JP6590257B2 - Dielectric constant evaluation method using time domain analysis - Google Patents

Description

  The present invention relates to a technique for correcting a reflected wave signal including noise derived from a jig in dielectric constant evaluation using time domain analysis in a reflection transmission method.

The reflection transmission method is used as a measurement method for dielectric constant evaluation necessary for the development of electromagnetic shielding materials and absorbers.
In the reflection transmission method, the dielectric constant is derived from the reflection / transmission characteristics (S parameter) of the electromagnetic wave incident on the sample (Non-Patent Document 1).

A coaxial / waveguide is used as a jig (jig) to enclose and measure a sample in order to evaluate the dielectric constant of high-frequency components with high loss in RF, microwave, millimeter wave, and submillimeter wave bands (10 MHz to over 300 GHz). Used.
When this measurement method is used, an unnecessary reflection component derived from the jig is included in the signal obtained by measuring the reflected wave, and thus the influence can be removed by using gating in the time domain analysis (Patent Document 1).

  The gating method in time domain analysis is used for millimeter wave band material evaluation and antenna measurement. From the time domain waveform obtained by performing FFT conversion on the measurement result in the frequency domain, for example, unnecessary reflections at the connection points / antenna of the jig This refers to acquiring only a direct wave signal without a component, and a highly accurate dielectric constant can be evaluated by a frequency domain waveform obtained by inverse FFT conversion (Non-patent Document 2).

However, when using the gating method in this time domain analysis on a sample sealed in a 40 mm long coaxial line at 1 to 18 GHz in the microwave band (about 10 GHz), the direct wave of the sample and the end face of the jig in the time domain The interval between the reflected waves becomes narrow, and the two cannot be clearly separated (FIG. 2).
If the dielectric constant is obtained without gating, ripples appear in the dielectric constant to be evaluated due to the influence of multiple reflection in the jig connection, and the dielectric constant of the sample cannot be evaluated correctly (FIG. 1).
In order to clearly separate the direct wave and reflected wave and apply time domain analysis, it is necessary to use a long sample jig, but if a conventional gating method is used for a sample enclosed in a 30 cm long coaxial line, Since the time domain waveform of the S parameter changes discontinuously at the gating boundary, a ripple appears in the frequency domain waveform obtained by inverse FFT transformation, and a ripple also appears in the dielectric constant to be evaluated. It cannot be evaluated correctly (Fig. 4, wave waveform).

International Publication No. 03/019207

Y. Kato and M. Horibe, “Study of reflection effect at fixture interfaces on permittivity measurements using the transmission / reflection method,” 84th ARFTG Conf. Digest, pp. 1-4, Dec. 2014. P. G. Bartley and S. B. Begley, “Improved Free-Space S-parameter Calibration,” IMTC 2005 proceedings, 372-375, 2005.

Further, when the gating method is used in the time domain analysis, when the influence of the jig length on the time domain waveform of the reflected wave at the jig end face is examined in detail, as shown in FIG. When the jig length is short due to the sample length and dielectric constant, the two peaks of the reflected wave originating from the jig appearing before and after the direct wave by the sample can be clearly separated when the jig length is long. It turned out that gating itself was difficult.
Therefore, the direct wave of the sample and the reflected wave of the end face of the jig can be distinguished by using the gating method so that only the direct wave can be used, or the influence of the reflected wave by the jig at the discontinuous point is suppressed or eliminated, and directly It becomes a problem to accurately evaluate the dielectric constant based on the waveform in the frequency domain obtained by performing the inverse FFT based only on the wave.

  In order to solve the above-mentioned problems, the present invention provides a Gating method in a conventional time-domain analysis using an S parameter measured by enclosing a sample in a jig, coaxial line or waveguide having a predetermined sufficient length. Based on the time domain waveform obtained by using the median as the initial estimated value of the dielectric constant of the sample based on the dielectric constant (vibrating value) obtained by evaluation by the technique, the gating region is The time domain waveform is corrected and extended so as to change substantially continuously outside the gating area by calculation.

When the dielectric constant was evaluated after returning the time domain waveform of the S parameter thus corrected to the frequency domain by inverse FFT, a dielectric constant characteristic consisting of a smooth curve as obtained by other measurement methods was obtained.
This analysis can achieve high accuracy in permittivity measurement mainly in the low frequency region.
The time domain analysis method developed below will be described with reference to the processing flowchart shown in FIG.

ここで、ｚ＝ｅｘｐ(−γｄ)、γ：試料領域の伝搬定数、γ₀：空気領域の伝搬定数、Γ：は、試料面における反射係数である。
Γはγとγ₀の関数であり、γ₀は試料に依らない定数であり、γは試料の誘電率の関数なので、測定されたＳパラメータを式(1)から(3)に代入し、誘電率について解くことで、試料の誘電率を求めることができる。 The S parameter of the jig enclosing the sample is measured (step S1).
When a sample to be measured having a length d is sealed in the center of a 2 L long coaxial line jig (FIG. 13B), the S parameter is expressed by the following equation from the transmission line theory.

Here, z = exp (−γd), γ: propagation constant of the sample region, γ ₀ : propagation constant of the air region, and Γ: a reflection coefficient on the sample surface.
Since Γ is a function of γ and γ ₀ , γ ₀ is a constant that does not depend on the sample, and γ is a function of the dielectric constant of the sample, the measured S parameter is substituted into equations (1) to (3), By solving for the dielectric constant, the dielectric constant of the sample can be determined.

In the actual measurement of the S parameter, the influence of multiple reflection at the connection portion of the jig appears.
However, since the reflection is assumed to be zero in the derivation of Equations (1) to (3), multiple reflection becomes an error when analyzing the dielectric constant from the S parameter, and as a result, ripples appear in the frequency characteristics of the dielectric constant. appear.
In order to remove the influence of multiple reflection, the existing time domain analysis method (gating method) analyzes as follows.
For example, if the reflected amount to be measured is converted to a time domain waveform by FFT, the raw data shown in FIG. 8 is obtained. In addition to the peaks caused by reflection on the sample surface (circle 2 in FIG. A peak due to reflection at the part appears (full 1, full 3).
In the gating method, only the time-domain waveform having a finite width around the peak (round 2) is left, and the outside thereof is set to zero, thereby removing the influence of reflection at the connecting portion of the jig (step S2).

When the time domain waveform obtained by the gating method is returned to the frequency domain waveform by inverse FFT and the dielectric constant is obtained from the S parameter according to the equations (1) to (3), the waveform shown in FIG. 4 is obtained (step S3).
Although the influence of multiple reflections has been eliminated, ripples resulting from discontinuous changes in the time domain waveform due to gating appear in the frequency characteristics of the dielectric constant.

In the method of the present invention, the time domain waveform is extended to the outside of the gating area to eliminate the discontinuous change, thereby realizing the dielectric constant measurement / analysis in which the ripple does not occur in the frequency characteristics of the dielectric constant.
First, the median value of the oscillating dielectric constant obtained by the gating method is set as the initial estimated value of the dielectric constant (FIG. 4) (step S4).
Substituting the initial estimate of the dielectric constant into equations (1) to (3), the length of the covered d is the center of an ideal coaxial line jig (length 2L) with zero reflection at the jig connection. The S parameter when the measurement sample is sealed is calculated.

The S parameter in the frequency domain is subjected to FFT, and among the obtained time domain waveforms, the data of the area outside the gating area is used to extend the gated time domain waveform to both outer sides (FIG. 6). (Step S5).
That is, as the time domain waveform of the S parameter, data obtained as the FFT of the measured value is used in the gating region, and data obtained as a result of calculation based on the initial estimated value of the dielectric constant is used outside the gating region.
By connecting both, continuous stretching of the gated time domain waveform can be performed.

  When the dielectric constant is obtained according to the equations (1) to (3) from the frequency domain waveform obtained by performing inverse FFT on the time domain waveform obtained in step S5, a gentle dielectric constant curve without ripples can be obtained ( Step S6).

In the present invention, the median value is set as the initial estimated value based on the dielectric constant obtained by the gating method, but how the dielectric constant finally obtained changes when other initial estimated values are selected. As shown in FIG. 5A, as shown in FIG. 5A, the median dielectric constant obtained by the gating method (round 1 in FIG. 5, the same applies hereinafter), minimum value (round 2), maximum value (round 3). 5B is obtained as the dielectric constant finally obtained by extending the time domain waveform of the S parameter based on the initial estimated values.
FIG. 5B shows that the dielectric constant can be determined with high accuracy regardless of which initial estimated value is used, and it was confirmed that the analysis of the present invention is not sensitive to how to select the initial estimated value.
Therefore, even if the accuracy of determining the initial estimated value is poor, the dielectric constant can be estimated with high accuracy as the final result.

By extending the gating method to the microwave band (about 10 GHz), which was difficult to apply in the past, a gentle dielectric constant curve (characteristic) close to the actual measurement value was obtained, and the measurement accuracy was improved.
In the millimeter wave band, it was confirmed that the measurement accuracy of the conventional gating method was exceeded.
As a result, the gating method can be utilized with high measurement accuracy in a wide band.

It is a graph showing the dielectric constant in the frequency domain which measured the sample enclosed in the 40-mm coaxial line. The dotted line represents a dielectric constant estimation line obtained by the least square method. The figure showing the time domain waveform of a reflected wave when the length of a jig is 5cm, 10cm, and 30cm. It is a process flowchart showing the time domain analysis method developed by this invention. It is the figure which showed the method of calculating | requiring the initial estimated value of a dielectric constant with the method of this invention. It is a figure showing the initial stage value dependency of the dielectric constant calculated | required by the method of this invention. It is a figure showing the time domain waveform of the reflected wave correct | amended with the method of this invention. A conceptual diagram (left) and a photograph (right) of the free space method measurement system. It is a figure showing the time domain waveform of a reflected wave. It is a figure showing the estimation result (A) of a dielectric constant, and the deviation (B) from a setting value. It is an image of a coaxial line jig with a length of 30 cm. It is a figure showing the dielectric constant measurement result of PTFE. Replacing corresponds to this analysis method, Gating corresponds to the existing time domain analysis method (gating), and Raw Data does not use time domain analysis. It is a figure showing the comparison between measurement methods. (A) is a diagram showing a general gating method, and (B) is a diagram showing a schematic diagram of a coaxial line jig having a length of 2 L in which a sample to be measured having a length d is sealed in the center.

  Although an Example is shown below, implementation of this invention is not restrict | limited to this example, When applicable, it is applicable also to another example.

According to the present invention, a PTFE sample was sealed in a coaxial line jig having a length of 30 cm shown in FIG. 10, and the dielectric constant was measured.
The measurement frequency is 1 to 18 GHz, and the sample length is about 5 mm.

FIG. 11 shows the measurement result of the dielectric constant.
In the figure, Replacing corresponds to this analysis method, Gating corresponds to the existing time domain analysis method (gating), and Raw data corresponds to the case where time domain analysis is not used.

  Looking at this, the raw data shows ripples due to multiple reflections at the joint end of the jig (particularly in the frequency range above 10 GHz).

On the other hand, a ripple is also seen in Gating, but this is due to a discontinuous change in the time domain waveform as a result of the gating operation.
Replacing shows a monotonous change with no ripple, and is considered to reflect the dielectric constant characteristics of the sample most accurately.

  FIG. 12 shows the results of comparison with other measurement methods.

  In FIG. 12, Coax (30 cm) is measured using a coaxial line jig with a length of 30 cm, and the dielectric constant is calculated by this analysis method. Waveguide is the result of using the X-band waveguide reflection transmission method. In other words, Coax (4 cm) was measured using a coaxial line jig having a length of 4 cm, and the dielectric constant was calculated without using time domain analysis.

  In the measurement using the Waveguide X-band waveguide reflection transmission method, reflection at the jig connecting portion is suppressed as compared with the coaxial line jig, and the measurement accuracy is considered to be the highest.

On the other hand, only a narrow band can be measured with a single jig.
In addition to the fact that the frequency band of the X-band waveguide is 8 to 13 GHz, FIG. 12 also compares in that frequency range.

  Since Coax (4cm) does not remove the influence of multiple reflections at the connection part of the coaxial line jig, fine vibrations can be seen in the measurement results.

  On the other hand, in Coax (30 cm), since the influence of multiple reflection is removed, no vibration is observed, and the change is monotonous like Waveguide.

  Moreover, the measurement results of Coax (30 cm) and Waveguide are in good agreement, and it was confirmed that this method gave results consistent with other measurement methods.

  Next, an embodiment in which the present invention is applied in place of a normal gating operation effective in the free space method used as a material measurement method in the millimeter wave band will be described.

In this method, two antennas are opposed to each other as shown in FIG.
Time domain analysis can be used to remove multiple reflections due to the lens antenna between the antennas when calculating the dielectric constant of the sample from the measured S-parameters.

  Considering measurement of a sample having a dielectric constant of 2 in the W band (75 to 110 GHz), the dielectric constant is estimated from the measured S-parameter data.

When the S parameter to be measured from the transmission line theory is calculated and the time domain waveform of the reflected wave is calculated, Raw data in FIG. 8 is obtained.
Here, peaks 1 (1 in FIG. 8; the same applies hereinafter) and 3 indicate reflection at the antenna, and peak 2 indicates reflection at the sample.

  When only the peak 2 is selectively left using the method of the present invention, the Replace shown in FIG. 8 is obtained.

The result of calculating the dielectric constant from the S parameter is shown in FIG.
Replace corresponds to this analysis method, Gate corresponds to normal time domain analysis (gating), and Raw does not use time domain analysis.

FIG. 9B shows a deviation between a set value and an estimated value when the present analysis method and a normal time domain analysis method (gating) are used.
It can be confirmed that the estimation result using this analysis method has the highest accuracy.

DESCRIPTION OF SYMBOLS 1 Transmission antenna 2 Sample 3 Reception antenna 4 Lens antenna 5 Jig

Claims (12)

This is a dielectric constant measurement device that uses a microwave band electromagnetic wave to encapsulate a sample in a coaxial line or waveguide jig having a predetermined length and both ends of a connecting portion, and evaluate the dielectric constant characteristics by a reflection transmission method using the gating method. And
Means for emitting a predetermined electromagnetic wave to the coaxial line or waveguide jig;
Means for measuring reflected and transmitted waves of the emitted electromagnetic wave and obtaining an S parameter;
Means for evaluating a dielectric constant characteristic of the sample based on the S parameter;
A frequency domain waveform obtained by inverse FFT from a time domain waveform obtained by applying the gating method from the acquired S parameter time domain waveform to remove multiple reflections at the connection portion of the coaxial line or waveguide jig. Based on the dielectric constant characteristics of the sample obtained from the above, set an initial estimate of the dielectric constant characteristics of the sample,
It is obtained by inverse FFT from the time domain waveform obtained by extending the time domain waveform of the S parameter to which the gating method is applied to both sides of the gate by the time domain waveform corresponding to the initial estimated value of the dielectric constant characteristic. A reflection transmission method dielectric constant measuring apparatus characterized by evaluating a dielectric constant characteristic of the sample based on a measured frequency domain waveform.   2. The reflection transmission method dielectric constant measuring apparatus according to claim 1, wherein the initial estimated value is a median value (central axis) of a dielectric constant curve of the sample obtained by applying the gating method.   The reflection transmission method dielectric constant measuring apparatus according to claim 2, wherein the microwave band is 1 to 18 GHz.   4. The reflection transmission method dielectric constant measuring apparatus according to claim 3, wherein the predetermined length is approximately 30 cm. A dielectric constant measuring apparatus for evaluating dielectric constant characteristics by a free space method using a gating method by placing a sample in the center between two lens antennas using millimeter wave electromagnetic waves,
Means for emitting a predetermined electromagnetic wave to the front lens antenna;
Means for measuring reflected and transmitted waves of the emitted electromagnetic wave and obtaining an S parameter;
Means for evaluating a dielectric constant characteristic of the sample based on the S parameter;
The dielectric constant of the sample obtained from the frequency domain waveform obtained by applying the gating method from the acquired S-parameter time domain waveform to remove multiple reflections between the two lens antennas and performing inverse FFT Set an initial estimate of the dielectric constant characteristics of the sample based on the characteristics,
It is obtained by inverse FFT from the time domain waveform obtained by extending the time domain waveform of the S parameter to which the gating method is applied to both sides of the gate by the time domain waveform corresponding to the initial estimated value of the dielectric constant characteristic. A reflection transmission method dielectric constant measuring apparatus characterized by evaluating a dielectric constant characteristic of the sample based on a measured frequency domain waveform.   6. The reflection transmission method dielectric constant measuring apparatus according to claim 5, wherein the initial estimated value is a median value (central axis) of a dielectric constant curve of the sample obtained by applying the gating method. This is a dielectric constant measurement method that uses a microwave band electromagnetic wave to enclose a sample in a coaxial line or waveguide jig having a predetermined length and both ends of a connecting portion, and evaluates the dielectric constant characteristics by the reflection transmission method using the gating method. And
Emitting a predetermined electromagnetic wave to the coaxial line or waveguide jig;
Measuring the reflected wave / transmitted wave of the emitted electromagnetic wave to obtain an S parameter;
Evaluating a dielectric constant characteristic of the sample based on the S parameter;
From the frequency domain waveform obtained by inverse FFT from the time domain waveform obtained by applying the gating method from the acquired S parameter time domain waveform to remove the multiple reflection of the connection part of the coaxial line jig. Obtaining a dielectric constant characteristic;
Further setting an initial estimate of the dielectric constant characteristic of the sample based on the dielectric constant characteristic of the sample obtained by applying the gating method;
It is obtained by inverse FFT from the time domain waveform obtained by extending the time domain waveform of the S parameter to which the gating method is applied to both sides of the gate by the time domain waveform corresponding to the initial estimated value of the dielectric constant characteristic. A reflection transmission method dielectric constant measurement method, comprising: evaluating a dielectric constant characteristic of the sample based on the measured frequency domain waveform.   8. The reflection transmission method dielectric constant measurement method according to claim 7, wherein the initial estimated value is a median value (central axis) of a dielectric constant curve of the sample obtained by applying the gating method.   9. The reflection transmission method dielectric constant measurement method according to claim 8, wherein the microwave band is 1 to 18 GHz. A dielectric constant measurement method for evaluating dielectric constant characteristics by a free space method using a gating method by placing a sample in the center between two lens antennas using millimeter wave electromagnetic waves,
Emitting a predetermined electromagnetic wave to the front lens antenna;
Measuring the reflected wave / transmitted wave of the emitted electromagnetic wave to obtain an S parameter;
A step of evaluating a dielectric constant characteristic of the sample based on the S parameter, and an inverse FFT that removes multiple reflections between the two lens antennas by applying the gating method from the time domain waveform of the acquired S parameter. Obtaining a dielectric constant characteristic of the sample obtained from the frequency domain waveform obtained by
Furthermore, an initial estimated value of the dielectric constant characteristic of the sample obtained by applying the gating method is set,
It is obtained by inverse FFT from the time domain waveform obtained by extending the time domain waveform of the S parameter to which the gating method is applied to both sides of the gate by the time domain waveform corresponding to the initial estimated value of the dielectric constant characteristic. A reflection transmission method dielectric constant measurement method, comprising: evaluating a dielectric constant characteristic of the sample based on a measured frequency domain waveform.   The reflection transmission method dielectric constant measurement method according to claim 10, wherein the initial estimated value is a median value (central axis) of a dielectric constant curve of the sample obtained by applying the gating method.   The calculation process of the S parameter acquired by measuring the reflected wave and the transmitted wave of the emitted electromagnetic wave in each step of the reflection transmission method dielectric constant measurement method according to any one of claims 7 to 11. And a storage medium on which the program is recorded.

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