CN1828314A - Substrate integration wave guide measuring method for microwave medium substrate dielectric constant - Google Patents

Abstract

The disclosed method comprises: preparing two integrated waveguides with different length on one substrate; linking same microstrip-substrate integrated waveguide converter between two ends; connecting with VNA by a HF SMA interface to measure scatter parameters; extracting single transmission parameter of a segment of pure waveguide by transfer matrix cascade method to obtain the target value. Compared with prior art, this invention improves precision and accuracy.

Description

The substrate integration wave-guide measuring method of microwave-medium substrate specific inductive capacity

Technical field

The present invention relates to a kind of method of accurate measurement microwave and millimeter wave dielectric substrate specific inductive capacity, thereby, finally improve integrated micro millimetre-wave circuit design accuracy and yield rate for the design of integrated micro millimetre-wave circuit provides accurate specific inductive capacity parameter.

Background technology

Along with the continuous development of microwave and millimeter wave technology, people have developed various microwave and millimeter wave integrated techniques and device.The printed microstrip circuit that PCB technology, LTCC technology are made, printed antenna etc., its electric property is closely related with the relative dielectric constant of dielectric substrate, and this makes the relative dielectric constant of the accurate measuring media substrate ever more important that becomes.In half a century in past, people are extensive use of and come Measuring Dielectric Constant based on the single port and the dual-port measuring method of transmission line technology.The core of this method is Nicolson-Ross and Weir (NRW) process.In this process, fill up one section waveguide or coaxial cable with dielectric sample, obtain the specific inductive capacity of medium then by the scattering parameter explicitly that records.Yet this explicit process is no longer stable when sample length is the half-wavelength integral multiple, and this instability is particularly evident in the low-loss medium.For this reason, Baker-Jarvis has proposed a kind of alternative manner of asking for specific inductive capacity, and he has analyzed the source of error in the measuring process simultaneously.After several years, Boughrie etc. have increased an intermediate steps on the basis of at large having analyzed the NRW formula, thereby have obtained a kind of dielectric constant measurement method iteration, stable that do not need.Above-mentioned several method has all only been considered the basic mode in the waveguide, and this is a kind of ideal situation.Owing to be difficult to fill up waveguide fully, therefore between dielectric sample and conductor border, certainly exist the space with dielectric sample.This space will motivate higher order mode, bring error for the result who measures.

In modern microwave and millimeter wave industry, very high to the accuracy requirement of the relative dielectric constant of dielectric substrate.So several new dielectric constant measurement methods are arisen at the historic moment.For avoiding producing the space, can directly put into free space to dielectric sample and measure.Afsar looks back and has compared several free space methods commonly used, and the principle of these methods is to measure the far field of the antenna system that sample constituted, and obtains specific inductive capacity thus.Obviously it needs sample to have very big cross section to reduce dispersive influence.Ghodgaonkar etc. adopted and focused on the specific inductive capacity that the horn-lens antenna system is measured free space medium sample afterwards.This method can be used for the sample of small cross sections, but because reference planes are uncertain, his method is difficult to well calibrate.

The another kind of method that solves the space problem is only to allow the partially filled waveguiding structure of dielectric sample, thereby avoids the appearance of void effect.The short circuited waveguide that cracks in the H plane that Bahl and Somlo use the part medium to fill is as test macro; York then leaves radial gap on the center line of rectangular metal waveguide broadside, then dielectric sample is inserted the slit, with this as test macro.All there is uncertainty in the formula of these methods, and when calculating specific inductive capacity, needs the process of a conjecture initial value.Recently Catal á-Civera[13] adopt the method for iteration from the scattering matrix of test gained, to try to achieve the complex permittivity of partially filled dielectric sample, do like this and guaranteed not exist in the formula uncertainty.But his method is too complicated, has limited its scope of application.

Summary of the invention

The invention provides a kind of substrate integration wave-guide measuring method that can improve the microwave-medium substrate specific inductive capacity of measurement precision.

The substrate integration wave-guide measuring method of microwave-medium substrate specific inductive capacity of the present invention, on same dielectric substrate, make the substrate integration wave-guide of two different lengths, be connected with identical little band-substrate integration wave-guide converter at its two ends, link to each other with vector network analyzer by the high frequency sub-miniature A connector again, after recording its scattering parameter with vector network analyzer respectively, utilize the Cascading Methods of transition matrix to extract the single transmission parameter of one section pure substrate integration wave-guide, and obtain the relative dielectric constant of dielectric sample thus.

The device that is used to implement the substrate integration wave-guide measuring method of above-mentioned microwave-medium substrate specific inductive capacity of the present invention, comprise that the surface is provided with the dielectric substrate of metal patch and microstrip transmission line is provided with two different lengths on dielectric substrate dielectric substrate integrated waveguide, the two ends of dielectric substrate integrated waveguide are connected with microstrip transmission line respectively.

Compared with prior art, the present invention has following advantage:

1) there is the space hardly in substrate integration wave-guide (SIW) structure between wave guide wall and filled media, uses this structure as tested object the accuracy of medium dielectric constant measurement method is improved.

2) designing and producing fully based on printed circuit board (PCB) (PCB) or LTCC (LTCC) technology and the conventional microwave vector network analyzer of maturation of test macro is simple and reliable.

3) measurement result is accurate, tradition based on the measuring method of dielectric-filled waveguide owing to exist medium with clearance between the wave guide wall and the accurate medium print of needs making, thereby cause the measuring process complexity, the measurement result precision is not high.Micro-wave dielectric constant measuring method of the present invention is owing to utilized the class guide properties of substrate integration wave-guide and the seamless characteristic between the conductive medium thereof, thereby measurement result is accurate.Emulation and actual test result have all been verified the accuracy of this method.

Description of drawings

Fig. 1 is the front view of the embodiment of the invention.

Fig. 2 is the vertical view of the embodiment of the invention.

Fig. 3 is the upward view of the embodiment of the invention.

Fig. 4 is a plated-through hole structural representation of the present invention.

Fig. 5 is at the dielectric constant measurement of X-band dielectric substrate figure as a result.

Fig. 6 is the arrangement plan of substrate integrated test system.

Fig. 7 is three part separation graph of substrate integrated test system.

Embodiment

Embodiment 1

A kind of substrate integration wave-guide measuring method of microwave-medium substrate specific inductive capacity, it is characterized in that on same dielectric substrate, making the substrate integration wave-guide of two different lengths, be connected with identical little band-substrate integration wave-guide converter 511 at its two ends, 512,521,522, link to each other with vector network analyzer by the high frequency sub-miniature A connector again, after recording its scattering parameter with vector network analyzer respectively, utilize the Cascading Methods of transition matrix to extract the single transmission parameter of one section pure substrate integration wave-guide, and obtain the relative dielectric constant of dielectric sample thus.

Embodiment 2

A kind of device that is used to implement the substrate integration wave-guide measuring method of above-mentioned microwave-medium substrate specific inductive capacity, comprise that the surface is provided with the dielectric substrate 1 and the microstrip transmission line 511 of metal patch 2,3,512,521,522, it is characterized in that on dielectric substrate 1, being provided with two different lengths and get dielectric substrate integrated waveguide 41,42, the two ends of dielectric substrate integrated waveguide 41,42 respectively with microstrip transmission line 511,512 and 521,522 connect.Above-mentioned dielectric substrate integrated waveguide 41,42 respectively is made of the two row metal through holes 6 that are located on the dielectric substrate 1; Microstrip transmission line is 50 ohm microstrip transmission lines.

Embodiment 3

A kind of dielectric constant measuring apparatus that is used for the microwave and millimeter wave dielectric substrate, comprise that the surface is provided with metal patch 2,3 dielectric substrate 1, on dielectric substrate 1, be provided with dielectric substrate integrated waveguide 41,42, above-mentioned dielectric substrate integrated waveguide 41,42 respectively are made of two row metal through holes 6, in the present embodiment, the two ends of dielectric substrate integrated waveguide 41,42 are connected respectively to 50 ohm microstrip 511,512 and 521,522, the microstrip line on both sides is connected to sub-miniature A connector, and plated-through hole is to offer through hole on dielectric substrate, metallic sheath 6 is set on through-hole wall and metallic sheath and the metal patch that is overlying on the dielectric substrate bilateral are coupled together.

As shown in Figure 1, be manufactured with the four lines metal throuth hole respectively on substrate to be measured, they have formed the substrate integration wave-guide of two different lengths, the outside diameter d=1mm of all metal throuth holes, Cycle Length p=2mm, substrate thickness b=1.5mm.The width of two substrate integration wave-guides that print on the substrate all is a=15.65mm, and the length of two substrate integration wave-guides is respectively 40mm and 20mm.

We measure the scattering parameter of these two substrate integration wave-guides respectively with composition test macros such as vector network analyzer, coaxial cable for high frequency, high frequency sub-miniature A connectors.Obtain one section single transmission parameter that does not contain the substrate integration wave-guide of uncontinuity by removing uncontinuity then, obtain the relative dielectric constant of this substrate by some mathematical computations more at last, the results are shown in accompanying drawing 5 at X-band.Clearly, the relative dielectric constant of substrate and nominal value 2.2 have a great difference, at the 10GHz place, measure the ε r ≈ 2.4 of gained.We have designed chip integrated waveguide slot array antenna according to the relative dielectric constant that records, and test result and simulation result meet finely, and this has also proved the correctness and the validity of the measuring method of the specific inductive capacity that this substrate is integrated.

With reference to Fig. 6, all there is uncontinuity in prior art in the junction and the place, little band-waveguide transitions two place of sub-miniature A connector and little band.The scattering parameter that vector network analyzer records is the whole test system scattering parameter of (comprising sub-miniature A connector, little band-waveguide transitions and substrate integration wave-guide), because the reflection that uncontinuity causes is difficult to the direct transmission parameter that extracts substrate integration wave-guide from this scattering parameter.For this reason, the present invention proposes a solution, adopt the substrate integration wave-guide of two different lengths to test, utilize the Cascading Methods of transition matrix to extract the single transmission parameter of one section pure substrate integration wave-guide exactly, and obtain the relative dielectric constant of dielectric sample thus.

With reference to Fig. 7, the present invention is divided into three parts to the substrate integration wave-guide test macro.Therefore I and III have comprised all uncontinuities, only contain pure substrate integrated wave guide structure like this in the part ii, can think single transmission parameter T=exp (the γ l of part ii _d), wherein γ represents the complex propagation constant of substrate integration wave-guide.We will test respectively the substrate integration wave-guide of two different lengths respectively, and first tested object only has I and these two parts of III; Second tested object comprises the long l that is _dSubstrate integration wave-guide.The I of two tested objects, III two parts remain unchanged.Suppose that the scattering parameter of measuring two tested objects that obtain is respectively [S] ⁽¹⁾[S] ⁽²⁾, then we can derive the satisfied formula of complex propagation constant of substrate integration wave-guide.

At first, the I of first tested object, III two parts are symmetrical, so first tested object is symmetrical reciprocal networks.Its scattering parameter S that satisfies condition ₁₁ ⁽¹⁾=S ₂₂ ⁽¹⁾, S ₁₂ ⁽¹⁾=S ₂₁ ⁽¹⁾, can obtain the normalization transition matrix of first tested object thus

${\left[A\right]}^{\left(1\right)}=\left[\begin{array}{cc}{A}_{11}^{\left(1\right)}& A_{12}^{\left(1\right)}\\ A_{21}^{\left(1\right)}& A_{11}^{\left(1\right)}\end{array}\right],$ Wherein $A_{11}^{\left(1\right)}=\frac{1}{{2S}_{21}^{\left(1\right)}}(1-{\left|\right[S]}^{\left(1\right)}|),$

$A_{12}^{\left(1\right)}=\frac{1}{{2S}_{21}^{\left(1\right)}}(1+{\left|\right[S]}^{\left(1\right)}|+S_{11}^{\left(1\right)}+S_{22}^{\left(1\right)}),A_{21}^{\left(1\right)}=\frac{1}{{2S}_{21}^{\left(1\right)}}(1+{\left|\right[S]}^{\left(1\right)}|-S_{11}^{\left(1\right)}-S_{22}^{\left(1\right)})\·---\left(1\right)$

Might as well establish part i the normalization transition matrix be

$\left[T_I\right]=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right],---\left(2\right)$

Because the structure of III part and part i is symmetry fully, and all satisfies reversibility condition.The normalization transition matrix of such III part can be write as

$\left[T_{\mathrm{III}}\right]=\left[\begin{array}{cc}{a}_{22}& a_{12}\\ a_{21}& a_{11}\end{array}\right]---\left(3\right)$

The normalization transition matrix of first tested object can be write as the matrix product of the normalization transition matrix of part i and III part, promptly

${\left[A\right]}^{\left(1\right)}=\left[\begin{array}{cc}{a}_{11}{a}_{22}+a_{12}{a}_{21}& 2a_{11}{a}_{12}\\ 2a_{22}{a}_{21}& a_{11}{a}_{22}+a_{12}{a}_{21}\end{array}\right]\·---\left(4\right)$

Equation (1) and equation (4) are compared, add the reciprocity condition that part i satisfies, just can obtain one about a ₁₁, a ₁₂, a ₂₁, a ₂₂System of equations:

$\left\{\begin{array}{c}{a}_{11}{a}_{22}+a_{12}{a}_{21}=A_{11}^{\left(1\right)}\\ 2a_{11}{a}_{12}=A_{12}^{\left(1\right)}\\ 2a_{22}{a}_{21}=A_{21}^{\left(1\right)}\\ a_{11}{a}_{22}-a_{12}{a}_{21}=1\end{array}\right.---\left(5\right)$

When analyzing second tested object, need introduce the part ii among Fig. 2.Obviously part ii satisfies symmetrical reversal condition, and its normalization transition matrix is like this

$\left[T_{\mathrm{II}}\right]=\left[\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{11}\end{array}\right],---\left(6\right)$

B wherein ₁₁ ²-b ₁₂b ₂₁=1.Total transition matrix that I, II, three part cascades of III obtain is:

${\left[A\right]}^{\left(2\right)}=\left[\begin{array}{cc}(a_{11}{a}_{22}+a_{12}{a}_{21})b_{11}+a_{12}{a}_{22}{b}_{21}+a_{11}{a}_{21}{b}_{12}& 2a_{11}{a}_{12}{b}_{11}+a_{12}^2{b}_{21}+a_{11}^2{b}_{12}\\ 2a_{21}{a}_{22}{b}_{11}+a_{22}^2{b}_{21}+a_{21}^2{b}_{12}& (a_{11}{a}_{22}+a_{12}{a}_{21})b_{11}+a_{12}{a}_{22}{b}_{21}+a_{11}{a}_{21}{b}_{12}\end{array}\right]---\left(7\right)$

Meanwhile according to the transition matrix of the measured value gained of the scattering parameter of second tested object

${\left[A\right]}^{\left(2\right)}=\left[\begin{array}{cc}{A}_{11}^{\left(2\right)}& A_{12}^{\left(2\right)}\\ A_{21}^{\left(2\right)}& A_{11}^{\left(2\right)}\end{array}\right],$ Wherein $A_{11}^{\left(2\right)}=\frac{1}{{2S}_{21}^{\left(2\right)}}(1-|{\left[S\right]}^{\left(2\right)}\left|\right),$

$A_{12}^{\left(2\right)}=\frac{1}{{2S}_{21}^{\left(2\right)}}(1+|{\left[S\right]}^{\left(2\right)}|+S_{11}^{\left(2\right)}+S_{22}^{\left(2\right)}),A_{21}^{\left(2\right)}=\frac{1}{{2S}_{21}^{\left(2\right)}}(1+|{\left[S\right]}^{\left(2\right)}|-S_{11}^{\left(2\right)}-S_{22}^{\left(2\right)})\·---\left(8\right)$

Formula (5) substitution formula (7) is obtained about b ₁₁, b ₁₂, b ₂₁Matrix equation be

$\left[\begin{array}{ccc}{A}_{11}^{\left(1\right)}& A_{12}^{\left(1\right)}/2& A_{21}^{\left(1\right)}/2\\ A_{12}^{\left(1\right)}& A_{12}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)& (A_{11}^{\left(1\right)}+1)/2\\ A_{21}^{\left(1\right)}& (A_{11}^{\left(1\right)}+1)/2& A_{21}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)\end{array}\right]\left[\begin{array}{c}{b}_{11}\\ {\mathrm{tb}}_{21}\\ {(1/t)b}_{12}\end{array}\right]=\left[\begin{array}{c}{A}_{11}^{\left(2\right)}\\ A_{12}^{\left(2\right)}\\ A_{21}^{\left(2\right)}\end{array}\right],$ T=a wherein ₂₂/ a ₁₁

(9)

We know that first tested object is reversible, so its transition matrix [A that satisfies condition ₁₁ ⁽¹⁾] ²-A ₁₂ ⁽¹⁾A ₂₁ ⁽¹⁾=1.We can obtain the determinant of the matrix of coefficients in formula (9) according to this condition:

$\left|\begin{array}{ccc}{A}_{11}^{\left(1\right)}& A_{12}^{\left(1\right)}/2& A_{21}^{\left(1\right)}/2\\ A_{12}^{\left(1\right)}& A_{12}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)& (A_{11}^{\left(1\right)}+1)/2\\ A_{21}^{\left(1\right)}& (A_{11}^{\left(1\right)}+1)/2& A_{21}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)\end{array}\right|={-A}_{11}^{{\left(1\right)}^2}+A_{12}^{\left(1\right)}{A}_{21}^{\left(1\right)}=-1,---\left(10\right)$

Simultaneously

$\left|\begin{array}{ccc}{A}_{11}^{\left(2\right)}& A_{12}^{\left(1\right)}/2& A_{21}^{\left(1\right)}/2\\ A_{12}^{\left(2\right)}& A_{12}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)& (A_{11}^{\left(1\right)}+1)/2\\ A_{21}^{\left(2\right)}& (A_{11}^{\left(1\right)}+1)/2& A_{21}^{{\left(1\right)}^2}/2(A_{11}^{\left(1\right)}+1)\end{array}\right|=-A_{11}^{\left(1\right)}{A}_{11}^{\left(2\right)}+(A_{12}^{\left(1\right)}{A}_{21}^{\left(2\right)}+A_{21}^{\left(1\right)}{A}_{12}^{\left(2\right)})/2\·---\left(11\right)$

According to Cramer's rule, can solve again

$b_{11}=A_{11}^{\left(1\right)}{A}_{11}^{\left(2\right)}-(A_{12}^{\left(1\right)}{A}_{21}^{\left(2\right)}+A_{21}^{\left(1\right)}{A}_{12}^{\left(2\right)})/2\·---\left(12\right)$

According to formula (12), we can derive the b of part ii ₁₁Only irrelevant with this a part of individual reflection coefficient Γ that the single transmission coefficient T is relevant and this is a part of.In fact can derive b simply ₁₁=(1+T ²)/2T.If b has been obtained in the calculating through the front ₁₁, we just can solve

$T=b_{11}\±\sqrt{b_{11}^2-1}---\left(13\right)$

In two of T separate selecting range less than 1 that, basis again

γ＝-ln(T)/l _d (14)

Obtain the complex propagation constant γ of part ii substrate integration wave-guide, γ=α+j β wherein, α and β represent the attenuation constant and the phase constant of substrate integration wave-guide respectively.

We know width be a substrate integration wave-guide can the equivalence become the rectangular metal waveguide that width is aRWG, b is constant for its thickness, the formula of normalization equivalent waveguide width

$\stackrel{\‾}{a}={\mathrm{\ξ}}_1+\frac{{\mathrm{\ξ}}_2}{\frac{p}{d}+\frac{{\mathrm{\ξ}}_1+{\mathrm{\ξ}}_2-{\mathrm{\ξ}}_3}{{\mathrm{\ξ}}_3-{\mathrm{\ξ}}_2}},$ TM _x ^OnPattern, (15)

Wherein

${\mathrm{\ξ}}_1=1.0198+\frac{0.3465}{\frac{a}{p}-1.0684},{\mathrm{\ξ}}_2=-0.1183-\frac{1.2729}{\frac{a}{p}-1.2010},{\mathrm{\ξ}}_3=1.0082-\frac{0.9163}{\frac{a}{p}+0.2152}\·---\left(16\right)$

Here a, p, d are respectively width, plated through-hole cycle and the diameters of substrate integration wave-guide.

Calculate the equivalent rectangular duct width a of substrate integration wave-guide _RWGAfterwards, just can further obtain the relative dielectric constant ε of the dielectric substrate at substrate integration wave-guide place _r:

${\mathrm{\ϵ}}_r={\left(\frac{c}{2\mathrm{\πf}}\right)}^2{k}^2,k^2={\mathrm{\β}}^2+{\left(\frac{\mathrm{\π}}{a_{\mathrm{RWG}}}\right)}^2\·---\left(17\right)$

It should be noted that we must guarantee that substrate integration wave-guide is operated in main mould workspace in order following formula is set up.That is to say that we must select the width of tested substrate integration wave-guide so that in the frequency band range of appointment meticulously, only can propagate TE in the waveguide ₁₀Pattern.

Claims (1)

1, a kind of substrate integration wave-guide measuring method of microwave-medium substrate specific inductive capacity, it is characterized in that on same dielectric substrate, making the substrate integration wave-guide of two different lengths, be connected with identical little band-substrate integration wave-guide converter (511 at its two ends, 512,521,522), link to each other with vector network analyzer by the high frequency sub-miniature A connector again, after recording its scattering parameter with vector network analyzer respectively, utilize the Cascading Methods of transition matrix to extract the single transmission parameter of one section pure substrate integration wave-guide, and obtain the relative dielectric constant of dielectric sample thus.

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