CN109713412B - Tunable E-plane cutting H-plane waveguide band-pass filter and design method thereof - Google Patents
Tunable E-plane cutting H-plane waveguide band-pass filter and design method thereof Download PDFInfo
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Abstract
The invention provides a tunable E-plane cutting H-plane waveguide band-pass filter and a design method thereof, and belongs to the technical field of filter design. The process of the method comprises the following steps: starting from the lumped parameter low-pass prototype, establishing a model with a chamfer; a new design formula of the band-pass filter with the chamfer lumped parameter coupling resonator is derived through frequency conversion; these coupling structures and resonators are then implemented with microwave structures, resulting in a microwave bandpass filter. The method ensures that the filter has low loss and no shift in frequency band. Compared with the traditional method, the method overcomes the defects of larger error and higher loss. The method is widely applied to the fields of short-range air defense, battlefield monitoring, missile guidance, airborne collision avoidance, high-resolution imaging, space target detection, battlefield friend-foe identification, millimeter wave communication and the like.
Description
Technical Field
The invention relates to a tunable E-plane cutting H-plane waveguide band-pass filter and a design method thereof, belonging to the technical field of filter design.
Background
Various objects in nature radiate electromagnetic waves, and theoretical analysis and experimental measurement of millimeter wave bands show that the millimeter wave radiating capability of different objects is greatly different. Therefore, if millimeter wave radiation information of an object can be obtained, the shape, volume, distance, even material and other characteristics of the object can be deduced to a certain extent, which has important significance for target detection and identification, combat cooperation, automatic navigation, anti-stealth technology and the like. Passive millimeter wave imaging techniques are one means of obtaining millimeter wave radiation images of a target or scene. Millimeter wave energy radiated by a scene or a target to be imaged is received by an antenna, and amplified and detected by a millimeter wave radiometer to obtain video information, wherein the video information reflects the difference of the millimeter wave energy radiated by various objects, so that the target can be distinguished.
The synthetic aperture radiometer has a higher spatial resolution than conventional radiometers while at the same time greatly increasing the number of channels of the receiver, and the performance of the synthetic aperture radiometer is also dependent on the consistency between the multiple receive channels. Therefore, improving the uniformity of parameters of each receiving channel becomes a necessary way to improve the performance of the radiometer.
Some passive elements in the design and development processes of the microwave millimeter wave front end system still cannot be realized on a single MMIC (Monolithic Microwave Integrated Circuit), and mainly comprise waveguide filters and the like. Waveguide filter performance is one of the main factors that determine radiometer performance.
The waveguide filter has the advantages of small conductor loss and dielectric loss; the power capacity is large; no radiation loss; simple structure and easy manufacture. In millimeter wave and sub-millimeter wave bands, the loss is increased and the manufacture is difficult because of the too small size of the metal waveguide tube, and the research on the accurate design and realization of the waveguide device in the millimeter wave band has important significance.
The waveguide filter is typically located between the receiver waveguide antenna and the millimeter wave front-end circuit and acts as an image filter to avoid the creation of images. Multiple solutions to the receiver consistency requirement of channel rf/microwave/millimeter wave radiometer systems necessarily place higher demands on the waveguide filter. In the processing process of the waveguide filter, chamfer angles exist at the mounting positions of the upper end and the lower end of the waveguide filter, and the existence of the chamfer angles can influence the consistency and the precision frequency response performance of the waveguide band-pass filter.
Disclosure of Invention
The invention provides a tunable E-plane cutting H-plane waveguide band-pass filter and a design method thereof, and particularly provides the tunable E-plane cutting H-plane waveguide band-pass filter for solving the defects of consistency and precision frequency response performance of the filter caused by chamfering in the processing and manufacturing of the existing waveguide band-pass filter:
a design method of a tunable E-plane cut H-plane waveguide band-pass filter, the steps of the design method comprising:
step one, using a waveguide section with half waveguide wavelength as a series resonator of an H filter, and using a parallel inductor formed by an inductance diaphragm as a coupling structure between resonators;
step two, obtaining an approximate conversion formula of the low-pass prototype-band-pass filter through an approximate conversion formula calculation model, wherein the approximate conversion formula of the prototype-band-pass filter is as follows:
series inductance L k Conversion to series LC circuits
Parallel capacitor C k Conversion to parallel LC circuits
L′ k And C k ' represents the converted inductance and capacitance values, respectively.
The conversion formula calculation model is as follows:
wherein ω', ω 1 ' represents the frequency variation and sideband frequencies of the lowpass prototype filter, lambda, respectively g0 ,λ g1 ,λ g2 ,λ g Are respectively with frequency omega 0 ,ω 1 ,ω 2 And ω corresponds to the waveguide wavelength, w λ Is the relative bandwidth;
step three, reactance of the resonance unit:
is carried into formulas (5) - (7),
obtaining waveguide filter impedance transformation formulas (8) - (10):
wherein K is 01 Representing a first order impedance transformer; r is R A Representing the impedance of the left side end of the equivalent circuit of the waveguide filter; x is X 1 A reactance slope parameter representing a first order half-wavelength series resonator; z is Z 0 Representing the input impedance; g 0 、g 1 Representing the source conductance and the first-order series inductor inductance or the capacitance of the first-order parallel capacitor, respectively; g j 、g j+1 Representing the capacitances of the series inductor inductances of the j-order and the j+1-order or the first-order parallel capacitors, respectively; g n 、g n+1 Representing the series inductor inductance or the capacitance of the parallel capacitor of the nth order and the load, respectively; x is X n Representing the reactance of the nth order diaphragm; r is R S Representing the load impedance; k (K) j，j+1 An impedance transformer represented as between j and j+1 steps; k (K) j，j+1 | j＝1→n-1 Representing j from 1 to n-1 impedance transformers; k (K) n，n+1 An impedance transformer representing the last order; k is an impedance converter, g is a chebyshev low-pass prototype filter parameter;
step four, the waveguide filter structure equivalent inductance is separated by an electrical length θ, wherein the impedance transformation comprising the parallel jX and the transmission line with a point length Φ is given by Ralph Levy:
step five, equivalent inductance membrane is T-shaped network structure, the transmission matrix of the T-shaped network structure is:
the equality relationship between the formula (11) and the formula (12) is obtained:
step six, according to formulas (14) and (15), and combining the conditions of the joint length phi:
obtaining an impedance transformer K, a point length phi and an impedance transformer model with chamfers:
wherein X is S Representing reactance parameters due to chamfering; x is X sj The reactance parameter generated by the j-order chamfer is the chamfer reactance; x is X j，j+1 The reactance parameter is expressed as reactance parameter generated by chamfering between the j and j+1 order resonators; …;
step seven, combining additional inductances introduced by chamfering to two sides of the parallel inductance, wherein the equivalent electrical length of each of the two sides is phi/2, and the electrical length of the actual resonant cavity is as follows:
wherein lambda is 0 Is the working frequency of the waveguide band-pass filter, L j Is the length of the BPF resonant cavity, X j-1 ， j The reactance parameter is expressed as reactance parameter generated by chamfering between the j-1 and j-order resonators;
step eight, according to a relation model of the length of the resonant cavity and the working frequency, obtaining the relation between the length of the resonant cavity and the working frequency, wherein the relation between the length of the resonant cavity and the working frequency is as follows:
L j ＝θ j λ 0 /2π (22)
thus, the parameter design of the filter is completed.
The tunable E-plane cutting H-plane waveguide band-pass filter formed by the design method comprises an H-plane waveguide band-pass filter and an upper cover: the H-plane waveguide band-pass filter adopts a rectangular structure; two groups of inductive diaphragms are arranged in the H-plane waveguide band-pass filter, and each group of inductive diaphragms comprises two rows of inductive diaphragms; the two groups of inductive diaphragms are distributed inside the H-plane waveguide band-pass filter in a mirror symmetry mode by taking the central axis on the long side of the H-plane waveguide band-pass filter as a symmetry axis; two rows of inductive diaphragms in each group of inductive diaphragms are arranged on long side walls of two sides of the H-plane waveguide band-pass filter in a mirror symmetry mode by taking a central axis of the wide side of the H-plane waveguide band-pass filter as a symmetry axis, and are perpendicular to the long side walls; the width of each row of inductance membranes is different, and the distance between two adjacent inductance membranes is different.
Further, in the two rows of inductance diaphragms which are symmetrically distributed, an air gap is reserved between every two corresponding inductance diaphragms; the width of each air gap is different.
Further, the two groups of inductive diaphragms comprise 6 inductive diaphragms, and the 6 inductive diaphragms are equally divided into two rows; in each row of inductance diaphragms, the directions from two ends of the filter to the center line of the long side of the filter are as follows: the first inductive diaphragm, the second inductive diaphragm and the third inductive diaphragm.
Further, the width of the first inductive diaphragm is smaller than the width of the second inductive diaphragm; the width of the second inductance membrane is smaller than that of the third inductance membrane; the distance between the first inductive diaphragm and the second inductive diaphragm is L 1 The method comprises the steps of carrying out a first treatment on the surface of the The distance between the second inductive diaphragm and the third inductive diaphragm is L 2 ；
The distance between the third inductive diaphragms in the two groups of inductive diaphragms is L 3 And the dimensional relationship between the distances is: l (L) 1 ＜L 2 ＜L 3 。
Further, in the two corresponding rows of inductive diaphragms, the width of the air gap between the two first inductive diaphragms is t 1 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two second inductance diaphragms is t 2 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two third inductance diaphragms is t 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the relation between each air gap width is: t is t 1 ＞t 2 ＞t 3 。
Further, the bottom end of the inductance diaphragm is fixedly arranged on the bottom surface of the H-plane waveguide band-pass filter; and a chamfer exists at the edges of the top end and the bottom end of the inductance membrane.
The invention has the beneficial effects that:
the tunable E-plane cutting H-plane waveguide band-pass filter and the design method thereof solve the problems of machining errors and frequency offset caused by chamfering caused by right angles between the inductive diaphragm and the waveguide cavity, and ensure that the waveguide band-pass filter has higher consistency and precision frequency response performance under the condition that chamfering exists in filter machining.
The invention provides a tunable E-plane cutting H-plane waveguide band-pass filter and a design method thereof, and provides a model of the waveguide band-pass filter with chamfer angles.
The tunable E-plane cutting H-plane waveguide band-pass filter and the design method thereof provide a new formula of the waveguide band-pass filter with chamfer angles.
The tunable E-plane cutting H-plane waveguide band-pass filter and the design method thereof provide a whole set of related design flow, so that the precise design of the waveguide filter is easy to realize, and the whole design flow becomes simple and smooth.
The tunable E-plane cutting H-plane waveguide band-pass filter and the design method thereof reduce the design difficulty of waveguide filters in millimeter wave and sub-millimeter wave bands to a certain extent, mainly avoid the problems of increased loss and difficult manufacture caused by the too small size of a metal waveguide tube, and have important significance for researching the accurate design and realization of waveguide devices in millimeter wave bands.
Drawings
FIG. 1 is a schematic diagram of a tunable E-plane cut H-plane waveguide band-pass filter;
FIG. 2 is a schematic diagram of an inductor membrane;
FIG. 3 is an equivalent circuit diagram of an inductive diaphragm;
FIG. 4 is a circuit diagram of a parallel inductance unit of a conduction band pass filter;
FIG. 5 is a cross-sectional view of a waveguide bandpass filter;
FIG. 6 is an equivalent circuit diagram of an inductive diaphragm with a chamfer;
FIG. 7 is a graph of actual electrical length of a filter versus chamfer reactance;
fig. 8 is a frequency shift versus center frequency diagram, wherein (a) represents a waveform diagram at a center frequency of 18GHz, (b) represents a waveform diagram at a center frequency of 26GHz, (c) represents a waveform diagram at a center frequency of 34GHz, and (d) represents a waveform diagram at a center frequency of 42 GHz;
fig. 9 is a frequency shift plot of different center frequencies at the same 3dB bandwidth, wherein (a) is a plot of BW 2.265%, (b) is a plot of BW 2.5%, (c) is a plot of BW 10%, (d) is a plot of BW 15%, (e) is a plot of BW 20%;
fig. 10 is a BPF installation and tuning diagram;
FIG. 11 is a graph of simulation and test results for a waveguide bandpass filter, wherein (a) is the center frequency 26GHzBPF frequency response; (b) center frequency 34ghz bpf frequency response.
Fig. 12 is a diagram of the filter.
Detailed Description
The invention will be further illustrated with reference to specific examples, but the invention is not limited to the examples.
Example 1:
a design method of a tunable E-plane cutting H-plane waveguide band-pass filter comprises the following steps:
according to the theory of a microwave filter network, all types of filters, such as a maximum flattening filter, a chebyshev filter, an elliptic function filter and the like, can be mapped into a normalized low-pass prototype filter. Chebyshev-type filters have the advantage of having in-band equi-ripple compared to the largest flat type filters. Although elliptic function type filters perform better, they are generally more difficult to implement, so chebyshev type bandpass filters are discussed herein.
The H filter uses a waveguide segment with half-wave guide wavelength as a series resonator and uses a parallel inductor formed by an inductive diaphragm as a coupling structure between resonators, as shown in fig. 1.
The approximate conversion formulas from the low-pass prototype-band-pass filters can be obtained from formulas (1) to (3), and such filters propagate only quasi-TE 10 mode waves.
ω′,ω 1 ' sideband frequencies of frequency variant and lowpass prototype filter, lambda respectively g0 ,λ g1 ,λ g2 ,λ g Are respectively with frequency omega 0 ,ω 1 ,ω 2 And ω corresponds to the waveguide wavelength, w λ Is the relative bandwidth. X is X j Reactance of the resonant cell. Z is Z 0 Is a 50 ohm characteristic impedance.
X is to be j Carrying in (5) to (7)
From this, waveguide filter impedance transformation formulas (8) to (10) can be obtained
K is called an impedance transformer and g is the chebyshev low-pass prototype filter parameter. The waveguide bandpass filter structure schematic diagram is shown in fig. 4 and 5, and the equivalent inductances are separated by a point length θ. Including parallel jX and a transmission line with a point length phi, the impedance transformation is given by Ralph Levy.
But the above design does not take into account the frequency offset problem caused by chamfering.
The process of designing the filter with chamfer is as follows:
the installation process of the waveguide band-pass filter adopts the mode that the left and right half internal structures are completely the same, and in order to analyze the property of the inserted inductance diaphragm, an equivalent equal T-shaped network is shown in figure 3.
The transmission matrix is
From the equality of formulas (11) and (12), it is possible to obtain (13) to (15)
Because phi is small
In the practical integrated inductive diaphragm processing, chamfering is unavoidable, and the cross-section of the chamfering is shown in fig. 1. b, t, L n And R is waveguide width, diaphragm thickness, nth th The step resonator length and chamfer radius. The equivalent circuit diagram is shown in fig. 3 and 6. Fig. 3 is an equivalent view of a chamfering-free diaphragm, and fig. 6 is an equivalent view of a chamfering-free diaphragm. X is X sj The reactance parameter generated by chamfering is now called chamfering reactance. Therefore, the formulas (18) to (20) can be obtained from the formulas (14) and (15).
From fig. 6, the additional inductances introduced by the chamfer are incorporated on both sides of the parallel inductance, each of which introduces an equivalent electrical length of phi/2. The electrical length of the actual resonant cavity can therefore be written as
Wherein lambda is 0 Is the working frequency of the waveguide band-pass filter, L j Is the BPF cavity length. From equation (22), the resonant cavity length is inversely proportional to the operating frequency.
L j ＝θ j λ 0 /2π (22)
The chamfering results in a shift in the center frequency of the waveguide bandpass filter as indicated by equations (18) - (22). The relationship between the actual electrical length of the cavity of the 26GHz waveguide bandpass filter with chamfer and chamfer reactance is obtained from equation (21), as shown in fig. 7. When (when)Chamfer reactance X s When the actual electric length of the resonant cavity is reduced, the center frequency of the waveguide band-pass filter is shifted towards the high frequency direction. When chamfer reactance X s When the resonant cavity is increased, the actual electrical length of the resonant cavity is increased, and the center frequency of the waveguide band-pass filter is shifted towards the low frequency direction. The values of the equivalent circuit are shown in table 1.
Table 1 values of elements in the equivalent circuit diagram of fig. 6
The chamfering effect of the 5-order waveguide bandpass filter with different center frequencies and 3dB bandwidths is shown in fig. 8 and 9. Fig. 10 (a) - (d) show that at fillet radii of 0.1 mm-0.7 mm, there are center frequencies of 18GHz, 26GHz, 34GHz and 42GHz, the frequency offset of which increases with increasing bandwidth. Fig. 9 (a) - (e) show that with different center frequencies 18GHz, 26GHz, 34GHz and 42GHz, the frequency shift increases with increasing center frequency and corner radius, respectively, for the same 3dB bandwidth. These conclusions are consistent with formulas (17) to (21).
And (3) realizing accurate design of the waveguide band-pass filter by using the direct coupling cavity theory of the modified formulas (17) - (21). 5-order chebyshev waveguide band-pass filter filters were designed with center frequencies of 26GHz and 34GHz, respectively, and specific dimensions thereof are shown in table 2. The modified parameters obtained by using the modified formulas (17) - (21) are all increased, and the fact that the size of the resonant cavity is inversely proportional to the resonant frequency is shown as the formula (21), so that the resonant frequency has low-frequency shift.
Table 2 comparison of Filter size parameters before and after correction formula
The 3dB BW of the two BPFs is measured to be 0.65GHz and 0.77GHz respectively, the passband is 0.5GHz, the in-band ripple and the insertion loss are both smaller than 0.5dB, the out-of-band image rejection is measured to be larger than 60dB, and all parameters meet the design requirements. The TRL calibration is used, the detailed measured data are shown in Table 3, tuning can be realized in the installation process by adjusting t 1-t 3, the frequency response is shown in fig. 10 (a) and (b), and therefore, the simulation and test samples have better consistency.
TABLE 3 BPF test data designed using correction formulas
Thus, a new design and processing technology of the waveguide band-pass filter can be obtained. This method takes into account the chamfering and its frequency shifting effects during machining and gives a modified formula to compensate for the frequency shift of the chamfer. The effectiveness of the design method can be obtained from the consistency between actual measurement and simulation data, and a theoretical basis is provided for designing the waveguide band-pass filter with the chamfer.
In the installation process, tuning is realized by adjusting t1 to t3 as shown in fig. 10, and the frequency response is shown in fig. 11 (a) and (b), so that the simulation and test samples have better consistency. The frequency response, the insertion loss and other parameters of the waveguide band-pass filter designed by the method are tested, the simulation and the measurement result are well matched, and the same kind of filter has good consistency. Through testing, the precise design method of the filter with the chamfer diaphragm can realize tuning of the filter and no deviation of frequency bands.
The embodiment provides an accurate design method of an inductance diaphragm waveguide band-pass filter with tunable K wave band and Ka wave band H face, which comprises the following steps:
(1) Starting from the lumped parameter low-pass prototype, a model with chamfers is built
(2) The new design formula of the band-pass filter with the chamfer lumped parameter coupling resonator is derived through frequency conversion
(3) These coupling structures and resonators are then implemented with microwave structures to obtain a microwave bandpass filter
In addition, in design, the practical problems of frequency offset caused by chamfering in machining and different loss caused by cutting of an E surface of an H surface are taken into consideration, and the accurate design method of the membrane filter with the chamfering is summarized, so that the low loss of the filter and the frequency band of the filter are ensured not to deviate. Compared with the traditional method, the method overcomes the defects of larger error and higher loss. The method is widely applied to the fields of short-range air defense, battlefield monitoring, missile guidance, airborne collision avoidance, high-resolution imaging, space target detection, battlefield friend-foe identification, millimeter wave communication and the like.
Example 2
The tunable E-plane cut H-plane waveguide band-pass filter formed by the design method, as shown in fig. 1, comprises an H-plane waveguide band-pass filter and an upper cover: the H-plane waveguide band-pass filter adopts a rectangular structure; two groups of inductive diaphragms are arranged in the H-plane waveguide band-pass filter, and each group of inductive diaphragms comprises two rows of inductive diaphragms; the two groups of inductive diaphragms are distributed inside the H-plane waveguide band-pass filter in a mirror symmetry mode by taking the central axis on the long side of the H-plane waveguide band-pass filter as a symmetry axis; two rows of inductive diaphragms in each group of inductive diaphragms are arranged on long side walls of two sides of the H-plane waveguide band-pass filter in a mirror symmetry mode by taking a central axis of the wide side of the H-plane waveguide band-pass filter as a symmetry axis, and are perpendicular to the long side walls; the width of each row of inductance membranes is different, and the distance between two adjacent inductance membranes is different.
In the two rows of inductance diaphragms which are symmetrically distributed, an air gap is reserved between every two corresponding inductance diaphragms; the width of each air gap is different.
The two groups of inductive diaphragms comprise 6 inductive diaphragms, and the 6 inductive diaphragms are equally divided into two rows; in each row of inductance diaphragms, the directions from two ends of the filter to the center line of the long side of the filter are as follows: the first inductive diaphragm, the second inductive diaphragm and the third inductive diaphragm.
The width of the first inductance membrane is smaller than that of the second inductance membrane; the width of the second inductance membrane is smaller than that of the third inductance membrane; the distance between the first inductive diaphragm and the second inductive diaphragm is L 1 The method comprises the steps of carrying out a first treatment on the surface of the The distance between the second inductive diaphragm and the third inductive diaphragm is L 2 The method comprises the steps of carrying out a first treatment on the surface of the The distance between the third inductive diaphragms in the two groups of inductive diaphragms is L 3 And the dimensions between the distancesThe relation is: l (L) 1 ＜L 2 ＜L 3 。
In the two corresponding rows of inductive diaphragms, the width of an air gap between the two first inductive diaphragms is t 1 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two second inductance diaphragms is t 2 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two third inductance diaphragms is t 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the relation between each air gap width is: t is t 1 ＞t 2 ＞t 3 . The bottom end of the inductance diaphragm is fixedly arranged on the bottom surface of the H-plane waveguide band-pass filter; and a chamfer exists at the edges of the top end and the bottom end of the inductance membrane. The tunable E-plane cuts the H-plane waveguide band-pass filter E-plane into the same two parts. That is, the filter as a whole can be understood as two identical half filter parts with a single row of inductive diaphragms snapped together; and due to the buckling mode, a convex butt joint wall surface exists between the two rows of inductance diaphragms. The specific structure is shown in fig. 12.
While the invention has been described in terms of preferred embodiments, it is not intended to be limited thereto, but rather to enable any person skilled in the art to make various changes and modifications without departing from the spirit and scope of the present invention, which is therefore to be limited only by the appended claims.
Claims (7)
1. A method for designing a tunable E-plane cut H-plane waveguide band-pass filter, the method comprising the steps of:
step one, using a waveguide section with half waveguide wavelength as a series resonator of an H filter, and using a parallel inductor formed by an inductance diaphragm as a coupling structure between resonators;
step two, obtaining an approximate conversion formula of the low-pass prototype-band-pass filter through an approximate conversion formula calculation model, wherein the approximate conversion formula of the prototype-band-pass filter is as follows:
series inductance L k Conversion to series LC circuits
Parallel capacitor C k Conversion to parallel LC circuits
L k ' and C k ' represents the converted inductance and capacitance values, respectively;
the conversion formula calculation model is as follows:
wherein ω', ω 1 ' represents the frequency variation and sideband frequencies of the lowpass prototype filter, lambda, respectively g0 ,λ g1 ,λ g2 ,λ g Are respectively with frequency omega 0 ,ω 1 ,ω 2 And ω corresponds to the waveguide wavelength, w λ Is the relative bandwidth;
step three, reactance of the resonance unit
Is carried into formulas (5) - (7),
obtaining waveguide filter impedance transformation formulas (8) - (10):
wherein K is 01 Representing a first order impedance transformer; r is R A Representing the impedance of the left side end of the equivalent circuit of the waveguide filter; x is X 1 A reactance slope parameter representing a first order half-wavelength series resonator; z is Z 0 Representing the input impedance; g 0 、g 1 Representing the source conductance and the first-order series inductor inductance or the capacitance of the first-order parallel capacitor, respectively; g j 、g j+1 Representing the capacitances of the series inductor inductances of the j-order and the j+1-order or the first-order parallel capacitors, respectively; g n 、g n+1 Representing the series inductor inductance or the capacitance of the parallel capacitor of the nth order and the load, respectively; xn represents the reactance of the nth order diaphragm; RS represents the load impedance; k (K) j，j+1 An impedance transformer represented as between j and j+1 steps; k (K) j，j+1|j＝1→n-1 Representing j from 1 to n-1 impedance transformers; k (K) n N+1 represents the impedance transformer of the last order; k is an impedance converter, g is a chebyshev low-pass prototype filter parameter;
step four, the equivalent inductance of the waveguide filter structure is separated by the electrical length theta, wherein the equivalent inductance comprises a parallel jX and has a point length ofThe impedance transformation of the transmission line of (a) is:
step five, equivalent inductance membrane is T-shaped network structure, the transmission matrix of the T-shaped network structure is:
the equality relationship between the formula (11) and the formula (12) is obtained:
step six, according to formulas (14) and (15), and combining the joint lengthsThe conditions of (2):
obtaining the impedance transformer K and the electrical lengthImpedance transformer model with chamfer:
wherein X is S Representing reactance parameters due to chamfering; x is X Sj The reactance parameter generated by the j-order chamfer is the chamfer reactance; x is X j，j+1 The reactance parameter is expressed as reactance parameter generated by chamfering between the j and j+1 order resonators;
step seven, combining the additional inductances introduced by chamfering into two sides of the parallel inductance, wherein the equivalent electrical length of each introduced into the two sides is as followsThe actual resonator electrical length is:
wherein lambda is 0 Is the working frequency of the waveguide band-pass filter, L j Is the resonant cavity length, X j-1，j The reactance parameter is expressed as reactance parameter generated by chamfering between the j-1 and j-order resonators;
step eight, according to a relation model of the length of the resonant cavity and the working frequency, obtaining the relation between the length of the resonant cavity and the working frequency, wherein the relation between the length of the resonant cavity and the working frequency is as follows:
L j ＝θ j λ 0 /2π (22)
thus, the parameter design of the filter is completed.
2. A tunable E-plane cut H-plane waveguide band-pass filter formed by the design method of claim 1, wherein the tunable E-plane cut H-plane waveguide band-pass filter comprises an H-plane waveguide band-pass filter: the H-plane waveguide band-pass filter adopts a rectangular structure; two groups of inductive diaphragms are arranged in the H-plane waveguide band-pass filter, and each group of inductive diaphragms comprises two rows of inductive diaphragms; the two groups of inductive diaphragms are distributed inside the H-plane waveguide band-pass filter in a mirror symmetry mode by taking the central axis on the long side of the H-plane waveguide band-pass filter as a symmetry axis; two rows of inductive diaphragms in each group of inductive diaphragms are arranged on long side walls of two sides of the H-plane waveguide band-pass filter in a mirror symmetry mode by taking a central axis of the wide side of the H-plane waveguide band-pass filter as a symmetry axis, and are perpendicular to the long side walls; the width of each row of inductance membranes is different, and the distance between two adjacent inductance membranes is different.
3. The tunable E-plane cut H-plane waveguide band pass filter of claim 2, wherein an air gap is left between each two corresponding inductive diaphragms in the two symmetrically distributed inductive diaphragms; the width of each air gap is different.
4. The tunable E-plane cut H-plane waveguide band pass filter of claim 2, wherein the two sets of inductive diaphragms include 6 inductive diaphragms, the 6 inductive diaphragms being uniformly distributed in two rows; in each row of inductance diaphragms, the directions from two ends of the filter to the center line of the long side of the filter are as follows: the first inductive diaphragm, the second inductive diaphragm and the third inductive diaphragm.
5. The tunable E-plane cut H-plane waveguide band pass filter of claim 4, wherein a width of the first inductive diaphragm is less than a width of the second inductive diaphragm; the width of the second inductance membrane is smaller than that of the third inductance membrane; first inductance membrane and second inductance membraneThe distance between the inductive diaphragms is L 1 The method comprises the steps of carrying out a first treatment on the surface of the The distance between the second inductive diaphragm and the third inductive diaphragm is L 2 The method comprises the steps of carrying out a first treatment on the surface of the The distance between the third inductive diaphragms in the two groups of inductive diaphragms is L 3 And the dimensional relationship between the distances is: l (L) 1 <L 2 ＜L 3 。
6. The tunable E-plane cut H-plane waveguide band pass filter of claim 4, wherein in the corresponding two rows of inductive diaphragms, an air gap between the two first inductive diaphragms has a width t 1 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two second inductance diaphragms is t 2 The method comprises the steps of carrying out a first treatment on the surface of the The width of the air gap between the two third inductance diaphragms is t 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the relation between each air gap width is: t is t 1 ＞t 2 ＞t 3 。
7. The tunable E-plane cut H-plane waveguide band-pass filter of claim 2, wherein the bottom end of the inductive diaphragm is fixedly mounted on the bottom surface of the H-plane waveguide band-pass filter; and a chamfer exists at the edges of the top end and the bottom end of the inductance membrane.
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| CN111224209A (en) * | 2019-12-08 | 2020-06-02 | 南京航空航天大学 | Waveguide band-pass filter based on waveguide re-cut-off characteristic and design method thereof |
| CN114824707B (en) * | 2022-04-28 | 2023-09-26 | 西南科技大学 | 5G millimeter wave reconfigurable waveguide filter and passband adjusting method thereof |
| CN115117580B (en) * | 2022-07-12 | 2024-04-30 | 安徽大学 | High rectangular coefficient semi-lumped millimeter wave filter chip based on cross coupling structure |
| CN114927844B (en) * | 2022-07-20 | 2022-11-15 | 南京天朗防务科技有限公司 | Waveguide filter of Ku wave band |
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