However, simply measuring the reflection characteristics with a network analyzer cannot satisfactorily measure the reflection characteristics of a transmission line made of a dielectric material to be measured. This is because the measurement result includes a joint portion between the connector portion and the transmission path as an inconsistent portion, and includes multiple reflections occurring at this portion.
There is a time domain method as a method for removing the mismatched portion, but when using the time domain method, it is necessary to widen the frequency range in order to increase the resolution, and the frequency characteristics of the material could not be observed. .
In the preferred embodiment of the present invention, the signal conductor and the ground conductor are short-circuited at four locations on the same transmission line (for example, a state in which a short-circuit reference is connected), and the S-parameter of one port is measured. Since the values are the same in the mismatching part of the connector part and the planar transmission path, the influence of the mismatching part of the connector part and the planar transmission path is accurately removed in error correction.
For this reason, it is possible to accurately measure the reflection characteristic of the transmission path of the dielectric material to be measured. By using this reflection characteristic, the characteristics of the transmission line are obtained and the dielectric constant and tan δ are calculated. Therefore, the dielectric constant and tan δ can be measured more accurately.

As the transmission line, it is preferable to use a planar transmission line that can short-circuit the signal conductor and the ground conductor at an arbitrary position in the transmission line by pressing the conductor from the upper surface.
This is because the flat transmission line can easily obtain a good short circuit state by pressing a conductor (short circuit reference) from above. When the signal conductor and the ground conductor are short-circuited, almost total reflection occurs, so that the scattering coefficient can be accurately measured without being influenced by the terminal end of the signal conductor.
Such planar transmission lines include coplanar waveguides and slot lines.

For each frequency range to be measured, the scattering coefficient of one port in a state where the signal conductor and the ground conductor are short-circuited is measured at least at four locations on the transmission path, and the transmission path characteristics ξ (ξ = α ^{− 2} exp (j2β), α: transmission, β: phase constant) should be calculated.
The signal conductor and the ground conductor are short-circuited at at least four locations on the transmission line, and the transmission line characteristic is obtained from the scattering coefficient. As the transmission line characteristics, there are a transmission factor α and a phase constant β. However, when ξ = α ⁻² exp (j2β), ξ is obtained as a complex number from the scattering coefficient. A phase constant β is obtained from the imaginary part. If the phase constant β is obtained, the effective dielectric constant ε _eff of the transmission line can be obtained by calculation, and tan δ can be obtained using the transmissivity α and the phase constant β.

From the transmission line characteristic ξ and the physical dimension of the transmission line, the relative dielectric constant ε _r of the transmission line material can be calculated.
Since the effective dielectric constant ε _eff has a value corresponding to the physical dimension of the transmission line, the dielectric constant ε _eff cannot be used even if the same dielectric material is used if the shape of the transmission line changes. The relative dielectric constant ε _r can be calculated from the effective dielectric constant ε _eff and physical dimensions. Therefore, it is possible to obtain the relative dielectric constant ε _r of the dielectric material itself that is not affected by the size and shape.

The position at which the signal conductor and the ground conductor are short-circuited is arbitrary, but when L ₁ , L ₂ , and L ₃ from the measurement point 1 to the port 1 side, the distance ratio is L ₁ : L ₂ : L ₃ = 1. : 2: 3 or 1: 2: 4 is preferable because the calculation formula of the transmission line characteristic ξ becomes simple.
In other cases, it becomes a complicated expression, so it is better to use iterative calculation.

The position where the signal conductor and the ground conductor are short-circuited, that is, the phase difference between each of the short-circuit reference connection positions is preferably set to be about 70 ° to 145 °. In this case, if the calibration accuracy is high and the measurement data is used well, the number of short-circuit reference measurements does not increase even in the wideband measurement.

From the measured value in the short-circuit state in the above-described dielectric constant measurement method of the present invention, the transmission channel characteristic ξ and the transmission channel error coefficient E _xx are calculated, and in the state where the measured electronic component is connected to the transmission channel, the scattering coefficient is calculated. (S parameter) is measured, the error coefficient E _xx of the transmission path is removed from the measured scattering coefficient of the electronic component to be measured, and the true value S _xxA of the scattering coefficient of the electronic component to be measured is obtained. The Z parameter Z _xxA of the electronic component can be obtained.
In other words, if calibration measurement in a short-circuit state is performed at four or more locations, the transmission channel error coefficient E _xx can be calculated simultaneously in addition to the transmission channel characteristics ξ. If the error coefficient E _xx of the transmission line is removed from the measurement value in a state where the subject (the electronic component to be measured) is connected to the transmission path, the true value of the electrical characteristic (S parameter) of the subject can be easily obtained. .
In this method, since the transmission line characteristic ξ and the error coefficient E _xx are obtained under the same conditions, the accuracy of the true value S _xxA and the Z parameter Z _xxA of the scattering coefficient of the electronic component to be measured obtained as a result is very high. .

The method is a method of calculating the impedance characteristic of the electronic component by simultaneously obtaining the transmission line characteristic ξ and the error coefficient E _xx , but in some cases, only the transmission line characteristic ξ of the board is obtained by the method of the present invention. error coefficient E _xx of the transmission path of the substrate and the same lot determined separately using existing calibration methods (e.g. TRL method), may be calculated impedance characteristic of the electronic component.
In this method, the transmission lines that can be used when obtaining the transmission line characteristics are limited to CPW and slot lines. However, the transmission lines that can be used during calibration are microstrip lines, CPWs, slot lines, etc., depending on the type of calibration. Can be appropriately selected.
However, in this case, the transmission path characteristics of the calibration board are not obtained at the same time as calibration, and the transmission path characteristics of the calibration board itself are not obtained. Somewhat inferior.

As described above, the relative dielectric constant ε _r of the transmission line material can be calculated from the transmission line characteristic ξ and the physical dimension of the transmission line. Therefore, even if the shape of the transmission line is changed, the effective dielectric constant ε _eff is obtained from the relative dielectric constant ε _r and the physical dimension of the transmission line, and the characteristic impedance Z ₀ of the transmission line is obtained from the ε _eff. it can. Therefore, if the dielectrics composing the substrate are the same, even if the measurement jig for which the dielectric constant is obtained is different from the measurement jig for measurement / calibration, the measurement treatment for measurement / calibration is used. The characteristic impedance Z _{0 of the} tool can be easily obtained.

A dielectric constant of the transmission line material obtained by the above-described dielectric constant measuring method, to calculate the characteristic impedance Z ₀ of the transmission line, the characteristic impedance Z ₀ of the transmission line and Z parameter Z _xxA of the measured electronic component described above Thus, the impedance Z _{DUT of the} electronic component to be measured can be calculated.
In order to accurately obtain the characteristic impedance of the electronic component to be measured, it is necessary to accurately grasp the dielectric constant of the transmission line. In the method of the present invention, an accurate dielectric constant of the transmission line can be obtained, so that the characteristic impedance Z ₀ of the transmission line can also be accurately grasped. Then, from the Z parameter Z _{xxA of the} electronic component to be measured obtained from the true value of the scattering coefficient and the characteristic impedance Z ₀ , the frequency Z _{DUT of the} electronic component to be measured is accurately and actually used. You can ask for it.

As described above, according to the preferred embodiment of the present invention, the reflection characteristic obtained by completely removing the mismatching portion between the connector and the transmission line can be measured, so that a more accurate dielectric constant and tan δ can be calculated.
In addition, since the dielectric constant and tan δ are obtained in the form of a transmission line in which a dielectric material is actually used, the dielectric constant in accordance with the actual use state can be obtained.
Furthermore, the dielectric constant and tan δ of the substrate can be obtained with high accuracy for each measurement frequency range.
In addition, since the accurate dielectric constant and tan δ can be measured by the method of the present invention, the following advantages can be obtained. That is, in the high-frequency impedance measurement of electronic components using a network analyzer, calibration methods such as the TRL calibration method that eliminates the error factors of the measurement system calibrate the error factors of the measurement system in order to obtain the impedance of the electronic components. Although it is necessary to multiply the obtained S parameter by the characteristic impedance of the jig transmission line, since the dielectric constant of the substrate is obtained directly and accurately, the accuracy of the characteristic impedance is improved. As a result, the impedance characteristic of the electronic component is improved. It can be obtained more accurately.

It is a top view of the measuring apparatus which is 1st Example of the dielectric constant measuring method concerning this invention. It is a fragmentary perspective view of CPW. It is a figure which shows the calculation algorithm for calculating | requiring tan (delta) from the transmission degree (alpha). It is a figure which shows the calculation algorithm for calculating | requiring the dielectric constant (epsilon) _r from effective dielectric constant (epsilon) _eff . It is an error model figure of the measuring jig shown in FIG. FIG. 2 is a plan view showing a state in which a subject is connected to the measurement jig shown in FIG. 1. It is a top view of the measuring apparatus which is 2nd Example of the dielectric constant measuring method concerning this invention. It is an error model figure of the measuring jig shown in FIG. It is a top view of the state which connected the through chip to the measuring jig shown in FIG. FIG. 8 is a plan view of a state in which a subject is connected to the measurement jig illustrated in FIG. 7. It is a top view of the measuring apparatus which is 3rd Example of the dielectric constant measuring method concerning this invention. It is an error model figure of the measuring jig shown in FIG. FIG. 12 is a plan view showing a state in which a subject is connected to the measurement jig shown in FIG. 11.

Hereinafter, preferred embodiments of the present invention will be described with reference to examples.

A first embodiment of a method for calculating transmission line characteristics according to the present invention will be described below. Here, a one-port measurement method using the reflection method will be described.
-Preparation of jig transmission line-
Here, a coplanar wave guide (hereinafter referred to as CPW) will be described as an example of the measuring jig 1. As shown in FIG. 1, the measuring jig 1 is formed by forming a transmission path composed of a signal conductor 3 and a ground conductor 4 on the upper surface of a jig substrate 2 made of a dielectric. A ground conductor may be formed on the back surface of the jig substrate 2. One end of the signal conductor 3 is an open end, and the other end is connected to the connector 5. The ground conductor 4 is formed so as to surround both sides of the signal conductor 3 in the width direction and the open end with a gap. A coaxial cable 6 is connected to the connector 5 and is connected to measurement ports 7a and 7b of a network analyzer 7 which is an example of a measuring instrument. The signal line 6a of the coaxial cable 6 is fixed to the signal conductor 3 by soldering or welding in order to eliminate connection variation. The measurement ports 7a and 7b are connected to the signal conductor 3 and the ground conductor 4 through the coaxial cable 6, respectively.

-Connection and measurement of short circuit reference-
In this calculation method, the calibration standards to be measured are all the same short-circuit standard 10, and the measurement jig 1 to be used is also the same jig.
The short-circuit reference 10 refers to general components that are electrically short-circuited, and may be a chip component, a metal piece, a tool, or the like. Desirably, the contact length in the longitudinal direction of the transmission path such as a knife edge is short. If the short-circuit standard is ideal, the reflection coefficient will be -1 (total reflection). However, even though the short-circuit standard actually has some inductance, the inductance value needs to be known. It is. Usually, in the microwave band, the short-circuit state can be relatively easily obtained as compared with the open state. When high measurement accuracy is required, the short-circuited reference inductance may be obtained by simple simulation or the like.

First, the signal conductor 3 and the ground conductor 4 are short-circuited by a short-circuit reference 10 at a location (measurement point 1: P1 in FIG. 1) where the subject is connected during measurement of the subject, and this point is used as a calibration surface. The measurement result at this time is S _11M1 and the true value of the reflection coefficient at the measurement point 1 is Γ _A1 . Γ _A1 is a true value of the short-circuit reference, and this may be set to −1 if the length of the short-circuit reference 10 in the length direction of the transmission line is sufficiently smaller than the measurement signal wavelength. The expected value of the true value should be obtained by simulation or the like.

Next, measurement is performed by connecting the short-circuit reference 10 between the signal conductor 3 and the ground conductor 4 at a position (measurement point 2: P2) on the transmission line that is L ₁ away from the measurement point 1 to the port 1 side. The measurement result is S _11M2 . At this time, the true value of the reflection coefficient of the short-circuit reference 10 at the measurement point 2 is Γ _A1 , but when the measurement point 1 is taken as the reference surface, the true value of the reflection coefficient is converted as shown in Equation 1. This is because the electromagnetic wave incident from the port 1 side is totally reflected by the short-circuit reference 10 and therefore has a shorter distance to transmit the transmission path by 2L _{1 than} the case where the short-circuit reference 10 is connected to the measurement point 1. Where α is the transmission rate [U / mm] per unit length, β is the phase constant [rad / mm] of the transmission channel, and α and β are unknown. Γ _A2 is the true value of the short-circuit reference 10 connected to the measurement point 2 when the measurement point 1 is the reference plane.

_Subsequently , measurement is performed by connecting the short-circuit reference 10 to a position (measurement point 3: P3) on the transmission line that is L ₂ away from the measurement point 1 on the port 1 side, and the measurement result at this time is S _11M3 . As in the case of the measurement point 2, if the measurement point 1 is taken as the reference plane, the true value of the reflection coefficient is expressed by Equation 2.

Furthermore the position of the transmission line which from the measurement point 1 spaced by a distance L ₃ to the port 1 side (measurement point 4: P4) was measured by connecting a short circuit reference 10, to the measurement results at this time is S _11M4. When the measurement point 1 is taken as the reference plane as in the case of the measurement point 2, the true value Γ _A4 of the reflection coefficient at the measurement point 4 is expressed by Equation 3.

Here, an expression including α and β is set as ξ as follows. ξ physically represents the transmission coefficient of the transmission line per unit length.

Using Equation 4, Equations 1 to 3 can be rewritten as Equations 5 to 7, respectively.

This time, the transmission path characteristic ξ and the error coefficients E ₁₁ , E ₁₂ , and E ₂₂ become unknown _numbers , and the measured value S _11M1 , S _11M2 , S _11M3 , and S _{11M4 at} the measurement points 1 to 4 _give four unknowns. You can ask for one.
Since the unknown ξ is obtained as a complex number, the transmission factor α (loss δ [dB / mm] = 20 log α) is obtained from the real part, and the phase constant β is obtained from the imaginary part.

For convenience of calculation, it is desirable that the distances L ₁ , L ₂ , L ₃ from the measurement point 1 connecting the short-circuit reference 10 to the measurement points 2 to 4 satisfy any one of the following relationships.
L ₁ : L ₂ : L ₃ = 1: 2: 3
L ₁ : L ₂ : L ₃ = 1: 2: 4
If the above relationship is satisfied, the transmission line characteristic ξ can be calculated explicitly using the following mathematical formula.

When the positions L ₁ , L ₂ , and L ₃ for measuring the short-circuit reference satisfy the relationship of L ₁ : L ₂ : L ₃ = 1: 2: 3, ξ can be obtained by Expression 8.

Ｌ₁：Ｌ₂：Ｌ₃の比が前記の条件を満たさない場合については、ξを求める式を陽に導いていないので、必要に応じて同様の式を誘導しておくか、あるいは反復計算によってξを求めるかすれば良い。On the other hand, when the relationship of L ₁ : L ₂ : L ₃ = 1: 2: 4 is satisfied, ξ can be obtained by Equation 9.

In the case where the ratio of L ₁ : L ₂ : L ₃ does not satisfy the above condition, the formula for obtaining ξ is not derived explicitly, so a similar formula is derived as necessary or iterative calculation is performed. It is sufficient to obtain ξ by

As described above, the calculation is facilitated when L ₁ : L ₂ : L ₃ = 1: 2: 3 or 1: 2: 4, but in other cases, the phase difference between the short-circuit reference connection positions is reduced. It is good to set it as 70 degrees-145 degrees.
That is, in this calculation method, the transmission line characteristics are obtained during calibration of one port, and the change in the reflection coefficient caused by the difference in the position where the short-circuit reference is connected to the jig transmission line is used. Depending on the relationship of the position of the short-circuit reference, the calibration accuracy may be lowered, so the position of the short-circuit reference needs to be determined carefully.
If a large phase difference between the short-circuit references is ensured, the accuracy of calibration is improved, but the frequency range that can be handled by one set of short-circuit references is narrowed, and many short-circuit references need to be measured when performing a wide-band measurement. In the case of TRL calibration in which calibration is performed using the phase difference between the short-circuit references, according to materials such as NIST, the phase difference between the short-circuit references should be ensured to be about 20 ° to 30 ° or more in order to obtain good measurement accuracy. It is said that there is.
When the phase difference between the short-circuit reference connection positions is about 70 ° to 145 °, the calibration accuracy is high, but the frequency range that can be handled by one set of short-circuit reference is considerably narrower than the above case, This is because, if the measurement data is used well, the number of short-circuit reference measurements will not increase even with wideband measurements.

-Calculation of dielectric constant ε _r , tan δ-
Next, the dielectric constant ε _r and tan δ of the substrate are obtained from the transmission path characteristics ξ of each frequency range obtained as described above, that is, the measured values of the transmissivity α and the phase constant β. Specifically, tan δ is obtained by performing a convergence calculation by a known numerical calculation method such as Newton's method so that the residual between the measured value of the transmission α and the calculated value is minimized, and from the measured value of the phase constant β. The same convergence calculation is performed so that the residual of the calculated dielectric constant ε _{eff of} the substrate and the calculated value is minimized, and the dielectric constant ε _{r of the} substrate is obtained.

A specific method for calculating the dielectric constants ε _r and tan δ of the substrate using the CPW transmission line will be described below.
The following equations are known as simulation equations for obtaining the characteristic impedance of the CPW transmission line.
Here, as shown in FIG. 2, W: the width of the signal conductor, s: the distance between the signal conductor and the ground conductor, h: the thickness of the dielectric, t: the thickness of the conductor, L: the length of the conductor, f : Frequency, ε _r : relative permittivity, c: speed of light, Z ₀ : characteristic impedance, ε _eff : effective permittivity, μ ₀ : vacuum permeability, ε ₀ : vacuum permittivity.

The equation for calculating Z ₀ is:

Here, Zc is given by the following equation. Zc is the characteristic impedance of CPW in the case of ε _r = 1, and K is the first type complete elliptic integral.

k and k ′ are given by the following equations.

K ₁ and k ₁ ′ are given by the following equations.

Next, the approximate expression of ε _eff is as follows.

Since the phase constant β is expressed as a function of the effective dielectric constant ε _eff as shown in Equation 15, the effective dielectric constant ε _eff can be calculated from the measured value of the phase constant β using this equation.

このため、伝送路の伝達度αは電磁界シミュレータを用いて算出する。The transmission α is expressed as the sum of the conductor loss α _e , the dielectric loss α _d and the radiation loss α _r. Of these, the dielectric loss α _d is expressed by the following equation: ε _eff and tan δ Expressed as a function.

For this reason, the transmission degree α of the transmission path is calculated using an electromagnetic field simulator.

FIG. 3 shows an algorithm by iterative calculation (Newton method) for obtaining tan δ. First, an initial value of tan δ is input (step S1), and α is calculated from the tan δ using an electromagnetic field simulator (step S2). Next, a difference | Δα | between the measured value of α and the calculated value obtained in step S2 is obtained (step S3), and it is determined whether or not | Δα | is sufficiently small (step S4). If it is determined that | Δα | is not sufficiently small, tan δ is corrected (step S5), and the operations after step S2 are repeated. If it is determined in step S4 that | Δα | is sufficiently small, tan δ when | Δα | ≈0 is set as the substrate characteristic (step S6).

When _{obtaining the} relative dielectric constant ε _r from the effective dielectric constant ε _eff, an algorithm based on iterative calculation (Newton method) is also used. FIG. 4 shows an example of the algorithm.
First, an initial value of ε _r is input (step S7), and ε _eff is calculated from the ε _r using an electromagnetic field simulator (step S8). Next, a difference | Δε _eff | between the effective dielectric constant ε _eff obtained above and the calculated value obtained in step S8 is obtained (step S9), and it is determined whether | Δε _eff | is sufficiently small (step S10). ). If it is determined that | Δε _eff | is not sufficiently small, ε _r is corrected (step S11), and the operations after step S8 are repeated. If it is determined in step S10 that | Δε _eff | is sufficiently small, ε _r when | Δε _eff | ≈0 is set as the relative dielectric constant of the substrate (step S12).

Further, simply, the relative dielectric constant ε _r can be calculated from the obtained effective dielectric constant ε _eff using Equation 14. That is, the relative dielectric constant ε _r of the material of the dielectric substrate itself can be calculated from the effective dielectric constant ε _eff and the physical dimension of the transmission line.

-Calculation of characteristic impedance-
The characteristic impedance Z ₀ can be calculated by Equation 10 from ε _eff obtained above and Zc obtained by Equations 11 and 12.

Since the characteristic impedance Z ₀ of the transmission line has been obtained as described above, a method for obtaining the impedance Z _{DUT of the} subject using this characteristic impedance will be described below.
-Calculation of error coefficient of calibration error model-
If ξ is obtained by Equation 8 or Equation 9, the values of Γ _A2 and Γ _A3 can be calculated by Equation 5 and Equation 6, so that the error coefficient of the transmission path can be obtained sequentially.
A calibration error model is shown in FIG. The reflection method is a method of observing how much of the electromagnetic wave incident on the subject 11 is reflected from one port (connector 5) and obtaining an impedance or the like from this. As shown in FIG. 4, there are only four error factors E ₁₁ , E ₂₁ , E ₁₂ , and E ₂₂ . Since the scattering coefficient measurement is a ratio measurement, if E ₂₁ = 1, there are three error factors E ₁₁ , E ₁₂ , and E ₂₂ . In the figure, S _11M is a measured value of the reflection coefficient, and S _11A is a true value of the scattering coefficient of the subject.

Now, the error coefficients E ₁₁ , E ₁₂ , and E ₂₂ are obtained by Equation 17 from the measurement result obtained by connecting the short-circuit reference 10 described above. D ₁ is an intermediate variable.

−Measurement and calibration of specimen−
When the error coefficient is obtained, as shown in FIG. 6, the subject 11 is connected between the signal conductor 3 and the ground conductor 4 at the measurement point 1, and its electrical characteristic, that is, the reflection coefficient S _11M is measured. Since the calibration error model is the same as the one-port correction error model, the same calculation as in the one-port correction can be performed to remove the influence of the error from the actual measurement result of the object. Equations for _obtaining the true value of the reflection coefficient S _11A of the object to be removed are described below. The calculation formula for removing the influence of the error factor is not limited to the following formula, and any known technique may be used.

このＺパラメータＺ_11A と、前記のように求めた基板の特性インピーダンスＺ₀とを、数式２０に示すようにそれぞれ同じ周波数での値同士で乗じることにより、被検体１１のインピーダンスＺ_DUT を求めることができる。-Conversion from S parameter to impedance-
Since the calibration method is a reflection method, the Z parameter Z _11A of the subject is calculated by Equation 19 using the true value S _11A of the reflection coefficient obtained by calibrating the error factor by the calibration method.

The impedance Z _DUT of the subject 11 is obtained by multiplying the Z parameter Z _11A and the characteristic impedance Z _{0 of the} substrate obtained as described above by values at the same frequency as shown in Equation 20. Can do.

なお、Ｓ_11A 、Ｚ_11A およびＺ_DUT はいずれも複素数である。

S _11A , Z _11A and Z _DUT are all complex numbers.

In this embodiment, as shown in FIG. 7, as the measurement jig 20, two signal conductors 22a and 22b are arranged on a straight line and one end is spaced from the upper surface of the dielectric substrate 21, and the signal conductors 22a and 22b are arranged. A CPW is used in which ground conductors 23 are arranged at intervals on both sides in the width direction of 22b. A ground conductor may also be provided on the back surface of the jig substrate 21. The connectors 24 and 25 are connected via coaxial cables 26 and 27 to measurement ports 28a to 28d of a network analyzer 28 which is an example of a measuring instrument. The signal lines of the coaxial cables 26 and 27 are fixed to the signal conductors 22a and 22b by soldering or welding.

Since the transmission line characteristic ξ is unknown as in the first embodiment, the transmission line characteristic ξ and the error coefficient can be obtained at the same time by short-circuiting the short-circuit reference 10 at four locations on the transmission line. The calculation method of the transmission path characteristic ξ is the same as that in the first embodiment.

In this embodiment, calibration measurement using the short-circuit reference 10 is performed at four points of measurement points 2 to 4 from the measurement point 1 and the measurement point 1 to the port 1 side, and thereafter, similarly at the four points on the port 2 side. Perform calibration measurement at.
Next, as shown in FIG. 8, measurement is performed in a through (direct connection between ports) state. An appropriate device (hereinafter referred to as a through chip) 13 for connecting the ports is connected in series between the signal conductors 22a and 22b. Measurements, reflection coefficient S _11MT, in S _22MT, the transfer coefficient and S _21MT, S _12MT. Note that the electrical characteristics of the through chip 23 may be unknown, for example, a chip resistor whose resistance value is unknown, but the transfer coefficient should not be directional. Since the transfer coefficient does not have directionality according to the reciprocity theorem, this condition is usually satisfied automatically.

FIG. 9 shows a calibration error model of this embodiment. This is also the same as the error model of TRL correction used conventionally. In the figure, S _11M and S _21M are measured values of the reflection coefficient and the transmission coefficient, and S _11A and S _{21A and the} like are true values of the scattering coefficient of the object. Further, although there are eight error coefficients E _xx and F _xx , the scattering coefficient measurement is a ratio measurement, and therefore, seven error factors may be determined. Specifically, E ₂₁ = 1 may be set.

Now, it is necessary to obtain each error coefficient in FIG. 9 from the measurement result obtained by connecting the short-circuit reference 10 described above. First, E ₁₁ , E ₁₂ , E ₂₂ , F ₁₁ , (F ₂₁ · F ₁₂ ), F ₂₂ is obtained by the following equation. Incidentally, F _xx are same as E _xx, described only E _xx. At this stage, for (F ₂₁ · F ₁₂ ), the product of the two error coefficients F ₂₁ and F ₁₂ is obtained, but these cannot be obtained separately. D ₁ is an intermediate variable.

Next, the measurement results S _21MT and S _12MT of the forward and reverse transfer coefficients of the through chip can be written as follows using the error factors of FIG. However, the true value of the through-chip scattering coefficient is assumed to be S _11A , S _21A , S _12A , S _22A .

Here, the ratio of S _21MT and S _12MT is considered. If the arrangement is made while paying attention to the fact that the transmission coefficients in the forward and reverse directions of the through chip are equal (S _21A = S _12A ) based on Expression 22, the following expression is obtained. It should be noted here that the through-chip scattering coefficients S _11A , S _21A , S _12A , and S _22A are all eliminated by division. In other words, even if the true value of the scattering coefficient of the through chip is unknown, if the through chip has no directionality, if the ratio of S _21MT and S _12MT (this is a measurable amount) is known, the relationship of the error coefficient is It is to be decided.

Based on Equation 21 and Equation 23, the total error coefficient can be determined as follows:

With the above, all error coefficients have been determined. The above is a discussion when a signal is applied from the port 1 side to the port 2 side (forward direction), but the reverse direction can be derived by setting F ₂₁ = 1 instead of E ₂₁ = 1.

−Measurement and calibration of specimen−
When the error coefficient is obtained, the subject 11 is connected to the transmission line as shown in FIG. 10 and its characteristics are measured. That is, the subject 11 is brought into contact with the subject measurement position on the transmission path, and the electrical characteristics (S _11M, S _21M, S _12M, S _22M ) are measured. At this time, when the subject 11 has two terminals, the signal conductors 22a and 22b may be connected in series as shown in FIG. 10A. However, in the case of three terminals or four terminals, FIG. What is necessary is just to connect between signal conductor 22a, 22b and the grounding conductor 23 like (b). Therefore, the measuring method according to this embodiment can be applied not only to a two-terminal electronic component but also to an electronic component having three or more terminals such as a filter.

Since the error model for calibration in the second embodiment is the same as the error model for TRL correction, the same calculation as TRL correction may be performed to remove the effect of error from the actual measurement result of the object. A mathematical expression for removing is described below. This equation is calculated based on the reflection coefficient in the case of 2-port measurement. However, in order to eliminate the influence of the error factor, it may be calculated from the four receiver outputs of the network analyzer. Also, in the case of three or more ports, the same equation as this equation may be used, or the influence of the error factor may be removed using a circuit simulation method. In short, any known technique may be selected. In Equation 25, D ₂ is an intermediate variable.

As described above, the dielectric constant of the transmission line material is obtained from the transmission line characteristic ξ, and further the characteristic impedance is obtained. On the other hand, the true value of the reflection coefficient of the subject from which the error factor obtained using Equation 25 is removed, and the transmission line The impedance of the subject can be calculated from the characteristic impedance.

このＺパラメータＺ_11A 、Ｚ_21Aと、前記のように求めた基板の特性インピーダンスＺ₀とを、数式２７に示すようにそれぞれ同じ周波数での値同士で乗じることにより、被検体１１のインピーダンスＺ_DUT を求めることができる。-Conversion from S parameter to impedance-
Since the calibration method is a two-port series method, the true value of the reflection coefficient S _11A and S _21A obtained by calibrating the error factor by the calibration method is used, and the subject's Z Parameters Z _11A and Z _21A are calculated.

By multiplying the Z parameters Z _11A and Z _21A and the characteristic impedance Z _{0 of the} substrate obtained as described above by values at the same frequency as shown in Equation 27, the impedance Z _DUT of the subject 11 is obtained. Can be requested.

実際には、被検体の対称性によりＺ_11AとＺ_21Aは同じ値になるため、Ｚ_DUTを求めるためには、数式２７のどちらを用いても構わない。なお、Ｓ_11A、Ｓ_21A、Ｚ_11A 、Ｚ_21AおよびＺ_DUT はいずれも複素数である。

Actually, since Z _11A and Z _21A have the same value due to the symmetry of the subject, either of Equation 27 may be used to obtain Z _DUT . S _11A , S _21A , Z _11A , Z _21A and Z _DUT are all complex numbers.

FIG. 11 shows a measuring jig 30 for measuring a subject by the shunt method. As the measurement jig 30, one signal conductor 32 is arranged on the upper surface of a jig substrate 31 made of a dielectric so as to extend continuously in the length direction, and is grounded at intervals on both sides in the width direction of the signal conductor 32. A CPW in which the conductor 33 is disposed is used. A ground conductor may also be provided on the back surface of the jig substrate 31. Connectors 34 and 35 are connected via coaxial cables 36 and 37 to measurement ports 38a to 38d of a network analyzer 38 which is an example of a measuring instrument. The signal lines of the coaxial cables 36 and 37 are fixed to both ends of the signal conductor 32 by soldering or welding.

Also in this embodiment, as in the first and second embodiments, the short-circuit reference 10 is shunt-connected to the transmission line at the position where the subject is measured (measurement point 11 in FIG. 11), and the signal conductor 32 and the ground conductor 33 are connected. _Are measured in a short-circuit state, and the reflection coefficient is measured as S _11M1 . Subsequently, calibration measurement is performed with the short-circuit reference connected at three measurement points 2 to 4 separated from the measurement point 1 in the port 1 direction or the port 2 direction.
In FIG. 11, the measurement points 2 to 4 are provided only on the port 1 side with respect to the measurement point 1, but may be provided separately on both sides (port 1 side and port 2 side) with the measurement point 1 in between. When it is provided on the port 2 side, the sign of the distance L is reversed with respect to the port 1 side. When the measurement points 2 to 4 are provided on both sides, effective data can be obtained even if the transmission path is short.

-Measurement in the through state-
Separately from the measurement based on the short-circuit standard 10, measurement is performed in a through state (direct connection state between ports). In the through state, the measurement is actually performed without connecting anything to the transmission line which is a measurement jig. Measurements, reflection coefficient at S _11MT, the transfer coefficient and S _21MT.

An error model of the calibration method of Example 3 is shown in FIG. This is not particularly new, and is the same as the error model of SOLT correction that has been used conventionally. In the figure, S _11M and S _21M are measured values of the reflection coefficient and the transmission coefficient, and S _11A and S _{21A and the} like are true values of the scattering coefficient of the object.
The unknown has four error factors for one-port measurement (E _DF , E _SF , E _RF ) and one transmission line characteristic ξ. Therefore, the short-circuit reference 10 can be short-circuited at four locations on the transmission line, and four equations can be _{created based on} the measurement values (S _11M1 , S _11M2 , S _11M3 , S _11M4 ) of the reflection coefficient at that time. (E _DF , E _SF , E _RF and ξ) can be determined.
If ξ is obtained in the same manner as in the first embodiment, E _DF , E _SF , and E _RF can be obtained by the following Expression 28. Denom is an intermediate variable.

以上はポート１側からポート２側へ信号を印加した場合（順方向）の議論であるが、逆方向についても全く同様である。The error coefficients (E _LF , E _TF ) in the through state are the measured values of the reflection coefficient and transmission coefficient (S _11MT , S _21MT ) in the ideal through state and the error coefficients (E _DF , E _SF , E _RF ) and can be derived by the following equation.

The above is the discussion when a signal is applied from the port 1 side to the port 2 side (forward direction), but the same applies to the reverse direction.

なお、伝送路特性ξから特性インピーダンスを求めることができるので、その後、被検体のインピーダンスを以下のように算出する。-Measurement of specimen-
When the error coefficient is obtained, as shown in FIG. 13, the subject 11 is connected between the signal conductor 32 and the ground conductor 33 at the subject measurement position P1, and the reflection coefficient and transmission coefficient in the forward / reverse direction of the subject. ( _{S11M, S21M, S12M, S22M} ) are measured. Using the measurement system error coefficients (E _DF , E _SF , E _RF , E _LF , E _TF ), the true value of the electrical characteristics of the object (S _11M , S _21M ) _S11A , _S21A ) can be obtained.

Since the characteristic impedance can be obtained from the transmission line characteristic ξ, the impedance of the subject is calculated as follows.

このＺパラメータＺ_11A 、Ｚ_21Aと、前記のように求めた基板の特性インピーダンスＺ₀とを、数式３２に示すようにそれぞれ同じ周波数での値同士で乗じることにより、被検体１１のインピーダンスＺ_DUT を求めることができる。-Conversion from S parameter to impedance-
Since the calibration method is a two-port shunt method, the true value of the reflection coefficient S _11A and S _21A obtained by calibrating the error factor by the calibration method is used to calculate the Z Parameters Z _11A and Z _21A are calculated.

The impedance Z _DUT of the subject 11 is obtained by multiplying the Z parameters Z _11A and Z _21A and the characteristic impedance Z _{0 of the} substrate obtained as described above by values at the same frequency as shown in Equation 32. Can be requested.

実施例２の場合と同様に、実際には被検体の対称性によりＺ_11AとＺ_21Aは同じ値になるため、Ｚ_DUTを求めるためには、数式３２のどちらを用いても構わない。なお、Ｓ_11A、Ｓ_21A、Ｚ_11A 、Ｚ_21AおよびＺ_DUT はいずれも複素数である。

As in the case of the second embodiment, Z _11A and Z _21A actually have the same value due to the symmetry of the subject. Therefore, either one of Equation 32 may be used to obtain Z _DUT . S _11A , S _21A , Z _11A , Z _21A and Z _DUT are all complex numbers.

In the first to third embodiments, the case where the measurement jig used for measuring the dielectric constant of the substrate and the measurement jig used for measuring and calibrating the object are the same CPW has been described. Even if the measurement jig used for the rate measurement and the measurement jig used for the measurement and calibration of the object are not the same, the impedance characteristic of the electronic component can be measured. Here, the measurement jig for dielectric constant measurement and the measurement jig for measurement / calibration are not the same, as long as the dielectric material used is the same, even if both transmission line shapes are different. It means good.
Specifically, first, a CPW transmission line is prepared as a measurement jig used for measuring the dielectric constant of the substrate, the dielectric constant is obtained by the same method as in Example 1, and the characteristic impedance of the transmission line is calculated.
Next, a measurement jig used for measuring and calibrating the specimen is made of the same dielectric material as the measurement jig used for dielectric constant measurement, and calibrated by the method of the present invention or a known method (for example, TRL calibration). And measure the S parameter of the electronic component. Note that a CPW, a microstrip line, a slot line, or the like can be used as a transmission line used for calibration, and is not particularly limited.
Furthermore, by multiplying the Z parameter calculated from the S parameter of the electronic component and the characteristic impedance of the transmission line by values at the same frequency, the impedance characteristic of the electronic component with higher accuracy than before can be obtained.

According to a preferred embodiment of the present invention, the following effects can be obtained.
(1) For each frequency range, the S-parameter of one port in the state where the signal conductor and the ground conductor are short-circuited (the state where the short-circuit reference is connected) is measured at least at four locations on the same substrate transmission line, and the error is measured. Since the mismatching between the connector and the planar transmission line is completely removed by correction, the characteristics of the transmission line (transmittance α and phase constant β) are obtained, so that a more accurate dielectric constant and tan δ can be measured.
(2) In the conventional dielectric constant measurement method, the dielectric material has to be processed in accordance with each measurement method, and it has not been possible to measure in the form of a transmission line that is actually used. Then, since the dielectric constant and tan δ can be measured in the form of the transmission line, the dielectric constant and tan δ of the transmission line actually used can be known.
(3) The dielectric constant obtained from the conventional dielectric constant measurement method is the relative dielectric constant of the material, but in the present invention, the effective dielectric constant ε _eff can be directly obtained, so the characteristic impedance is directly calculated from this ε _eff. can do.
(4) Since the relative dielectric constant of the material obtained by the conventional dielectric constant measurement method has a significant figure of about two digits, which is lower than the dimensional accuracy, the accuracy of the characteristic impedance calculated using it must be low. Although the effective figure of the effective dielectric constant ε _eff obtained by the present invention is equivalent to the dimensional accuracy, it is possible to obtain a characteristic impedance with higher accuracy than before.
(5) In the resonance method often used in the conventional dielectric constant measurement method, the frequency characteristics of the dielectric constant and tan δ cannot be obtained. In the present invention, the dielectric constant and tan δ for each measurement frequency range are obtained. Can do.
(6) Conventionally, the dielectric constant data of the purchased material lot could not be accurately grasped. However, in the present invention, the dielectric constant and tan δ data of the purchased material lot can be accurately grasped.

Furthermore, since the dielectric constant measurement method has been established by the present invention, the following can be performed.
(1) In high-frequency impedance measurement of electronic components using a network analyzer, calibration methods such as the TRL calibration method that eliminates error factors in the measurement system calibrate the error factors in the measurement system in order to obtain the impedance of the electronic component. It is necessary to multiply the Z parameter calculated from the S parameter obtained in this way by the characteristic impedance of the transmission line used for the measurement, but since the dielectric constant for each frequency range can be obtained with high accuracy, the accuracy of the characteristic impedance is As a result, the impedance characteristics of electronic components can be accurately obtained.
(2) If the dielectric constant and tan δ of the substrate actually used are determined in advance according to the present invention, the design accuracy in high-frequency circuit design can be improved.
(3) In the measurement of the high-frequency dielectric constant and tan δ of the dielectric, conventionally, the dielectric material had to be processed according to the measurement method and equipment, but the dielectric constant and tan δ were relatively easily processed. Measurement of high-frequency materials became easy.
(4) The dielectric constant and tan δ of the material used for the high-frequency transmission board can be easily measured.

Claims (10)

Preparing a measuring jig having a transmission path whose electrical characteristics per unit length are unknown, comprising a signal conductor and a ground conductor on a dielectric substrate;
Measuring the electrical characteristics by short-circuiting the signal conductor and the ground conductor in at least four locations in the length direction of the transmission path;
From the measured value in the short circuit state, calculating the characteristics of the transmission path;
Calculating at least one of a dielectric constant and tan δ of the transmission line material from characteristics of the transmission line, and measuring a dielectric constant of the transmission line material. The dielectric of the transmission line material according to claim 1, wherein the transmission line is a planar transmission line capable of short-circuiting the signal conductor and the ground conductor at an arbitrary position in the transmission line by pressing the conductor from the upper surface. Rate measurement method. For each frequency range to be measured, the scattering coefficient of one port with the signal conductor and the ground conductor short-circuited is measured at least at four locations on the transmission line.
A transmission path characteristic ξ (ξ = α ⁻² exp (j2β), α: transmission [U / mm], β: phase constant [rad / mm]) is calculated using the scattering coefficient. Item 3. A dielectric constant measurement method for a transmission line material according to Item 1 or 2. 4. The method of measuring a dielectric constant of a transmission line material according to claim 3, wherein a relative dielectric constant ε _r of the transmission line material is calculated from the transmission line characteristic ξ and a physical dimension of the transmission line. The distance at which the signal conductor and the ground conductor are short-circuited is L ₁ , L ₂ , and L ₃ from the measurement point 1 to the port 1 side, and the scattering coefficients at the measurement points 2 to 4 are S _11M1 , S _{11M2, and} S _11M3 . 4. The transmission according to claim 3, wherein a calculation formula of the transmission line characteristic ξ when the distance ratio is L ₁ : L ₂ : L ₃ = 1: 2: 3 is as follows: Method for measuring the dielectric constant of road materials.

The distance at which the signal conductor and the ground conductor are short-circuited is L ₁ , L ₂ , and L ₃ from the measurement point 1 to the port 1 side, and the scattering coefficients at the measurement points 2 to 4 are S _11M1 , S _{11M2, and} S _11M3 . 4. The transmission according to claim 3, wherein the calculation formula of the transmission line characteristic ξ when the distance ratio is L ₁ : L ₂ : L ₃ = 1: 2: 4 is as follows: Method for measuring the dielectric constant of road materials.

The method of measuring a dielectric constant of a transmission line material according to claim 3, wherein a phase difference between positions where the signal conductor and the ground conductor are short-circuited is about 70 ° to 145 °. A step of calculating a transmission path error coefficient E _xx together with the transmission path characteristic ξ from the measured value in the short-circuit state in the dielectric constant measurement method according to claim 1;
Measuring the scattering coefficient S _xx with the measured electronic component connected to the transmission line;
Removing the error coefficient E _xx of the transmission line from the measured scattering coefficient S _{xx of the} electronic component to be measured to obtain a true value S _xxA of the scattering coefficient of the electronic component to be measured;
_Obtaining a Z parameter Z _xxA from a true value S _xxA of a scattering coefficient of the electronic component to be measured. Calculating the transmission line characteristic ξ from the measured value in the short-circuit state in the dielectric constant measurement method according to claim 1;
Preparing a measurement / calibration measurement jig formed of the same material as the dielectric substrate of the measurement jig, and obtaining an error coefficient E _xx of the transmission path of the measurement jig;
Measuring the scattering coefficient S _xx in a state where the electronic device to be measured is connected to the transmission path of the measurement / calibration measuring jig;
Removing the error coefficient E _xx of the transmission line from the measured scattering coefficient S _{xx of the} electronic component to be measured to obtain a true value S _xxA of the scattering coefficient of the electronic component to be measured;
_Obtaining a Z parameter Z _xxA from a true value S _xxA of a scattering coefficient of the electronic component to be measured.
Calculating the characteristic impedance of the transmission line from the dielectric constant of the transmission line material obtained by the dielectric constant measurement method according to claim 1;
The step of obtaining the impedance of the electronic component to be measured from the Z parameter Z _{xxA of the} electronic component to be measured obtained by the electrical property measuring method of the electronic component according to claim 8 or 9, and the characteristic impedance of the transmission path. A method for measuring electrical characteristics of electronic parts, comprising:

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