Linear topology with phase compensation characteristics and high temperature superconducting filter

Abstract

The embodiment of the application relates to the technical field of filter design, and discloses a straight-line topology structure with phase compensation characteristics, design and a superconducting filter. The topology structure is based on a standard straight-line topology structure comprising a source suspension branch, a straight-line coupling main path and a load suspension branch. Four continuous resonators are selected on the straight-line coupling main path. A first resonator and a fourth resonator of the four continuous resonators are cross-coupled to form the straight-line topology structure with the phase compensation characteristics. The four continuous resonators form a CQ structure. Therefore, under the condition of fully utilizing the simplicity of the straight-line topology structure, the introduction, independent control and adjustment of the phase compensation real zero point are realized, the group delay in the passband of the filter is compensated while the sideband suppression capability is improved, and therefore the signal fidelity of a communication system is improved.

Description

Technical Field

[0001] This application relates to the field of filter design technology, and in particular to a linear topology with phase compensation characteristics, its design, and a superconducting filter. Background Technology

[0002] With the rapid development of modern communication technology and the increasing congestion of the radio spectrum, bandwidth utilization and anti-interference capabilities face new challenges. Microwave filters, as the management gateway for spectrum resources, will require narrower bandwidth and superior sideband suppression capabilities. Therefore, filters with high quality factor (Q-value) characteristics will play a significant role, such as HTS (high temperature superconducting filter), cavity filters, and high Q-value filter chips. In particular, high-temperature superconducting thin film materials have extremely low surface resistivity in the microwave band, making them ideal for fabricating planar microwave filters, effectively balancing the requirements for insertion loss and filter order.

[0003] By setting up CQ (cross quadrangle), CT (cross triangle), extracted pole, and NRNs (non-resonating nodes), the sideband suppression and sideband roll-off of the filter can be improved. The principle is to introduce cross-coupling or add additional stub units between non-adjacent resonators to introduce transmission zeros, that is, to increase the physical structure coupling units of the filter, thereby changing the characteristics of the frequency response.

[0004] Another simple and effective topology for introducing real-frequency transmission zeros is the linear topology. The linear topology is particularly suitable for HTS design because it can achieve miniaturization of the filter size, can be well adapted to the low-temperature working environment of liquid nitrogen temperature range, effectively reduce the heat load of the refrigerator, and is easy to design and meet the precision requirements of the manufacturing process.

[0005] However, the aforementioned sideband suppression improvement schemes will worsen the group delay within the filter's passband, especially for narrowband filters, which will directly affect the signal fidelity of the communication system. Summary of the Invention

[0006] The purpose of this application is to provide a linear topology structure, design, and superconducting filter with phase compensation characteristics. It can fully utilize the simplicity of the linear topology structure to achieve the introduction, independent control, and adjustment of phase compensation real zeros, thereby improving the sideband suppression capability and compensating for the group delay in the filter passband, thus improving the signal fidelity of the communication system.

[0007] To address the aforementioned technical problems, embodiments of this application provide a linear topology with phase compensation characteristics. This linear topology is based on a standard linear topology including a source suspension branch, a linearly coupled main path, and a load suspension branch. Four consecutive resonators are arbitrarily selected on the linearly coupled main path, and the first and fourth resonators are cross-coupled to form the linear topology with phase compensation characteristics. The source suspension branch is provided with… A resonator is provided in the linear coupling main circuit. A resonator, wherein the load suspension branch is provided with One resonator It is an integer greater than 4. and All are integers not less than 0, and the four consecutive resonators constitute a CQ structure.

[0008] Embodiments of this application also provide a design method for a high-temperature superconducting filter, comprising the following steps: Step 1: Determine the type of response function, topology, and number of resonators of the high-temperature superconducting filter according to the preset performance indicators; wherein, the type of response function is a bounded GC response or a reduced GC response, the topology is the linear topology with phase compensation characteristics described above, and the performance indicators include the expected center frequency, bandwidth, relative bandwidth, insertion loss, return loss, order, reflection, sideband suppression, and group delay of the high-temperature superconducting filter; Step 2: Based on the topology and the number of resonators, derive the transmission coefficient and reflection coefficient patterns and the number of zeros and poles corresponding to the response function. Then, combine the return loss to synthesize the transmission coefficient and reflection coefficient patterns to obtain the expressions for the transmission coefficient and reflection coefficient patterns and the zero-pole characteristics. Step 3: Starting from 0, increase the coupling coefficient value of the cross-coupling in the CQ unit, and adjust the coupling coefficient of the adjacent coupling in the CQ unit through iterative optimization until the group delay suppression requirement is met; Step 4: Based on the coupling coefficients in the CQ unit that meet the group delay suppression requirement, adjust the coupling coefficients of other adjacent couplings in the topology until the group delay requirement is met, and obtain the normalized coupling coefficient matrix corresponding to the topology at this time. Step 5: Perform inverse normalization on the normalized coupling coefficient matrix to obtain the general parameters required to realize the physical structure size of the filter. The general parameters include the physical coupling coefficients for realizing the filter, as well as the quality factor of the input port and the quality factor of the output port. Step 6: Based on the general parameters, determine the distance between each of the resonators, the first distance between the resonator connected to the source and the first loading tap structure, and the second distance between the resonator connected to the load and the second loading tap structure. Step 7: Determine the filter circuit size based on the calculation results in Step 6, and then process and package the filter circuit.

[0009] An embodiment of this application also provides a high-temperature superconducting filter, which is designed according to the high-temperature superconducting filter design method described above and fabricated on a double-sided yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer structure thin film substrate. One side of the three-layer structure thin film substrate is etched with circuits using standard photolithography and ion etching processes, and the other side of the three-layer structure thin film substrate is used for grounding. The high-temperature superconducting filter is packaged in a metal shielding box.

[0010] The embodiments of this application provide a linear topology, design, and superconducting filter with phase compensation characteristics. Without requiring additional units, it enables the introduction, independent control, and adjustment of finite-frequency transmission zeros and phase-compensated real zeros. This achieves the design of a filter with multiple transmission zeros and linear phase compensation characteristics while ensuring maximum filter structure simplicity, minimum circuit design complexity, and minimum device size. The designed high-temperature superconducting filter has two pairs of symmetrical finite-frequency transmission zeros, improving sideband suppression capability; simultaneously, it has a pair of real zeros to compensate for group delay, thus achieving both improved sideband suppression capability and compensation for group delay within the filter's passband, thereby enhancing the signal fidelity of the communication system. Furthermore, the results for parameters such as in-band insertion loss and band-side roll-off rate of the designed high-temperature superconducting filter highly agree with theoretical simulation values, demonstrating significant application potential in modern wireless communication systems.

[0011] In some alternative embodiments, the CQ structure , , , satisfy That is, the coupling coefficients of all four pairs of couplings in the CQ structure are not equal to 0; among them, Let be the coupling coefficient between the first and second resonators in the CQ structure. Let be the coupling coefficient between the second and third resonators in the CQ structure. The coupling coefficient between the third and fourth resonators in the CQ structure is given. The coupling coefficient between the first and fourth resonators in the CQ structure is given. The first resonator in the CQ structure is the first resonator in the linear topology with phase compensation characteristics. i One resonator, the i greater than and less than Integers.

[0012] In some alternative embodiments, , ,and .

[0013] In some optional embodiments, the resonators in the source suspension branch and the load suspension branch are used to determine the frequency positions of finite transmission zeros, and the resonators in the CQ structure are used to determine the frequency positions of real zeros, which are complex zeros.

[0014] In some alternative embodiments, the physical coupling coefficients of the filter have the simplicity of being all positive or negative, meaning that the coupling between all resonators adopts the same coupling characteristics.

[0015] In some optional embodiments, the high-temperature superconducting filter includes several resonators, which are miniaturized resonators fabricated on a yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate with folded half-wavelength microstrip lines.

[0016] In some alternative embodiments, the resonant frequency of the resonator is controlled by adjusting the length of the resonator, and the coupling coefficient between the two resonators is adjusted by adjusting the distance between the two resonators. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0018] Figure 1 This is a schematic diagram of a standard linear topology; Figure 2 This is a schematic diagram of a linear topology with phase compensation characteristics provided in one embodiment of this application; Figure 3This is a schematic diagram of another linear topology with phase compensation characteristics provided in one embodiment of this application; Figure 4a This is a schematic diagram of the S-parameter frequency response curve of an 8th-order bounded GC function topology provided in one embodiment of this application; Figure 4b This is a schematic diagram of the group delay frequency response curve of an 8th-order bounded GC function topology provided in one embodiment of this application; Figure 5 This is a zero-pole distribution diagram of an 8th-order filter with two pairs of transmission zeros provided in one embodiment of this application; Figure 6a This is a schematic diagram of the S-parameter frequency response curve of a 10th-order reduced GC function topology provided in one embodiment of this application; Figure 6b This is a schematic diagram of the group delay frequency response curve of a 10th-order reduced GC function topology provided in one embodiment of this application; Figure 7 This is a zero-pole distribution diagram of a 10th-order filter with two pairs of transmission zeros provided in one embodiment of this application; Figure 8 This is a flowchart illustrating a design method for a high-temperature superconducting filter according to an embodiment of this application; Figure 9 This is a schematic diagram of a miniaturized resonator based on a folded half-wavelength microstrip line provided in one embodiment of this application; Figure 10a This is a graph illustrating the coupling characteristics between adjacent resonators according to an embodiment of this application; Figure 10b This is a graph illustrating the characteristics of cross-coupling between non-adjacent resonators provided in one embodiment of this application; Figure 11 This is a schematic diagram of the frequency response S-parameters and group delay characteristics of a high-temperature superconducting filter designed according to an embodiment of this application; Figure 12 This is a schematic diagram of a high-temperature superconducting filter fabricated according to an embodiment of this application; Figure 13 yes Figure 12 The S-parameter characteristic curve of the high-temperature superconducting filter measured at 77K. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this application to help readers better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the various embodiments below is for the convenience of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0020] To facilitate the explanation of the technical solution of this application, the following sections will first introduce the standard linear topology, the characteristic analysis of the high-temperature superconducting filter (hereinafter referred to as the linear filter) designed based on the standard linear topology, the constraints between the transmission zero and the reflection zero, the characteristics of the bounded GC response (Generalized Chebyshev) and reduced GC response filters, and the comprehensive analysis of several typical linear filters.

[0021] I. Characteristic Analysis of Standard Linear Topology and High-Temperature Superconducting Filters Designed Based on This Topology A standard linear topology can be as follows: Figure 1 As shown, it consists of cascaded components coupled along a straight line. The topology consists of a resonator node, an input (source) node, and an output (load) node. The source (S) and load (L) nodes connect to the topology. Each resonator node is divided into three units. Figure 1 The hollow circles represent the source and load, the solid black dots represent resonator nodes, and the line segments between two resonator nodes represent the coupling between the two resonators. The first unit, composed of several resonator nodes, can be considered as a suspension of the source, called... The source of the second unit is a suspended branch; the second unit is composed of... It consists of several resonator nodes, called the linear coupling main path; The third unit, composed of several resonator nodes, can be considered as a suspension of the load, called... The load suspension branch of the step, .

[0022] when or At that time, the standard linear topology changes to a single suspended topology; when At this time, the standard linear topology degenerates into the original straight standard structure. In practical engineering applications, it is usually set as follows: and At the same time, set .

[0023] Suppose that for source S corresponding to Extreme points At the location, the load L corresponds to Extreme points At this point, the source and load branches are equivalently short-circuited, therefore in this... Extreme points , Extreme points The input and output admittances of the filter are: , ( k = 0, 1, 2) , ( l = 0, 1, 2) In the formula, Indicates the source input admittance. Indicates the source output admittance. Indicates the load input admittance. This represents the load output admittance, or in other words, it can be expressed as (denoted as satisfying the first condition):

[0024]

[0025] k = 0, 1, 2 l = 0, 1, 2 In the formula, , , All are S-parameters.

[0026] At this time, admittance extreme points and The poles are exactly the filter's poles. n TZs = n S + n L One transmission zero point. Produced by the source, Generated by load, in There are no transmission zeros in the linearly coupled main path composed of resonator nodes. Therefore, the poles and extreme points They are independent of each other, that is k and l It can take any value, or it can take the same value. Although and In principle, it is arbitrary, but when a stub generates two or more transmission zeros, it is subject to... and The alternating singularity characteristic of the filter means that at least one of a pair of adjacent poles or transmission zeros is composed of... (or Only by generating zeros can effective attenuation of the sideband amplitude be achieved, especially when two transmission zeros are close together. Therefore, we limit the number of transmission zeros generated by each stub to two or fewer, and when a stub generates two transmission zeros, the two transmission zeros must not be on the same side of the stopband or have the same sign (both positive or both negative). Therefore, it is necessary to ensure that... and Since all the values ​​are less than 2, the design is relatively convenient and can already meet the actual engineering needs.

[0027] The zero-point distribution of a typical multi-transmission zero-point frequency response can be categorized into the following situations: 1) Single zero point ,or .

[0028] 2) A pair of symmetrical zeros ,or .

[0029] 3) Two zeros with the same sign ,when At that time, the two zero points coincided.

[0030] 4) Two zeros with different signs ,when At that time, the two zero points are symmetrical.

[0031] 5) Three zeros ; or, .

[0032] 6) Two pairs of symmetrical zeros ,when At that time, the two pairs of zeros coincide.

[0033] The synthesis of low-pass prototypes with linear topologies can be achieved through characteristic polynomials. F ( s ), P ( s )and E ( sTo analyze this, the scattering parameters of the filter (denoted as the second condition) are defined as follows:

[0034]

[0035]

[0036] In the formula, the complex frequency variable s = j Ω, * denotes the conjugate matrix. P ( s )yes n TZ normalized polynomial of order, F ( s )and E ( s )yes Normalized polynomial of order. F ( s )and P ( s The roots of ) are the reflection zeros (RZs) and the transmission zeros (TZs). E ( s ) is a strict Hurwitz polynomial, whose roots are the poles of the filter. E ( s ), F ( s )and P ( s )satisfy: , The coefficients of the transfer function, Let be the coefficients of the reflection function. Simultaneously, according to the characteristics of a linear filter, the characteristic polynomial must also satisfy the following constraint condition (denoted as the third condition):

[0037]

[0038]

[0039] k = 0, 1, 2 l = 0, 1, 2 Thus, the characteristic polynomial F ( s ), P ( s )and E ( s The constraints at the poles correspond one-to-one with the responses of filters based on standard linear topologies.F ( s ), P ( s )and E ( s If the above constraints are met, it can be implemented based on a standard linear topology, and vice versa.

[0040] Filters implemented based on standard linear topologies require only a minimal number of coupling elements and do not require additional components to generate transmission zeros. Furthermore, they do not require special settings for coupling elements or resonators, such as the coupling between all resonators being either positive or negative.

[0041] II. Constraints and Limitations Between Transmission Zero Point and Reflection Zero Point For a standard linear topology, given the above characteristic function polynomials, to achieve the generalized Chebyshev filter response, The conditions that need to be met are:

[0042] In the formula, RL Indicates return loss. RL It is about and The increasing function, that is, the generalized Chebyshev response of the standard linear topology. S In the parameters, With return loss RL It has fixed constraints and is determined by... F ( j )and P ( j This is jointly determined. Therefore, for a standard linear topology, because the frequency response needs to satisfy either the first or third condition, the reflection polynomial... F ( s ) and the transmission polynomial P ( s It is constrained, namely, the transmission zero point. ( and The determination of the reflection zero point and the generalized Chebyshev filter functions TZs and RZs are mutually constrained and cannot be arbitrarily set. Simply put, due to the physical constraints of the standard linear topology, the generalized Chebyshev filter functions TZs and RZs are no longer freely generated.

[0043] III. Characteristics of Bounded GC Response and Reduced GC Response Filters In the linear filter of GC response RL The horizontal level and the position of the transmission zero point affect each other, which means that free allocation is not allowed. RLTherefore, by changing the characteristics of the reflection zero, the degree of freedom of the transmission zero can be restored, thereby meeting the requirements of different out-of-band suppression, i.e., relaxing the band rejection. S 11 and S 22 The characteristics required. Two typical GC responses are bounded GC response and reduced GC response. Depending on the specific application scenario, different response schemes for linear topologies can be used: 1) When the transmission zero point is small or there are no fixed requirements, the standard GC response can be used, that is, all RZs are pure imaginary numbers.

[0044] 2) When the value of the transmission zero is small (the transmission zero is close to the sideband), RZs can be partially or completely degenerated into an imaginary number with a non-zero real part. A non-zero value generates a new response, which is a bounded GC response.

[0045] 3) When the value of the transmission zero is large (the transmission zero is far from the sideband), one or two RZs can be degenerated into pure real numbers, while the other RZs remain pure imaginary numbers. In this case, the number of pure imaginary RZs is reduced, and the generated response is the reduced GC response.

[0046] Bounded GC response is defined by the polynomial modeling. RL The scope, thereby broadening The degrees of freedom of TZs, their typical characteristics are The minimum value in the passband ( RL min ) and maximum value ( RL max The TZs value is determined by the RZs value. Within a certain TZs setting range, it can be adjusted... RL min and RL max The value of makes the polynomial of the standard linear topology satisfy the third condition mentioned above. However, the bounded GC response has two limitations: firstly, this response is only applicable to the case of one or a pair of transported zeros mentioned above; secondly, when the number of transported zeros is three or more, it is difficult to find a solution that can achieve the bounded GC response. RL min and RL max On the one hand, the bounded GC response has a limited degree of freedom in releasing TZs, meaning that TZs cannot be chosen at any frequency position within the stopband. At the same time, the bounded GC response has two advantages: firstly, the sign of the real part of RZ does not affect the magnitude of the S-parameters (it only determines the phase), which means that when the third condition is met, there exists... Several different F(s) polynomials can be satisfied; on the other hand, in Under the condition that the second condition is met, The real part of each RZs can take different values, and there are multiple solutions to RZs, which increases the complexity of solving the problem. RL The selectivity. Given the bounded GC response of a standard linear topology, RL Given the boundedness of RZs and the multiple solutions of RZs, optimization methods are typically used to obtain efficient matrix functions.

[0047] Although bounded GC response through release RL The range of values ​​increases the degrees of freedom for RZs and TZs to some extent, but constraints still exist in these allocations. When the TZs value is large, or when there is significant asymmetry or multiple transmission zeros in the desired response, it can lead to... RL The value is extremely large, which is difficult to achieve in engineering implementation. Therefore, it can be achieved by moving several reflection zeros to the complex plane and solving the reduced GC response function. The non-Chebyshev isoripple response of order, in which the polynomial F ( s )have RZs, usually It equals 1 or 2, while the rest... RZs is a purely imaginary number. Therefore, the characteristic function of the reduced GC response has in the passband... The maximum and minimum values, and RL The number of TZs can be freely set. Among them, the number of RZs... The selection of RZs can follow these rules: one RZs allows two additional degrees of freedom, which can be used to support up to two RZs generated from any one of the suspension branches. The free setting. When extracting one or two freely adjustable TZs from a single suspension branch, adding one RZs is sufficient. When extracting one or two freely adjustable TZs from two suspension branches, two RZs need to be added. This typically occurs in the following situations: 1) , ,in, , ,or , .

[0048] 2) , ,in, , ,or , ,or .

[0049] in," , , "and" , , "This is a commonly used structure in engineering." This refers to the number of transmission zeros, under which paired transmission zeros can be introduced.

[0050] When implementing the reduced GC response of a filter using a standard linear topology, the following steps are required: 1) According to Preliminary numerical assessment Choose the value. or .

[0051] 2) Select After the value is given, assume the real number Given a fixed initial value, calculate the RZs value that determines the GC response. F ( s It is worth noting that at this time F ( s It has roots of complex numbers and roots of purely imaginary numbers.

[0052] 3) According to RL The value of the reflection function is used to select and update its coefficients. And according to the above text The conditions to be met must be satisfied, and the coefficients of the transfer function must be calculated. .

[0053] 4) Use the formula ,calculate E ( s ).

[0054] 5) Check if the current conditions meet the third condition.

[0055] 6) If the current condition does not meet the third condition, return to step 3) to update. and If the current conditions meet the third condition, the calculation process ends.

[0056] Thus, based on the standard linear topology, a method with... The number of complex zeros and A pure imaginary number reflection zero point, within the band RL The reduced GC frequency response, which can be freely set by TZs, is obtained and satisfies the third condition. In practical engineering applications, , , RL and There are only a few typical cases, so efficient solutions are easily obtained. The main advantage of filters designed based on standard linear topologies is that their implementation does not require special internal units. Furthermore, the sign of the coupling does not affect the characteristics of the response. Therefore, the actual size of a linear filter can be implemented in exactly the same way as a directly cascaded, all-pole filter.

[0057] IV. Comprehensive Analysis of Several Typical Linear Filters Standard linear topologies can effectively introduce transmission zeros of limited frequencies through the application of a source or load. Based on the above method, we can synthesize a pair of The function polynomial and zero-pole characteristics corresponding to the bounded GC response of the 8th-order filter are shown in Tables I and II below. At this point, , , , , RL = 22dB. Similarly, following the design process described above, we can easily synthesize a design with two pairs of... The reduced GC response function polynomial and zero-pole characteristics of the 10th-order filter are shown in Tables III and IV below. , , , RL =20dB. Once the polynomial used to describe the linear topology is determined, it can be used to complete the coupling coefficient synthesis of the filter.

[0058] Table 1: Transmission coefficient and reflection coefficient polynomials of an 8th-order filter with a pair of transmission zeros. RL =22dB, 9707

[0059] Table 2: Zero-point characteristics of an 8th-order filter with a pair of transmission zeros

[0060] Table 3: Polynomials for the transfer coefficients and reflection coefficients of a 10th-order filter with two pairs of finite zeros. RL =20dB, 0.9138

[0061] Table 4: Zero-point characteristics of a 10th-order filter with two pairs of transmission zeros

[0062] As can be seen from the above introduction on linear filters, although linear filters can improve sideband suppression, this approach will worsen the group delay in the filter's passband, especially for narrowband filters, which will directly affect the signal fidelity of the communication system.

[0063] To address the aforementioned technical problems of poor group delay within the filter passband and low signal fidelity in communication systems, one embodiment of this application proposes a linear topology with phase compensation characteristics. The implementation details of this linear topology with phase compensation characteristics are described below. These details are provided for ease of understanding and are not essential for implementing this solution.

[0064] This embodiment of the linear topology with phase compensation characteristics is based on a standard linear topology including a source suspension branch, a linearly coupled main path, and a load suspension branch. Four consecutive resonators are selected on the linearly coupled main path, and the first and fourth resonators are cross-coupled to form a linear topology with phase compensation characteristics. The source suspension branch is provided with… A resonator, with a linearly coupled main circuit equipped with... A resonator, with a load suspension branch set up. One resonator It is an integer greater than 4. and All are integers not less than 0. The four consecutive resonators selected on the linearly coupled main path constitute the CQ structure.

[0065] The linear topology with phase compensation characteristics proposed in this embodiment can introduce, independently control, and adjust finite-frequency transmission zeros and phase-compensated real zeros without the need for additional units. It achieves the design of a filter with multiple transmission zeros and linear phase compensation characteristics while ensuring maximum filter structure simplicity, minimum circuit design complexity, and minimum device size. The high-temperature superconducting filter (which can be called a linear linear-phase filter) designed based on this topology has two pairs of symmetrical finite-frequency transmission zeros, improving sideband suppression capability, and a pair of real zeros to compensate for group delay. This achieves both improved sideband suppression capability and compensation for group delay within the filter's passband, thereby improving the signal fidelity of the communication system. Furthermore, the in-band insertion loss, band roll-off rate, and other parameters of the high-temperature superconducting filter designed based on this topology are in high agreement with theoretical simulation values, showing great promise for application in modern wireless communication systems.

[0066] Figure 2 A linear topology with phase compensation characteristics is shown, in which... Specifically, the source suspension branch has 2 resonators, the linearly coupled main path has 6 resonators, and the load suspension branch has 2 resonators. The 2nd, 3rd, 4th, and 5th resonators on the linearly coupled main path (i.e., the 4th, 5th, 6th, and 7th resonators in total) are selected to form the CQ structure. Based on this linear topology with phase compensation characteristics, a 10th-order reduced GC response can be achieved.

[0067] Figure 3 Another linear topology with phase compensation characteristics is shown, in which... Specifically, the source suspension branch has 2 resonators, the linearly coupled main path has 6 resonators, and the load suspension branch has 0 resonators. The 2nd, 3rd, 4th, and 5th resonators on the linearly coupled main path (i.e., the 4th, 5th, 6th, and 7th resonators in total) are selected to form the CQ structure. Based on this linear topology with phase compensation characteristics, an 8th-order bounded GC response can be achieved.

[0068] In specific implementations, the CQ structure , , , satisfy That is, the coupling coefficients of all four pairs of couplings in the CQ structure are not equal to 0, among which, denoted as the coupling coefficient between the first and second resonators in the CQ structure. denoted as the coupling coefficient between the second and third resonators in the CQ structure. is the coupling coefficient between the third and fourth resonators in the CQ structure. Let be the coupling coefficient between the first and fourth resonators in the CQ structure. The first resonator in the CQ structure is the fourth resonator in the linear topology with phase compensation characteristics. i One resonator i greater than and less than Integers.

[0069] In other words, the CQ structure is not located at a fixed position on the main linear coupling path, for example... The linearly coupled main circuit can be configured by selecting the 1st, 2nd, 3rd, and 4th resonators on the linearly coupled main circuit to form a CQ structure, or by selecting the 2nd, 3rd, 4th, and 5th resonators on the linearly coupled main circuit to form a CQ structure, or by selecting the 3rd, 4th, 5th, and 6th resonators on the linearly coupled main circuit to form a CQ structure.

[0070] Figure 2 and Figure 3In the linear topology with phase compensation characteristics, the 4th, 5th, 6th, and 7th resonators are selected to form the CQ structure, which is composed of... , , and This constitutes the CQ structure.

[0071] In practical implementation, a linear topology with phase compensation characteristics... , ,and Such a setup is easy to implement in actual engineering projects.

[0072] In the specific implementation, the resonators in the source suspension branch and the load suspension branch are used to determine the frequency position of the finite transmission zeros, and the resonators in the CQ structure are used to determine the frequency position of the real zeros, which are the complex zeros.

[0073] The following section analyzes the characteristics of the linear topology with phase compensation proposed in this embodiment.

[0074] for Figure 3 The linear topology with phase compensation characteristics shown, based on the function polynomials and zero characteristics in Tables 1 and 2, can extract the following frequency response: Figure 4a and Figure 4b As shown, Figure 4a The S-parameter frequency response curves of an 8th-order bounded GC function topology are shown. Figure 4b The group delay frequency response curve is for an 8th-order bounded GC function topology. This corresponds to... M 47 The curve is equal to 0. The coupling coefficients of the topology are synthesized as follows: Figure 4a As shown, at this time, M 45 =0.532、 M 56 =0.539、 M 67 =0.578, the corresponding zero-pole distribution is as follows Figure 5 As shown, from Figure 5 You can see It has a real part rather than being a purely imaginary number. Based on this, if we... M 47 The value gradually increases from 0 to 0.20, while the corresponding adjustment is made in the CQ unit. M 45 , M 56 , M 67And keeping other coupling coefficients in the topology unchanged, the corresponding frequency response polynomials and zero-pole characteristics are shown in Tables 5 and 6. Figure 3 It can be seen that the filter's The positions remain unchanged, but two real number transmission zeros have been added. , The value remained almost unchanged. Additionally, through... Figure 4a It can also be seen that the roll-off of the near-side zone remains unchanged, while the roll-off of the far-side zone becomes slower, and the roll-off within the passband... RL =22 remains unchanged, through Figure 4b It can also be seen that the group delay within the passband can be well compensated. Therefore, the location of the null point in finite frequency transmission is... Zeros and poles within the passband and within the passband RL Determined by the topology's response, the CQ unit can independently control the real zeros. The frequency. Therefore, based on the standard linear topology, a linear topology with phase compensation characteristics obtained by introducing phase-compensated CQ cells can realize the complex zeros of the bounded GC response. and real zeros Independent introduction and tuning.

[0075] Table 5: Transmission coefficient and reflection coefficient polynomials of an 8th-order filter with two pairs of transmission zeros. RL =22dB, 9267

[0076] Table 6: Zero-point characteristics of an 8th-order filter with two pairs of transmission zeros

[0077] Similarly, for Figure 3 The linear topology with phase compensation characteristics shown, based on the function polynomials and zero characteristics in Tables 3 and 4, can extract the following frequency response: Figure 6a and Figure 6b As shown, Figure 6a The S-parameter frequency response curves of the 10th-order reduced GC function topology are shown. Figure 6b This is the group delay frequency response curve for the topology of the 10th-order reduced GC function. At this point, it corresponds to... M 47 The curve is equal to 0. The coupling coefficients of the topology are synthesized as follows: Figure 6a As shown, at this time, M 45 =0.526、 M 56 =0.521、 M 67=0.524, the corresponding zero-pole distribution is as follows Figure 7 As shown, from Figure 7 You can see All are purely imaginary numbers. Based on this, if we... M 47 The value gradually increases from 0 to 0.20, while the corresponding adjustment is made in the CQ unit. M 45 , M 56 , M 67 And keeping other coupling coefficients in the topology unchanged, the corresponding frequency response polynomials and zero-pole characteristics are shown in Tables 7 and 8. Similarly, the filter has finite propagation zeros. With the position unchanged and the near-sideband roll-off unchanged, two real-valued transmission zeros are added. The group delay within the passband is compensated, but the sideband roll-off in the far sideband is slightly reduced. RL =20 remains unchanged. All are purely imaginary numbers. Furthermore, when M 47 During the adjustment from 0 to 0.20, the phase state upgrades from uncompensated to overcompensated, demonstrating universality. Therefore, it can be concluded that, based on a linear topology, introducing a phase-compensated CQ cell can achieve the complex zeros of the reduced GC response. and real zeros Independent introduction and tuning.

[0078] Table 7: Polynomials for the transfer coefficients and reflection coefficients of a 10th-order filter with four pairs of finite zeros. RL =20dB, 0.9486

[0079] Table 8: Zero-point characteristics of a 10th-order filter with three pairs of transmission zeros

[0080] Based on the above analysis, the finite propagation zeros of a linear-phase filter... Location by and The resonator determines the real zero point. The frequency position is determined by The CQ structure in the complex number is determined by this, and the two have complementary influences. Thus, the complex zeros... and real zeros The position can be easily and freely adjusted.

[0081] Table 9 shows the coupling coefficients of the CQ structures for bounded GC functions and reduced GC functions.

[0082] Table 9: Coupling coefficients of the CQ structures of bounded GC functions and reduced GC functions

[0083] Based on this, another embodiment of this application proposes a design method for a high-temperature superconducting filter, which is applied to radar and communication systems. The implementation details of the high-temperature superconducting filter design method of this embodiment are described in detail below. The following implementation details are provided for ease of understanding and are not necessary for implementing this solution.

[0084] The specific process of the high-temperature superconducting filter design method in this embodiment can be described as follows: Figure 8 As shown, it includes: Step 101: Determine the type of response function, topology, and number of resonators of the high-temperature superconducting filter according to the preset performance indicators. The type of response function is a bounded GC response or a reduced GC response. The topology is a linear topology with phase compensation characteristics. The performance indicators include the expected center frequency, bandwidth, relative bandwidth, insertion loss, return loss, order, reflection, sideband suppression, and group delay of the high-temperature superconducting filter.

[0085] Step 102: Based on the topology and the number of resonators, derive the transmission coefficient and reflection coefficient patterns and the number of zeros and poles corresponding to the response function. Then, combine the return loss to synthesize the transmission coefficient and reflection coefficient patterns to obtain the expressions for the transmission coefficient and reflection coefficient patterns and the zero-pole characteristics.

[0086] With a total order of In the topology, it can be and Treating a part as an independent unit Each part is treated as an independent unit, which facilitates independent control of the transmission zero point of the two parts, so as to better meet the performance requirements of high-temperature superconducting filters under different characteristic environments.

[0087] High-temperature superconducting filters, with their extremely high quality factor, offer significant advantages in narrowband and high sideband suppression scenarios. However, the group delay characteristics within the passband deteriorate in narrowband or ultra-narrowband filter designs. Therefore, a linear topology with phase compensation is the most suitable choice for narrowband high-temperature superconducting filter designs. A set of preset performance indicators (units are indicated in parentheses) are given below: 1) Center frequency (MHz): 4000 MHz.

[0088] 2) Bandwidth (MHz): 80 MHz.

[0089] 3) Relative bandwidth, Fractional Bandwidth (%): 2%.

[0090] 4) Insertion loss (dB): less than or equal to 0.25 dB.

[0091] 5) Order of filter: 10.

[0092] 6) Reflection (dB): less than or equal to -10 dB.

[0093] 7) Sideband suppression, Suppression (dB): greater than or equal to 50 dB.

[0094] 8) Group delay (ns, @70% of BW): less than or equal to 5ns.

[0095] 9) Return loss (dB): 20dB.

[0096] Based on the relative bandwidth and sideband suppression in this set of preset performance indicators, the response function of the high-temperature superconducting filter can be determined to be a reduced GC response. Through phase analysis, the following parameters are used... The normalized coupling coefficients of a set of 10th-order filters, at this time , , = [1.21 j -1.21 j ], = [1.50 j -1.50 j The characteristic polynomial of the function at this point is obtained through fine-tuning: P ( s ) = [-0.075j, 0.032j, -0.268j, 0.120j, -0.200j, 0.107j, 0.046j]; F ( s ) = [1.000, -1.436, 1.675, -2.943, 0.558, -1.940, -0.242, -0.429, -0.112, -0.0160]; E ( s) = [1.000, 3.891, 8.216, 13.206-0.118j, 15.374-0.153j, 14.312-0.163j, 10.155-0.128j, 5.502, 2.117, 0.503, 0.051].

[0097] Step 103: Starting from 0, increase the coupling coefficient of cross-coupling in the CQ unit, and adjust the coupling coefficient of adjacent coupling in the CQ unit through iterative optimization until the group delay suppression requirement is met.

[0098] Step 104: Based on the coupling coefficients in the CQ cell that meet the group delay suppression requirement, adjust the coupling coefficients of other adjacent couplings in the topology until the group delay requirement is met, and obtain the normalized coupling coefficient matrix corresponding to the topology at this time.

[0099] In the specific implementation, by continuously adjusting the coupling coefficients in the topology, the coupling coefficients that satisfy the group delay suppression requirement and the sideband suppression requirement are found, and the normalized coupling coefficient matrix corresponding to the topology is obtained.

[0100] Step 105: Denormalize the normalized coupling coefficient matrix to obtain the general parameters required to realize the physical structure size of the filter. The general parameters include the physical coupling coefficients for realizing the filter, as well as the quality factor of the input port and the quality factor of the output port.

[0101] A crucial step in filter design is to inverse normalize the coupling coefficient matrix to obtain the general parameters required for the physical structure dimensions of the path filter.

[0102] The low-pass prototype can be mapped to a band-pass filter using the transformation given by the following equation:

[0103] In the formula, ω It is the angular frequency under low-pass conditions. f It is the frequency in the bandpass circuit. CF It is the center frequency. BW It refers to bandwidth, and the coupling coefficient under the physical structure (physical coupling coefficient). Coupling terms with normalization The relationship is as follows:

[0104] Input / output ports S and L The correspondence between the quality factor and the normalized coupling coefficient term is as follows:

[0105]

[0106]

[0107]

[0108] In the formula, and This is the quality factor for the input port. and This is the quality factor of the output port.

[0109] Therefore, according to the above text Figure 4b The normalized coupling coefficients in Table 9 are used. Through inverse normalization transformation, the general parameters of the 10th-order linear-phase filter are calculated as shown in Table 10 below, and all physical coupling coefficients are positive, meaning that the coupling between all resonators adopts the same coupling characteristics. Therefore, compared to typical cross-coupling alternatives, this filter does not require negative coupling, which effectively solves the problems of spurious resonance and fabrication tolerance.

[0110] Table 10: General parameters of a 10th-order linear phase filter

[0111] Step 106: Based on the general parameters, determine the distance between each resonator, the first distance between the resonator connected to the source and the first loading tap structure, and the second distance between the resonator connected to the load and the second loading tap structure.

[0112] When designing high-temperature superconducting filters, methods such as... Figure 9 The miniaturized resonator shown is based on a folded half-wavelength microstrip line, fabricated on a yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate with a thickness of 0.5 mm and a dielectric constant of 9.8. The resonator has the same linewidth and slot width, both being 0.1 mm. Figure 9 middle, d 1 = 0.55, d 2 = 0.88, d 3 = 0.81, d 4 = 0.81, d 5 = 0.90, d 6 = 0.81, d 7 = 0.82, d 8 = 0.87, d 9 = 0.58, t = 0.45, w= 0.80. This resonator has a loop-shaped structure, which facilitates coupling between adjacent resonators, making it a relatively practical topology. The resonant frequency of a microstrip resonator depends on the length of the microstrip line; therefore, the resonant frequency can be controlled by adjusting the resonator length. Under the condition of extremely weak external coupling, the amplitude and phase characteristics of the coupling between the two resonators are as follows: Figure 10a and Figure 10b As shown. Figure 10a The coupling characteristics between adjacent resonators are shown. Figure 10b The characteristics of cross-coupling between non-adjacent resonators are shown. Analysis of the phase change in the transfer function response reveals that the coupling between the two resonators is electrical coupling, and the coupling coefficient between them can be calculated using the following formula:

[0113] In the formula, f p1 and f p2 This represents the resonant frequency of two resonators in an electromagnetic simulation. Therefore, in... Figure 9 Distance between middle resonators d i ( i When the distance between the two resonators (e.g., 1, 2, ..., 9) increases, the coupling coefficient between the two resonators decreases, and vice versa. Therefore, the coupling coefficient between the two resonators can be adjusted by adjusting the distance between them, thus obtaining the general parameters in Table 10.

[0114] Under the condition of weak coupling on the outside, the cross-coupling characteristics between the two resonators are further analyzed, such as... Figure 10b As shown, the two resonators are electrically coupled. Similarly, this can be achieved by adjusting... Figure 9 The length of the cross-coupling line is used to control the cross-coupling strength between the two resonators. The distance between the cross-coupling line and the resonator is 0.08 mm to achieve a greater coupling degree.

[0115] The location of the feed port directly affects the no-load quality factor of the resonator. The value can be calculated using the following formula:

[0116] The input and output microstrip lines employ a 50-ohm structure with a linewidth of 0.46 mm. It is particularly noteworthy that in the linear topology, the input ports simultaneously implement… Q S2 and Q S3The numerical extraction between the two factors will affect each other, and the length of the input and output ports (named taps) will also interfere with the extraction of the two quality factors. Therefore, a more effective method is to use indirect coupling with less mutual interference.

[0117] The specific steps for extracting the parameters are as follows: 1) First, couple the tap to resonator 2 (or 3), and then adjust the length and distance of the tap to obtain the desired result. Q S2 (or Q S3 The initial value of ).

[0118] 2) Shorten the length of resonator 2 (or 3) and introduce resonator 3 (or 2).

[0119] 3) Obtain the desired result by adjusting the distance between the tap and resonator 3 (or 2). Q S3 (or Q S2 The initial value of ).

[0120] 4) Restore the length of resonator 2 (or 3), shorten the length of resonator 3 (or 2), and repeat the adjustment. Q S2 (or Q S3 ).

[0121] Valid values ​​are obtained by iterating through steps 3) and 4). Q S2 , Q S3 This method is also applicable to Q L8 and Q L9 Extraction. By distinguishing the lengths of the two resonators, the impact of mutual interference between them is reduced. Three parameters—tap length, tap distance between the two resonators—are used to adjust two parameters, increasing the degrees of freedom and feasibility.

[0122] By successively calculating and extracting the spacing corresponding to the coupling coefficient between two resonators, extracting the spacing between the tap and resonators 2, 3, 8, and 9, and the coupling length of the cross-coupled lines, the physical dimensions of each part of the filter can finally be constructed. The final layout of the entire planar circuit and its corresponding frequency response can then be determined. S The parameters and group delay characteristics are shown in Figure 11. The coupling characteristics between resonators can be entirely electrical or magnetic coupling, which significantly reduces the design complexity. The filter's... S The parameter response matches the theoretical calculation well, and the group delay can reach the expected value of less than or equal to 5ns.

[0123] Step 107: Determine the filter circuit size based on the calculation results of step 106, and process and package the filter circuit.

[0124] Finally, the filter was fabricated on a double-sided yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate, with dimensions of 7.74 mm × 9.66 mm (0.258). λ go × 0.322 λ go ), λ go For a wavelength of 4 GHz at the center frequency on the substrate, one side of the thin film is etched with circuitry using standard photolithography and ion etching processes, while the other side is used for grounding. The filter is then packaged in a metal shielding box. The final fabricated filter is shown below. Figure 12 As shown, Figure 13 The S-parameter characteristics measured at 77K are shown.

[0125] Experimental results show that the fabricated high-temperature superconducting filter has four transmission zeros at 3.919 GHz, 3.953 GHz, 4.046 GHz, and 4.063 GHz, which significantly improves the sideband roll-off. The insertion loss in the passband is only 0.15 dB, and the return loss in this frequency range is better than 17.8 dB. With a center frequency of 4 GHz, a relative bandwidth of 2%, a band-side roll-off greater than 40 dB / GHz, and a group delay ripple of less than 5 ns in 70% of the bandwidth, the filter successfully achieves the expected performance and verifies the effectiveness of the proposed linear topology with phase compensation characteristics.

[0126] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this patent. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, but without changing the core design of the algorithm and process, are also within the scope of protection of this patent.

[0127] Another embodiment of this application relates to a high-temperature superconducting filter. The high-temperature superconducting filter designed according to the design method of the high-temperature superconducting filter described above is fabricated on a double-sided yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer structure thin film substrate. One side of the three-layer structure thin film substrate is used for circuit etching by photolithography and ion etching processes, and the other side of the three-layer structure thin film substrate is used for grounding. The high-temperature superconducting filter is packaged in a metal shielding box.

[0128] In a specific implementation, the high-temperature superconducting filter includes several resonators, which are miniaturized resonators fabricated on a yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate with folded half-wavelength microstrip lines.

[0129] In practice, the resonant frequency of the resonator is controlled by adjusting the length of the resonator, and the coupling coefficient between the two resonators is adjusted by adjusting the distance between them.

[0130] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. A linear topology with phase compensation characteristics, characterized in that, Based on a standard linear topology including a source suspension branch, a straight-coupled main path, and a load suspension branch, four consecutive resonators are selected on the straight-coupled main path, and the first resonator of the four consecutive resonators is cross-coupled with the fourth resonator to form a linear topology with phase compensation characteristics. The source suspension branch is provided with A resonator is provided in the linear coupling main circuit. A resonator, wherein the load suspension branch is provided with One resonator It is an integer greater than 4. and All are integers not less than 0, and the four consecutive resonators constitute a CQ structure; The linear topology with phase compensation characteristics is used for the design of high-temperature superconducting filters. The design method of high-temperature superconducting filters includes: Step 1: Determine the type of response function, topology, and number of resonators of the high-temperature superconducting filter according to preset performance indicators; wherein, the type of response function is a bounded GC response or a reduced GC response, the topology is a linear topology with phase compensation characteristics, and the performance indicators include the expected center frequency, bandwidth, relative bandwidth, insertion loss, return loss, order, reflection, sideband suppression, and group delay of the high-temperature superconducting filter; Step 2: Based on the topology and the number of resonators, derive the transmission coefficient and reflection coefficient patterns and the number of zeros and poles corresponding to the response function. Then, combine the return loss to synthesize the transmission coefficient and reflection coefficient patterns to obtain the expressions of the transmission coefficient and reflection coefficient patterns and the zero-pole characteristics. Step 3: Starting from 0, increase the coupling coefficient value of the cross-coupling in the CQ unit, and adjust the coupling coefficient of the adjacent coupling in the CQ unit through iterative optimization until the group delay suppression requirement is met; Step 4: Based on the coupling coefficients in the CQ unit that meet the group delay suppression requirement, adjust the coupling coefficients of other adjacent couplings in the topology until the group delay requirement is met, and obtain the normalized coupling coefficient matrix corresponding to the topology at this time. Step 5: Denormalize the normalized coupling coefficient matrix to obtain the general parameters required to realize the physical structure size of the filter. The general parameters include the physical coupling coefficients for realizing the filter, as well as the quality factor of the input port and the quality factor of the output port. Step 6: Based on the general parameters, determine the distance between each of the resonators, the first distance between the resonator connected to the source and the first loading tap structure, and the second distance between the resonator connected to the load and the second loading tap structure. Step 7: Determine the filter circuit size based on the calculation results of Step 6, and then process and package the filter circuit. The physical coupling coefficients of the filters are all positive, meaning that the coupling between all resonators adopts the same coupling characteristics.

2. The linear topology with phase compensation characteristics according to claim 1, characterized in that, The CQ structure , , , satisfy That is, the coupling coefficients of the four pairs of couplings in the CQ structure are all not equal to 0; in, Let be the coupling coefficient between the first and second resonators in the CQ structure. Let be the coupling coefficient between the second and third resonators in the CQ structure. The coupling coefficient between the third and fourth resonators in the CQ structure is given. The coupling coefficient between the first and fourth resonators in the CQ structure is given. The first resonator in the CQ structure is the first resonator in the linear topology with phase compensation characteristics. i One resonator, the i greater than and less than Integers.

3. The linear topology with phase compensation characteristics according to any one of claims 1 to 2, characterized in that, , ,and .

4. The linear topology with phase compensation characteristics according to any one of claims 1 to 2, characterized in that, The resonators in the source suspension branch and the load suspension branch are used to determine the frequency positions of finite transmission zeros, and the resonators in the CQ structure are used to determine the frequency positions of real zeros, which are complex zeros.

5. A high-temperature superconducting filter, characterized in that, A high-temperature superconducting filter with a linear topology having phase compensation characteristics, designed according to any one of claims 1 to 4, is fabricated on a double-sided yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate. One side of the three-layer thin film substrate is etched with circuits using standard photolithography and ion etching processes, and the other side of the three-layer thin film substrate is used for grounding. The high-temperature superconducting filter is packaged in a metal shielding box.

6. The high-temperature superconducting filter according to claim 5, characterized in that, The high-temperature superconducting filter includes several resonators, which are miniaturized resonators fabricated on a yttrium barium copper oxide / magnesium oxide / yttrium barium copper oxide three-layer thin film substrate with folded half-wavelength microstrip lines.

7. The high-temperature superconducting filter according to claim 6, characterized in that, The resonant frequency of the resonator is controlled by adjusting its length, and the coupling coefficient between the two resonators is adjusted by adjusting the distance between them.

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