JP2007198975A - Both-end open type half wavelength resonator and method of measuring dielectric constant using it - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of measuring a dielectric constant by suppressing deterioration of a non-load Q value in particular, even when thickness is 50 μm or less by measuring the dielectric constant of a dielectric thin layer arranging a conductor on upper and lower faces at high precision and to provide a both-end open type half wavelength resonator. <P>SOLUTION: The both-end open type half wavelength resonator A1 comprises providing a rectangular strip conductor 3 on one face of the dielectric thin layer 1, providing a ring-like ground conductor 4 on the other face of the dielectric thin layer 1, and being arranged so that at least one end in a long axis direction of the slip conductor 3 and a part of the ground conductor 4 are overlapped in viewing from a layered direction. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an open-ended half-wave resonator for measuring a dielectric constant in a microwave band in a region sandwiched between conductors disposed on upper and lower surfaces of a thin dielectric layer, and a dielectric constant measuring method using the same. It is.

  In recent years, with the development and popularization of mobile communication technology, there is a strong demand for a dielectric constant measurement method for dielectric substrates for microwave circuit configuration. Various methods for measuring dielectric constants of microwaves on dielectric substrates have been proposed. Among them, the cavity resonator method (JIS R 1641, established in 2002) is recognized as a high-precision measurement method. In this cavity resonator method, the dielectric constant in the surface direction of the substrate is measured.

  On the other hand, when ceramics are used as electronic parts, metallized and ceramics are often fired simultaneously by a simultaneous firing technique to constitute electronic parts. In this case, the dielectric constant of ceramics may change due to differences in firing conditions compared to firing with ceramics alone or due to interdiffusion with metallization, so dielectric constant measurement is sandwiched between cofired bodies, especially metallized. It is necessary to measure with ceramics (sample). However, since the cavity resonator method is to measure by sandwiching a measurement sample between a pair of metal bottomed cylindrical members, the sample that can be measured needs to be a substrate of a single ceramic, Measurement of the co-fired ceramic substrate is not possible.

Therefore, a measurement method using a microstrip line ring resonator has been proposed as a method for measuring the dielectric characteristics of a ceramic substrate co-fired with metallization, particularly a ceramic substrate sandwiched between metallizations (for example, non-patented). Reference 1). This microstrip line ring resonator is formed by forming a ring-shaped conductor on the upper surface of the ceramic layer and a solid ground conductor on the lower surface. In this measurement method, the thickness of the ring-shaped conductor having the same shape is provided. The microstrip line ring resonators are formed by simultaneously firing different ceramic substrates, and the difference between the unloaded Q values of these microstrip line ring resonators is measured to determine the conductivity of the metallization and the dielectric of the ceramic layer. The tangent is determined. This method uses the fact that the conductor loss increases when the ceramic layer is thin as a measurement principle, and further assumes that the dielectric properties of the ceramic layers having different thicknesses are equal.
Aly E. Fathy, et al., “An Innovative Semianalytical Technique for Ceramic Evaluation at Microwave Frequencies,” IEEE Trans. MTT., Vol. 50, pp. 2247-2252, Oct. 2002.

  However, in a ceramic substrate co-fired with metallization, when the thickness of the ceramic layer is thin, the change in dielectric properties due to diffusion from the metallization becomes relatively large. It was. In addition, when the thickness of the ceramic layer is 50 μm or less, the above-mentioned microstrip line ring resonator has a very large conductor loss, so that there is a problem that the unloaded Q value is lowered and measurement is difficult. .

  The present invention provides a dielectric constant measuring method capable of measuring the dielectric constant of a thin dielectric layer having conductors on the upper and lower surfaces with high accuracy, and in particular, suppressing the decrease in no-load Q value even when the thickness is 50 μm or less. An object is to provide an open-ended half-wave resonator.

  According to the present invention, a rectangular strip conductor is provided on one surface of the thin dielectric layer, and an annular ground conductor is provided on the other surface of the thin dielectric layer, and at least one of the strip conductors in the major axis direction is provided. An open both-end half-wave resonator, wherein the end portion and a part of the ground conductor are arranged so as to overlap each other when viewed from the stacking direction.

  Such an open-ended half-wave resonator can be effectively used in a dielectric constant measurement method described later. According to this open-ended half-wavelength resonator, the capacitance at both ends can be increased, which is effective for reducing the size of a filter or the like. In addition, the conductor loss can be reduced as compared with a microstrip line resonator having both ends open as shown in FIG. 4 described later, which is effective in reducing the loss. It is effective not only for the dielectric constant measurement method described later, but also as a resonator serving as a basic structure of an electronic component such as a filter using a ceramic substrate.

  In the first dielectric constant measurement method of the present invention, the open-ended half-wave resonator is excited to measure at least one of a resonance frequency and an unloaded Q value, and the resonance frequency and the unloaded Q are measured. The dielectric constant in the thickness direction of the dielectric thin layer is calculated from at least one of the measured values. The half-wavelength in the open both-end half-wave resonator means that the length of the strip conductor in the major axis direction is a half-wavelength.

  According to such a dielectric constant measurement method, since the ratio of the electric field energy to the resonance space is high at the portion where the strip conductor and the ground conductor overlap in the stacking direction, the dielectric thin layer sandwiched between these conductors Dielectric constant can be measured with high accuracy. Further, since the ground conductor is formed in an annular shape and the conductor non-forming region exists inside the ground conductor, conductor loss can be suppressed and the unloaded Q value can be increased. Thereby, measurement can be facilitated and measurement accuracy can be improved. In addition, the open-ended half-wave resonator for dielectric constant measurement and the dielectric thin layer can be integrally fabricated as a planar circuit, eliminating measurement errors associated with resonator assembly compared to using a three-dimensional resonator. be able to. That is, the resonator is manufactured by, for example, applying a metallized paste for forming a strip conductor and a ground conductor by screen printing or the like on the upper and lower surfaces of a green sheet for forming a dielectric, using a common simultaneous firing technique, and firing this Therefore, it is possible to manufacture easily, and it is possible to minimize the measurement error accompanying the manufacture of the resonator.

The second dielectric constant measuring method of the present invention is a first open-ended half-wave resonator comprising the open-ended half-wave resonator and having a different area of a conductor non-forming region surrounded by the annular ground conductor. And the second open-ended half-wave resonator are excited to measure at least _one of a resonance frequency f ₁ and an unloaded Q value Q ₁ of the first open-ended half-wave resonator and And measuring at least one of a resonance frequency f ₂ and an unloaded Q value Q ₂ of the two open-ended half-wavelength resonators, and measuring the resonance frequency f ₁ and the resonance frequency f ₂ and the unloaded Q value Q ₁ and it is characterized in that to calculate the dielectric constant in the thickness direction of the dielectric thin layer from at least one of the measured values of the unloaded Q value Q _2.

In this dielectric constant measurement method, the conductor loss of the open-ended half-wave resonator depends on the area of the conductor non-forming region surrounded by the annular ground conductor, and the first open-ended type having a different area of the conductor non-forming region is different. The fact that there is a difference between the unloaded Q value of the half-wave resonator and the unloaded Q value of the second open-ended half-wave resonator is utilized. In this method, at least one of the resonance frequency f ₁ and the unloaded Q value Q ₁ of the _first open-ended half-wave resonator is measured, and the resonance of the second open-ended half-wave resonator is measured. At least one of the frequency f ₂ and the unloaded Q value Q ₂ is measured, and using these data, the electrical conductivity of the conductor and the relative dielectric constant of the dielectric thin layer are obtained by numerical analysis such as FEM (finite element method). At least one of the ratio and the dielectric loss tangent can be calculated.

In the second dielectric constant measurement method, in the first open-ended half-wave resonator, the area of the region where at least one end in the major axis direction of the strip conductor and a part of the ground conductor overlap when viewed from the stacking direction. And by appropriately adjusting the area of the region where at least one end in the major axis direction of the strip conductor in the second open-ended half-wave resonator and a part of the ground conductor overlap when viewed from the stacking direction, The difference between the resonance frequencies f ₁ and f ₂ can be reduced, and a decrease in accuracy due to the frequency dependence of the conductivity of the conductor, the relative dielectric constant of the dielectric thin layer, and the dielectric loss tangent can be easily suppressed. Also, by making the thickness of the dielectric thin layer the same between the first open-ended half-wave resonator and the second open-ended half-wave resonator, the effect of diffusion from metallization is made equal. Thus, even when the thickness of the dielectric thin layer is extremely thin, a highly accurate dielectric constant can be obtained.

Furthermore, the third dielectric constant measuring method of the present invention is a double-ended open type comprising a solid ground conductor in place of the open-ended half-wave resonator and the annular ground conductor of the open-ended half-wave resonator. The microstrip line resonator is excited to measure at least one of the resonance frequency f ₃ and the no-load Q value Q ₃ of the open both-end half-wave resonator and the resonance of the open both-end microstrip line resonator. At least one of the frequency f ₄ and the no-load Q value Q ₄ is measured, and at least one of the resonance frequency f _{3, the} resonance frequency f ₄ , the no-load Q value Q _3, and the no-load Q value Q ₄ The dielectric constant in the thickness direction of the dielectric thin layer is calculated from one measured value.

Also in this dielectric constant measurement method, the open-ended microstrip line resonator has a very large conductor loss, and the unloaded Q value of the open-ended half-wave resonator and the unloaded Q of the open-ended microstrip line resonator. The fact that there is a difference between values is used. In this method, at least one of the resonance frequency f ₃ and the no-load Q value Q ₃ of the open-ended half-wave resonator is measured, and the resonant frequency f _{4 of the} open-ended microstrip line resonator is measured. Measure at least one of the load Q values Q ₄ and use these data to calculate at least one of the electrical conductivity of the conductor, the relative dielectric constant of the dielectric thin layer, and the dielectric loss tangent by numerical analysis such as FEM it can.

In the third dielectric constant measurement method, the area of the region where at least one end in the major axis direction of the strip conductor and a part of the ground conductor overlap in the open direction half-wave resonator as viewed from the stacking direction is appropriately adjusted. By doing so, the difference between the resonance frequencies f ₃ and f ₄ can be reduced, and the accuracy degradation due to the frequency dependence of the conductivity of the conductor, the relative dielectric constant of the dielectric thin layer and the dielectric loss tangent can be easily suppressed. it can. Also, by making the thickness of the dielectric thin layer the same between the open-ended half-wave resonator and the open-ended microstrip line resonator, the influence of diffusion from metallization can be made equal, and the dielectric A highly accurate dielectric constant can be obtained even when the thin layer is extremely thin.

  According to the open-ended half-wave resonator of the present invention and the dielectric constant measurement method using the same, the dielectric constant of a thin dielectric layer in which conductors are arranged on the upper and lower surfaces can be measured with high accuracy. Even if it becomes below, the fall of a no-load Q value can be suppressed.

(Double-ended open half-wave resonator)
An embodiment of an open-ended half-wave resonator according to the present invention will be described with reference to FIG.

  An open-ended half-wavelength resonator A1 of the present invention shown in FIG. 1 includes a dielectric thin layer (sample layer) 1, a rectangular strip conductor 3 provided on the upper surface of the dielectric sample 1, and a dielectric thin layer. (Sample layer) It is comprised from the cyclic | annular ground conductor 4 provided in the lower surface of 1. FIG.

  Specifically, the dielectric thin layer (sample layer) 1 has a substantially square shape when viewed from the stacking direction, and an elongated shape is formed on the upper surface of the dielectric thin layer (sample layer) 1 when viewed from the stacking direction. The strip conductor 3 is formed, and an annular ground conductor 4 is formed along the peripheral portion when viewed from the stacking direction on the lower surface of the dielectric thin layer (sample layer) 1. It arrange | positions so that a part of conductor 4 may overlap seeing from a lamination direction.

  Since the electric field energy is high in a region overlapping the ground conductor 4 that is the end of the strip conductor 3 when viewed from the stacking direction, the thickness of the dielectric thin layer 1 at the portion sandwiched between the strip conductor 3 and the ground conductor 4 The dielectric constant in the direction can be measured with high accuracy. Further, since the overlapping region is at both ends of the strip conductor 3, conductor loss is unlikely to occur, and a decrease in Q value can be suppressed.

  Note that the overlapping region when viewed from the stacking direction is not limited to both ends of the strip conductor 3, but may be one end. Further, the strip conductor 3 and the ground conductor 4 do not necessarily have to be exposed on the surface layer, and when the dielectric thin layer (sample layer) 1 is very thin as 50 μm or less, the lower surface of the ground conductor 4 is further warped. It is desirable to provide a dielectric support layer 2 for suppressing the occurrence of the above. The dielectric support layer 2 does not have to have the same composition and structure as the dielectric thin layer (sample layer) 1 and may be formed with a conductor or the like. In particular, in order to suppress the occurrence of warping, it is desirable that the open-ended half-wave resonator A1 as a whole has a vertically symmetrical structure.

(First dielectric constant measurement method)
The first dielectric constant measuring method of the present invention will be described with reference to FIG.
First, an open-ended half-wave resonator A1 shown in FIG. 1 is prepared as a measurement sample.
Then, the both-end open half-wave resonator A1 is excited using, for example, a microwave of 3 to 30 GHz to measure the resonance frequency and no-load Q value of the both-end open half-wave resonator. As shown in FIG. 1, a half-wave resonator A1 having both ends open is excited by a loop antenna 6 formed at the tip of one coaxial cable 5, and detected by the loop antenna 6 formed at the tip of the other coaxial cable 5. The resonance frequency f ₀ and the no-load Q value _Qu are measured with a measuring instrument such as a network analyzer. In order to excite both-end open half-wave resonator A1, not only a loop antenna but also a microstrip line, strip line, coplanar line, slot line, and NRD guide may be employed.

  Here, when the radiation loss of the open-ended half-wave resonator A1 cannot be ignored, it is desirable to install the shielding conductor 7 so as to surround the open-ended half-wave resonator A1, as shown in FIG. As this shielding conductor 7, a box shape, a hollow rectangular structure, etc. are suitable.

Then, calculated from the resonance frequency f ₀ the dielectric thin layer (sample layer) dielectric constant of 1 epsilon ', dielectric thin layer than the unloaded Q value Q _u (sample layer) calculates a dielectric loss tangent tan [delta. Hereinafter, a method for calculating these dielectric constants will be described.

  Here, in order to calculate the relative dielectric constant of the dielectric thin layer (sample layer) 1, the relationship between the relative dielectric constant and the resonance frequency is obtained by numerical analysis such as FEM within an assumed range. Approximation with an appropriate function, and the relative dielectric constant is calculated from this approximate function and the measured value of the resonance frequency. In order to calculate the conductivity of the conductor and the dielectric loss tangent of the dielectric thin layer (sample layer) 1, the resonator form factor G and the electric field energy concentration rate Pe of the dielectric sample are calculated by FEM, etc. The dielectric loss tangent of the sample is calculated from the measured values of G and Pe and the unloaded Q value.

First, the relative dielectric constant ε of the thin dielectric layer (sample layer) 1 is measured from the measured value of the resonance frequency f ₀ of the open-ended half-wavelength resonator A1 by numerical analysis such as the finite element method (FEM) or the mode matching method. Ask for '. Here, the case where the finite element method is used will be described.

The resonant frequency f ₀ of the open-ended half-wave resonator A 1 shown in FIG. 1 is that the dielectric constant ε ′ of the dielectric thin layer (sample layer) 1, the thickness T, and the dielectric constant ε of the dielectric support layer 2. 's, thickness Ts, thickness Tc of strip conductor 3 and ground conductor 4, width Wc and length Lc of strip conductor 3, width Wo of a conductor non-formation region surrounded by ground conductor 4, major axis of strip conductor 3 The length of the region where each end in the direction overlaps the ground conductor 4 when viewed from the stacking direction (the length of the strip conductor 3 in the major axis direction) is a function of Lr and Ll. Therefore, T, ε's, Ts, Tc, Wc, Lc, Wo, Lr, Ll are fixed to measured values or design values, and the dielectric constant ε 'of the dielectric thin layer (sample layer) 1 is expected. Several points are set within a range, and the corresponding resonance frequency f ₀ is calculated by the finite element method. From these calculation results, the relative dielectric constant ε ′ is calculated from an approximate expression that approximates the relationship between the resonant frequency f ₀ and the relative dielectric constant ε ′ with an appropriate function and the measured value of the resonant frequency f ₀ .

Next, the dielectric loss tangent tan δ of the dielectric thin layer (sample layer) 1 is obtained from the measured value of the no-load Q value Q _u by the following formula 1.

In Equation 1 above, μ is the magnetic permeability of the conductor, and for a non-magnetic conductor, μ is equal to the vacuum magnetic permeability μ ₀ = 4π × 10 ⁻⁷ H / m. _Pe is the concentration factor of the electric field energy in the dielectric thin layer (sample layer) 1, _Pes is the concentration factor of the electric field energy in the dielectric support layer 2, and G is the form factor of the open-ended half-wave resonator A1. For example, the literature “J. Krupka, K. Derzakowski, A. Abramowicz, ME Tobar and RG Geyer,“ Use of whispering-gallery modes for complex permittivity determinations of ultra-low-loss dielectric materials, ”IEEE Trans. Microwave Theory Tech , vol. 47, pp.752-759, June 1999 ”. Further, tan δs is a dielectric loss tangent of the dielectric support layer 2.

The concentration ratio of the electric field energy is defined as a fraction of the electric field energy stored in each part with respect to the electric field energy stored in the open-ended half-wave resonator A1. _Pe and _Pes are given by Equation 2 and Equation 3 below.

Further, G, which is the shape factor of the open both-end half-wave resonator A1, is given by the following equation 4.

Expressions 2 to 4 are obtained by a numerical analysis method such as a finite element method (FEM) or a mode matching method. The calculated P _{e, P es,} and _G, the measured value and literature values of the conductivity due to alternative sigma, a further measurement values and literature values for tan [delta _s by alternative into Equation 1 to obtain the tan [delta.

Another method for obtaining σ is “A. Nakayama, Y. Terashi, H. Uchimura and, A. Fukuura,“ Conductivity measurement at the interface between the sintered conductor and dielectric substrate at microwave frequencies, ”IEEE Trans. Microwave Theory Tech. , vol. MTT-50, No.7, pp. 1665-1674, July 2002. " As another method for obtaining the tanδ _s JIS-R1641: 2002 it is preferable.

(Second dielectric constant measurement method)
The second dielectric constant measuring method of the present invention will be described with reference to FIGS.
First, as a measurement sample, both ends open half-wave resonator A1 as shown in FIG. 1 and both ends open half-wave resonator A1 shown in FIG. 1 as shown in FIG. 3 are surrounded by an annular ground conductor 4. An open-ended half-wave resonator A2 having a different conductor non-forming area is manufactured. The conductor non-formation region is a region represented by the inner periphery of the annular ground conductor 4, and is a region indicated by a one-dot chain line in FIGS. 1 (a) and 3 (a).

At the time of measurement, similarly to the first dielectric constant measurement method, a resonator is excited by a loop antenna 6 formed at the tip of one coaxial cable 5, and detected by the other loop antenna 6, and measured by a network analyzer or the like. vessel at the resonance frequency f ₁ and the resonance frequency f ₂ and unloaded unloaded Q value across the open-type half-wavelength resonator A2 shown in FIG. 3 as well as measuring the Q ₁ across an open type half-wavelength resonator A1 shown in FIG. 1 to measure the Q value _{Q 2.}

Next, a method for calculating the dielectric constant will be described. First, from the measured values of the resonance frequencies f ₁ and f ₂ of the resonator, the relative permittivity ε ′ of the dielectric thin layer sample 1 in each resonator is obtained by numerical analysis such as a finite element method (FEM) or a mode matching method. Ask for. The resonance frequency f ₁ of the open-ended half-wave resonator A1 shown in FIG. 1 is as described above, the relative dielectric constant ε ′ of the dielectric thin layer sample 1, the thickness T, and the relative dielectric constant ε ′ of the support layer 2. s, thickness Ts, strip conductor 3 and ground conductor 4 thickness Tc, strip conductor 3 width Wc, length Lc, ground conductor 4 opening width Wo, and strip conductor 3 lengthwise end portions This is a function of lengths (electrode lengths) Lr and Ll overlapping with the ground conductor 4 in the vertical direction. Therefore, T, ε's, Ts, Tc, Wc, Lc, Wo, Lr, Ll are fixed to measured values or design values, and the relative dielectric constant ε ′ of the sample layer 1 is set at several points within the expected range. Then, the corresponding resonance frequency f ₁ is calculated by the finite element method. Similarly, to calculate from the measured values of the resonance frequency f _2, the dielectric thin layer of open-ended shaped half-wavelength resonator A2 (sample layer) dielectric constant of 1 epsilon '.

Next, the electrical conductivity σ of the conductor and the dielectric loss tangent tan δ of the dielectric thin layer (sample layer) 1 are obtained from the measured values of the no-load Q values Q ₁ and Q ₂ using Equation 1. The numerical analysis such as the finite element method (FEM) and mode matching method for each of the resonators, _{P e, P es} given by Equation 2, 3, 4, seek G, Substituting this in Equation 1. By solving the simultaneous equations thus obtained, the electrical conductivity σ of the conductor and the dielectric loss tangent tan δ of the dielectric thin layer (sample layer) 1 can be obtained.

(Third dielectric constant measurement method)
A third dielectric constant measuring method of the present invention will be described with reference to FIGS.
First, as a measurement sample, a solid ground is used instead of the open-ended half-wave resonator A1 as shown in FIG. 1 and the annular ground conductor in the open-ended half-wave resonator A1 shown in FIG. A microstrip line resonator A3 having both ends open as a conductor 41 is manufactured.

At the time of measurement, similarly to the first and second dielectric constant measurement methods, a resonator is excited by a loop antenna 6 formed at the tip of one coaxial cable 5, and detected by the other loop antenna 6, and then a network analyzer. the resonance frequency f of the open ends form the microstrip line resonator A3 of the measuring instrument with measuring the resonance frequency f ₃ and the unloaded Q value Q ₃ of open-ended shaped half-wavelength resonator A1 shown in FIG. 1 and the like shown in FIG. 4 ₄ and no-load Q value Q ₄ are measured.

The calculation method of the dielectric constant is the same as the calculation method described in the second dielectric constant measurement method, and the resonance frequencies f ₁ and f ₂ in the calculation method described in the second dielectric constant measurement method are set to f ₃ and with substituting f _4, the unloaded Q value Q ₁ and Q ₂ may be calculated by changing the Q ₃ and Q ₄ in the calculation method described in the second dielectric constant measurement method.

  In the dielectric constant measurement method of the present invention, the temperature dependency of the resonance frequency and the no-load Q value can be easily measured by measuring under different temperature atmospheres. The temperature dependence of the relative permittivity and dielectric loss tangent of the body sample can be obtained. Further, in the dielectric constant measuring method of the present invention, the direct current voltage is easily applied between the strip conductor and the ground conductor, thereby obtaining the direct-current electric field dependence of the relative dielectric constant and dielectric loss tangent of the dielectric thin layer sample. You can also.

1 shows a double-ended open half-wave resonator used in the measurement method of the present invention, where (a) is a plan view seen from above, and (b) and (c) are cross-sectional views. It is explanatory drawing for demonstrating the structure which provided the shielding conductor in the both-ends open type half wavelength resonator. The other example of the open both-ends type half wave resonator used for the measuring method of the present invention is shown, (a) is a top view seen from the top, and (b) and (c) are sectional views. 1 shows a microstrip line resonator with open ends used in the measurement method of the present invention, (a) is a plan view seen from above, and (b) and (c) are sectional views.

Explanation of symbols

1 ... Dielectric thin layer (sample layer)
2 ... Dielectric support layer 3 ... Strip conductor 4 ... Ground conductor 41 ... Solid ground conductor 5 ... Coaxial cable 6 ... Loop antenna 7 ... Shielding conductors A1, A2,. -Open-end half-wave resonator A3 ... Open-end microstrip line resonator

Claims (4)

A rectangular strip conductor is provided on one surface of the thin dielectric layer, an annular ground conductor is provided on the other surface of the thin dielectric layer, and at least one end in the major axis direction of the strip conductor and the An open-ended half-wave resonator, wherein a part of a ground conductor is disposed so as to overlap when viewed from the stacking direction. The at least one of a resonance frequency and an unloaded Q value is measured by exciting the open-ended half-wave resonator according to claim 1, and a measured value of at least one of the resonance frequency and the unloaded Q value. A dielectric constant measuring method, comprising: calculating a dielectric constant in a thickness direction of the dielectric thin layer from A first open-ended half-wave resonator and a second open-ended half-wavelength comprising the open-ended half-wave resonator according to claim 1 and having different conductor non-formation areas surrounded by the annular ground conductor. The resonator is excited to measure at least _one of a resonance frequency f ₁ and an unloaded Q value Q ₁ of the _first open-ended half-wave resonator and the open-ended second half-wave resonator And measuring at least one of the resonance frequency f ₂ and the no-load Q value Q ₂ , and at least one of the resonance frequency f _{1, the} resonance frequency f ₂ , the no-load Q value Q _1, and the no-load Q value Q ₂ A dielectric constant measuring method, wherein a dielectric constant in a thickness direction of the dielectric thin layer is calculated from any one of the measured values. An open-ended half-wave resonator according to claim 1 and an open-ended microstrip line resonator provided with a solid ground conductor in place of the annular ground conductor of the open-ended half-wave resonator. the resonance frequency f ₃ and unloaded Q value resonant frequency of the open-ended type microstrip line resonator with measuring at least one of Q ₃ f ₄ and the unloaded Q value Q of the open-ended type half-wavelength resonator Te _At least one of the resonance frequency f _{3, the} resonance frequency f ₄ , the unloaded Q value Q _3, and the measured value of at least one of the unloaded Q value Q _4. A dielectric constant measuring method comprising calculating a dielectric constant in a thickness direction of a layer.

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