CN102608431B - Coaxial-dielectric circular waveguide resonant cavity with frequency range of 1GHz-8GHz and dielectric parameter testing method - Google Patents

Abstract

The invention discloses a coaxial-dielectric circular waveguide resonant cavity for measurement of a dielectric medium with frequency range of 1GHz-8GHz, and a dielectric testing method. An adjustable short-circuiter with a travel of 100mm is arranged at one end of an air coaxial measuring line formed by an outer conductor, an inner conductor and an axially moving probe, and an input coupling loop is arranged on the adjustable short-circuiter. A cylindrical dielectric sample is arranged at a gap between the inner conductor and a metal short circuit board at the other end of the coaxial measuring line, and the cylindrical dielectric sample and the coaxial line outer conductor form a dielectric circular waveguide. TEM (transverse electromagnetic) wave in the coaxial line and TM 01 wave in the sample are combined in resonance to obtain a complex dielectric constant of a material. The difficulty in preparation of the coaxial line and insertion and tight fit of ring samples is overcome, electromagnetic field distribution of the sample is unrelated to sample size and operating frequency, and error of matching of the sample radial size with a metal wall is no longer a main factor causing uncertainty of measurement. The dielectric material with the relative dielectric constant of 1-100 (or higher) can be measured.

Description

1GHz～8GHz coaxial cable-medium circular waveguide resonator cavity and dielectric parameter method of testing

Technical field

The present invention relates to resonator cavity dielectric method of testing, relate in particular to a kind of coaxial cable-medium circular waveguide resonator cavity and dielectric parameter method of testing for 1GHz～8GHz dielectric medium measurement.

Background technology

At microwave frequency band, the basic electricity parameter of non-magnetic media, i.e. relative dielectric constant ε _r, dielectric loss angle tangent tan δ, be research material and development respective media components and parts, as substrate, dielectric resonator, dielectric filter, diectric antenna, microstrip antenna, LTCC (LTCC), microwave module, the integrated basis of microwave.As everyone knows, at the dielectric medium measurement of frequency 1GHz～8GHz, current conventional coaxial cable transmission testing method is the reflection-transmission measurement of annulus sample or the reflection-transmission measurement of cylindrical sample.The former,, due to the tolerance clearance of sample and coaxial cable inner and outer conductor, causes considerable measured deviation, and raises fast with the increase of specific inductive capacity.The latter is because coaxial cable-be full of in medium circular waveguide unitized construction exists a series of TM _0pmould, makes to calculate extremely complicated.This method adopts the resonance principle of coaxial cable-circular waveguide unitized construction, make interval between coaxial cable and coaxial inner conductor inner wire and short circuit metal plate be full of medium and the combined cavity that forms at minimum mode resonance.That by this non-continuous face of coaxial cable-medium circular waveguide, has been encouraged like this, only has TM ₀₁mould.Cause in coaxial cable, only having TEM guided wave and TM ₀₁disappearance ripple, only has TM in medium circular waveguide ₀₁disappearance ripple or guided wave.Thereby realize at TM ₀₁under mould, measure the ε of material _rwith tan δ.This has not only overcome the difficulty of preparing and insert close-fitting circular sample in coaxial cable, and it is irrelevant to have realized in sample electromagnetic field distribution and sample size and frequency of operation, and the mismatch error of sample radial dimension and metallic walls is no longer the principal element that causes measuring uncertainty.Can for Measuring Dielectric Constant from close to 1 to the dielectric material that is about 100.Be particularly suitable for the measurement of one side metallization board substrate and foamed material.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, dielectric parameter proving installation and the method for testing thereof of coaxial cable-medium circular waveguide resonator cavity of a kind of 1GHz～8GHz is provided.

1GHz～8GHz frequency range comprises coaxial outer conductor, coaxial inner conductor, mobile probe, adjustable short-circuiting device, input coupling ring, cylindrical dielectric sample, short circuit metal plate, microwave input signal and output standing wave signal for the measurement mechanism of coaxial cable-medium circular waveguide resonator cavity of dielectric medium measurement; Coaxial outer conductor and coaxial inner conductor are that coaxial configuration, coaxial outer conductor are provided with axial slits, be provided with mobile probe and form air coaxial slotted line in axial slits; One end of air coaxial slotted line is provided with the adjustable short-circuiting device that stroke is 100mm, and adjustable short-circuiting device is provided with input coupling ring; Air coaxial slotted line other end end is provided with short circuit metal plate, is provided with in ， interval, interval and is full of cylindrical dielectric sample between coaxial inner conductor and short circuit metal plate, and cylindrical dielectric sample, short circuit metal plate and coaxial outer conductor form medium circular waveguide; Input coupling ring and microwave input signal join, and the output standing wave signal amplitude while detecting resonance from mobile probe, obtains voltage standing wave ratio (VSWR), and the length relevant with output standing wave signal phase is read by the scale of adjustable short-circuiting device.

Described coaxial outer conductor internal diameter is 2.3～3.5 with the ratio of coaxial inner conductor external diameter.Axial slits length on described coaxial outer conductor is that 200mm, width are 1mm, from the distance of cylindrical dielectric sample surfaces, are 10mm.The thickness of described cylindrical dielectric sample is 1～12mm.

The dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of 1GHz～8GHz is: utilize mode resonance minimum time, making only has TEM guided wave and TM in coaxial cable ₀₁, in medium, only there is TM in disappearance ripple ₀₁disappearance ripple or guided wave; With measuring distance and the voltage standing wave ratio (VSWR) of first node to sample surfaces, evaluation material is at TM ₀₁ε under mould _rwith tan δ, the concrete steps of method are as follows:

(1) first node under measurement resonance is to the distance l of sample surfaces ₀:

At given frequency v _runder, put into dielectric sample, regulate short-circuiting device to reach cavity resonant, the reading L of adjustable short-circuiting device while writing down coaxial cable-medium circular waveguide state _i, with short circuit metal plate, replace sample, again regulate short-circuiting device, make under same frequency resonance again, adjustable short-circuiting device reading L while writing down coaxial cable-short board state ₀, show that first node to the distance of sample surfaces is:

l ₀＝c/(2v _r)-(L ₀-L _i) (1)

Here, c is the airborne light velocity,

(2) measure the voltage standing wave ratio (VSWR) s under resonance:

With sensor-microwave power meter of receiving output probe, the mobile probe on traverse measurement line, while measuring coaxial cable-medium circular waveguide state at above-mentioned resonance frequency v _rthe power meter reading P of lower standing wave peak value and valley _imaxand P _imin, have

s _i＝(P _imin/ _Pimax) ^1/2 (2)

With short circuit metal plate, replace cylindrical dielectric sample, regulate short-circuiting device, make under same frequency resonance again, the mobile probe on traverse measurement line again, measures standing wave peak value under coaxial cable-short board state and the power meter reading P of valley _0maxand P _0min, have

s ₀＝(P _0min/P _0max) ^1/2 (3)

The voltage standing wave ratio (VSWR) that must be caused by dielectric sample is:

s＝s _i-s ₀·2v _rl ₀/c (4)

(3) complex permittivity of Calculating material

by the resonance-standing wave parameter l recording ₀and s, by formula

$j\frac{{2k}_{0}a{\widehat{\mathrm{\ϵ}}}_r}{\ln (a/b)}(y_0-y_q{x}_q)=\frac{1-\mathrm{js}\·\tan (2\mathrm{\π}{v}_r{l}_0/c)}{s-j\tan (2\mathrm{\π}{v}_r{l}_0/c)}---\left(18\right)$

The plural iterative program of writing, solves complex permittivity

in formula (18):

$y_0=\frac{\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{\mathrm{\λ}}_i^2{a}^3}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}---\left(6\right)$

$y_q=-\frac{\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{a}^3({\mathrm{\λ}}_i^2-{\mathrm{\ξ}}_q^2)}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}---\left(7\right)$

x _q＝y _q/A _qn (8)

$A_{\mathrm{qn}}=\frac{{\mathrm{\λ}}_i^2\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{a}^3{({\mathrm{\λ}}_i^2-{\mathrm{\γ}}_q^2)}^2}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}\text{+}\frac{1}{{\widehat{\mathrm{\ϵ}}}_r}\·\frac{1}{4a{\mathrm{\γ}}_q}[\frac{a^2{Z}_1^2\left({\mathrm{\ξ}}_{q}a\right)}{b^2{Z}_1^2\left({\mathrm{\ξ}}_{q}b\right)}-1]---\left(9\right)$

And, the linear combination of Bessel's function

Z ₁(ξ _qa)＝J ₁(ξ _qa)+J ₀(ξ _qa)N ₁(ξ _qa)/N ₀(ξ _qa) (10)

Z ₁(ξ _qb)＝J ₁(ξ _qb)-J ₀(ξ _qb)N ₀(ξ _qb)/N ₀(ξ _qb) (11)

Above-mentioned various in: 2a is coaxial outer conductor internal diameter, and 2b is coaxial inner conductor external diameter, and d is cylindrical sample thickness, J ₀, J ₁and N ₀, N ₁respectively the another rank of the first kind and Equations of The Second Kind, first-order bessel function, ξ _qby formula

J ₀(ξ _qa)N ₀(ξ _qb)-J ₀(ξ _qb)N ₀(ξ _qa)＝0 (12)

First solution that the iterative program of writing obtains, and have

${\mathrm{\γ}}_q=\sqrt{{\mathrm{\ξ}}_q^2-k_0^2}---\left(13\right)$

λ _i＝2.4048/a (14)

${\mathrm{\γ}}_i=\sqrt{{\mathrm{\λ}}_i^2-k^2}---\left(15\right)$

K ₀＝ω/c，

ω＝2πv _r (16)

In formula: γ _qcoaxial pair TM ₀₁wave propagation constant, is real number, propagates disappearance ripple; γ _ithat medium circular waveguide is to TM ₀₁the complex propagation constant of ripple; ω is resonance circular frequency; k ₀it is airborne wave number; K is the wave number in medium; Formula (14) is the another rank of first kind Bessel's function J ₀(λ _ia) first solution of=0.

The beneficial effect that the present invention compared with prior art has:

1: measure simple procedure: only first node under need measurement resonance is to the distance l of sample surfaces ₀with voltage standing wave ratio (VSWR) s.

(1) first node under measurement resonance is to the distance l of sample surfaces ₀:

At given frequency v _runder, put into dielectric sample, regulate short-circuiting device to reach cavity resonant, the reading L of the adjustable short-circuiting device while writing down coaxial cable-medium circular waveguide state _i.With short circuit metal plate, replace sample, again regulate short-circuiting device, make under same frequency resonance again, the adjustable short-circuiting device reading L while writing down coaxial cable-short board state ₀.Show that first node to the distance of sample surfaces is:

l ₀＝c/(2v _r)-(L ₀-L _i) (1)

Here, c is the airborne light velocity.

(2) measure the voltage standing wave ratio (VSWR) s under resonance:

With sensor-microwave power meter of receiving output probe, the mobile probe on traverse measurement line, while measuring coaxial cable-medium circular waveguide state, at above-mentioned resonance frequency v _runder standing wave peak value and the power meter reading P of valley _imaxand P _imin, have

s _i＝(P _imin/P _imax) ^1/2 (2)

With short circuit metal plate, replace sample, regulate short-circuiting device, make under same frequency resonance again, the mobile probe on traverse measurement line again, measures standing wave peak value under coaxial cable-short board state and the power meter reading P of valley _0maxand P _0min, have

s ₀＝(P _0min/P _0max) ^1/2 (3)

The voltage standing wave ratio (VSWR) that must be caused by dielectric sample is

s＝s _i-s ₀·2v _rl ₀/c (4)

2: measured parameter and relative complex permittivity

between have (the disresonance state comparing) relatively simply too much and strict relationship.

, when at minimum mode resonance, in coaxial cable, there is TEM guided wave and TM in the unitized construction cavity of this coaxial cable-medium circular waveguide ₀₁(q=1), in medium, only there is TM in disappearance ripple ₀₁(i=1) disappearance ripple or guided wave.The electromagnetic field equation of separating resonance structure, the normalization input admittance that obtains coaxial inner conductor-cylindrical dielectric interface is

$y_e=j\frac{{2k}_{0}a{\widehat{\mathrm{\ϵ}}}_r}{\ln (a/b)}(y_0-y_q{x}_q)---\left(5\right)$

In formula:

$y_0=\frac{\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{\mathrm{\λ}}_i^2{a}^3}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}---\left(6\right)$

$y_q=-\frac{\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{a}^3({\mathrm{\λ}}_i^2-{\mathrm{\ξ}}_q^2)}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}---\left(7\right)$

x _q＝y _q/A _qn (8)

$A_{\mathrm{qn}}=\frac{{\mathrm{\λ}}_i^2\coth \left({\mathrm{\γ}}_{i}d\right)}{{\mathrm{\γ}}_i{a}^3{({\mathrm{\λ}}_i^2-{\mathrm{\γ}}_q^2)}^2}\·\frac{J_0^2\left({\mathrm{\λ}}_{i}b\right)}{J_1^2\left({\mathrm{\λ}}_{i}a\right)}\text{+}\frac{1}{{\widehat{\mathrm{\ϵ}}}_r}\·\frac{1}{4a{\mathrm{\γ}}_q}[\frac{a^2{Z}_1^2\left({\mathrm{\ξ}}_{q}a\right)}{b^2{Z}_1^2\left({\mathrm{\ξ}}_{q}b\right)}-1],(n=q)---\left(9\right)$

And, the linear combination of Bessel's function

Z ₁(ξ _qa)＝J ₁(ξ _qa)+J ₀(ξ _qa)N ₁(ξ _qa)/N ₀(ξ _qa) (10)

Z ₁(ξ _qb)＝J ₁(ξ _qb)-J ₀(ξ _qb)N ₁(ξ _qb)/N ₀(ξ _qb) (11)

Above-mentioned various in: 2a is coaxial outer conductor internal diameter, and 2b is coaxial inner conductor external diameter.D is cylindrical sample thickness.J ₀, J ₁and N ₀, N ₁respectively the another rank of the first kind and Equations of The Second Kind, first-order bessel function.ξ _qby formula

J ₀(ξ _qa)N ₀(ξ _qb)-ξ _q(ξ _qb)N ₀(ξ _qa)＝0 (12)

First solution that the iterative program of writing obtains.And have

${\mathrm{\γ}}_q=\sqrt{{\mathrm{\ξ}}_q^2-k_0^2}---\left(13\right)$

λ _i＝2.4048/a (14)

${\mathrm{\γ}}_i=\sqrt{{\mathrm{\λ}}_i^2-k^2}---\left(15\right)$

With

k ₀＝ω/c，

ω＝2πv _r (16)

In formula: γ _qcoaxial pair TM ₀₁wave propagation constant, is real number, propagates disappearance ripple; γ _ithat medium circular waveguide is to TM ₀₁the complex propagation constant of ripple; ω is resonance circular frequency; k ₀it is airborne wave number; K is the wave number in medium; Formula (14) is the another rank of first kind Bessel's function J ₀(λ _ia) first solution of=0.

The reduced admittance on formula (5) left side can be used measuring voltage standing-wave ratio (SWR) s and the distance l of first node to sample surfaces ₀obtain, have

$y_e=\frac{1-\mathrm{js}\·\tan (2\mathrm{\π}{v}_r{l}_0/c)}{s-j\tan (2\mathrm{\π}{v}_r{l}_0/c)}---\left(17\right)$

Like this, for non magnetic (μ _r=1) material, combined type (5) and formula (17),

$j\frac{{2k}_{0}a{\widehat{\mathrm{\ϵ}}}_r}{\ln (a/b)}(y_0-y_q{x}_q)=\frac{1-\mathrm{js}\·\tan (2\mathrm{\π}{v}_r{l}_0/c)}{s-j\tan (2\mathrm{\π}{v}_r{l}_0/c)}---\left(18\right)$

The iterative program of writing by formula (18), complex permittivity that just can evaluation material

3: be that the perparation of specimen is easy and measuring error is little.

The interval of coaxial cable and its inner conductor terminal and short circuit metal plate is full of the closed housing of cylindrical dielectric, and its cylindrical sample is easily prepared.Under disresonance state, in coaxial cable, there is TEM mould and TM _0q, in medium, only there is TM in mould _0imould.This has not only overcome the difficulty of preparing and insert close-fitting circular sample in coaxial cable, and it is irrelevant to have realized this place's electromagnetic field distribution and sample size and frequency of operation, and the mismatch error of sample radial dimension and metallic walls is no longer the principal element that causes measuring uncertainty.When at minimum mode resonance, in coaxial cable, be TEM guided wave and TM ₀₁(q=1), in medium, only there is TM in disappearance ripple ₀₁(i=1) disappearance ripple or guided wave, simplified calculating greatly.The standing-wave ratio (SWR) that adopts the place ahead, coaxial cable-medium circular waveguide interface while measuring minimum mode resonance, can further suppress the impact of higher mode on amplitude measurement, improves the measurement accuracy degree of tan δ.

4: be frequently or under random resonance frequency to measure at the point of appointment.

Manufacture the coaxial configuration of different size, with the adjustable short-circuiting device regulating in resonator cavity, can within the scope of 1GHz～8GHz, under your required arbitrary constant frequency, realize resonance, thereby can adopt inexpensive some source frequently.And when the adjustable short-circuiting device of resonator cavity is during in certain fixed position, can change the frequency of synthesized source, within the scope of 1GHz～8GHz, find resonance frequency to measure.Different thickness of sample have different ε _rmeasurement range, Measurement Resolution and accuracy.

5: in applicating medium sample, propagate the characteristic (add select same shaft size) of disappearance ripple or guided wave, arbitrary frequency that can be within the scope of 1GHz～8GHz, from specific inductive capacity close to 1 to up to ε _rthe material of ≈ 100 is measured.

Accompanying drawing explanation

Fig. 1 is the coaxial cable-medium circular waveguide resonator cavity schematic diagram for 1GHz～8GHz frequency range dielectric medium measurement;

Fig. 2 is MPC-14 system (ε under disappearance ripple _r< 28.7) ε _r～l ₀curve: 3GHz, s=0.001, d=3mm (indigo plant) and d=1mm (pink);

Fig. 3 is MPC-14 system (ε under guided wave _r> 28.7) ε _r～l ₀curve: 3GHz, s=0.001, d=8mm (indigo plant), d=10mm (pink).

Embodiment

As shown in Figure 1,1GHz～8GHz frequency range comprises coaxial outer conductor 1, coaxial inner conductor 2, mobile probe 3, adjustable short-circuiting device 4, input coupling ring 5, cylindrical dielectric sample 6, short circuit metal plate 7, microwave input signal 8 and output standing wave signal 9 for the measurement mechanism of coaxial cable-medium circular waveguide resonator cavity of dielectric medium measurement; Coaxial outer conductor 1 and coaxial inner conductor 2, for coaxial configuration, coaxial outer conductor 1 are provided with axial slits, are provided with mobile probe 3 and form air coaxial slotted line in axial slits; One end of air coaxial slotted line is provided with the adjustable short-circuiting device 4 that stroke is 100mm, and adjustable short-circuiting device 4 is provided with input coupling ring 5; Air coaxial slotted line other end end is provided with short circuit metal plate 7, between coaxial inner conductor 2 and short circuit metal plate 7, be provided with interval, in interval, be full of cylindrical dielectric sample 6, cylindrical dielectric sample 6, short circuit metal plate 7 form medium circular waveguide with coaxial outer conductor 1; Input coupling ring 5 joins with microwave input signal 8, and output standing wave signal 9 amplitudes while detecting resonance from mobile probe 3, obtain voltage standing wave ratio (VSWR), and the length relevant with output standing wave signal 9 phase places is read by the scale of adjustable short-circuiting device 4.

Described coaxial outer conductor 1 internal diameter is 2.3～3.5 with the ratio of coaxial inner conductor 2 external diameters.Axial slits length on described coaxial outer conductor 1 is that 200mm, width are 1mm, from the distance on cylindrical dielectric sample 6 surfaces, are 10mm.The thickness of described cylindrical dielectric sample 6 is 1～12mm.

The dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of 1GHz～8GHz is: utilize mode resonance minimum time, making only has TEM guided wave and TM in coaxial cable ₀₁, in medium, only there is TM in disappearance ripple ₀₁disappearance ripple or guided wave; With measuring distance and the voltage standing wave ratio (VSWR) of first node to sample surfaces, evaluation material is at TM ₀₁ε under mould _rwith tan δ, the concrete steps of method are as follows:

(1) first node under measurement resonance is to the distance l of sample surfaces ₀:

At given frequency v _runder, put into dielectric sample 6, regulate short-circuiting device 4 to reach cavity resonant, the reading L of adjustable short-circuiting device 4 while writing down coaxial cable-medium circular waveguide state _i, with short circuit metal plate 7, replace samples 6, again regulate short-circuiting device 4, make under same frequency resonance again, adjustable short-circuiting device 4 reading L while writing down coaxial cable-short board state ₀, show that first node to the distance of sample surfaces is:

l ₀＝c/(2v _r)-(L ₀-L _i) (1)

Here, c is the airborne light velocity,

(2) measure the voltage standing wave ratio (VSWR) s under resonance:

With sensor-microwave power meter of receiving output probe, the mobile probe 3 on traverse measurement line, while measuring coaxial cable-medium circular waveguide state at above-mentioned resonance frequency v _rthe power meter reading P of lower standing wave peak value and valley _imaxand P _imin, have

s _i＝(P _imin/P _imax) ^1/2 (2)

With short circuit metal plate 7, replace cylindrical dielectric samples 6, regulate short-circuiting device 4, make under same frequency resonance again, the mobile probe 3 on traverse measurement line again, measures standing wave peak value under coaxial cable-short board state and the power meter reading P of valley _0maxand P _0min, have

s ₀＝(P _0min/P _0max) ^1/2 (3)

The voltage standing wave ratio (VSWR) that must be caused by dielectric sample is:

s＝s _i-s ₀·2v _rl ₀/c (4)

(3) complex permittivity of Calculating material

by the resonance-standing wave parameter l recording ₀and s, by formula

$j\frac{{2k}_{0}a{\widehat{\mathrm{\&epsiv;}}}_r}{\ln (a/b)}(y_0-y_q{x}_q)=\frac{1-\mathrm{js}\&CenterDot;\tan (2\mathrm{\&pi;}{v}_r{l}_0/c)}{s-j\tan (2\mathrm{\&pi;}{v}_r{l}_0/c)}---\left(18\right)$

The plural iterative program of writing, solves complex permittivity

in formula (18):

$y_0=\frac{\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{\mathrm{\&lambda;}}_i^2{a}^3}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}---\left(6\right)$

$y_q=-\frac{\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{a}^3({\mathrm{\&lambda;}}_i^2-{\mathrm{\&xi;}}_q^2)}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}---\left(7\right)$

x _q＝y _q/A _qn (8)

$A_{\mathrm{qn}}=\frac{{\mathrm{\&lambda;}}_i^2\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{a}^3{({\mathrm{\&lambda;}}_i^2-{\mathrm{\&gamma;}}_q^2)}^2}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}\text{+}\frac{1}{{\widehat{\mathrm{\&epsiv;}}}_r}\&CenterDot;\frac{1}{4a{\mathrm{\&gamma;}}_q}[\frac{a^2{Z}_1^2\left({\mathrm{\&xi;}}_{q}a\right)}{b^2{Z}_1^2\left({\mathrm{\&xi;}}_{q}b\right)}-1]---\left(9\right)$

And, the linear combination of Bessel's function

Z ₁(ξ _qa)＝J ₁(ξ _qa)+J ₀(ξ _qa)N ₁(ξ _qa)/N ₀(ξ _qa) (10)

Z ₁(ξ _qb)＝J ₁(ξ _qb)-J ₀(ξ _qb)N ₁(ξ _qb)/N ₀(ξ _qb) (11)

Above-mentioned various in: 2a is coaxial outer conductor internal diameter, and 2b is coaxial inner conductor external diameter, and d is cylindrical sample thickness.J ₀, J ₁and N ₀, N ₁respectively the another rank of the first kind and Equations of The Second Kind, first-order bessel function, ξ _qby formula

J ₀(ξ _qa)N ₀(ξ _qb)-J ₀(ξ _qb)N ₀(ξ _qa)＝0 (12)

First solution that the iterative program of writing obtains, and have

${\mathrm{\&gamma;}}_q=\sqrt{{\mathrm{\&xi;}}_q^2-k_0^2}---\left(13\right)$

λ _i＝2.4048/a (14)

${\mathrm{\&gamma;}}_i=\sqrt{{\mathrm{\&lambda;}}_i^2-k^2}---\left(15\right)$

k ₀＝ω/c，

ω＝2πv _r (16)

In formula: γ _qcoaxial pair TM ₀₁wave propagation constant, is real number, propagates disappearance ripple; γ _ithat medium circular waveguide is to TM ₀₁the complex propagation constant of ripple; ω is resonance circular frequency; k ₀it is airborne wave number; K is the wave number in medium; Formula (14) is the another rank of first kind Bessel's function J ₀(λ _ia) first solution of=0.

The invention belongs to the relative complex permittivity of low/high-k, medium/low loss microwave dielectric material

measuring coaxial cable-medium circular waveguide resonator cavity test macro.The same shaft size of available MPC-14, APC-7 are with shaft size or other same shaft size (for example: 2a=30.0 * 10 ^-3m, 2b=13.0 * 10 ^-3m; 2a=50.0 * 10 ^-3m, 2b=21.7 * 10 ^-3m) implement.

Embodiment: table 1, Fig. 2 be in some situation of Propagation disappearance ripple, and table 2, Fig. 3 are in some situation of Propagation guided wave.Table 3 is measurement data and the result of calculation of teflon sample in MPC-14 coaxial system, under two frequencies.

Table 1. γ _iwhile being real number, some coaxial system can be used for Measuring Dielectric Constant situation (s=0.001)

^*ε r _maxrepresent the maximum limit that can measure.

Table 2. γ _iwhile being imaginary number, some coaxial system can be used for Measuring Dielectric Constant situation (s=0.001)

^*ε _rminrepresent the minimum limit value that can measure.

The measurement result of table 3 teflon sample (Φ 4.25mm * 1.5mm)

Claims (4)

1. the dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of a 1GHz～8GHz, it is characterized in that: adopt 1GHz～8GHz frequency range for the measurement mechanism of coaxial cable-medium circular waveguide resonator cavity of dielectric medium measurement, utilize mode resonance minimum time, making only has TEM guided wave and TM in coaxial cable ₀₁, in medium, only there is TM in disappearance ripple ₀₁disappearance ripple or guided wave; With measuring distance and the voltage standing wave ratio (VSWR) of first node to cylindrical dielectric sample surfaces, ask material at TM ₀₁ε under mould _rwith tan δ, the concrete steps of method are as follows:

(1) first node under measurement resonance is to the distance l of cylindrical dielectric sample surfaces ₀:

At given frequency ν _runder, put into cylindrical dielectric sample (6), adjustable short-circuiting device (4) reaches cavity resonant, the reading L of adjustable short-circuiting device (4) while writing down coaxial cable-medium circular waveguide state _i, with short circuit metal plate (7), replace cylindrical dielectric sample (6), again regulate adjustable short-circuiting device (4), make under same frequency resonance again, adjustable short-circuiting device (4) reading L while writing down coaxial cable-short board state ₀, show that first node to the distance of cylindrical dielectric sample surfaces is:

l ₀=c/(2ν _r)-(L ₀-L _i) （1）

Here, c is the airborne light velocity,

(2) measure the voltage standing wave ratio (VSWR) s under resonance:

With sensor-microwave power meter of receiving output probe, the mobile probe (3) on mobile air coaxial slotted line, while measuring coaxial cable-medium circular waveguide state at above-mentioned resonance frequency ν _rthe power meter reading P of lower standing wave peak value and valley _imaxand P _imin, have

s _i＝(P _imin/P _imax) ^1/2 （2）

With short circuit metal plate (7), replace cylindrical dielectric sample (6), regulate adjustable short-circuiting device (4), make under same frequency resonance again, mobile probe (3) on mobile air coaxial slotted line again, measures standing wave peak value under coaxial cable-short board state and the power meter reading P of valley _0maxand P _0min, have

s ₀＝(P _0min/P _0max) ^1/2 （3）

The voltage standing wave ratio (VSWR) that must be caused by cylindrical dielectric sample is:

s＝s _i-s ₀·2ν _rl ₀/c （4）

(3) complex permittivity of Calculating material

by the resonance-standing wave parameter l recording ₀and s, by formula

$j\frac{2k_{0}a{\widehat{\mathrm{\&epsiv;}}}_r}{\ln (a/b)}(y_0-y_q{x}_q)=\frac{1-\mathrm{js}\&CenterDot;\tan (2\mathrm{\&pi;}{v}_r{l}_0/c)}{s-j\tan (2\mathrm{\&pi;}{v}_r{l}_0/c)}---\left(18\right)$

The plural iterative program of writing, solves complex permittivity in formula (18):

$y_0=\frac{\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{\mathrm{\&lambda;}}_i^2{a}^3}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}---\left(6\right)$

$y_q=-\frac{\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{a}^3({\mathrm{\&lambda;}}_i^2-{\mathrm{\&xi;}}_q^2)}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}---\left(7\right)$

x _q＝y _q/A _qn （8）

$A_{\mathrm{qn}}=\frac{{\mathrm{\&lambda;}}_i^2\coth \left({\mathrm{\&gamma;}}_{i}d\right)}{{\mathrm{\&gamma;}}_i{a}^3{({\mathrm{\&lambda;}}_i^2-{\mathrm{\&gamma;}}_q^2)}^2}\&CenterDot;\frac{J_0^2\left({\mathrm{\&lambda;}}_{i}b\right)}{J_1^2\left({\mathrm{\&lambda;}}_{i}a\right)}+\frac{1}{{\widehat{\mathrm{\&epsiv;}}}_r}\&CenterDot;\frac{1}{4a{\mathrm{\&gamma;}}_q}[\frac{a^2{Z}_1^2\left({\mathrm{\&xi;}}_{q}a\right)}{b^2{Z}_1^2\left({\mathrm{\&xi;}}_{q}b\right)}-1]---\left(9\right)$

And, the linear combination of Bessel's function

Z ₁(ξ _qa)＝J ₁(ξ _qa)+J ₀(ξ _qa)N ₁(ξ _qa)/N ₀(ξ _qa) （10）

Z ₁(ξ _qb)＝J ₁(ξ _qb)-J ₀(ξ _qb)N ₁(ξ _qb)/N ₀(ξ _qb) （11）

Above-mentioned various in: 2a is coaxial outer conductor internal diameter, and 2b is coaxial inner conductor external diameter, and d is cylindrical dielectric thickness of sample, J ₀, J ₁and N ₀, N ₁respectively the another rank of the first kind and Equations of The Second Kind, first-order bessel function, ξ _qby formula

J ₀(ξ _qa)N ₀(ξ _qb)-J ₀(ξ _qb)N ₀(ξ _qa)＝0 （12）

First solution that the iterative program of writing obtains, and have

${\mathrm{\&gamma;}}_q=\sqrt{{\mathrm{\&xi;}}_q^2-k_0^2}---\left(13\right)$

λ _i＝2.4048/a （14）

${\mathrm{\&gamma;}}_i=\sqrt{{\mathrm{\&lambda;}}_i^2-k^2}---\left(15\right)$

$k_0=\mathrm{\&omega;}/c,k^2=k_0^2{\widehat{\mathrm{\&epsiv;}}}_r,\mathrm{\&omega;}=2\mathrm{\&pi;}{v}_r---\left(16\right)$

In formula: γ _qcoaxial pair TM ₀₁wave propagation constant, is real number, propagates disappearance ripple; γ _ithat medium circular waveguide is to TM ₀₁the complex propagation constant of ripple; ω is resonance circular frequency; k ₀it is airborne wave number; K is the wave number in medium; Formula (14) is the another rank of first kind Bessel's function J ₀(λ _ia) first solution of=0;

The measurement mechanism of the described coaxial cable-medium circular waveguide resonator cavity for 1GHz～8GHz frequency range dielectric medium measurement comprises coaxial outer conductor (1), coaxial inner conductor (2), mobile probe (3), adjustable short-circuiting device (4), input coupling ring (5), cylindrical dielectric sample (6), short circuit metal plate (7), microwave input signal (8) and output standing wave signal (9); Coaxial outer conductor (1) and coaxial inner conductor (2) are coaxial configuration, and coaxial outer conductor (1) is provided with axial slits, be provided with mobile probe (3) and form air coaxial slotted line in axial slits; One end of air coaxial slotted line is provided with the adjustable short-circuiting device (4) that stroke is 100mm, and adjustable short-circuiting device (4) is provided with input coupling ring (5); Air coaxial slotted line other end end is provided with short circuit metal plate (7), between coaxial inner conductor (2) and short circuit metal plate (7), be provided with interval, in interval, be full of cylindrical dielectric sample (6), cylindrical dielectric sample (6), short circuit metal plate (7) form medium circular waveguide with coaxial outer conductor (1); Input coupling ring (5) joins with microwave input signal (8), output standing wave signal (9) amplitude while detecting resonance from mobile probe (3), obtain voltage standing wave ratio (VSWR), the length relevant with output standing wave signal (9) phase place is read by the scale of adjustable short-circuiting device (4).

2. the dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of a kind of 1GHz～8GHz according to claim 1, is characterized in that described coaxial outer conductor (1) internal diameter and the ratio of coaxial inner conductor (2) external diameter are 2.3～3.5.

3. the dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of a kind of 1GHz～8GHz according to claim 1, is characterized in that the axial slits length on described coaxial outer conductor (1) is that 200mm, width are 1mm, from the surperficial distance of cylindrical dielectric sample (6), are 10mm.

4. the dielectric parameter method of testing of coaxial cable-medium circular waveguide resonator cavity of a kind of 1GHz～8GHz according to claim 1, is characterized in that the thickness of described cylindrical dielectric sample (6) is 1mm～12mm.

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