Parameter Design Method of Array Resonant Circuit

Abstract

The present application provides a parameter design method for an array resonant circuit, wherein the array resonant circuit includes m resonant units, and the parameter design method includes: simulating n resonant units among the m resonant units according to the expression of the resonant frequency with respect to the inductance value L of the resonant inductor, the first microbridge number of the resonant capacitor, the second microbridge number of the coupling capacitor, and multiple constant parameters K, and determining the value of the combination of L and K; n is greater than or equal to 3 and less than m; and determining the value of L and the multiple constant parameters K according to the first expression of the quality factor with respect to the inductance value L, the first microbridge number, the second microbridge number, and multiple constant parameters K, in combination with the value of the combination of L and K. In this way, the relationship between the resonant frequency and the quality factor with respect to the first microbridge number and the second microbridge number can be determined by a small amount of simulation combined with formula calculation.

Description

Technical Field

[0001] The present application relates to the technical field of dynamic inductance detectors, and in particular to a parameter design method for an array resonant circuit. Background Art

[0002] Resonant circuits are one of the key design elements in modern electronic devices. The main application in the field of astronomy is dynamic inductance detectors, which have shown great potential in the fields of photon detection and reading, single photon counting, and dark matter detection. The dynamic inductance detector is an array resonant circuit, including multiple resonant units, each of which is a pixel of the dynamic inductance detector.

[0003] At present, the dynamic inductance detector has reached 20,000 pixels, and the future development trend is likely to be to the direction of million or ten million pixel detectors. The design parameters of each pixel unit in the dynamic inductance detector are different to achieve the distribution of the resonant frequency within the specified frequency range and keep the resonator quality factor within a certain range.

[0004] In the design of array resonant circuits, the resonant inductor is generally kept constant, and the resonant frequency is tuned by changing the number of microbridges of the resonant capacitor, and the resonator quality factor is adjusted by changing the number of microbridges of the coupling capacitor. Because it works under superconducting temperature conditions, the impedance in the resonant circuit is very small and negligible, which increases the difficulty of extracting the resonant circuit quality factor using traditional formulas. In addition, it is time-consuming and labor-intensive to simulate and design one by one in the design of large-scale array resonant circuits. Summary of the invention

[0005] The present application provides a parameter design method for an array resonant circuit to solve at least some of the problems in the related art.

[0006] The present application provides a parameter design method for an array resonant circuit, wherein the array resonant circuit comprises m resonant units, wherein the resonant units comprise resonant capacitors, resonant inductors and coupling capacitors, wherein both the resonant capacitors and the coupling capacitors are interdigital capacitors, and the parameter design method comprises:

[0007] According to the resonant frequency of the resonant unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and multiple constant parameters K, simulating n resonance units among the m resonance units to determine the value of the combination of L and K; wherein n is greater than or equal to 3 and less than m;

[0008] According to the quality factor of the resonant unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, and combining the value of the combination of L and K to determine the value of L and a plurality of constant parameters K; wherein the first expression is based on the quality factor About the resonant frequency The second expression of Δf is obtained, where Δf is the resonant frequency The second frequency corresponding to the transmission coefficient S21 on the left and right sides when it takes a value of -3dB and the first frequency The difference between , Δf is a positive value.

[0009] Determine the design value of one of the first design parameter and the second design parameter according to the design value of the other one, wherein the first design parameter includes the resonant frequency and the quality factor, and the second design parameter includes the number of the first microbridges and the second microbridge number .

[0010] Optionally, multiple constant parameters K include , , and The expression of the resonant frequency is based on the resonant frequency with respect to the inductance value L of the resonant inductor, the capacitance value C of the resonant capacitor and the capacitance value of the coupling capacitor. The initial expression of the capacitance value C of the resonant capacitor is related to the number of the first microbridge of the resonant capacitor. The expression C = * + , the capacitance value of the coupling capacitor The number of second microbridges with respect to the coupling capacitor The expression = * + Got it.

[0011] Optionally, the capacitance value C of the resonant capacitor is expressed as C= * + , the capacitance value of the coupling capacitor The expression = * + It is obtained by transforming the calculation formula of the interdigital capacitance, which is A* *( -( -1)* )* , where A is the correction factor, is the equivalent dielectric constant, N is the number of microbridges of the interdigital capacitor, is the width of a single microbridge, is the distance between two adjacent microbridges, is the length of the interdigital capacitor, and t is the equivalent distance between the two electrodes of the capacitor.

[0012] Optionally, the n resonance units include a first resonance unit, a second resonance unit and a third resonance unit;

[0013] The simulating n resonance units among the m resonance units includes:

[0014] The first resonance unit, the second resonance unit and the third resonance unit are simulated, wherein the first microbridges of the first resonance unit and the second resonance unit are the same in number, and the second microbridges are different in number; the first resonance unit and the third resonance unit are different in number, and the first microbridges are the same in number;

[0015] Determining the value of the combination of L and K includes:

[0016] Determine L* , L* , L* The value of .

[0017] Optionally, the quality factor About the resonant frequency The second expression of Δf is .

[0018] Optionally, the quality factor of the resonance unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, including the first frequency with respect to the inductance value L of the resonant inductor, the first microbridge number of the resonant capacitor , the number of second microbridges of the coupling capacitor and multiple constant parameters K, and the second frequency is related to the inductance value L of the resonant inductor, the first microbridge number of the resonant capacitor , the number of second microbridges of the coupling capacitor and expressions for multiple constant parameters K;

[0019] The quality factor of the resonance unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, and determining the values ​​of L and the plurality of constant parameters K in combination with the value of the combination of L and K, comprising:

[0020] The resonant frequency in the simulation results , first frequency Substitute the value of into the expression of the first frequency and change the resonant frequency in the simulation results to , Second Frequency Substitute the value of into the expression of the second frequency, combine the value of the combination of L and K, and determine the value of L and multiple constant parameters K.

[0021] Optionally, determining the expression of the first frequency and the expression of the second frequency includes: determining an expression of the admittance of the resonance unit, wherein the expression of the admittance includes a value of a combination of the inductance values ​​L and K;

[0022] Determine the equation for the transmission coefficient S21 with respect to admittance;

[0023] When the transmission coefficient S21 takes a value of -3dB, determine an equation of the admittance expression with respect to the first frequency, the inductance value L, and a plurality of constant parameters K, and then determine an expression of the first frequency;

[0024] When the transmission coefficient S21 takes a value of -3dB, the equation of the admittance expression with respect to the second frequency, the inductance value L, and a plurality of constant parameters K is determined, and then the expression of the second frequency is determined.

[0025] Optionally, the expression of the transmission coefficient with respect to the admittance of the resonance unit is obtained according to the following steps:

[0026] According to the structure of the two-port network where the resonance unit is located, an expression of the transmission coefficient with respect to the admittance of the resonance unit is obtained, wherein the two-port network includes a source end and a load end, and the impedances of the source end and the load end are matched.

[0027] Optionally, determining the design value of one of the first design parameter and the second design parameter according to the design value of the other of the first design parameter and the second design parameter includes:

[0028] According to the expression of the resonant frequency and the number of the first microbridges The design value and the number of the second microbridge , determining a design value of the resonant frequency of the resonant unit;

[0029] Determine a design value of the first frequency and a design value of the second frequency according to the design value of the resonant frequency, an expression of the first frequency, and an expression of the second frequency;

[0030] The design value of the quality factor is determined according to the design value of the resonant frequency, the design value of the first frequency, and the design value of the second frequency in combination with an expression of the quality factor with respect to the resonant frequency, the first frequency, and the second frequency.

[0031] Optionally, the parameter design method further includes:

[0032] The resonance unit is simulated based on the substrate thickness of the resonance unit, the range of the resonance frequency, the range of the quality factor and the structure of the resonance inductor to determine the upper and lower limits of the first number of microbridges and the upper and lower limits of the second number of microbridges based on the range of the resonance frequency and the range of the quality factor.

[0033] The parameter design method of the array resonant circuit provided in the embodiment of the present application does not need to simulate and design each resonant unit in the array resonant circuit. It only needs to simulate a small number of resonant units in the array resonant circuit. Combined with circuit knowledge and formula calculations, the key parameters of the large-scale array resonant circuit can be extracted, which greatly reduces the design difficulty and design resource requirements and improves the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0035] Figure 1 A schematic diagram of an array resonant circuit shown in an embodiment of the present application;

[0036] Figure 2 for Figure 1 A circuit diagram of the resonance unit shown;

[0037] Figure 3 for Figure 1 A schematic diagram of the structure of the resonance unit shown;

[0038] Figure 4 for Figure 2 A schematic diagram of the resonance frequency shift of the resonance unit shown;

[0039] Figure 5 A schematic diagram of a flow chart of a parameter design method for an array resonant circuit provided in an embodiment of the present application;

[0040] Figure 6It is a schematic diagram of the structure of the interdigital capacitor shown in the embodiment of the present application;

[0041] Figure 7 for Figure 1 A schematic diagram of related parameters of the quality factor of the resonance unit shown;

[0042] Figure 8 It is a circuit diagram of a two-port network of a resonance unit shown in an embodiment of the present application.

[0043] Reference numerals:

[0044] Array resonant circuit 1, resonant unit 10, substrate 11, resonant capacitor 12, resonant inductor 13, coupling capacitor 14, feed line 15, finger capacitor 16, first electrode 161, second electrode 162, finger 163, two-port network 17. DETAILED DESCRIPTION

[0045] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0046] Please refer to Figure 1-Figure 4 , Figure 1 A schematic diagram of an array resonant circuit 1 shown in an embodiment of the present application; Figure 2 for Figure 1 A circuit diagram of the resonance unit 10 shown; Figure 3 for Figure 2 The structural schematic diagram of the resonance unit 10 shown; Figure 4 for Figure 2 The schematic diagram of the resonance frequency shift of the resonance unit 10 is shown.

[0047] The array resonant circuit 1 includes a substrate 11, a feed line 15 and a plurality of resonant units 10, wherein the feed line 15 and the plurality of resonant units 10 are arranged on the substrate 11, and each resonant unit 10 is a pixel of a dynamic inductance detector. Each resonant unit 10 includes a resonant capacitor 12, a resonant inductor 13 and a coupling capacitor 14, wherein the resonant capacitor 12 and the resonant inductor 13 are connected in parallel and coupled to the feed line 15 via the coupling capacitor 14. The array resonant circuit 1 includes m resonant units 10, wherein the resonant capacitor 12 and the coupling capacitor 14 are both interdigital capacitors 16.

[0048] The working principle of the resonance unit 10 is that when the photon energy is greater than the energy band gap (hv>2Δ), the photon energy is absorbed by the superconductor, causing the Cooper pairs inside the superconductor to be destroyed. When light is incident on the superconductor, the Cooper pairs inside it are broken up to form quasiparticles, and the density of quasiparticles and Cooper pairs will affect the change of the surface impedance of the superconductor, including the influence on the inductance value of the resonant inductor 13. The resonant inductor 13 is used to absorb electromagnetic radiation and resonate with the resonant capacitor 12, and is coupled to the feed line 15 through the coupling capacitor 14. The strength of the incident photon is reflected in the relative frequency offset. Figure 4 As shown, in Figure 4 In the figure, there are two resonant waveforms, one of which is the resonant waveform before photon irradiation, and the other is the resonant waveform after photon irradiation. The resonant waveforms before and after photon irradiation have changed, and the resonant frequency has shifted.

[0049] The microwave superconducting dynamic inductance detector has reached 20,000 pixels, and the future development trend is likely to be to improve towards the direction of million or ten million pixel detectors. The design parameters of each pixel unit in the detector are different to achieve the distribution of the resonance frequency within the specified frequency range and keep the resonator quality factor within a certain range. In the design of the array resonant circuit 1, the general resonant inductor 13 remains unchanged, and the resonant frequency tuning is achieved by changing the number of microbridges of the resonant capacitor 12, and the resonator quality factor is adjusted by changing the number of microbridges of the coupling capacitor 14. In the related art, it is necessary to simulate all the resonant units 10 one by one to complete the parameter design of all the resonant units 10, which has high design difficulty and great demand for design resources. And because the dynamic inductance detector works under superconducting temperature conditions, the impedance in the array resonant circuit 1 is very small and can be ignored, which increases the difficulty of extracting the quality factor of the resonant circuit using traditional formulas. Therefore, such a large-scale array resonant circuit 1 relies on traditional simulation design, which is time-consuming and labor-intensive.

[0050] Please refer to Figure 5 , Figure 5 A flow chart of a parameter design method for an array resonant circuit 1 provided in an embodiment of the present application. Figure 5 In the illustrated embodiment, the parameter design method includes steps 21 to 23.

[0051] Step 21, according to the resonant frequency of the resonant unit 10 Regarding the inductance L of the resonant inductor 13 and the number of the first microbridges of the resonant capacitor 12 , the number of second microbridges of coupling capacitor 14 and multiple constant parameters K, simulate n resonance units 10 out of m resonance units 10 to determine the value of the combination of L and K; wherein n is greater than or equal to 3 and less than m.

[0052] Step 22, according to the quality factor of the resonance unit 10 Regarding the inductance L of the resonant inductor 13 and the number of the first microbridges of the resonant capacitor 12 , the number of second microbridges of coupling capacitor 14 and a first expression of a plurality of constant parameters K, and combining the values ​​of the combination of L and K to determine the values ​​of L and the plurality of constant parameters K, wherein the first expression is based on the quality factor About resonant frequency The second expression of Δf is obtained, where Δf is the resonant frequency The second frequency corresponding to the transmission coefficient S21 on the left and right sides when it takes a value of -3dB and the first frequency The difference between , Δf is a positive value.

[0053] Step 23, determining a design value of one of the first design parameter and the second design parameter according to the design value of the other design parameter, wherein the first design parameter includes a resonant frequency and quality factor , the second design parameter includes the number of first microbridges and the number of second microbridges .

[0054] In this way, the parameter design method of the array resonant circuit 1 provided by the present application does not need to simulate and design each resonant unit 10 in the array resonant circuit 1. It only needs to simulate a small number of resonant units 10 in the array resonant circuit 1, and combined with circuit knowledge and formula calculation, it can extract the key parameters of the large-scale array resonant circuit 1, greatly reducing the design difficulty and design resource requirements. The parameter design of each resonant unit 10 of the large-scale array resonant circuit 1 is realized, improving the design efficiency of the large-scale array superconducting dynamic inductance detector and expanding its application range.

[0055] In this embodiment, the multiple constant parameters K include , , and The resonant frequency is related to the inductance L of the resonant inductor 13 and the number of the first microbridges of the resonant capacitor 12. , the number of second microbridges of coupling capacitor 14 The expression of multiple constant parameters K is = ,in, is the resonant frequency, L is the inductance of the resonant inductor 13, , , and is a constant parameter.

[0056] The resonant frequency is related to the inductance L of the resonant inductor 13 and the number of first microbridges of the resonant capacitor 12. , the number of second microbridges of coupling capacitor 14 The expressions of the constant parameters K are based on the resonant frequency with respect to the inductance value L of the resonant inductor 13, the capacitance value C of the resonant capacitor 12 and the capacitance value C of the coupling capacitor 14. The initial expression of the capacitance C of the resonant capacitor 12 is related to the number of the first microbridge of the resonant capacitor 12. The expression C = * + , the capacitance value of coupling capacitor 14 The number of second microbridges with coupling capacitor 14 The expression = * + Got it.

[0057] The resonant frequency is related to the inductance L of the resonant inductor 13, the capacitance C of the resonant capacitor 12 and the capacitance of the coupling capacitor 14. The initial expression is = ,in, is the capacitance value of the resonant capacitor 12, is the capacitance value of the coupling capacitor 14.

[0058] Please refer to Figure 6 , Figure 6 This is a schematic diagram of the structure of the interdigital capacitor 16 shown in an embodiment of the present application. The interdigital capacitor 16 includes a first electrode 161 and a second electrode 162. The first electrode 161 includes a plurality of interdigits 163, and the second electrode 162 includes a plurality of interdigits 163. The plurality of interdigits 163 of the first electrode 161 and the plurality of interdigits 163 of the second electrode 162 are arranged alternately. The sum of the number of the first interdigits 163 and the number of the second interdigits 163 is the number of microbridges.

[0059] The calculation formula of the interdigital capacitance 16 is A* *( -( -1)* )* , where A is the correction factor, is the equivalent dielectric constant, N is the number of microbridges of the interdigital capacitor 16, is the width of a single microbridge, is the distance between two adjacent microbridges, is the length of the interdigital capacitor 16, and t is the equivalent distance between the two electrodes of the capacitor. The calculation formula of the interdigital capacitor 16 is transformed to obtain A* *( ) / t*N+A* *G*H / t.

[0060] The capacitance value C of the resonant capacitor 12 is expressed as C= * + , the capacitance value of coupling capacitor 14 The expression = * + It is obtained by transforming the calculation formula of the interdigital capacitance 16. Specifically, in the resonant capacitor 12, let A* *( ) / t= , A* *G*H / t= , the number of the first microbridge of the resonant capacitor 12 is , we can get the expression of capacitance value C of resonant capacitor 12: C= * + In the coupling capacitor 14, let A* *( ) / t= , A* *G*H / t= , the number of the second microbridge of coupling capacitor 14 is , the capacitance value of coupling capacitor 14 can be obtained The expression = * + .

[0061] In this embodiment, the n resonance units 10 include a first resonance unit, a second resonance unit and a third resonance unit; and the n resonance units 10 among the m resonance units 10 are simulated, including:

[0062] The first resonant unit, the second resonant unit and the third resonant unit are simulated, wherein the first resonant unit and the second resonant unit have the same number of first microbridges and different number of second microbridges. The first resonant unit and the third resonant unit have different number of second microbridges and the same number of first microbridges.

[0063] Determine the value of the combination of L and K, including:

[0064] Determine L* , L* , L* The value of .

[0065] In this way, by simulating the three resonance units 10, namely the first resonance unit, the second resonance unit and the third resonance unit, the values ​​of the first microbridge number and the second microbridge number in the first resonance unit, the second resonance unit and the third resonance unit, as well as the resonance frequencies of the first resonance unit, the second resonance unit and the third resonance unit and the values ​​of the first frequency and the second frequency are recorded.

[0066] Substitute the first microbridge number of the resonant capacitor 12 in the first resonant unit, the second microbridge number of the coupling capacitor 14, and the resonant frequency of the first resonant unit into the expression of the resonant frequency: = Substitute the first microbridge number of the resonant capacitor 12 in the second resonant unit and the second microbridge number of the coupling capacitor 14 and the resonant frequency of the second resonant unit into the expression of the resonant frequency = Substitute the first microbridge number of the resonant capacitor 12 in the third resonant unit and the second microbridge number of the coupling capacitor 14 and the resonant frequency of the third resonant unit into the expression of the resonant frequency = In; L* can be calculated by combining , L* , L* The value of .

[0067] Please refer to Figure 7 , Figure 7 for Figure 1 Schematic diagram of parameters related to the quality factor of the resonance unit 10 shown. Figure 7 As shown, the resonant frequency can be read out according to the simulation results , first frequency and the second frequency The value of quality factor About resonant frequency and Δf is .

[0068] The quality factor of the resonance unit 10 Regarding the inductance L of the resonant inductor 13 and the number of the first microbridges of the resonant capacitor 12 , the number of second microbridges of coupling capacitor 14 and the expressions of multiple constant parameters K, including the inductance L of the resonant inductor 13 and the first microbridge number of the resonant capacitor 12 at the first frequency , the number of second microbridges of coupling capacitor 14 and the expressions of the multiple constant parameters K, and the second frequency with respect to the inductance value L of the resonant inductor 13, the first microbridge number of the resonant capacitor 12 , the number of second microbridges of coupling capacitor 14 and multiple constant parameters K.

[0069] According to the quality factor of the resonance unit 10 Regarding the inductance L of the resonant inductor 13 and the number of the first microbridges of the resonant capacitor 12 , the number of second microbridges of coupling capacitor 14 and a first expression of a plurality of constant parameters K, combined with the value of the combination of L and K, to determine the value of L and the plurality of constant parameters K, including:

[0070] The resonant frequency in the simulation results , first frequency Substitute the value of into the expression of the first frequency and change the resonant frequency in the simulation results to , Second Frequency Substitute the value of into the expression of the second frequency, combine the value of the combination of L and K, and determine the value of L and multiple constant parameters K.

[0071] Please refer to Figure 8 , Figure 8 This is a circuit diagram of a two-port network 17 in which the resonance unit 10 is located as shown in an embodiment of the present application. The two-port network 17 of the resonance unit 10 includes a source end and a load end. The resonance unit 10 is located between the source end and the load end. The source end is port1 and the load end is port2.

[0072] Determining the expression of the first frequency and the expression of the second frequency includes: determining an expression of the admittance of the resonance unit 10, wherein the expression of the admittance includes a value of a combination of the inductance values ​​L and K;

[0073] Determine the equation for the transmission coefficient S21 with respect to admittance;

[0074] When the transmission coefficient S21 takes a value of -3dB, determine the equation of the admittance expression with respect to the first frequency, the inductance value L, and a plurality of constant parameters K, and then determine the expression of the first frequency;

[0075] When the transmission coefficient S21 takes a value of -3dB, the equation of the admittance expression with respect to the second frequency, the inductance value L, and a plurality of constant parameters K is determined, and then the expression of the second frequency is determined.

[0076] The expression of the transmission coefficient with respect to the admittance of the resonant unit 10 is obtained according to the following steps:

[0077] According to the structure of the two-port network 17 where the resonance unit 10 is located, an expression of the transmission coefficient with respect to the admittance of the resonance unit 10 is obtained, wherein the two-port network includes a source end and a load end, and the impedance of the source end and the load end are matched.

[0078] Specifically, in this embodiment, the admittance of the resonance unit 10 is obtained according to the structure of the two-port network 17 where the resonance unit 10 is located, combined with the admittance formulas of capacitance and inductance and the calculation formulas of admittance in series circuits and parallel circuits.

[0079] First, the expression of the admittance of the resonant unit 10 is determined according to the structure of the resonant unit 10. Because the resonant unit 10 includes a resonant capacitor 12, a resonant inductor 13 and a coupling capacitor 14, the resonant capacitor 12 and the resonant inductor 13 are connected in parallel and coupled to the feed line 15 through the coupling capacitor 14. The admittance of the resonant capacitor 12 is j C, the admittance of the resonant inductor 13 is -j / L, the admittance of the coupling capacitor 14 is j In a parallel circuit, the total admittance after parallel connection is the sum of the admittances of each component. In a series circuit, the total admittance after series connection is the reciprocal of the sum of the reciprocals of the admittances of each component. In summary, the admittance expression of the resonant unit 10 is =j ,in, is the admittance of the resonance unit 10.

[0080] Then, according to the structure of the two-port network 17 of the resonant unit 10, the expression of the transmission coefficient with respect to the admittance of the resonant unit 10 is obtained. Specifically, the transmission (ABCD) cascade matrix is ​​used to calculate the transmission (ABCD) matrix between port1 and port2, and then the ABCD parameter matrix is ​​converted into an S parameter matrix to obtain the transmission coefficient The expression of = .in, is the transmission coefficient from Port1 to Port2, and A, B, C, and D are the parameters of the output transmission (ABCD) matrix.

[0081] In this embodiment, the impedance matching between the source end and the load end is Then there is = , where β is the phase shift constant, is the length of the feed lines 15 on both sides of the resonant unit 10. When the resonant frequency range is low, the influence introduced by the short feed line 15 can be ignored. For example, in the embodiment of the present application, the resonant frequency range is 1.5-2 GHz, then 2, 1, then = In this way, the expression of the transmission coefficient with respect to the admittance of the resonant unit 10 is obtained: = .

[0082] After obtaining the expression of the transmission coefficient of the two-port network 17 of the resonant unit 10 from Port 1 to Port 2 with respect to the admittance of the resonant unit 10, the equation of the admittance expression with respect to the first frequency, the inductance value L, and the plurality of constant parameters K is determined in combination with the transmission coefficient S21 in the quality factor expression when the value is -3dB, and then the expression of the first frequency is determined;

[0083] When the transmission coefficient S21 takes a value of -3dB, the equation of the admittance expression with respect to the second frequency, the inductance value L, and a plurality of constant parameters K is determined, and then the expression of the second frequency is determined.

[0084] Since the expression of the transmission coefficient with respect to the admittance of the resonance unit 10 is = , the admittance is in the numerator of the expression for the transmission coefficient, and the expression for the admittance =j is a pure imaginary number, which makes calculation inconvenient. So the value is j = , and the transmission coefficient is obtained about The expression of = = .

[0085] dB( ) = -3dB, mag( )= = , solving the equation gives =4( ), we can know that when At a certain time, The value of is also a fixed value. .

[0086] According to the assignment j = , =j , can be obtained = , Admittance expression about the first frequency , inductance value L and multiple constant parameters K = , which is also the equation for the first frequency about the admittance expression, the inductance value L and a plurality of constant parameters K. And determine the admittance expression about the second frequency , inductance value L and multiple constant parameters K = - , which is also an equation for the second frequency regarding the admittance expression, the inductance value L and a plurality of constant parameters K.

[0087] Solve the frequency in the admittance expression , inductance value L and multiple constant parameters K, solve the frequency in the admittance expression , inductance L and multiple constant parameters K, combined with the known resonant frequency , first frequency , Second Frequency , and the value of the combination of L and K, determine the value of L and multiple constant parameters K, including:

[0088] The first frequency Substitute the value of into the admittance expression about the first frequency , inductance L and multiple constant parameters K, the second frequency Substitute the value of into the admittance expression about the second frequency , inductance value L and multiple constant parameters K, the values ​​of L and multiple constant parameters K are determined by combining the values ​​of the combination of L and K.

[0089] Specifically, the first frequency in the simulation results can be Substitute the value of the first microbridge number and the value of the second microbridge number into the admittance expression about the first frequency , inductance value L and multiple constant parameters K = . The second frequency in the simulation results Substitute the value of the first microbridge number and the value of the second microbridge number into the admittance expression for the second frequency , inductance value L and multiple constant parameters K = - The values ​​of L and a plurality of constant parameters K are determined in combination with the values ​​of L and K.

[0090] In this example of the present application, determining the design value of one of the first design parameter and the second design parameter according to the design value of the other of the first design parameter and the second design parameter includes:

[0091] According to the expression of the resonant frequency and the number of the first microbridge The design value of the second microbridge number , determine the design value of the resonant frequency of the resonant unit 10. Specifically, the expression of the resonant frequency is = .

[0092] Solve the equations for the first frequency according to the admittance expression related to the resonant frequency, the first frequency or the second frequency, the inductance value L and the multiple constant parameters K. , Second Frequency Specifically, you can Calculate the first frequency The value of Calculate the second frequency The value of .

[0093] According to the design value of the resonant frequency, the first frequency , Second Frequency The quality factor can be determined based on = , calculate the quality factor of the resonance unit 10 .

[0094] In the present application example, according to the design value of one of the first design parameter and the second design parameter, the design value of the other of the first design parameter and the second design parameter is determined, including the resonant frequency of the resonant unit 10. Design value and quality factor The design value of the first microbridge number of the resonant unit 10 is determined The design value of the second microbridge number design value.

[0095] According to the resonant frequency of the resonant unit 10 and design quality factor The design value of the first microbridge number of the resonant unit 10 is determined The design value of the second microbridge number When the design value of the second microbridge is It is not an integer and needs to be rounded down. The rounded second microbridge number As the final second microbridge number design value.

[0096] In the embodiment of the present application, the parameter design method further includes:

[0097] Determine the number of first microbridges The upper and lower limits of the second microbridge number Avoid the resonant frequency range exceeding the set resonant frequency range, and avoid the quality factor exceeding the set quality factor range.

[0098] In an embodiment of the present application, the upper and lower limits of the number of first microbridges and the upper and lower limits of the number of second microbridges are determined, including: simulating the resonance unit 10 according to the thickness of the substrate 11 of the resonance unit 10, the range of the resonance frequency, the range of the quality factor and the structure of the resonance inductor 13, so as to determine the upper and lower limits of the number of first microbridges and the upper and lower limits of the number of second microbridges according to the range of the resonance frequency and the range of the quality factor.

[0099] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the application disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0100] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A parameter design method for an array resonant circuit, characterized in that: The array resonant circuit includes m resonant units, the resonant unit includes a resonant capacitor, a resonant inductor and a coupling capacitor, the resonant capacitor and the coupling capacitor are both interdigital capacitors, and the parameter design method includes: According to the resonant frequency of the resonant unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and multiple constant parameters K, simulating n resonance units among the m resonance units to determine the value of the combination of L and K; wherein n is greater than or equal to 3 and less than m; According to the quality factor of the resonant unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, and combining the value of the combination of L and K to determine the value of L and a plurality of constant parameters K; wherein the first expression is based on the quality factor About the resonant frequency The second expression of Δf is obtained, where Δf is the resonant frequency The second frequency corresponding to the transmission coefficient S21 on the left and right sides when it takes a value of -3dB and the first frequency The difference between , Δf is a positive value; Determine the design value of one of the first design parameter and the second design parameter according to the design value of the other one, wherein the first design parameter includes the resonant frequency and the quality factor, and the second design parameter includes the number of the first microbridges and the second microbridge number .

2. The parameter design method according to claim 1, characterized in that: Multiple constant parameters K include , , and The expression of the resonant frequency is based on the resonant frequency with respect to the inductance value L of the resonant inductor, the capacitance value C of the resonant capacitor and the capacitance value of the coupling capacitor. The initial expression of the capacitance value C of the resonant capacitor is related to the number of the first microbridge of the resonant capacitor. The expression C = * + , the capacitance value of the coupling capacitor The number of second microbridges with respect to the coupling capacitor The expression = * + Got it.

3. The parameter design method according to claim 2, characterized in that: The capacitance value C of the resonant capacitor is expressed as C= * + , the capacitance value of the coupling capacitor The expression = * + It is obtained by transforming the calculation formula of the interdigital capacitance, which is A* *( -( -1)* )* , where A is the correction factor, is the equivalent dielectric constant, N is the number of microbridges of the interdigital capacitor, is the width of a single microbridge, is the distance between two adjacent microbridges, is the length of the interdigital capacitor, and t is the equivalent distance between the two electrodes of the capacitor.

4. The parameter design method according to claim 2, characterized in that: The n resonance units include a first resonance unit, a second resonance unit and a third resonance unit; The simulating n resonance units among the m resonance units includes: The first resonance unit, the second resonance unit and the third resonance unit are simulated, wherein the first microbridges of the first resonance unit and the second resonance unit are the same in number, and the second microbridges are different in number; the first resonance unit and the third resonance unit are different in number, and the first microbridges are the same in number; Determining the value of the combination of L and K includes: Determine L* , L* , L* The value of .

5. The parameter design method according to claim 1, characterized in that: The quality factor About the resonant frequency The second expression of Δf is .

6. The parameter design method according to claim 1, characterized in that: The quality factor of the resonant unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, including the first frequency with respect to the inductance value L of the resonant inductor, the first microbridge number of the resonant capacitor , the number of second microbridges of the coupling capacitor and multiple constant parameters K, and the second frequency is related to the inductance value L of the resonant inductor, the first microbridge number of the resonant capacitor , the number of second microbridges of the coupling capacitor and expressions for multiple constant parameters K; The quality factor of the resonance unit Regarding the inductance value L of the resonant inductor and the number of the first microbridges of the resonant capacitor , the number of second microbridges of the coupling capacitor and a first expression of a plurality of constant parameters K, and determining the values ​​of L and the plurality of constant parameters K in combination with the value of the combination of L and K, comprising: The resonant frequency in the simulation results , first frequency Substitute the value of into the expression of the first frequency and change the resonant frequency in the simulation results to , Second Frequency Substitute the value of into the expression of the second frequency, combine the value of the combination of L and K, and determine the value of L and multiple constant parameters K.

7. The parameter design method according to claim 6, characterized in that: The determination of the expression of the first frequency and the expression of the second frequency includes: Determine an expression for the admittance of the resonance unit, wherein the expression for the admittance includes a value of a combination of the inductance values ​​L and K; Determine the equation of the transmission coefficient S21 with respect to the admittance; When the transmission coefficient S21 takes a value of -3dB, determine an equation of the admittance expression with respect to the first frequency, the inductance value L, and a plurality of constant parameters K, and determine an expression of the first frequency; When the transmission coefficient S21 takes a value of -3dB, the equation of the admittance expression with respect to the second frequency, the inductance value L, and a plurality of constant parameters K is determined, and the expression of the second frequency is determined.

8. The parameter design method according to claim 7, characterized in that: The expression of the transmission coefficient with respect to the admittance of the resonant unit is obtained according to the following steps: According to the structure of the two-port network where the resonance unit is located, an expression of the transmission coefficient with respect to the admittance of the resonance unit is obtained; wherein the two-port network includes a source end and a load end, and the impedances of the source end and the load end are matched.

9. The parameter design method according to claim 1, characterized in that: The step of determining the design value of the other of the first design parameter and the second design parameter according to the design value of one of the first design parameter and the second design parameter comprises: According to the expression of the resonant frequency and the number of the first microbridges The design value and the number of the second microbridge Determine the design value of the resonant frequency of the resonant unit based on the design value of Determine a design value of the first frequency and a design value of the second frequency according to the design value of the resonant frequency, an expression of the first frequency, and an expression of the second frequency; The design value of the quality factor is determined according to the design value of the resonant frequency, the design value of the first frequency, and the design value of the second frequency in combination with an expression of the quality factor with respect to the resonant frequency, the first frequency, and the second frequency.

10. The parameter design method according to claim 1, characterized in that: The parameter design method also includes: The resonance unit is simulated based on the substrate thickness of the resonance unit, the range of the resonance frequency, the range of the quality factor and the structure of the resonance inductor to determine the upper and lower limits of the first number of microbridges and the upper and lower limits of the second number of microbridges based on the range of the resonance frequency and the range of the quality factor.

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