DE102018132534A1 - Device and method for determining a non-linearity of a dielectric material - Google Patents

Abstract

The invention relates to a device and a method for determining a non-linearity of the charge shift that is caused in a dielectric material in response to an electric field, in particular for determining a coefficient α = χ / ε of a series representation associated with an i-order susceptibility χ the electrical flux density D (E) = εε (E + ∑αE) within the dielectric material exposed to the electrical field E with relative permittivity ε.

Description

Field of the Invention

The invention relates to an apparatus and a method for determining a non-linearity of the charge shift that is caused in a dielectric material in response to an electric field.

Background of the Invention

The growing demand for high-speed data in mobile applications requires new solutions in many areas of technology and science. In particular, in networks for wireless communication in the GHz frequency range, the necessary number of channels that are used simultaneously is increasing. The fifth generation of mobile radio standards (5G) currently under development aims to increase the data volume by a factor of 100 or more compared to the LTE4 technology used today. This ambitious goal requires new specifications for cellular networks.

The data speed (in bit / s) is directly proportional to the bandwidth (in Hz = 1 / s) that is available for information transmission. At higher frequencies, there is more relative bandwidth available. In the electromagnetic spectrum, there are two windows in the transparency of the atmosphere that can be used for wireless applications, one in the optical range (λ ≈ a few nm) and one in the microwave range (Lambda ≈ a few cm). While the optical window is not used for mobile communication, the microwave window is used by a number of known technologies, in particular radio, GPS, satellite television, WLAN, radar and mobile phone connections. With regard to the achievement of the 5G standard, the frequency space will have to be expanded to higher frequencies and used more efficiently.

The use of dielectrics in microwave circuits has several advantages: On the one hand, they can be used as dielectric resonators (DR) for filters. Because of their miniaturized size, they do better than conventional microwave cavity resonators. In addition, antennas can be equipped with dielectrics, which allows smaller designs and reduces their sensitivity to changes in the electromagnetic properties of the surrounding space.

Dielectrics that are used in microwave applications are mainly (sintered) ceramics. Dielectric resonators with high dielectric constants and low dielectric losses have been developed as well as temperature-resistant systems. However, due to their sintering production process, they show some artifacts with disadvantages: a certain degree of porosity and inhomogeneity. Glass ceramics, on the other hand, are made from a homogeneous liquid glass melt. Due to the different process, they do not show the disadvantages of sintered ceramics, but they have another disadvantage: their dielectric loss is about 10 times greater than that of sintered ceramics.

The most important properties that characterize a dielectric material for GHz applications are its relative dielectric constant ε _r , its loss tan δ and its temperature coefficient τ _f . A dielectric resonator for mobile communication systems should have a high dielectric constant ε _r , a low loss tan δ and a vanishing temperature coefficient τ _{f of} the resonance frequency.

There are various methods for determining these properties, as well as numerous research that is concerned with realizing this property. Mobile radio technology, however, faces the challenge of intermodulation, which cannot be described by the properties mentioned above. Intermodulation arises from the nonlinear response of an otherwise passive device and is therefore referred to as passive intermodulation (PIM) to distinguish it from nonlinear responses from active devices such as amplifiers. Intermodulation can have various causes, for example dielectrics that react non-linearly to an applied electrical field. In general, it is difficult to experimentally isolate the various sources of PIM.

Nowadays, PIM is usually measured on a system basis. Shitvov et al. measure the PIM generation in a microstrip line, for example, whereby the PIM generation can start from the conductor or from the substrate (Alexey Shitvov, Dmitry Kozlov, Alexander Schuchinsky: Nonlinear Characterization for Microstrip Circuits with Low Passive Intermodulation, IEEE Transactions on Microwave Theory and Tequniques 66 : 2, 865-874, 2018).

An exception to the system measurements is the work of Nishikawa et. AI. for sintered ceramics (JPH02147962A), which describes a structure in which the intermodulation is solely due to a dielectric material. Building on this, the master thesis written by Florian Bergmann, which deals with the characterization of the nonlinearity of glass ceramics as a material property (2018, Florian Bergmann, "Measuring extremely small nonlinear electric responses in glasses and glass ceramics", SCHOTT AG).

For materials with low dielectric constants ε _r , however, these approaches reach their limits. This applies in particular to most substrate materials. In these cases, the structure of a according to Nishikawa et. al. described resonator with a natural resonance no longer feasible.

Object of the invention

It is therefore an object of the invention to provide an apparatus and a method which make it possible to determine passive intermodulation (PIM) on a material basis in materials with low dielectric constants (relative permittivity) ε _r . In particular, a device and a method should therefore be specified which make it possible to determine a non-linearity of the charge shift which is caused in a dielectric material in response to an electric field.

General description of the invention

The invention relates to an apparatus for determining a non-linearity of charge displacement, which is caused in a dielectric material in response to an electric field, in particular for determining a ter i-a susceptibility order χ _i in context property coefficients α _i = χ _i / ε _r a series representation of the electrical flux density D (E) = ε ₀ ε _r (E + ∑ _{i = 3.5, ...} α _i E ⁱ ) within the dielectric material exposed to the electric field E with relative permittivity ε _r .

The device comprises a resonator arrangement with at least one resonator element which contains the dielectric material with relative permittivity ε _r .

The device further comprises an injection device for introducing at least one signal, which serves to expose the resonator arrangement to the electric field E.

In addition, the device comprises an extraction device for extracting at least one signal which corresponds to a resonance of the resonator arrangement.

The dielectric material with relative permittivity ε _r represents a perturbation in a system which resonates even without this material or in a resonator arrangement which also resonates without this material. The natural frequency of the resonance is therefore in particular not determined solely by the material of the permittivity ε _r to be characterized becomes.

enthält, welches vorzugsweise das dielektrische Material mit relativer Permittivität ε_r zumindest teilweise umgibt.In particular, in addition to the dielectric material with relative permittivity ε _r , the resonator element contains at least one further dielectric material with greater relative permittivity ${\epsilon }_r^{\text{'}}>{\epsilon }_r$

contains, which preferably at least partially surrounds the dielectric material with relative permittivity ε _r .

However, it is also possible to provide a structure with three Fabry-Perrot resonators arranged at an angle of approximately 120 degrees, in the center of which there is a sample or the ε _r material.

enthalten.The resonator element preferably comprises at least three disks arranged adjacent, in particular adjoining one another, such that a middle disk is axially surrounded by a left disk and a right disk, the middle disk containing the dielectric material with relative permittivity ε _r and / or one of the two or more surrounding disks the dielectric material with relative permittivity ${\epsilon }_r^{\text{'}}$

contain.

enthalten.In principle, however, it can also be provided that the resonator element comprises at least three concentrically arranged, in particular adjacent, disks, such that an annular middle disk is radially surrounded by an inner disk and an annular outer disk, the middle disk being the dielectric material with relative permittivity ε _r and / or one or the two surrounding disks contains the dielectric material with relative permittivity ${\epsilon }_r^{\text{'}}$

contain.

The dielectric material has in particular a relative permittivity ε _r <20, preferably ε _r <15, particularly preferably ε _r <10, again more preferably ε _r <5.

vorzugsweise ${\epsilon }_r^{\text{'}}>\mathrm{10,}$

besonders bevorzugt ${\epsilon }_r^{\text{'}}>\mathrm{15,}$

nochmals bevorzugter ${\epsilon }_r^{\text{'}}>20$

auf. Das dielektrische Material mit relativer Permittivität ε_r, insbesondere die umgebenden äußeren Scheiben des Resonatorelements, können als Glaskeramik ausgebildet sein, insbesondere eine Glaskeramik die Ba₄Ti₁₀Al₂O₂₇ als Kristallphase enthält.The further dielectric material in particular has a relative permittivity ${\epsilon }_r^{\text{'}}>\mathrm{5,}$

preferably ${\epsilon }_r^{\text{'}}>\mathrm{10,}$

particularly preferred ${\epsilon }_r^{\text{'}}>\mathrm{15,}$

even more preferred ${\epsilon }_r^{\text{'}}>\mathrm{20th}$

on. The dielectric material with relative permittivity ε _r , in particular the surrounding outer panes of the resonator element, can be designed as a glass ceramic, in particular a glass ceramic which contains Ba ₄ Ti ₁₀ Al ₂ O ₂₇ as the crystal phase.

The resonator arrangement preferably comprises a plurality of, in particular three, coupled resonator elements, the plurality of coupled resonator elements a plurality, in particular three, Have resonances, preferably with frequencies ω ₁ , ω ₂ , ω ₃ , where ω ₃ = 2ω ₂ - ω ₁ applies.

The device preferably further comprises a, in particular tubular, waveguide, which houses the resonator element (s), in particular a cylindrical one. The natural frequencies ω ₁ , ω ₂ , ω ₃ are preferably in the cut-off region of the waveguide, so that electromagnetic waves cannot propagate with the frequencies.

It can preferably be provided that the injection device has at least two separate input elements, in particular arranged on the end face of the waveguide, for introducing at least two different signals in order to expose the resonator arrangement to an electric field E = E ₁ + E ₂ formed as a superposition.

The resonator element or elements preferably have a thickness between 1 and 4 centimeters * ω _mess / GHz and / or a diameter between 3 and 9 centimeters * ω _mess / GHz, the values of the disk thickness and diameter being the length multiplied by the measurement frequency ω _mess (in GHz) are given. In order to be able to determine the non-linearities at higher frequencies, a smaller structure can be used, with manufacturing inaccuracies being a limiting factor when the frequencies are too high and accordingly too small.

The frequencies ω ₁ , ω ₂ , ω ₃ are preferably so close together that the dielectric properties, in particular the dielectric loss, do not change appreciably. Accordingly, (ω ₁ - ω ₂ ) / ω ₁ <0.1, preferably (ω ₁ - ω ₂ ) / ω ₁ <0.05 can be provided. In particular, there are three equidistant resonance frequencies, which are preferably close to each other (relative distance less than 0.1, better 0.05).

The adjacent left, middle and right pane can have a thickness between 0.4 and 3 centimeters * ω _mess / GHz, 0.1 and 3 centimeters * ω _mess / GHz or 0.4 and 3 centimeters * ω _mess / GHz .

In the case of concentrically arranged disks, the inner, middle and outer disks can have a diameter between 0 and 5 centimeters * ω _mess / GHz, 0 and 6 centimeters * ω _mess / GHz or 3 and 12 centimeters * ω _mess / GHz.

The resonator element or elements, in particular the adjacently arranged disks or the inner one of the concentrically arranged disks, can have a, in particular centrally formed, storage opening.

Correspondingly, the device can further comprise a bearing device in order to hold the resonator element (s), in particular by means of the bearing opening, and preferably to space them from the waveguide.

The storage device can comprise a material or consist of a material which has a relative permittivity ε _r <2, preferably ε _r <1.5, particularly preferably ε _r <1.1, again more preferably ε _r <1.05.

The invention further relates to a composite resonator element for a device for determining a non-linearity of the charge shift, which is caused in a dielectric material in response to an electric field, in particular as described above.

The composite resonator element comprises three adjacently arranged, in particular adjoining, disks, such that a middle disk is axially surrounded by a left-hand disk and a right-hand disk, or at least three concentrically arranged, in particular adjoining, disks, such that an annular middle disk Disc is radially surrounded by an inner disc and an annular outer disc.

According to the invention, the middle pane contains a dielectric material with relative permittivity ε _r and one or the two surrounding panes contains a further dielectric material with greater relative permittivity ${\epsilon }_r^{\text{'}}>{\epsilon }_r.$

The invention also relates to a method for determining a non-linearity of charge displacement, which is caused in a dielectric material in response to an electric field, in particular for determining a ter i-a susceptibility order χ _i in context property coefficients α _i = χ _i / ε _r a series representation of the electrical flux density D (E) = ε ₀ ε _r (E + ∑ _{i = 3.5, ...} α _i E ⁱ ) within the dielectric material exposed to the electric field E with relative permittivity ε _r , in particular by means of a device as described above.

enthält einem elektrischen Feld E ausgesetzt, derart, dass eine Resonanz der Resonatoranordnung angeregt wird und ein Signal, welches einer Resonanz der Resonatoranordnung entspricht, entnommen, um die Nichtlinearität, insbesondere den Koeffizienten α_i zu bestimmen.The method uses a resonator arrangement with at least one resonator element, which has a dielectric material with relative permittivity ε _r and a further dielectric material with greater relative permittivity ${\epsilon }_r^{\text{'}}>{\epsilon }_r$

contains an electric field E, such that a resonance of the resonator arrangement is excited and a signal corresponding to a resonance of the resonator arrangement is taken to determine the non-linearity, in particular the coefficient α _i .

The resonator arrangement used can have several resonances, in particular three resonances with frequencies ω ₁ , ω ₂ , ω ₃ , where ω ₃ = 2ω ₂ - ω ₁ applies, in particular in that the resonator arrangement comprises several, in particular three, coupled resonator elements.

It can be provided that the resonator arrangement is exposed to an electrical field E = E ₁ + E ₂ formed as a superposition from a first electrical field with a frequency ω ₁ and a second electrical field with a frequency ω ₂ and the excited resonance of the resonator arrangement Intermodulation corresponds to the frequency ω ₁ and the frequency ω ₂ , in particular with the frequency ω ₃ = 2ω ₂ - ω ₁ .

The extracted signal preferably corresponds to the resonance with the frequency ω ₃ . Furthermore, a further signal is preferably extracted which corresponds to a different resonance of the resonator, in particular the resonance with the frequency ω ₁ .

The nonlinearity, in particular the coefficients α _i, can be determined by means of one or more signals which serve to expose the resonator arrangement to the electric field E and / or one or more signals which correspond to a resonance of the resonator.

To determine the non-linearity, in particular the coefficient α _i , an energy stored in the resonance of the resonator element can be calculated.

Detailed description of an embodiment

In the case of high electric field strengths, a linear relationship between the electric flux density and the applied electric field can generally no longer be assumed, but higher-order terms must be taken into account. The first nonlinear non-vanishing term for an isotropic medium is third order: $$D\left(E\right)={\epsilon }_0{\epsilon }_r\left(E+{\displaystyle \sum _{i=\mathrm{3.5,}...}{\alpha }_i{E}^i}\right)$$

Of particular interest is the cubic non-linearity α ₃ . This is low for dielectrics compared to ferroelectrics. The challenge when measuring small non-linearities is that devices with high electrical field strengths generally show non-linear behavior so that the non-linearity of the material to be tested can no longer be determined. Approaches to measuring small non-linearities should therefore take into account the application of high electric fields to the source in question. Compared to the generation of harmonics, the generation of intermodulation has the favorable property that it only takes place where both intermodulating frequencies are present. For this reason, intermodulation methods enable a test setup in which both frequencies are only available in a certain area of the setup. For this purpose, there is a separate introduction on the input side and the earliest possible separation of the intermodulation signal from the original frequencies on the output side. In addition, metallic contact with the material to be exposed to a field can pose the problem of causing intermodulation itself. The feed is therefore preferably carried out without contact. In order to obtain high electric fields, cylindrical dielectric resonators can be used and placed in a cylindrical waveguide. The waveguide can be operated below the cutoff frequency so that no propagating waves can arise and the fields are (only) concentrated in the dielectric resonators. In particular, three such resonators of the same resonance frequency can be coupled. They can have three different resonance frequencies, which fulfill the following intermodulation relationship: $${\omega }_{\mathrm{3rd}}=\mathrm{2nd}{\omega }_{\mathrm{2nd}}-{\omega }_1$$

If an intermodulation signal is generated in the arrangement, it can therefore be stored in particular in the third mode and thereby increase its amplitude by the Q factor of the resonators. This increases the sensitivity of the setup to small intermodulation signals. Separate input and isolated dielectric resonators tuned to the input frequencies can ensure that the signal from the other input does not enter the first frequency input system and that there is no intermodulation before the input. The exclusion of intermodulation after the output can be achieved by detecting in the area of the central resonator, where the second mode has a node. The detection can thus be limited to ω ₁ and ω ₃ at the location of the central resonator in order to prevent further intermodulation generation of ω ₃ after the output. With a comparable structure, Nishikawa et. al. Sintered ceramics with low non-linearity (Youhei Ishikawa, Hiroshi Tamura, Toshio Nishikawa, Kikuo Wakino: Extremely low distortion dielectric ceramics, Ferroelectrics 135: 1, 371-383, 1992).

If these dielectric resonators are placed in a cut-off waveguide, the measurement method is limited to materials with a high dielectric constant (eg ε _r > 20), because Resonators made of materials with a high dielectric constant (eg ε _r <10) would not fit in the cut-off waveguide. However, the distribution of the intermodulation generation is strongly concentrated in the middle of a disk, since it is proportional to the sixth power of the electric field: E ⁶ (x). The concentration takes place in the radial and longitudinal directions.

By inserting a thin disk made of a low ε _r material in this concentration, the behavior in relation to the generation of intermodulations can change significantly, but not the other relevant properties of the resonance, such as frequency and Q factor, since they only differ from the second Depend on the power of the electric field. The concentration in the radial direction can be used by omitting a thin tube from the material with a high ε _r and replacing it with a material with a low ε _r . Concentration in the longitudinal direction enables a generally simpler handling, since a thin disk can be inserted in the middle of the length of the resonator, which is generally easier to manufacture than a thin hollow tube.

The boundary conditions of the low ε _r do not lead to a discontinuity in the electrical field in the pane, since the electrical field of the TE _01δ mode, a transverse electrical mode, does not have a vertical component on the surface, but only a parallel component that is continuous Behavior on dielectric surfaces shows. However, the electric field drops within the disc. As a result, the thickness of the pane to be inserted can be limited or an optimal pane thickness can arise.

The arrangement makes it possible in particular to measure the relative amplitude of the first and third modes. The ratio of the energies can be stated as follows: $$\frac{W_{\mathrm{3rd}}}{W_1}=\frac{Q_{\mathrm{3rd}}}{\mathrm{2nd}\pi }\frac{{\displaystyle \int dx{\left[\frac{\mathrm{3rd}}{\mathrm{4th}}\alpha \left(x\right)E_{\mathrm{2nd}}^{\mathrm{2nd}}\left(x\right)\right]}^{\mathrm{2nd}}{\epsilon }_r\left(x\right)E_1^{\mathrm{2nd}}\left(x\right)}}{{\displaystyle \int dx{\epsilon }_r\left(x\right)E_1^{\mathrm{2nd}}\left(x\right)}}$$

Herein ε _{r is} the relative location-dependent dielectric constant and α = α _{3 is} the location-dependent non-linearity of the third order, which can thus be determined from the equation. The equation determines the limit of sensitivity for measuring the nonlinearity of the low ε _r material in the disk compared to the surrounding high ε _r material. For a material ε _r = 3, the ratio of the relative dielectric constant is approximately 0.1 for a resonator material with ε _r = 32. The field distributions can be calculated using computer simulation software.

The ratio of the sixth power of the field distribution for a 12 mm thick disk between two 12 mm resonators is again about 0.3. Therefore, it becomes possible to measure nonlinearities of materials with a low ε _r with a 30 times higher sensitivity to the nonlinearity of the high ε _r material.

The nonlinearity of the high ε _r material can be carried out without using the disk method, but with resonators made of one material, as described by Nishikawa et al. described. With a slightly higher ε _r = 5 it can be possible to achieve a 20-fold sensitivity to the non-linearity of the high ε _r material. Since the non-linearity for different materials can vary over several orders of magnitude, this limit of sensitivity is sufficient for testing many materials. Using glass ceramics as in the master thesis written by Florian Bergmann (2018, Florian Bergmann, "Measuring extremely small nonlinear electric responses in glasses and glass ceramics", SCHOTT AG), which has a cubic nonlinearity of (2 ± 2) 10 ^-16 m ² / V ² , the sensitivity 30 times lower results in a sensitivity of about 10 ^-14 m ² / V ² .

In order to be able to measure disc material which is not perfect, i.e. contains thickness variations (TTV = total thickness variations) in the range of up to 0.5mm or warping up to 2mm, which is the case with many plastic substrates, it is advantageous to use one to make fixed spacers between the two resonator plates with high ε _r , which can be formed for example by a glass tube in the center of the panes. It can accordingly be provided that the surrounding disks are held at a defined distance from one another by a spacer (which is in particular not the middle disk) and the middle disk is located between the surrounding disks spaced apart by the spacer. With three axially adjacent disks, the spacer can be located in particular in the center of the disks. In addition, the spacer can preferably be tubular, for example as a glass tube. In this way, the frequency can be hit precisely enough with real substrate materials that show TTV and / or warp.

In summary, it is thus possible to quantify the smallest nonlinearities, in particular up to a size of α = 10 ^-14 m ² / V ^2, on a material basis. With a resonator structure, the non-linearities of materials with dielectric constants, for example up to ε _r = 3, can be determined. For this purpose, thin layers of a material are inserted between two thick plates made of a material with a high ε _r , which enables a high field concentration in the material layer and offers the possibility of constructing resonators of a suitable size for use in a cut-off waveguide. Characterized non-linearities can be taken into account in the simulation software and enable PIM predictions before the construction of an overall system.

Claims (22)

Apparatus for determining a non-linearity of the charge shift that is caused in a dielectric material in response to an electric field, in particular for determining a coefficient α _i = χ _i / ε _{r associated} with a susceptibility of i-th order χ _i electrical flux density D (E) = ε ₀ ε _r (E + ∑ _{i = 3.5, ...} α _i E ⁱ ) within the dielectric material exposed to the electrical field E with relative permittivity ε _r , the device comprising: a Resonator arrangement with at least one resonator element, which contains the dielectric material with relative permittivity ε _r , an injection device for introducing at least one signal, which serves to expose the resonator arrangement to the electric field E, an extraction device for extracting at least one signal, which resonates the resonator arrangement corresponds, the dielectric material with relative perm itivity ε _{r represents} a disturbance in a system that resonates even without this material. Apparatus for determining a non-linearity of the charge shift that is caused in a dielectric material in response to an electric field, in particular for determining a coefficient α _i = χ _i / ε _{r associated} with a susceptibility of i-th order χ _i electrical flux density D (E) = ε ₀ ε _r (E + ∑ _{i = 3.5, ...} α _i E ⁱ ) within the dielectric material exposed to the electrical field E with relative permittivity ε _r , in particular according to Claim 1 , The device comprising: a resonator arrangement with at least one resonator element which contains the dielectric material with relative permittivity ε _r , an injection device for introducing at least one signal which serves to expose the resonator arrangement to the electric field E, an extraction device for removing at least one Signal, which corresponds to a resonance of the resonator arrangement, the resonator element in addition to the dielectric material with relative permittivity ε _r at least one further dielectric material with greater relative permittivity $\left({\epsilon }_r^{\text{'}}>{\epsilon }_r\right)$

contains, which preferably at least partially surrounds the dielectric material with relative permittivity ε _r . Device according to Claim 1 or 2nd , wherein the resonator element comprises at least three adjacently arranged, in particular adjacent, disks, such that a middle disk is axially surrounded by a left-hand disk and a right-hand disk, or wherein the resonator element comprises at least three concentrically arranged, in particular adjoining, disks, such that an annular middle disk is radially surrounded by an inner disk and an annular outer disk, and wherein the middle disk contains the dielectric material with relative permittivity ε _r and / or one or the two surrounding disks contains the dielectric material with relative permittivity ${\epsilon }_r^{\text{'}}$

contain. Device according to one of the Claims 1 to 3rd , wherein the dielectric material has a relative permittivity ε _r <20, preferably ε _r <15, particularly preferably ε _r <10, again more preferably ε _r <5 and / or wherein the further dielectric material has a relative permittivity ${\epsilon }_r^{\text{'}}>\mathrm{5,}$

preferably ${\epsilon }_r^{\text{'}}>\mathrm{10,}$

particularly preferred ${\epsilon }_r^{\text{'}}>\mathrm{15,}$

even more preferred ${\epsilon }_r^{\text{'}}>\mathrm{20th}$

having. Device according to one of the Claims 1 to 4th , wherein the dielectric material with relative permittivity ε _r , in particular the surrounding panes of the resonator element, are designed as glass ceramics, in particular as glass ceramics, which contain Ba ₄ Ti ₁₀ Al ₂ O ₂₇ as the crystal phase. Device according to one of the Claims 1 to 5 , wherein the resonator arrangement comprises several, in particular three, coupled resonator elements and wherein the resonator arrangement and / or the several coupled resonator elements have several, in particular three, resonances, preferably with frequencies ω ₁ , ω ₂ , ω ₃ , where ω ₃ = 2ω ₂ - ω ₁ applies. Device according to one of the Claims 1 to 6 wherein the resonator arrangement has several, in particular three, resonances which are in particular equidistant and / or preferably have a relative distance from one another of less than 0.1, preferably less than 0.05, in particular for example (ω ₁ -ω ₂ ) / ω ₁ <0.1, preferably (ω ₁ - ω ₂ ) / ω ₁ <0.05. Device according to one of the Claims 1 to 7 , wherein the device further comprises a, in particular tubular, waveguide, which houses the one or more, in particular cylindrical, resonator elements. Device according to one of the Claims 1 to 8th , wherein the injection device has at least two separate input elements, in particular arranged on the end face of the waveguide, for introducing at least two different signals in order to expose the resonator arrangement to an electric field E = E ₁ + E ₂ formed as a superposition. Device according to one of the Claims 1 to 9 , wherein the resonator _element or elements have a thickness between 1 and 4 centimeters times ω _mess / GHz, where ω _mess denotes the measurement frequency, and / or wherein the resonator _element or elements have a diameter between 3 and 9 centimeters times ω _mess / GHz and / or wherein the adjacent left, middle and right pane have a thickness between 0.4 and 3 centimeters times ω _mess / GHz, 0.1 and 0.3 centimeters times ω _mess / GHz or 0.4 and 3 centimeters times ω _mess / GHz and / or wherein the concentrically arranged inner, middle and outer disk have a diameter between 0 and 5 centimeters times ω _mess / GHz, 0 and 6 centimeters times ω _mess / GHz or 3 and have 13 centimeters times ω _mess / GHz. Device according to one of the Claims 1 to 10th , wherein the resonator element or elements, in particular the adjacently arranged disks or the inner of the concentrically arranged disks, have a, in particular centrally formed, storage opening. Device according to one of the Claims 1 to 11 , wherein the device further comprises a bearing device to hold the resonator element (s), in particular by means of the bearing opening, and preferably to space them from the waveguide and / or the bearing device comprises a material or consists of a material which has a relative permittivity ε _r <2, preferably ε _r <1.5, particularly preferably ε _r <1.1, even more preferably ε _r <1.05. Device according to one of the Claims 1 to 12 , wherein the surrounding disks are held at a defined distance from one another by a spacer and the middle disk is located between the surrounding disks spaced from one another by the spacer and wherein the spacer is preferably located at least in the center of the disks, in particular in the storage opening, and wherein the spacer is preferably tubular, for example as a glass tube. Composite resonator element for a device for determining a non-linearity of the charge shift which is caused in a dielectric material in response to an electric field, in particular according to one of the Claims 1 to 10th , comprising: at least three adjacently arranged, in particular adjoining, disks, such that a middle disk is axially surrounded by a left-hand disk and a right-hand disk, or at least three concentrically arranged, in particular adjoining, disks, such that an annular middle disk is radially surrounded by an inner disk and an annular outer disk and the middle disk contains a dielectric material with relative permittivity ε _r and one or the two surrounding disks contains a further dielectric material with greater relative permittivity ${\epsilon }_r^{\text{'}}>{\epsilon }_r$

contain. Composite resonator element after Claim 14 , wherein the surrounding disks are held at a defined distance from one another by a spacer and the middle disk is located between the surrounding disks spaced from one another by the spacer and wherein the spacer is preferably located at least in the center of the disks, in particular in the storage opening, and wherein the spacer is preferably tubular, for example as a glass tube. Method for determining a non-linearity of the charge shift that is caused in a dielectric material in response to an electric field, in particular for determining a coefficient α _i = χ _i / ε _{r associated} with a susceptibility of i-th order χ _i electrical flux density D (E) = ε ₀ ε _r (E + ∑ _{i = 3.5, ...} α _i E ⁱ ) within the dielectric material exposed to the electrical field E with relative permittivity ε _r , in particular by means of a device according to a of the Claims 1 to 10th , wherein a resonator arrangement with at least one resonator element, which has a dielectric material with relative permittivity ε _r and a further dielectric material with greater relative permittivity ${\epsilon }_r^{\text{'}}>{\epsilon }_r$

contains an electric field E, such that a resonance of the resonator arrangement is excited and a signal which corresponds to a resonance of the resonator arrangement is taken in order to determine the nonlinearity, in particular the coefficient α _i . Procedure according to Claim 16 , wherein the resonator arrangement has several resonances, in particular three resonances with frequencies ω ₁ , ω ₂ , ω ₃ , where ω ₃ = 2ω ₂ - ω ₁ applies, in particular in that the resonator arrangement comprises several, in particular three, coupled resonator elements Procedure according to Claim 16 or 17th , wherein the resonator arrangement is exposed to an electric field E = E ₁ + E ₂ formed as a superposition from a first electrical field with a frequency ω ₁ and a second electrical field with a frequency ω ₂ and the excited resonance of the resonator arrangement to an intermodulation of the frequency ω ₁ and the frequency ω ₂ , in particular with the frequency ω ₃ = 2ω ₂ - ω ₁ . Procedure according to one of the Claims 17 or 18th , wherein the extracted signal corresponds to the resonance with the frequency ω ₃ . Procedure according to one of the Claims 16 to 19th , wherein a further signal is extracted which corresponds to a different resonance of the resonator, in particular the resonance with the frequency ω ₁ . Procedure according to one of the Claims 16 to 20th , the nonlinearity, in particular the coefficient α _i , being determined by means of one or more introduced signals which serve to expose the resonator arrangement to the electric field E and / or one or more extracted signals which correspond to a resonance of the resonator. Procedure according to one of the Claims 16 to 21st , an energy stored in the resonance of the resonator element being calculated to determine the non-linearity, in particular the coefficient α _i .