CN101546347A - Parameter determination method of rectangular waveguide lowpass - Google Patents
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Abstract
The invention discloses a parameter determination method of a rectangular waveguide lowpass, belonging to the technical field of electric elements and mainly solving the problem of the design precision of the rectangular waveguide lowpass. The parameter determination method comprises the following steps: firstly, selecting a rectangular waveguide model according to an electrical property index of the rectangular waveguide lowpass and initially determining the structural parameters of a rectangular waveguide electrical length and a rectangular waveguide capacitive diaphragm; then, utilizing Jonathan Schwartz-Christopher inverse transform to solve an S' matrix of the rectangular waveguide capacitive diaphragm through an improved hybrid genetic algorithm; then utilizing genetic algorithm optimization to approximately equalize the S' matrix and an S matrix obtained by a generalized impedance conversion coefficient K so as to finally determine the structural parameter of the rectangular waveguide capacitive diaphragm; and finally, utilizing the S' matrix of the rectangular waveguide capacitive diaphragm to correct the waveguide length between two diaphragms so as to finally determine the cavity length of a rectangular waveguide. The invention can accurately determine the parameters without repeated debugging and can be used for designing the rectangular waveguide lowpass with high precision.
Description
Technical Field
The invention belongs to the technical field of electrical components, in particular to a parameter determination method of a rectangular waveguide low-pass filter, which is used for guiding the design of a high-performance rectangular waveguide low-pass filter.
Background
The rectangular waveguide low-pass filter design comprises the steps of firstly obtaining a low-pass prototype circuit according to the electrical performance indexes of the filter, then carrying out circuit transformation to obtain a generalized impedance transformer K, and finally realizing the impedance transformer and branch elements of the circuit by using a waveguide microwave structure, wherein the design comprises the coupling capacitor diaphragm design and the transmission section waveguide design. For a rectangular waveguide low-pass filter which adopts a capacitive diaphragm to realize coupling, designing the parameters of the capacitive diaphragm according to a generalized impedance transformation coefficient K is a very critical step.
Fig. 1 is a schematic structural diagram of a rectangular waveguide low-pass filter, in which a capacitor diaphragm implements a parallel capacitor and a waveguide segment implements a series inductor.
Fig. 2 shows a capacitive diaphragm structure in a rectangular waveguide and an equivalent circuit thereof. TE transported in rectangular waveguide10Mode electromagnetic waves excite higher order modes at the discontinuity diaphragm, which are cut off in the waveguide and quickly decay away short of the diaphragm. Due to TE10The mode field has only a y component and no x component, and the discontinuity is only in the y direction, which is continuous, so that the electric field lines are distributed in the form of fringe fields on both sides of the diaphragm. In this way, net electrical energy is stored in the vicinity of the diaphragm, while the diaphragm is extremely thin and lossless, so that the discontinuous diaphragm can be equivalent to a lumped capacitive element, denoted by accommodating jB.
For the existing filter, a method for measuring the reflection coefficient is commonly used in engineering to determine the corresponding susceptance value. When the waveguide is terminated by a matching load, the reflection coefficient caused by the susceptance jB is
In the formula <math> <mrow> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mo>=</mo> <mfrac> <mi>B</mi> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mfrac> </mrow></math>
Is a normalized susceptance. The above formula can be solved <math> <mrow> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>Γ</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>Γ</mi> </mrow> </mfrac> <mo>.</mo> </mrow></math>
Wangxinluo, Lemna minor, is described in detail in section seven of chapter II microwave technology and antennas. However, this method cannot give the relationship between susceptance and diaphragm size, and cannot be directly applied to the design of a filter.
At present, when a waveguide filter is designed, the following methods for calculating susceptance of a capacitive diaphragm are mainly used:
1 quasi-static field method
The quasi-static field method is a common method for solving the discontinuity of the waveguide. The electrostatic field is characterized by an operating wavelength λ → ∞, which, although not infinite, is not infinite for the waveguide. However, for evanescent waves in a waveguide, there is λ → λcAnd the higher the order of evanescent wave, the cut-off wavelength lambdacThe smaller, the existing lambda [. lambda. ]cThus, for λcIt is as if the operating wavelength were lengthened, so that the field of the evanescent wave can be approximately represented by the electrostatic field. Angle-keeping transformerThe transformation is a method for obtaining quasi-static field solution directly from the problem of static field solution, and can be carried out by utilizing various functions. Zhang Jun analyzes this in section II of chapter IV of the first book, entitled "discontinuity problem of guided waves". For the parallel plate waveguide of FIG. 1(a) containing symmetric capacitive diaphragms, the pass function <math> <mrow> <mi>w</mi> <mo>=</mo> <mi>u</mi> <mo>+</mo> <mi>jv</mi> <mo>=</mo> <mi>arcsin</mi> <mrow> <mo>[</mo> <mi>csc</mi> <mrow> <mo>(</mo> <mfrac> <mi>πd</mi> <mrow> <mn>2</mn> <mi>b</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>sin</mi> <mfrac> <mi>π</mi> <mi>b</mi> </mfrac> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <mi>jz</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </mrow></math>
The conversion is carried out to obtain a simple parallel plate waveguide, an equivalent capacitance C is obtained, and then B is equal to omega C, so that the parallel susceptance B of the equivalent network can be obtained, and the normalized susceptance value is
In the formula ofgIs the waveguide wavelength, b is the waveguide height, and d is the spacing between the two diaphragms.
2 method of variation
The variational method is a method for processing the extreme value of the functional, and finally, an extreme value function is sought, so that the functional obtains a maximum value or a minimum value. The key theorem is the euler-lagrange equation, which corresponds to the critical point of the functional. In an actual engineering problem, if an actual pending problem can be represented as <math> <mrow> <mi>J</mi> <mrow> <mo>[</mo> <mi>y</mi> <mo>]</mo> </mrow> <mo>=</mo> <msubsup> <mo>∫</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <msub> <mi>x</mi> <mn>1</mn> </msub> </msubsup> <mi>F</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>y</mi> <mo>′</mo> <mo>)</mo> </mrow> <mi>dx</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>y</mi> <mo>=</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow></math>
The real value of the requirement is the extreme value of the functional, which is also called the stable value. When solving the problem of waveguide discontinuity, the parameters of the equivalent network are often expressed as an integral expression of an unknown tangential electric field or current at the discontinuity, and the actual electric field or current makes the integral expression take an extreme value and satisfies the boundary condition at the discontinuity, and the parameters of the equivalent network can be determined by a variational method. Sangster A.J et al, In Progress In electronics Research IEE, 1965, volume method for the analysis of road side packaging, vol.112. The waveguide coupling is analyzed by adopting a variational method, and the first approximation value of the normalized susceptance of the symmetric capacitive diaphragm is as follows:
3 mode matching method
The mode matching method considers the higher mode at the discontinuous part, the diaphragm part with the thickness is treated as a small waveguide, and the waveguide containing the symmetrical capacitive diaphragm can be regarded as the cascade of two waveguide double-sided steps and a small waveguide with the length of t, wherein t is the thickness of the diaphragm. During analysis, the field in the region to be studied is regarded as the superposition of infinite modes, and the scattering matrix on the interface can be obtained by using the continuous boundary condition of the electric field and the magnetic field on the interface of the two regions and applying the orthogonality of mode functions. Mode matching is mainly the analysis of microwave devices with regular geometry. R.Safavi-Naini and R.H.Macphi. et al, published in IEEE Transactions on M TT, 1982, Vol.82, No. 11, "Scattering iterative-to-iterative waveguide junctions" applied mode matching for waveguide discontinuity analysis.
The existing method has the following defects:
1) the conformal transformation in the quasi-static field method adopts function transformation to solve the equivalent susceptance B, and does not take the factors such as the thickness of the diaphragm, the processing inclination angle and the like into consideration, and if the factors such as the thickness and the inclination angle are added, the rectangular wave containing the symmetrical capacitance diaphragm is difficult to be directly transformed into the pure parallel plate waveguide through the transformation function.
2) The variation method does not take into account factors such as the thickness of the diaphragm and the machining inclination angle.
3) The mode matching mainly analyzes the microwave device with a regular geometric structure, and the microwave device is not accurately analyzed for the irregular deformation conditions such as inclination angle.
Disclosure of Invention
The invention aims to avoid the defects of the prior method and provide a parameter determination method of a rectangular waveguide low-pass filter so as to improve the design precision of the rectangular waveguide low-pass filter.
In order to achieve the above object, the method for determining parameters of a rectangular waveguide low-pass filter according to the present invention comprises the steps of: a parameter pre-determining step: selecting the type of the rectangular waveguide according to the frequency requirement of the rectangular waveguide low-pass filter; determining the electrical length theta of the rectangular waveguide between the two capacitive diaphragms according to the relative bandwidth BW of the rectangular waveguide low-pass filter0(ii) a Obtaining a low-pass prototype circuit only containing a capacitance element according to the electrical performance index and circuit transformation of the rectangular waveguide low-pass filter, further obtaining a generalized impedance transformation coefficient K, determining the capacitive reactance X of a parallel capacitor, and preliminarily determining the window width d, the film thickness m and the machining inclination angle alpha of a capacitance film in the rectangular waveguide by searching an equivalent susceptance graph loaded by the rectangular waveguide capacitor;
membrane parameter optimization: determining an S matrix of the rectangular waveguide single-section capacitor diaphragm according to the generalized impedance transformation coefficient K; performing SchwarzCristorfer inverse transformation on a diaphragm section polygon formed by preliminarily determining the window width d, the diaphragm thickness m, the processing inclination angle alpha and the waveguide height B of the capacitance diaphragm in the rectangular waveguide, and solving the normalized equivalent susceptance B of the capacitance diaphragm; determining an S' matrix of the capacitance diaphragm according to the equivalent susceptance B: <math> <mrow> <msubsup> <mi>S</mi> <mn>11</mn> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mn>12</mn> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> </mfrac> <mo>;</mo> </mrow></math>
optimizing by utilizing a genetic algorithm to enable the matrix S 'to be approximately equal to the matrix S, and finally determining the window width d', the film thickness m 'and the processing inclination angle alpha' of the single-section capacitance film;
repeating the diaphragm parameter optimization step, and determining the parameters of the rest capacitance diaphragms of the rectangular waveguide low-pass filter;
and correcting the cavity length of the waveguide: and obtaining the corrected waveguide length between the two diaphragms as follows through the S' matrix of the capacitive diaphragms:
λgis the wave guide wavelength, theta0To initially determine the electrical length of the rectangular waveguide between the two capacitive diaphragms,
x is normalized parallel reactance of capacitance diaphragm equivalent circuit, namely <math> <mrow> <mi>j</mi> <mover> <mi>X</mi> <mo>‾</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>S</mi> <mn>12</mn> </msub> <mo>′</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>S</mi> <mn>11</mn> <mo>′</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>S</mi> <mn>12</mn> <mrow> <mo>′</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow></math>
And repeating the step of correcting the cavity length of the waveguide, and determining the waveguide length between the other two capacitive diaphragms of the rectangular waveguide low-pass filter to complete the design of the whole rectangular waveguide low-pass filter.
Compared with the prior art, the invention has the following advantages:
1) the invention considers the dimensional tolerance and the processing inclination angle in the processing process of the diaphragm, and the actual contour line of the diaphragm is approximated to be a polygon by utilizing the polygon approximation, thereby not only retaining important information, but also improving the analysis speed.
2) When the polygon conformal transformation is solved, an improved genetic algorithm is adopted, so that the result is optimal, and the calculation speed is increased.
3) The invention considers the thickness and inclination angle factors of the rectangular waveguide capacitive diaphragm caused by processing, carries out Schwarz-CriserStoffer inverse transformation on the rectangular waveguide capacitive diaphragm to solve equivalent susceptance and an S 'matrix, and utilizes genetic algorithm optimization to ensure that the S' matrix is approximately equal to the S matrix obtained through a generalized impedance transformation coefficient K, thereby accurately determining the structural parameters of the rectangular waveguide capacitive diaphragm.
4) The method can accurately analyze the influence of the tolerance of the diaphragm on the electrical property in the processing process.
Simulation tests prove that the method can improve the precision of the parameter design of the capacitive diaphragm of the rectangular waveguide low-pass filter and improve the performance of the whole filter.
Drawings
FIG. 1 is a schematic structural diagram of a conventional rectangular waveguide low-pass filter;
FIG. 2 is a schematic diagram of a conventional waveguide capacitive diaphragm structure and an equivalent circuit;
FIG. 3 is an equivalent circuit diagram of a conventional rectangular waveguide low-pass filter;
FIG. 4 is a schematic diagram of the present invention implementing the inverse Schwarz-CriserStoffer transform process;
FIG. 5 is a flow chart of the design steps of the present invention;
FIG. 6 is a flow chart of the steps for the optimal solution of the inverse Schwarz-CriserStoffer transform of the present invention;
FIG. 7 is a comparison graph of the calculation results of the single-section capacitive diaphragm and the simulation results of the single-section capacitive diaphragm according to the present invention;
FIG. 8 is a diagram of the HFSS simulation characteristics of a 2GHz rectangular waveguide low-pass filter designed by the method of the invention.
The specific implementation mode is as follows:
referring to fig. 5, the method comprises the following specific steps:
The main electrical performance indexes of the rectangular waveguide low-pass filter include: the cut-off frequency omega, the maximum attenuation in the pass band, the minimum attenuation in the stop band and the relative bandwidth BW are input into a computer program of a computer.
And 2, pre-determining structural parameters of the rectangular waveguide low-pass filter.
2.1, selecting the type of the rectangular waveguide according to the frequency requirement of the rectangular waveguide low-pass filter;
and 2.2, designing a low-pass prototype circuit by a calculation program according to the electrical performance index of the rectangular waveguide low-pass filter to obtain the parameters of the prototype circuit: g0……gn+1N is the circuit order;
step 2.3, the low-pass prototype circuit is converted into a low-pass prototype circuit only containing a capacitance element, and the low-pass prototype circuit is processed by a formula <math> <mrow> <msub> <mi>K</mi> <mn>01</mn> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> <msqrt> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <msub> <mi>g</mi> <mn>0</mn> </msub> <msub> <mi>g</mi> <mn>1</mn> </msub> </mrow> </mfrac> </msqrt> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>Z</mi> <mn>0</mn> </msub> <mi>ω</mi> </mfrac> <msqrt> <mfrac> <mn>1</mn> <mrow> <msub> <mi>g</mi> <mi>i</mi> </msub> <msub> <mi>g</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </msqrt> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>K</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> <msqrt> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <msub> <mi>g</mi> <mi>n</mi> </msub> <msub> <mi>g</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </msqrt> <mo>,</mo> </mrow></math>
Calculating to obtain generalized impedance transformation coefficient K, Z0Is the waveguide characteristic impedance; according to the relative bandwidth BW of the rectangular waveguide low-pass filter, the filter is obtained by the formula <math> <mrow> <mi>BW</mi> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>θ</mi> <mn>0</mn> </msub> </mrow> <mi>π</mi> </mfrac> <mo>,</mo> </mrow></math>
Calculating to obtain the electrical length theta of the rectangular waveguide between the two capacitive diaphragms0As shown in fig. 3;
step 2.4, according to the generalized impedance transformation coefficient K, passing through the formula <math> <mrow> <mover> <mi>X</mi> <mo>‾</mo> </mover> <mo>=</mo> <mfrac> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
And K is normalization K, determining the capacitive reactance X of the normalized parallel capacitor, and preliminarily determining the window width d, the film thickness m and the processing inclination angle alpha of the capacitor film in the rectangular waveguide by searching the equivalent susceptance graph loaded by the rectangular waveguide capacitor.
And 3, determining an A matrix and an S matrix of the single-section capacitor diaphragm according to the generalized impedance transformation coefficient K.
According to the characteristics of the two-port microwave network, determining that an A matrix and an S matrix of a single-section capacitor diaphragm are respectively as follows:
in the formula <math> <mrow> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mo>=</mo> <mfrac> <mi>K</mi> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>S</mi> <mn>11</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>S</mi> <mn>12</mn> </msub> <mo>=</mo> <mi>j</mi> <mfrac> <mrow> <mo>-</mo> <mn>2</mn> <mover> <mi>K</mi> <mo>‾</mo> </mover> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
j is the imaginary part.
And 4, performing Schwarz-CriserStoffer inverse transformation on the polygonal cross section of the capacitor diaphragm.
Referring to fig. 4, performing a schwarzkristoff inverse transformation on a diaphragm section polygon formed by preliminarily determining a window width d, a diaphragm thickness m, a machining inclination angle alpha and a waveguide height b of a rectangular waveguide capacitive diaphragm according to the following steps:
step 4.1, transforming the polygon in the complex plane z to the upper half plane of the complex plane by using the inverse Schwarz-Crisleffer transform, and transforming the polygon boundary to the real axis, i.e. the polygon plane ABCDz in FIG. 4(a)0Z2Z3Z4Transformation to the upper complex half plane A 'B' C 'D' T in FIG. 4(B)0T2T3T4。
From the symmetry of the polygon and the nature of the conformal transformation, the coordinates of the T-point in the T-plane are symmetric about the y-axis. When the side length ratio of adjacent edges on the T plane is too large or too small, which may cause strong peak phenomenon of the integrand to make the integrand part not integrable, inserting some dummy vertices correctly can solve the problem well, and at the same time, can improve the precision, accelerate the speed of numerical integration and iterative convergence, for example, adding dummy vertex Z in fig. 4(a)1，Z5. Selecting T according to polygonal conformal transformation rule0＝0，T1＝1，Tn-1Given as ∞, the transformation equation is obtained as:
step 4.2, establishing T in a calculation transformation formula ZjThe optimization model of the values is:
find T2，T3，T4，...，Tn-2
wherein:
In the formula ZiThe coordinates of each vertex of the polygonal cross section of the capacitor diaphragm in the z plane,
Tithe coordinates of each vertex of the polygonal cross section of the capacitor diaphragm in the plane t,
|Zj+1-Zji is from Z in the Z planejTo Zj+1Length of side, ZLjIt is shown that,
|Tj+i-Tji is the corresponding side length in the T plane, in TLjIt is shown that,
Yjis the relative side length of the jth edge represented by the vertex,
Yjis the relative side length of the jth side expressed as the side length;
and 4.3, optimizing an objective function AIM in the model to make the objective function AIM smaller than a given precision requirement so as to obtain all TjThe optimization process is shown in fig. 6:
first, an unknown parameter set T is determinedi，(i＝2，3，......n-2)，C1，C2The fitness function AIM and constraint conditions are adopted, so that the optimization search always runs in a feasible solution space;
secondly, generating an initial population in a feasible solution area according to a random selection rule of a genetic algorithm, judging whether a fitness function meets a termination condition, if so, stopping, if not, selecting, crossing and mutating according to the genetic rule until the condition is met, and obtaining an optimal solution as an initial point;
finally, the optimal solution of the model, namely T, is obtained by optimizing again by using a sequential quadratic programming method2，T3，T4，...，Tn-2。
And 5, solving the equivalent susceptance value and the S' matrix.
In step 5.1, the upper half complex plane of the T plane is transformed into a plate capacitor of the ω plane by using the formula ω ═ μ + jv ═ arcsin (μ '+ jv'), i.e., the upper half complex plane a 'B' C 'D' T in fig. 4(B)0T1T2T3T4T5Switching to the plate capacitor A "B" C "D" E "F" G "H" I "in FIG. 4 (C);
step 5.2, substituting the TA coordinates into the formula to obtain omegaA＝uA+jvA；
Step 5.3, calculating the total capacitance C of the capacitor according to the width and the length of the capacitor,
as seen from FIG. 4(c), capacitance per unit width of the parallel plate between AD and AF <math> <mrow> <msub> <mi>C</mi> <mi>AD</mi> </msub> <mo>=</mo> <mi>ϵ</mi> <mfrac> <msub> <mi>v</mi> <mi>A</mi> </msub> <mi>π</mi> </mfrac> <mo>,</mo> </mrow></math>
Due to CADIncluding AB segment parallel plate capacitor CABIf the coordinate of point a is y-b/2 and z is L/2, the coordinate of point a is defined as
Therefore, the capacitance introduced by the addition of the diaphragm should be CAD-CABThus, introduced by the membraneThe capacitance C should be
Step 5.4, calculating the equivalent susceptance according to the total electric C <math> <mrow> <mi>B</mi> <mo>=</mo> <mi>ωC</mi> <mo>=</mo> <mn>2</mn> <mi>ωϵ</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>v</mi> <mi>A</mi> </msub> <mi>π</mi> </mfrac> <mo>-</mo> <mfrac> <mi>L</mi> <mrow> <mn>2</mn> <mi>b</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>4</mn> <mi>λ</mi> </mfrac> <msub> <mi>Y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mi>A</mi> </msub> <mo>-</mo> <mfrac> <mi>Lπ</mi> <mrow> <mn>2</mn> <mi>b</mi> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow></math>
Then, the equivalent characteristic admittance Y is used0B is normalized
And 5.5, obtaining S' matrix parameters of the single-section capacitance diaphragm according to the normalized equivalent susceptance as follows:
and 6, optimizing and solving the structural parameters of the rectangular waveguide capacitive diaphragm.
And 6.1, establishing an optimization model as follows:
find d，m，α
min ΔSi11，ΔSi12
wherein, <math> <mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mn>11</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mn>12</mn> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mfrac> <mrow> <mo>-</mo> <mn>2</mn> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mn>11</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mn>12</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow></math>
in the formula (d)i，mi，αiRespectively the window width, the film thickness and the processing inclination angle of the ith capacitor film, BiTo normalize the equivalent susceptance, Δ Si11，ΔSi12Respectively, is a reflection coefficient Si11And a transmission coefficient Si12An error;
and 6.2, optimizing by using a genetic algorithm to enable the matrix S 'to be approximately equal to the matrix S, and finally determining the window width d', the film thickness m 'and the processing inclination angle alpha' of the single-section capacitance film.
And 7, repeating the steps of performing Schwarz-CriserStoffe inverse transformation on the polygonal section of the rectangular waveguide diaphragm to solve the equivalent susceptance and the S' matrix and the step of optimizing the structural parameters of the rectangular waveguide capacitive diaphragm, and determining all the capacitive diaphragm parameters of the rectangular waveguide low-pass filter.
And 8, correcting the length of the waveguide cavity.
And 8.1, obtaining the parallel reactance of the equivalent circuit according to the S' parameter of the capacitor diaphragm:
and 8.2, obtaining the phase angle of the K converter according to the parallel reactance: phi is ai＝-arctan(2Xi)；
And 8.3, correcting the electrical length as follows: <math> <mrow> <msub> <mi>θ</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>φ</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>φ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mover> <mi>X</mi> <mo>‾</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mover> <mi>X</mi> <mo>‾</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>;</mo> </mrow></math>
and 8.4, correcting the length of the waveguide cavity as follows: <math> <mrow> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>λ</mi> <mi>g</mi> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>φ</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>φ</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow></math>
and 9, repeating the waveguide cavity length correction step, determining the waveguide cavity length between all the two capacitive diaphragms of the rectangular waveguide low-pass filter, and finishing the design of the whole rectangular waveguide low-pass filter.
The effectiveness of the invention can be illustrated by simulation data:
1. a single-section rectangular waveguide capacitive diaphragm with a main mode frequency range of 1.4-2.8GHz is selected, the thickness is 1mm, the processing inclination angle is 1 degree, simulation tests are carried out, and S matrix parameters of the method, S matrix parameters of the traditional method and S matrix parameters obtained through Ansoft HFSS simulation are respectively obtained, and the S matrix parameters are shown in figure 7.
2. According to the electrical performance indexes: the cut-off frequency is 2.0 GHz; the maximum attenuation in the pass band is 0.2dB, the attenuation at the stop band of 3.5GHz is more than 60dB, a 2.0GHz waveguide low-pass filter is designed, and simulation verification is carried out by using HFSS, so that the amplitude-frequency characteristic curve shown in FIG. 8 can be obtained.
In FIG. 7, the S matrix parameters of the conventional method are compared with the S matrix parameters obtained by the Ansoft HFSS simulation, S11，S12The average errors are-18.29% and 3.04%, respectively; comparing the S matrix parameters of the invention with the S matrix parameters obtained by AnsoftHFSS simulation, S11，S12The average errors were 2.12% and-0.1%, respectively. Therefore, the coincidence of the transmission coefficient and the reflection coefficient obtained by the method is more accurate compared with the traditional method, and the design precision is improved.
As can be seen from FIG. 8, the cut-off frequency of the filter designed by the method of the present invention is 2.0GHz, and the reflection coefficient S in the pass band11The attenuation in the stop band is less than-20 dB and more than 60dB, and the design performance requirement is met. Repeated debugging is not needed, and the design efficiency is improved.
Claims (4)
1. A parameter determination method for a rectangular waveguide low-pass filter comprises the following steps:
A. a parameter pre-determining step:
selecting the type of the rectangular waveguide according to the frequency requirement of the rectangular waveguide low-pass filter; determining the electrical length theta of the rectangular waveguide between the two capacitive diaphragms according to the relative bandwidth BW of the rectangular waveguide low-pass filter0(ii) a Obtaining a low-pass prototype circuit only containing a capacitance element according to the electrical performance index of the rectangular waveguide low-pass filter and circuit transformation, further obtaining a generalized impedance transformation coefficient K, and determining the capacitive reactance of the parallel capacitorX, preliminarily determining the window width d, the diaphragm thickness m and the processing inclination angle alpha of the capacitive diaphragm in the rectangular waveguide by searching an equivalent susceptance graph loaded by the rectangular waveguide capacitor:
B. membrane parameter optimization:
determining an S matrix of the rectangular waveguide single-section capacitor diaphragm according to the generalized impedance transformation coefficient K;
performing SchwarzCristorfer inverse transformation on a diaphragm section polygon formed by preliminarily determining the window width d, the diaphragm thickness m, the processing inclination angle alpha and the waveguide height B of the capacitance diaphragm in the rectangular waveguide, and solving the normalized equivalent susceptance B of the capacitance diaphragm;
determining an S' matrix of the capacitance diaphragm according to the equivalent susceptance B: <math> <mrow> <msubsup> <mi>S</mi> <mn>11</mn> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mn>12</mn> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <mover> <mi>B</mi> <mo>‾</mo> </mover> </mrow> </mfrac> <mo>;</mo> </mrow></math>
optimizing by utilizing a genetic algorithm to enable the matrix S 'to be approximately equal to the matrix S, and finally determining the window width d', the film thickness m 'and the processing inclination angle alpha' of the single-section capacitance film;
repeating the diaphragm parameter optimization step, and determining the parameters of the rest capacitance diaphragms of the rectangular waveguide low-pass filter;
C. and (3) waveguide cavity length correction:
and obtaining the corrected waveguide length between the two diaphragms as follows through the S' matrix of the capacitive diaphragms:
λgis the wave guide wavelength, theta0To initially determine the electrical length of the rectangular waveguide between the two capacitive diaphragms,
x is the parallel reactance of the equivalent circuit of the capacitance diaphragm, i.e. <math> <mrow> <mi>j</mi> <mover> <mi>X</mi> <mo>‾</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mn>2</mn> <mi>S</mi> </mrow> <mn>12</mn> </msub> <mo>′</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>S</mi> <mn>11</mn> <mo>′</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>S</mi> <mn>12</mn> <mo>′</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow></math>
And repeating the waveguide cavity length correction step, and determining the waveguide length between the other two capacitance diaphragms of the rectangular waveguide low-pass filter to complete the design of the whole rectangular waveguide low-pass filter.
2. The method for determining parameters of a rectangular waveguide low-pass filter according to claim 1, wherein said step of optimizing the diaphragm parameters comprises performing an inverse schwarzkristhroff transform on a diaphragm cross-section polygon formed by preliminarily determining the window width d, the diaphragm thickness m, the machining tilt angle α and the waveguide height b of the capacitive diaphragm in the rectangular waveguide, and solving the equivalent susceptance of the capacitive diaphragm, and comprises the following steps:
firstly, a hybrid optimization algorithm combining a genetic algorithm and a sequence quadratic programming method is used for inverse transformation of Schwarz-CriserStoffer <math> <mrow> <mi>Z</mi> <mo>=</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <msubsup> <mo>∫</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mi>T</mi> </msubsup> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mi>T</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <msub> <mi>v</mi> <mi>i</mi> </msub> </mrow> </msup> <mi>dt</mi> <mo>+</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> </mrow></math>
And carrying out optimization solution to obtain transformed vertex coordinates: t is1，T2，T3，T4，...，Tn-2；
Secondly, substituting the coordinates of each vertex into a Schwarz-CriserStoffer inverse transformation formula Z, and transforming the polygonal plane to an upper half complex plane in a complex plane;
and thirdly, converting the upper half complex plane into a plate capacitor, and calculating the diaphragm capacitance and the equivalent susceptance value according to the length and the width of the plate capacitor.
3. The parameter determination method for the rectangular waveguide low-pass filter according to claim 2, wherein the inverse schwarz-cristoffer transform of the first step <math> <mrow> <mi>Z</mi> <mo>=</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <msubsup> <mo>∫</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mi>T</mi> </msubsup> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mi>T</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <msub> <mi>v</mi> <mi>i</mi> </msub> </mrow> </msup> <mi>dt</mi> <mo>+</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> </mrow></math>
Carrying out optimization solution according to the following steps:
step 1, establishing an optimization model as follows:
find T2，T3，T4，...，Tn-2
wherein:
In the formula ZiThe coordinates of each vertex of the polygonal cross section of the capacitor diaphragm in the z plane,
Tithe coordinates of each vertex of the polygonal cross section of the capacitor diaphragm in the plane t,
|Zj+1-Zji is from Z in the Z planejTo Zj+1Length of side, ZLjIt is shown that,
|Tj+1-Tji is the corresponding side length in the T plane, in TLjIt is shown that,
Yjis the relative side length of the jth edge represented by the vertex,
Yjis the relative side length of the jth side expressed as the side length;
and 2, adopting an improved hybrid genetic algorithm to carry out optimization solution on the model:
firstly, carrying out constraint condition processing on a genetic algorithm, namely adopting a method of reducing a search space to ensure that optimization search always runs in a feasible solution space and an initial point is obtained by optimization solution;
secondly, optimizing again by using a sequence quadratic programming method to obtain the optimal solution of the model, namely: t is2，T3，...，Tn-2°
4. The parameter determination method for the rectangular waveguide low-pass filter according to claim 1, wherein said optimization using genetic algorithm in the patch parameter optimization step makes the S' matrix approximately equal to the S matrix, and the optimization solution is performed by an optimization model such that:
find di，mi，αi
min ΔSi11，ΔSi12
wherein, <math> <mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mn>11</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mn>12</mn> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mfrac> <mrow> <mo>-</mo> <mn>2</mn> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <msub> <mover> <mi>K</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mn>11</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow></math>
<math> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mn>12</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <mn>2</mn> <mo>+</mo> <mi>j</mi> <msub> <mover> <mi>B</mi> <mo>‾</mo> </mover> <mi>j</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow></math>
in the formula (d)i，mi，αiRespectively the window width, the film thickness and the processing inclination angle of the ith capacitor film, BjTo normalize the equivalent susceptance, Δ Si11，ΔSi，2Respectively, is a reflection coefficient Si11And a transmission coefficient Si12The error of (2).
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| CN103077271A (en) * | 2012-09-12 | 2013-05-01 | 电子科技大学 | 8 mm substrate integrated waveguide circulator parameter determination method |
| CN109713412A (en) * | 2018-12-20 | 2019-05-03 | 常州机电职业技术学院 | Tunable E-plane cutting H-plane waveguide bandpass filter and design method thereof |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101944145A (en) * | 2010-08-31 | 2011-01-12 | 电子科技大学 | Finite element simulation method capable of removing microwave tube high-frequency circuit in pseudo-DC mode |
| CN101944145B (en) * | 2010-08-31 | 2012-08-08 | 电子科技大学 | Finite element simulation method capable of removing microwave tube high-frequency circuit in pseudo-DC mode |
| CN103077271A (en) * | 2012-09-12 | 2013-05-01 | 电子科技大学 | 8 mm substrate integrated waveguide circulator parameter determination method |
| CN103077271B (en) * | 2012-09-12 | 2016-08-03 | 电子科技大学 | 8 millimeters of substrate integrated wave guide ring device parameter determination method |
| CN109713412A (en) * | 2018-12-20 | 2019-05-03 | 常州机电职业技术学院 | Tunable E-plane cutting H-plane waveguide bandpass filter and design method thereof |
| CN109713412B (en) * | 2018-12-20 | 2024-03-29 | 常州机电职业技术学院 | Tunable E-plane cutting H-plane waveguide band-pass filter and design method thereof |
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