CN106093810A - A kind of method of material electromagnetic parameter test and the ambiguity solution for material electromagnetic parameter test - Google Patents

A kind of method of material electromagnetic parameter test and the ambiguity solution for material electromagnetic parameter test Download PDF

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CN106093810A
CN106093810A CN201610353303.0A CN201610353303A CN106093810A CN 106093810 A CN106093810 A CN 106093810A CN 201610353303 A CN201610353303 A CN 201610353303A CN 106093810 A CN106093810 A CN 106093810A
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frequency
value
group delay
electromagnetic parameter
formula
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CN106093810B (en
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胡大海
赵锐
杜刘革
王亚海
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CLP Kesiyi Technology Co Ltd
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China Electronics Technology Instruments Co Ltd CETI
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00Arrangements or instruments for measuring magnetic variables
    • G01R33/12Measuring magnetic properties of articles or specimens of solids or fluids
    • G01R33/1253Measuring galvano-magnetic properties
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
    • G01R27/2617Measuring dielectric properties, e.g. constants
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00Arrangements or instruments for measuring magnetic variables
    • G01R33/12Measuring magnetic properties of articles or specimens of solids or fluids
    • G01R33/1223Measuring permeability, i.e. permeameters

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Abstract

The present invention proposes and a kind of carries out the method for material electromagnetic parameter test and a kind of ambiguity solution for material electromagnetic parameter test based on free-space Method.A kind of method carrying out material electromagnetic parameter test based on free-space Method, including: step (), the calculating of initial n value, step (two), the calculating of follow-up all n values.The present invention does not has particular/special requirement to the solution of ambiguity in material electromagnetic parameter test to the thickness of testing sample;To the initial frequency tested without particular/special requirement;Avoid the loaded down with trivial details iterative that all frequencies are carried out by group delay method;It is applicable to microwave and millimeter wave and is particularly suited for terahertz wave band free-space Method material electromagnetic parameter test.

Description

A kind of method of material electromagnetic parameter test and many for material electromagnetic parameter test Value sex chromosome mosaicism solution
Technical field
The present invention relates to technical field of measurement and test, carry out material electromagnetic parameter test particularly to one based on free-space Method Method, further relate to a kind of ambiguity solution for material electromagnetic parameter test.
Background technology
Microwave dielectric material has been widely used in the every field of microwave as electromagnetic transmission medium, as microwave leads to The systems such as letter, satellite communication, missile guidance, electronic countermeasure, radar navigation, remote sensing, remote measurement use microwave dielectric material the most in a large number. The electromagnetic parameter of dielectric material refers to complex dielectric permittivity and the complex permeability of material, and they characterize the mutual of material and electromagnetic field Effect.Electromagnetic parameter testing has the most important meaning along with the extensively application of dielectric material.Free-space Method, transmission are instead Method of penetrating as typical material dielectric constant method of testing, have compared with additive method convenient test, can carry out wide-band width measurement, It is applicable to electricity spy and magnetic meets the advantages such as material non-destructive testing.
As a example by typical NRW transmission/bounce technique principle, its basic calculating formula is as follows:
S 11 = Γ ( 1 - T 2 ) 1 - T 2 Γ 2 - - - ( 1 )
S 21 = T ( 1 - Γ 2 ) 1 - T 2 Γ 2 - - - ( 2 )
Γ = η r - 1 η r + 1 - - - ( 3 )
T=e-jγd (4)
Wherein, S11、S21It is scattering parameter, can be obtained by vector network analyzer, ηrSpace for testing sample Natural impedance, γ is the propagation constant of sample, and d is testing sample thickness.More than simultaneous four formula, solves reflection coefficient and transmission system Number,
Γ = k ± k 2 - 1 - - - ( 5 )
T = S 11 + S 21 - Γ 1 - ( S 11 + S 21 ) Γ - - - ( 6 )
k = S 11 2 - S 21 2 - Γ 2 S 11 - - - ( 7 )
Wherein, formula (5) sign selects | Γ | < 1, according to space wave impedance and propagation constant and dielectric constant, pcrmeability Between relationγ=2 π/λ, formula (3), (4) can turn to
η r = 1 + Γ 1 - Γ = μ r ϵ r - - - ( 8 )
γ = j 1 d ln ( 1 T ) = 2 π λ · μ r ϵ r - - - ( 9 )
More than simultaneous two formula, then obtains relative dielectric constant and pcrmeability computing formula:
μ r = 1 + Γ 1 - Γ · j 1 d ln ( 1 T ) · λ 2 π - - - ( 10 )
ϵ r = - 1 μ r [ λ 2 π d ln ( 1 T ) ] 2 - - - ( 11 )
Solve formula (10), (11) the i.e. electromagnetic parameter of derived sample.
Formula (10) according to calculating pcrmeability is known, the pcrmeability of sample to be calculated must solve the logarithm of transmission coefficient T, And T is plural number, plural number has following character,
N=int (d/ λg) (14)
Visible, although the value of 1/T is it is believed that but ln (1/T) is but the most uncertain, imaginary part difference 2n The value of τ, n is by waveguide wavelength λgWith the thickness d of sample determine how to determine that the value of n is in material electromagnetic parameter test Ambiguity.
Conventional imaginary part penalty method is a kind of fairly simple solution solving ambiguity, the propagation of air Constant is:
γ 0 = j ω ϵ 0 μ 0 - - - ( 15 )
Propagation constant in sample is
γ = γ 0 ϵ r μ r - - - ( 16 )
From formula (15), (16), between imaginary part and test frequency f of propagation constant γ should be linear correlation and The function being incremented by, the imaginary part of propagation constant γ shown in Fig. 2 dotted line becomes in periodicity along with the increase of test frequency f Change, therefore can carry out imaginary part compensation by linear increasing function principle, the imaginary part of propagation constant γ and survey after compensation The graph of a relation of examination frequency f is as illustrated in solid line in figure 2.
Imaginary part penalty method determines the method for n, (the f when measuring frequency and raisingm< fm+1), if there being imag (γ (fm+1)) < imag(γ(fm)), then know that the imaginary part of propagation constant γ there occurs periodically change, therefore, frequency fm+1Corresponding n Value should add 1 (i.e. n=n+1) accordingly.Measure frequency uses the mode of frequency sweep to measure as far as possible so that the void of propagation constant Fractional part changes in the range of π.The method is fairly simple relative to group delay method, but be will be to survey for the shortcoming of the method The initial frequency of amount is estimated, and original frequency fixed pattern really isDo not knowing the electricity of dielectric material Initial frequency it is difficult to estimate in the case of magnetic parameter.
Free-space Method carries out the ambiguity solution of material electromagnetic parameter test, the most commonly used method Mainly there is a following deficiency:
(1) limit testing sample thickness, typically make the testing sample thickness half less than waveguide wavelength, can by formula (14) Seeing, after meeting this condition, the value of n only has 0, the most there is not ambiguity.The shortcoming one of the method is to need to estimate The waveguide wavelength of sample, is difficult to accomplish in the case of sample electromagnetic property the unknown, and two is to be not suitable for high frequency measurement, high frequency condition Under, wavelength is too small, and thickness of sample is difficult to half-wavelength.
(2) principle of phase group time delay method is n from 0 incremental calculation sample permittivity successively, when electromagnetic wave is by be measured During sample, its group delay has two kinds of computational methods, and one is by the dielectric constant currently calculated and pcrmeability, according to group delay with The relation of dielectric constant, pcrmeability, thickness and operating frequency calculates group delay;Two is to be directly read by vector network analyzer The electromagnetic wave group delay by sample.When the group delay that two kinds of methods obtain is consistent, then it represents that current n is right value.Should The shortcoming of method is that each frequency will carry out successive ignition, comparatively laborious, and judges that the group delay that two kinds of methods calculate is No unanimously needing specification error scope, the tolerance gap of different frequent points is crossed conference and is had a strong impact on judged result, thus affects calculating Precision.
(3) imaginary part penalty method, the propagation constant imaginary part of actual test presents periodically become along with the increase of test frequency Changing, the rule should being incremented by along with frequency according to propagation constant imaginary part, when propagation constant imaginary part reduces suddenly, then to n Add 1.The method is fairly simple relative to group delay method, but the shortcoming of the method is to enter the initial frequency measured Row estimation, and original frequency fixed pattern really isIn the case of not knowing the electromagnetic parameter of dielectric material It is difficult to estimate initial frequency.
Summary of the invention
For solving above-mentioned deficiency of the prior art, it is an object of the invention to propose one and carry out based on free-space Method The method of material electromagnetic parameter test and a kind of ambiguity solution for material electromagnetic parameter test, first use phase Position group delay method solves the initial value of n, then uses " imaginary part compensation " method to solve follow-up all n values.
The technical scheme is that and be achieved in that:
A kind of method carrying out material electromagnetic parameter test based on free-space Method, comprises the following steps:
Step (one), the calculating of initial n value:
First frequency f of test bandwidth is calculated initially with phase place-group delay method0Corresponding n, in working frequency points f0Time, N starts from scratch and circulates successively, adds 1 and is incremented by, and under previous cycle, n is known, calculates current dielectric according to formula (10)~(13) Constant εrAnd magnetic permeability μr,
μ r = 1 + Γ 1 - Γ · j 1 d ln ( 1 T ) · λ 2 π - - - ( 10 )
ϵ r = - 1 μ r [ λ 2 π d ln ( 1 T ) ] 2 - - - ( 11 )
And calculate the electromagnetic wave theoretical group delay numerical value by sample according to formula (17),
τ c a l = d d d f ϵ r u r f 2 c 2 = 1 c 2 fϵ r u r + f 2 1 2 d ( ϵ r u r ) d f ϵ r u r f 2 c 2 d - - - ( 17 )
Or, after group delay is calibrated by scattering parameter, the phase of the S21 at testing sample two ends is calculated, meter Calculate formula such as formula (18),
τ m e a = - 1 2 π d φ d f - - - ( 18 )
Step (two), the calculating of follow-up all n values:
After initial n value calculates, carrying out calculated for subsequent all of n value according to imaginary part penalty method, imaginary part compensates periodically to become The basis for estimation that S21 phase place is n value changed, particularly as follows:
From the beginning of second some m >=2 of frequency, when measuring frequency and raising, i.e. fm< fm+1If there being phase (S21 (fm)) > phase(S21(fm+1)), then know that the phase bit position of S21 there occurs periodically change, now, frequency fm+1Corresponding n value phase That answers adds 1, i.e. n=n+1.
Alternatively, calculate group delay according to formula (17), (18), when the two result has relatively large deviation, increase the numerical value of n, Continue calculate sample electromagnetic parameter and calculate group delay according to formula (17), meet error precision until the result of calculation with formula (18) Time, then it represents that under previous cycle, n value is correct.
Alternatively, measuring frequency uses the mode of frequency sweep to measure so that the phase place of S21 becomes in the range of ± 2 π Change.
The invention allows for a kind of ambiguity solution for material electromagnetic parameter test, based on above-mentioned The method of material electromagnetic parameter test, comprise the following steps:
(1) first, test fixture is only carried out Two-port netwerk scattering parameter calibration, after calibration so that vector network divides The S21 parameter that analyzer reads is the electromagnetic wave S21 by testing sample;
(2) setting cycle initial value n=0, frequency fmFirst frequency number scale be m=0;
(3) theoretical group delay τ is calculated respectively according to formula (17), (18)calWith test group delay τmea
(4) step-up error item error, it may be judged whether meet condition | τcalmea|/|τcal|≤error, if then representing Current n value is initial n value, otherwise carries out n=n+1, and returns step (3) and recalculate theory group delay τcalWith test group Delay, τmea
(5) m=m+1 is made;
(6) judging whether m is last frequency, if then performing step (8) to jump out circulation, otherwise performing step (7);
(7) the phase place phase (S21 (f of current S21 is judgedm)) phase place of whether the most corresponding more than previous frequency S21 phase(S21(fm-1)), if then taking n (m)=n (m-1), and return step (5), if otherwise taking n (m)=n (m-1)+1 and returning Return step (5);
(8) complete solving of ambiguity, export all n values.
Alternatively, step-up error item error takes 1%.
The invention has the beneficial effects as follows:
(1) thickness of testing sample do not had particular/special requirement;
(2) to the initial frequency tested without particular/special requirement;
(3) the loaded down with trivial details iterative that all frequencies are carried out by group delay method is avoided;
(4) it is applicable to microwave and millimeter wave and is particularly suited for terahertz wave band free-space Method material electromagnetic parameter test.
Accompanying drawing explanation
In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to Other accompanying drawing is obtained according to these accompanying drawings.
Fig. 1 is test scene schematic diagram;
Fig. 2 is existing imaginary part the principle of compensation schematic diagram;
Fig. 3 be the present invention carry out the method electromagnetic wave of material electromagnetic parameter test through treating test sample based on free-space Method Product principle schematic;
Fig. 4 is change situation schematic diagram before and after phase compensation of the present invention;
Fig. 5 is that the present invention is to the flow chart of the solution of ambiguity in material electromagnetic parameter test.
Detailed description of the invention
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments wholely.Based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under not making creative work premise Embodiment, broadly falls into the scope of protection of the invention.
Ambiguity be free-space Method, transmission bounce technique solve matter of utmost importance that electromagnetic parameter have to solve it One, in electromagnetic parameter solution procedure, need to solve phase information, phase place has the periodicity of 2n π, therefore there is ambiguity and asks Topic.Three kinds of solutions are currently mainly had about ambiguity:
One is the thickness limiting testing sample, typically makes thickness of sample be less than the half of waveguide wavelength, after meeting this condition, The value of n only has 0, the most there is not ambiguity.The method is usually used in microwave band transmission bounce technique or free space Method material electromagnetic parameter test, but it is no longer desirable for high frequency measurement, as a example by Terahertz frequency range, waveguide wavelength is the highest also at millimeter Magnitude, sample is the thinnest is difficult to and considerably increases thickness uncertainty, has a strong impact on measuring accuracy;
Two is by estimating the dielectric constant of testing sample and pcrmeability, thus calculates the waveguide wavelength of testing sample, The value of n is calculated further according to correlation formula.Obviously, when the electromagnetic property of detected materials is unknown, and the method is inapplicable;
Three is to solve ambiguity by the method adjusting propagation constant imaginary part, and a difficult problem for the method maximum is needs Limit thickness of sample or limit test initial frequency to ensure that the initial value of n is as zero.
It is an object of the invention to propose a kind of method and carrying out material electromagnetic parameter test based on free-space Method Kind to the solution of ambiguity in material electromagnetic parameter test, do not increase any hardware cost, to material thickness without spy Different require, to job initiation frequency without particular/special requirement, be particularly suited for ultra broadband THz material electromagnetic parameter test.
Electromagnetism by testing sample sight as it is shown on figure 3, on the basis of combining imaginary part penalty method and group delay method advantage, The method of material electromagnetic parameter test of the present invention includes following two steps:
One, the calculating of initial n value.
The present invention calculates first frequency f of test bandwidth initially with phase place-group delay method0At the beginning of corresponding n, i.e. n Initial value.In working frequency points f0Time, n starts from scratch and circulates successively, adds 1 and is incremented by, and under previous cycle, n is known, the most permissible Current DIELECTRIC CONSTANT ε is calculated according to formula (10)~(13)rAnd magnetic permeability μr, and (17) calculating electromagnetic wave passes through sample according to the following formula Theoretical group delay numerical value
τ c a l = d d d f ϵ r u r f 2 c 2 = 1 c 2 fϵ r u r + f 2 1 2 d ( ϵ r u r ) d f ϵ r u r f 2 c 2 d - - - ( 17 )
Additionally, after group delay can also be calibrated by scattering parameter, the phase of the S21 at testing sample two ends calculates Obtain, specific formula for calculation such as formula (18),
τ m e a = - 1 2 π d φ d f - - - ( 18 )
Two kinds of computational methods, the actual electromagnetic ripple sample by fixed thickness is had according to group delay seen from formula (17), (18) Group delay should be unique, therefore both result of calculation should be consistent, when the two result has relatively large deviation, increase Add the numerical value of n, continue calculate sample electromagnetic parameter and calculate group delay according to formula (17), until full with the result of calculation of formula (18) During the most certain error precision of foot, then it represents that under previous cycle, n value is correctly, thus solves initial frequency f0Ambiguity ?.Solving because only that a frequency needs iteration to compare, the calculating speed the step for of therefore is quickly and accurately.
Two, the calculating of follow-up all n values.
After initial n value calculates, calculated for subsequent all of n value can be carried out according to imaginary part penalty method, during due to phase group Prolonging method iteration comparatively laborious, in wideband frequency range, error judgment is difficult to unanimously, and the calculating of follow-up n value no longer uses this side Method, but use the imaginary part penalty method improved, the basis for estimation that it is n value with periodically variable S21 phase place that imaginary part compensates. Scattering parameter is after full two-port network is calibrated, and the phase place of S21 is along with the rising place of presenting the periodically change of operating frequency Trend, as shown in Fig. 4 dotted line, after being similar to the phase compensation that imaginary part compensates, change is become shown in Fig. 4 by the phase place of S21 Bold portion.
The method that concrete phase compensation method determines n is, from the beginning of second point of frequency (m >=2), when measuring frequency and raising (fm< fm+1), if there being phase (S21 (fm)) > phase (S21 (fm+1)), then know that the phase bit position of S21 there occurs periodically Change, now, frequency fm+1Corresponding n value should add 1 (i.e. n=n+1) accordingly.Measure frequency and use the side of frequency sweep as far as possible Formula measures so that the phase place of S21 changes in the range of ± 2 π.The method is fairly simple relative to group delay method, due to N value corresponding to starting point is calculated by previous step, therefore need not press formula againLimit initial frequency Rate, it is to avoid estimate initial frequency in the case of do not know the electromagnetic parameter of dielectric material.
Utilize the said method of the present invention, the invention allows for one ambiguity in material electromagnetic parameter test and ask The solution of topic, as it is shown in figure 5, comprise the following steps:
(1) first, test fixture is only carried out Two-port netwerk scattering parameter calibration, after calibration so that vector network divides The S21 parameter that analyzer reads is the electromagnetic wave S21 by testing sample;
(2) setting cycle initial value n=0, frequency fmFirst frequency number scale be m=0;
(3) theoretical group delay τ is calculated respectively according to formula (17), (18)calWith test group delay τmea
(4) step-up error item error, typically takes 1%, it may be judged whether meet condition | τcalmea|/|τcal|≤error, If then representing that current n value is initial n value, otherwise carry out n=n+1, and return step 3 and recalculate theoretical group delay τcal With test group delay τmea
(5) m=m+1 is made;
(6) judging whether m is last frequency, if then performing step 8 to jump out circulation, otherwise performing step 7;
(7) the phase place phase (S21 (f of current S21 is judgedm)) phase place of whether the most corresponding more than previous frequency S21 phase(S21(fm-1)), if then taking n (m)=n (m-1), and return step 5, if otherwise taking n (m)=n (m-1)+1 and returning Step 5
(8) complete solving of ambiguity, export all n values.
The thickness of testing sample is not had by the present invention by the solution of ambiguity in material electromagnetic parameter test Particular/special requirement;To the initial frequency tested without particular/special requirement;Avoid the loaded down with trivial details iteration that all frequencies are carried out by group delay method Solve;It is applicable to microwave and millimeter wave and is particularly suited for terahertz wave band free-space Method material electromagnetic parameter test.
The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all essences in the present invention Within god and principle, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (5)

1. the method carrying out material electromagnetic parameter test based on free-space Method, it is characterised in that comprise the following steps:
Step (one), the calculating of initial n value:
First frequency f of test bandwidth is calculated initially with phase place-group delay method0Corresponding n, in working frequency points f0Time, n from Zero starts to circulate successively, adds 1 and is incremented by, and under previous cycle, n is known, calculates current dielectric according to formula (10)~(13) normal Number εrAnd magnetic permeability μr,
μ r = 1 + Γ 1 - Γ · j 1 d ln ( 1 T ) · λ 2 π - - - ( 10 )
ϵ r = - 1 μ r [ λ 2 π d ln ( 1 T ) ] 2 - - - ( 11 )
And calculate the electromagnetic wave theoretical group delay numerical value by sample according to formula (17),
τ c a l = d d d f ϵ r u r f 2 c 2 = 1 c 2 fϵ r u r + f 2 1 2 d ( ϵ r u r ) d f ϵ r u r f 2 c 2 d - - - ( 17 )
Or, after group delay is calibrated by scattering parameter, the phase of the S21 at testing sample two ends is calculated, and calculates public affairs Formula such as formula (18),
τ m e a = - 1 2 π d φ d f - - - ( 18 )
Step (two), the calculating of follow-up all n values:
After initial n value calculates, carrying out calculated for subsequent all of n value according to imaginary part penalty method, imaginary part compensates with periodically variable S21 phase place is the basis for estimation of n value, particularly as follows:
From the beginning of second some m >=2 of frequency, when measuring frequency and raising, i.e. fm< fm+1If there being phase (S21 (fm)) > phase(S21(fm+1)), then know that the phase bit position of S21 there occurs periodically change, now, frequency fm+1Corresponding n value phase That answers adds 1, i.e. n=n+1.
A kind of method carrying out material electromagnetic parameter test based on free-space Method, its feature exists In, calculate group delay according to formula (17), (18), when the two result has relatively large deviation, increase the numerical value of n, continue to calculate sample Electromagnetic parameter also calculates group delay according to formula (17), when meeting error precision until the result of calculation with formula (18), then it represents that when Under front circulation, n value is correct.
A kind of method carrying out material electromagnetic parameter test based on free-space Method, its feature exists In, measure frequency and use the mode of frequency sweep to measure so that the phase place of S21 changes in the range of ± 2 π.
4. the ambiguity solution for material electromagnetic parameter test, it is characterised in that based on claim 1 to The method of the material electromagnetic parameter test described in 3 any one, comprises the following steps:
(1) first, test fixture is only carried out Two-port netwerk scattering parameter calibration, after calibration so that vector network analyzer The S21 parameter read is the electromagnetic wave S21 by testing sample;
(2) setting cycle initial value n=0, frequency fmFirst frequency number scale be m=0;
(3) theoretical group delay τ is calculated respectively according to formula (17), (18)calWith test group delay τmea
(4) step-up error item error, it may be judged whether meet condition | τcalmea|/|τcal|≤error, if then representing current n Value is initial n value, otherwise carries out n=n+1, and returns step (3) and recalculate theoretical group delay τcalWith test group delay τmea
(5) m=m+1 is made;
(6) judging whether m is last frequency, if then performing step (8) to jump out circulation, otherwise performing step (7);
(7) the phase place phase (S21 (f of current S21 is judgedm)) phase place phase of whether the most corresponding more than previous frequency S21 (S21(fm-1)), if then taking n (m)=n (m-1), and return step (5), if otherwise taking n (m)=n (m-1)+1 and returning step Suddenly (5);
(8) complete solving of ambiguity, export all n values.
5. the ambiguity solution for material electromagnetic parameter test as claimed in claim 4, it is characterised in that set Put error term error and take 1%.
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