FI122901B - Method, measurement apparatus and computer program product for measuring the electromagnetic properties of materials - Google Patents

Description

METHOD, MEASUREMENT EQUIPMENT AND COMPUTER SOFTWARE PRODUCT FOR MEASURING THE ELECTROMAGNETIC PROPERTIES OF MATERIALS

BACKGROUND OF THE INVENTION

Field of the Invention:

The present invention relates to the measurement of electromagnetic parameters of materials, in particular to complex refractive index, complex wave impedance, complex electrical permittivity and complex magnetic permeability.

Description of Related Technology:

Recently, there is an increasing need for rapid and accurate information on the electromagnetic properties of materials in the design and development processes of a wide range of industries from food processing to telecommunication systems. Understanding and measuring such parameters of materials as complex refractive index n and complex electrical permittivity ε is also essential for basic scientific research.

Untuned techniques such as transmittance and reflectance measurements are currently used to characterize the electromagnetic properties of materials, cf. e.g., L. Chen, V. V. Varadan, C. K. Ong, C. P. o Neo: Microwave Electronics: Measurement and Materials

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^ Characterization, John Wiley and Sons, 2004. The foundations of these techniques have already been established in the pioneering articles of Nicolson, Ross, and Weir by AM in the 1970s and 30s (AM Nicolson and GF Ross: Measurement of the Intrinsic Properties of Materials by Time). domain techniques, IEEE Trans Instr. Meas., Vol. IM-o 19, pp. 377-382, Nov. 1970; William Weir: Automated 0X1 35 ic Measurement of Complex Dielectric Constant and Microwave Frequencies, Proc. , Vol. 2, 62, pp. 33-36, January 1974). These techniques are relatively simple and accurate. Their advantage is the broadband characterization of materials and equipment. For nearly four decades, they have been widely used to measure the permittivity and permeability of a variety of synthetic and natural materials.

A known disadvantage of the original Nicolson-Ross-Weir (NRW) method is that the measurements of the S-10 parameters must be converted from calibration reference levels to material surfaces. The location of the reference levels strongly affects the phases of the transmission and reflection signals, so uncertainties in the S-parameter transformations can lead to significant errors. The accuracy of this conversion can be improved in many ways, for example by adding more steps to the calibration process or by performing additional computation algorithms that complicate the measurement. In addition to the Nicolson-Ross-Weir algorithm, other methods based on transmittance / reflection measurements have similar difficulties.

An important step was made in 1990 when

Baker-Jarvis and coworkers demonstrated that it is possible to derive S-parameter equations that are invariant with respect to the reference level (see J. Baker-Jarvis, EJ Venzura, WA, Kissick: Improved Technique for Determining Complex Permittivity with Transmission / reflection method, IEEE Tran. Microw. Theory o ^ Tech., Vol. 38, pp. 1096-1103, August 1990). With the help of some of these 30 equations, they showed that it was possible to separate the values of the material parameters using an iterative algorithm. This algorithm requires

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consider some initial values of permittivity and permeability as input, and there is one of its limits

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g 35 tests: a good guess is needed, otherwise the algorithm may produce false results.

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Another disadvantage when using the Baker-Järvis method is that it cannot be used to determine the permeability of magnetic materials.

SUMMARY OF THE INVENTION

The present invention provides a method for measuring electromagnetic parameters of materials.

The method combines the ideas of NRW and Baker-Järvis techniques. More specifically, the scattering parameters are combined into a set of reference-level invariant equations (as in Baker-Jarvis), and the equations are used in combination with group rate data (as in NRW). The result is 15 simple, explicit, and comparatively invariant methodologies that can be used to characterize hand dielectric and magnetic materials. Compared to NRW, this method has the advantage of using in-20 variants with respect to the reference level, so it is easier to implement and, moreover, errors due to the location of the reference levels are not generated. Compared to the Baker-Järvis algorithm, the improvement is obtained by using additional sample information obtained from group speed measurements. This removes the uncertainty in the step definition. In addition, since our results are not dependent on choosing good initial values for s and u such as Baker-c \ j q in Järvys,

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unknown dielectric materials and additional

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? 30 materials with magnetic properties at high frequencies.

ir The method is characterized in that it comprises τ_ the following steps: oo measure the length of the material sample, o 35 determine the distance between the gates of the measuring device, 4 determine the scattering parameters by measuring the transmission and reflection signals between the gates of the measuring device and without where the reflection coefficient depends on the scattering parameters, but the equation used to calculate the reflection coefficient is independent of the distances between the material sample and the gates of the measuring device, 10 is calculated distances between the gates, and calculate the electromagnetic parameters of the material based on progression.

In one embodiment of the present invention, the propagation ratio P and the square of the reflection coefficient Γ2, which are invariant with respect to the reference plane, are calculated as follows: p2 - ä (i + B j + (1 -Bf ± -j- AÄ'B '+ [ - (l -Bf]

2 AB ~ 2 AB

1. - | -i2 2 inL C C

„1 + Γ A _ ύ11ύ22 P = R-e λ d = - Μ 25 1 + 5Γ2, where S2lSn.

O 14 (Lair-L) CO B - eX (^ 21 ^ 12 _ ^ 11 ^ 22); and * ^ 21, where S ± j indicates the transmission and reflection signals 30 measured from port j to port i of the measuring device, and λ indicates the wavelength of the signal in the region between the ports outside the material.

Section 05 In one embodiment of the present invention

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the method further comprising calculating a complex refractive index 5 or a complex wave impedance based on the propagation ratio and / or reflection coefficient.

In one embodiment of the present invention, the complex refractive index 5 is explicitly calculated from the equation ilnfL \ P J and / or the complex 1 + Γ wave impedance from the equation z = -——.

In one embodiment of the present invention, the complex electrical permittivity and complex magnetic permeability are calculated based on the propagation ratio and / or reflection coefficient.

In one embodiment of the present invention, the complex electrical permeability is calculated from equation n-1 to z, and the complex magnetic permeability is calculated from the equation Pr-nz. In one embodiment of the present invention, the electrical permittivity f = n ^ of a non-magnetic material is calculated from the equation <.

In one embodiment of the present invention, the magnetic permeability of an unknown material is determined by checking whether the square of the square of the reflection coefficient negative or positive is physically correct by comparing the sign of the calculated scattering parameters with the measured scattering parameters.

In one embodiment of the present invention

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Electrical permittivity and magnetic properties of 25 materials

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, the permeability is determined by the electrical permittivity-00? and magnetic permeability, irrespective of the sign of the reflection coefficient.

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In one embodiment of the present invention, the group velocity or group delay is measured by a measuring device

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§ in space between gates, o cm In one embodiment of the present invention, the physically correct solution for the calculated electromagnetic parameters is selected by comparing the calculated group delay with the measured group delay.

According to another aspect of the present invention, the invention comprises a computer program product 5 for measuring electromagnetic parameters. A computer program product is characterized in that it comprises computer program code means stored on a computer-readable medium, the code means being arranged to execute the steps of any of the methods described above when executing said program on a computer.

In one embodiment of the present invention, a computer program product is implemented for use in a vector circuit analyzer.

According to a third aspect of the present invention, the invention comprises measuring apparatus for measuring electromagnetic parameters of a material.

The measuring apparatus is further characterized by comprising: 20 measuring means configured to measure the length of the material sample, measuring means configured to determine the distance between the gates of the measuring device, measuring means configured to determine the scattering parameters by measuring the transmission and reflection signals with and without a material sample, ^ processing means configured to calculate the reflection coefficient of the material, where the reflection-oo cp 30 coefficient depends on the scattering parameters, but the equation used to calculate the reflection ^ coefficient is independent of the material port and the gauge ports

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distances, the processing means configured to glass in g 35 the propagation ratio of the transverse electromagnetic wave propagating through the material, the propagation ratio being dependent on the scattering parameters and the reflectivity, 7 but the equation used for is configured to calculate the electromagnetic parameters of the material based on the reflection coefficient and the propagation ratio.

In one embodiment of the present invention, the measuring apparatus further comprises means configured to perform any of the above-described embodiments of the method.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows a pattern of multiple reflections between two interfaces of different materials, Figure 2 shows a model of a transmission tube containing material of length L, where Lj (j = 1, 2) indicates the distance from the reference plane of measurement of the S parameter and the at the interface between the materials, Figure 3 shows a reference plane invariant measurement model, where L indicates the sample length and Lair indicates the distance between the calibration levels of the S parameter measurement, Figure 4 illustrates a measuring arrangement for micromanaging the electromagnetic parameters of materials. 18 GHz, Figure 5 shows Nicolson-Ross-Weir

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o method (NRW) and a reference level according to the invention

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a comparative permittivity of the Complex 30 permittivity obtained by the invariant invariant method (RPI) for a 20 mm PVC sample, and g Figure 6 shows the Nicolson-Rossin-Weir method (NRW) and the comparative level g invariant method of the invention (RPI) comparing the lexical permittivity of the obtained component 35 with a 20 mm

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0X1 for a PTFE sample.

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DETAILED DESCRIPTION OF THE APPLICATIONS

Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

5 First, the measurement is modeled within the classical electric dynamics. We present a novel algorithm that is invariant to the reference plane and demonstrate how it can be used to determine complex refractive index and complex permittivity and permeability.

We begin by deriving the mathematical relationship between S parameters and material parameters. We illustrate the scattering of transverse electromagnetic waves using the multi-beam-15 pattern illustrated in Figure 1. In this figure, parts 12 and 14 contain a first material having an electrical permittivity ει and a magnetic permeability μι. The second material is located between the two portions in space 13 and has a length L, an electrical permittivity 20 of 82, and a magnetic permeability of µ2. The interfaces between the two materials are shown by reference numerals 10 and 11.

In this model, the total reflectance and transmittance can be calculated using the superposition principle 25. Since a transverse electromagnetic wave (TEM) traveling at distance L generates a phase change of 2nL / X, where λ is the wavelength in the region, the etch ratio of the TEM wave passing through the 0 L material is given by the following equation: Z 30 ^ P = e ~ ^ L, (1)

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Q_ _ where y2 = ΐω / ν2 = icon2 / c = ϊω- ^ μ2ε2.

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o 35 The total reflection coefficient is ^ rfi _ P2) r = Γ + 7 'T TP2 + T T r3P4 + t_i_L (2) 1 toi 1 ^^ 21 ^ 121 ^ ^ - ^ 21- ^ 121 *' 2n2 '' Z '

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9 J _ | g2Ml where Γ = - '. (3) j _l_ £ 2 ^ 1 V ^ lf ^ 2 and Γ12 = 1 + Γ = - (4) 1+ g ^ 2 Vei ^ 2 V ε2 ^ 1 5 Similarly, the total coefficient of penetration for η: η and P is p (l-r2) r '= TW (5) 10 Figure 2 shows a standard model for transmission / reflectance measurement. The transmission tube is divided into three areas 22, 23, and 24. The reference level of the first port is indicated by reference numeral 20, while the reference level of the second port is indicated by reference numeral 21. The location of the reference levels determines L1 and L2. Typically, the regions L 1 and L 2 are assumed to be filled with air, and the center region L is filled with material with a relative permittivity ε μ er = - and a relative permeability μΓ-—. The complex refractive index of Ma-£ μ0 20 can be expressed as n = · Assuming the permittivity

Door a] a permeability μι are the same as free space? permittivity εο and free space permeability μο, the T equation (3) can be rewritten to the following form c 25:

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S r = 77T (6) σ> ζΛΛ o o

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10 where z = ^ μΓ Ier is the impedance relative to the vacuum (total impedance Z = μ / ε = Z0z, where Z0 = · ^ μ0 / ε0 = 120πΩ is the specific impedance of the vacuum).

The remainder of this section focuses mainly on the determination of these two variables, z and n, based on test data. Based on the multi-reflection model, the S parameters are expressed as Γ: η and P as follows: 10 sn = e-2 '· 1 · r „, = e-2’ · 1 · (7)

Si 2 β - 'Λ Τ ^ ζ ζ) (8) and (9) where γι = ίωηλ le «ico / c (c is the speed of light in vacuum).

When there is no sample inside the transmission tube, Γ = 0, γι = γ2, and thus: S ° 21 = e ~ ri (L1 + l2 + L) = e ~ r '(A ^ (10) 20

From equation 10, the length of the air tube Lair can be experimentally determined by calibrating the vector circuit analyzer and then measuring the transmission through the empty air tube to obtain the step.

^ 25 In the next step, Γ and P are expressed by the parameters S-o w. This corresponds to the Nicolson-Rossino-Weir algorithm with the fundamental difference that neither Γ ^ nor P is determined by Li and L 2. In fact, in air ducts operating at relatively high frequencies, the measurements of L1 and L2in are subject to relatively high uncertainties. These errors are σ> further inherited in the phase coefficients of the S parameters, / / i ivföLj S (2riLJ) = - ^ f (11) 11 where 7e {1,2}, which results in larger errors in the phase coefficients at higher frequencies.

Figure 3 shows a schematic model for measuring the invasive variant relative to the reference plane. The first material is housed in spaces 32 and 34 and is preferably air. Between the air spaces is another material 33 of length L and permeability and permeability of £ 2 and µ2. The calibration levels are indicated by reference numerals 30 and 31 and their spacing is Lair.

We begin by defining two variables related to the quantities being measured, namely: 15 rLJd! 1, (12) & A (i_rh /> 'and B = -SnS2) = lhp-, (13) where ^ is the wavelength of the signal in the region outside the material. .

The S parameters are experimentally measured with a vector circuit analyzer (VNA), the air tube length Lair is obtained from equation (10), and the sample length L is measured before the sample is inserted into the air tube.

^ 25 By solving equation (13) for P2, δ

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oh R + r2 9 (14) ^ 1 + ΒΓ2

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tr and placing this back in Equation 12 gives: $ 30 r2 (i -b) 2 I ^> + r2) Mr2) · (15) (M v 12

The actual results of the invention will now be approached, and the first embodiment of the invention will illustrate how the complex refractive index n can be measured by the present method.

5 Equation (15) can finally solve the square of the reflection coefficient (Γ2) r2 -A (l + B2) + (i-Bf J-4A2B2 + [4 + g:) - (i-yf

2 AB 2 AB

10 where the sign of this equation is selected such that | Γ | ^ 1. These expressions P2 and Γ2 are obviously invariant with respect to the reference level.

A very useful, simpler expression of P can be obtained by defining another quantity 15 R, which is directly related to the scattering parameters: R = s ± _ylp (^) S ° 21l-P2T2 where Sy and S ° - are the signals measured from port j to port i between gates and without material.

The quantities L1 and L2 can be solved by equation (17): solving the equation for the propagation ratio P and placing P2 from equation (14) into equation 25 (17) gives the position δ

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§ P = R-T ^ nL = R-5 - / *. (18) ° \ + BT2 \ + BT2 a. After these calculations, assuming that there is free space on each side of the 30 samples, the complex refractive index can be determined as follows: S, - c lii § η = φ ^ = —— In- , (19) c \ i iItjjL \ P) 13 or explicit walls as follows: 1 1. f 1 + Γ2 λ n = 1 - In -TR. (20)

YLL [l + BT2) 5 The logarithmic function shown in Equations (19) and (20) is a polyvalent function that results in an infinite number of discrete values of n. The right solution must be chosen among these values. One way to do this is to check whether or not the selected solution gives correct values for another measurand. In addition, this measurand must not be determined by Li and L2.

By definition, group delay is a measure of the pulse signal propagation time through the transmission tube. The propagation time of the wave-15 packet is defined as: x ** = -, (21) v, where x is the propagation length and vg is the group speed of the wave pulse 20. In this case, τ1 = ~~ '(22) and ^ OC Lair -L T d (fn \ o 25 * g = —- + L— -, (23)

c \! c df {c J

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o ^ where τ ° is the group delay through the empty tube and zg is the g group delay through the tube

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L-length sample. By comparing the calculated group delay-53 to the measured group delay, LO | τ measured _ ^ calculated | _ q (2 4)

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Another variable 14 that can be used as an alternative to group delay is the group delay relative to the empty air tube: τ = - {\ - n-f-Y (25) df) 5, which is derived by subtracting equation (23) from equation (22).

The following exemplary embodiment of the invention describes how to distinguish the material parameters sr and 10 μΓ (relative permittivity and relative permeability). In practice, an interesting situation is the case where the experimenter already has some information about the material. For example, if chemical analysis provides further evidence that materi-15 does not contain magnetic elements, it can be assumed that μΓ = 1 and simply determine the permittivity from er = n2. As will be shown below, this achieves better accuracy than the more general method described below, which requires the determination of z.

However, in many situations, especially with respect to materials under investigation which contain magnetic elements, magnetic impurities, or magnetic nanoparticles, it is not possible to know in advance what the electromagnetic properties are. Use in these situations

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In addition to ^ n, the relative impedance z. This is an additional application for the magnetic materials of the invention, whereby the properties of the materials sr and Pr are given by: xn £ μΓ = nz and £ r = -, (26) z oö ^ where 8 1 + Γ ί \ CM Z = T ^ r 27 15

The refractive index Γ is determined from equation (16). But this equation gives Γ only up to the sign, since + Γ are both in equation (16) 5. Γ: η To get the correct sign, you need to go back to Equation (7) or (8) and check which, + Γ or -Γ, matches the equation. It should be noted that this does not produce any additional errors as it is only a sign check.

In other words, to obtain the correct sign Γ: η, the S-parameters calculated on the basis of ± Γ: η are compared with the measured S-parameters. Equations (26) and (27) can then directly obtain complex electrical permittivity and magnetic permeability 15, provided that the complex refractive index is known from the above method.

It should be noted that even without such verification, only a minimum amount of information on the properties of the material may be sufficient. Assume that Γ is the right rat-20 ripple, which results in the right set of material parameters sr and μΓ. The properties of the conformal mapping, equation (27), mean that the opposite sign -Γ corresponds to the relative impedance z'1. The effect on the final result in equation (26) is simply that the values of permittivity and permeability are changed. In many practical situations, an experienced experimenter can easily identify which is permittivity and which is permeability,

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^ when two complex numbers are given with a minimum of 30 information on the chemical composition of the material.

The following is an example of an experiment in which the above method is verified. In this example, the electrical permittivity S 35 of polytetrafluoroethylene (PTFE) and polyvinyl chloride (PVC) is measured in the frequency range 2-18 GHz. However, it should be noted that although this test is performed in a limited frequency range, the method is generally frequency independent.

Referring to Figure 4; the present method measures the electromagnetic para-5 meters of materials in the microwave frequency range. A 7 mm precision coaxial air tube 44 is used as a sample holder for conducting transverse electromagnetic waves between the measurement ports; sample 45 can be seen in the middle of the air tube. The group delays and scattering parameters mi-10 were determined using a vector circuit analyzer (VNA) 40.

The air tube equipment was connected to the VNA ports 41 from 7 mm to 2.92 mm (K) adapters. In this example, the measurement frequency range is limited to the operating frequencies of the 7 mm air tube, that is, up to 18 GHz. In principle, the method can also be used in other frequency ranges, provided that transverse electromagnetic waves are propagated and isotropically propagated through the region between the measurement ports in that frequency range.

20 Prior to measurement, a 2-port calibration was performed. An empty air tube was then measured to obtain S ° ij, which is used to infer a Lair 17.3193 cm between the calibration levels 42, 43. A specimen in the form of a rotary piece was then inserted between the inner and outer conductors of the il-25 map tube, and the measurements were repeated.

Measurements for 20.00 mm PVC and 20.00 mm PTFE samples give the complex permittivity spectra illustrated in Figures 5 and 6. It will be appreciated that, compared to the Nicolson-Ross-Weir algorithm (NRW), the method of the invention (RPI) results in fewer errors and stable results also around the three Fabryn-Perot resonance frequencies in the aforementioned frequency range.

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g 35 This is a practical demonstration that the present method produces significantly fewer errors 17 than the NRW algorithm when used to characterize non-magnetic materials.

Numerical analysis and experiments show that the uncertainties of the method of the invention are relatively small at higher frequencies. This characteristic is an intrinsic property of the transmission / reflection method because a significant change in the S parameter step due to the presence of the material requires that the sample length be greater than a certain size 10 relative to the signal wavelength.

The present algorithm is preferably implemented as a computer program that can be executed on a suitable processing device. The processing device may be a microprocessor, preferably implemented in a vector silicon analyzer.

In addition, the algorithm has been experimentally verified for several materials. It can be seamlessly integrated with any vector circuit analyzer on the market.

It will be obvious to a person skilled in the art that as technology advances, the basic idea of the invention can be implemented in many different ways. The invention and its applications are thus not limited to the examples described above; instead, they may vary within the scope defined by claims 25.

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Claims (15)

A method for measuring electromagnetic parameters of materials, characterized in that the method comprises the steps of: measuring the length of the material sample, determining the distance between the ports of the measuring device, material reflection coefficient, where the reflection coefficient depends on the scattering parameters, but the equation used to calculate the reflection coefficient is independent of the distances between the material sample and the measuring device ports, and the distances between the ports of the gauge, and calculate ma the electromagnetic parameters of the material based on the reflection coefficient and the propagation ratio. Method according to claim 1, characterized in that the method further comprises the step δ: CM ^ calculating the propagation ratio P and the reflection coefficient? '30 men square Γ which are invariant with respect to the reference plane and are obtained from the following equations: X en CL 2 _-4l + £ 2) + (l-£) 2 V-4A2B2 + λ {ί + Β2) - {\ - Β) 2 \ oo I —-- m 2 AB 2 AB CD i. τ-ι2 2iizL COSP = R ^ '~ l + BT, where, i4n (Lair-L) β _ ^ 21 B = e 1 (SA-S "Sn) r and S" where Sij indicates the measuring device from port j to port i the transmission and reflection signals and λ indicate the signal wavelength in the region between the ports 5 outside the material. The method according to claims 1-2, characterized in that the method further comprises the step of: calculating a complex refractive index or a complex wave impedance based on the propagation ratio and / or the reflection coefficient. The method according to claim 3, characterized in that the method further comprises the step of: explicitly calculating a complex orn = —— lnf-1 factor based on the equation * '2vfL \ PJ and / or a complex wave impedance of the equation z = | + ^ basis. Method according to claims 1-2, characterized in that the method further comprises the step of calculating the complex electrical permittivity and the complex magnetic permeability on the basis of the propagation ratio and / or the reflection coefficient. The method according to claim 5, CVJ «- 25, characterized in that the method further comprises the following step: co cp is calculated by the complex electric permittivity 2 n zr - g based on z and the complex magnetic permeability of the equation Pr ~ nz basis. o 30 Method according to claim 5, characterized in that the electrical permittivity of the non-magnetic material is calculated on the basis of the equation r ~. Method according to claims 1-7, characterized in that the magnetic permeability of the unknown material is determined by checking whether the square of the reflection coefficient negative 5 or positive square is physically correct by comparing the sign of the calculated scattering parameters with the measured scattering parameters. Method according to claims 1-7, characterized in that the electrical permittivity and the magnetic permeability of the material are determined on the basis of the electrical permittivity and the magnetic permeability separable irrespective of the sign of the reflection coefficient. Method according to claim 1, characterized in that the method further comprises the step of: measuring the group speed or the group delay along the space between the ports of the measuring device. The method of claim 10, characterized in that the physically correct solution for the calculated electromagnetic parameters is selected by comparing the calculated group delay with the measured group delay. A computer program product for measuring the electrical magnetic parameters of a material, characterized in that the computer program product comprises computer program code means stored on a computer readable medium, the code means arranged to perform any method according to claims 1-11 of cp 30. steps ^ when executing said program on a computer, A computer program product according to claim 12, characterized in that the computer program product is designed for use in a vector silicon analyzer. o o {M 14. Measuring apparatus for measuring the electromagnetic parameters of a material, characterized in that the apparatus comprises: measuring means configured to measure the length of the material sample, measuring means configured to determine the distance between the gates of the measuring device, measuring means configured to determine scattering parameters. 10 reflection signals material sample positioned between the gauge device ports and without material sample, processing means configured to calculate the material reflection coefficient, wherein the reflection coefficient depends on the scattering parameters, but the equation used to calculate the reflection coefficient 15 is calculate the propagation ratio of the transverse electric magnetic wave propagating through the material, where the propagation ratio depends on sir hollow parameters and reflection coefficient, but the equation used to calculate the propagation ratio is independent of the distances between the material sample and gauge ports, and processing means configured to calculate the electromagnetic parameters of the material based on the reflectance and propagation ratio. CM i- A measuring apparatus according to claim 14, characterized in that the apparatus further comprises means configured to carry out the method according to claims 2-11. x cc CL oö LO 05 O O CM