A method for implementing a transfer function using an RLC circuit

Abstract

A method for implementing a transfer function using an RLC circuit, comprising: splitting the transfer function of the reduced-order simulation model into a first polynomial containing high-order frequency terms and a second polynomial containing a constant term and the sum of a rational proper fraction; calculating the roots of the first polynomial equal to zero; calculating a set of coefficients corresponding to all the roots according to the first polynomial and the set of all its roots; calculating the values of the RLC elements corresponding to each root according to each root and its corresponding coefficient; placing the calculated RLC elements into the circuit topologies corresponding to each root to construct the RLC circuit corresponding to the first polynomial; constructing the RLC circuit corresponding to the second polynomial, and connecting the RLC circuit corresponding to the first polynomial in parallel with the RLC circuit corresponding to the second polynomial to implement the transfer function of the reduced-order simulation model. The method of the present invention supplements the circuit implementation process of the transfer function containing high-order frequency terms, enabling more types of transfer functions to be circuit-represented by RLCs.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation of large-scale linear circuits, and in particular to a method for realizing a transmission function by utilizing an RLC circuit. Background Art

[0002] In circuit simulation, large-scale linear circuits are often encountered. For example, RC circuits in EMIR can contain hundreds of millions of nodes. Although the circuit contains a huge number of nodes, the number of ports connecting the linear circuit to the outside world is often far smaller than the number of internal nodes. Therefore, model reduction is a widely used technique.

[0003] Among various model-order reduction methods, one involves calculating the system's transfer function and then representing it with an RLC circuit using RLC elements. This new RLC circuit can be considered an approximation of the original circuit. Because the scale of the new RLC circuit is much smaller than the original, circuit-order reduction is achieved.

[0004] Since the transfer function is often a function of frequency, it comes from the user doing a series expansion near the frequency point of interest. In this way, the transfer function can be written as

[0005]

[0006] Here H(s) is the transfer function, s = j2πf, and f is the frequency. i , i=0,...,N are the coefficients and order of the polynomial expansion. And c k and p k , k=1,...,M are the residues and extreme points of rational proper fractions.

[0007] For passive circuits, the transfer function can usually be expressed as the sum of a linear term, a constant term, and a rational fraction, i.e., formula (2).

[0008]

[0009] For active circuits, the polynomial expansion may contain higher-order terms. If the transfer function is written in the form of formula (2), the literature [1] can be found to convert it into an RLC circuit, but for the case of containing higher-order terms, there is no such work.

[0010] This patent proposes a characterization method using RLC circuits for transfer functions containing high-order frequency terms. This allows transfer function order reduction methods to be applied more broadly. In this patent, the transfer function is circuit admittance.

[0011] References:

[0012] [1]Zhenyu Qi,Hao Yu,Pu Liu,Sheldon X.-D.Tan,and Lei He,Wideband Passive Multiport Model Order Reduction and Realization of RLCM Circuits,IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,Vol.25,p1496-p1509(2006). Summary of the Invention

[0013] To solve the deficiencies of the prior art, the object of the present invention is to provide a method for implementing a transfer function using an RLC circuit, which is used to implement a circuit for a transfer function containing high-order frequency terms. This method expands the situation of circuit implementation of transfer functions that are only applicable to passive circuits, that is, the transfer function can contain not only first-order terms, constant terms, and rational proper fractions of frequency, but also high-order terms of frequency in the transfer function.

[0014] To achieve the above object, the method for implementing a transfer function using an RLC circuit provided by the present invention includes:

[0015] Split the transfer function of the reduced-order simulation model into a first polynomial containing high-order frequency terms and a second polynomial containing the sum of a constant term and a rational proper fraction;

[0016] Calculate the roots of the first polynomial equal to zero;

[0017] According to the first polynomial and the set of all its roots, calculate the set of coefficients corresponding to all roots;

[0018] According to each root and its corresponding coefficient, calculate the values of the RLC components corresponding to each root;

[0019] Place the calculated RLC components into the circuit topologies corresponding to each root to construct the RLC circuit corresponding to the first polynomial;

[0020] Construct the RLC circuit corresponding to the second polynomial, and connect the RLC circuit corresponding to the first polynomial in parallel with the RLC circuit corresponding to the second polynomial to implement the transfer function of the reduced-order simulation model.

[0021] Further, the step of splitting the transfer function of the reduced-order simulation model into a first polynomial containing high-order frequency terms and a second polynomial containing the sum of a constant term and a rational proper fraction is carried out using the following model:

[0022] H(s) = H1(s) + H2(s)

[0023]

[0024]

[0025] Wherein, H(s) is the transfer function, H1(s) is the first polynomial containing high-order terms of frequency, H2(s) is the second polynomial containing the sum of the constant term and the rational proper fraction, a i , i = 0,..., N are the coefficients and orders of the polynomial expansion, c k and p k , k = 1,..., M are the residues and poles of the rational proper fraction.

[0026] Furthermore, the first polynomial can be expressed as follows:

[0027]

[0028] Wherein, N c is the number of pairs of conjugate complex roots, N is the total number of roots, α k and are a pair of conjugate complex roots, from 2N c +1 to N are used to label the real roots, N - 2N c is the number of real roots, α l is the l-th real root.

[0029] Furthermore, the step of calculating the set of coefficients corresponding to all roots according to the first polynomial and the set of all its roots further includes:

[0030] For the n-th root, calculate its corresponding coefficient according to the following formula,

[0031]

[0032] Wherein, H′1(s) is the polynomial obtained by differentiating the first polynomial with respect to s, H′1(α n ) is the value of the polynomial after differentiating the first polynomial at α n , N is the total number of roots of the first polynomial equal to zero, α n is the n-th root of the first polynomial equal to zero, β n is the coefficient corresponding to the n-th root of the first polynomial.

[0033] Furthermore, the coefficient set is

[0034]

[0035] Wherein, B is the coefficient set, β k and is the coefficient corresponding to the k-th pair of conjugate complex roots, β l is the coefficient corresponding to the l-th real root, N c is the number of pairs of conjugate complex roots, and N is the total number of roots.

[0036] Further, the step of calculating the RLC element values corresponding to each root according to each root and its corresponding coefficient further includes:

[0037] For the real root and its corresponding coefficient, the corresponding RLC elements include a resistor and a capacitor, and the values of the corresponding resistor and capacitor are calculated according to the following formula:

[0038]

[0039] where C l , R l are the capacitor and resistor corresponding to the l-th real root, α l , β l are the root and coefficient corresponding to the l-th real root.

[0040] Further, the step of calculating the values of the RLC elements corresponding to each root according to each root and its corresponding coefficient further includes:

[0041] For the conjugate complex root and its corresponding coefficient, the corresponding RLC elements include a first resistor, a second resistor, a capacitor, and an inductor, and the values of the first resistor, the second resistor, the capacitor, and the inductor are calculated according to the following formula:

[0042]

[0043]

[0044] where C k , R 1k , R 2k , L k are the capacitor, the first resistor, the second resistor, and the inductor corresponding to the k-th pair of conjugate complex roots; β kr = Re(β k ), α kr = Re(α k ), k = 1, 2,..., N c ; N c is the number of pairs of conjugate complex roots; α k and are the k-th pair of conjugate complex roots; β k and are the coefficients corresponding to the k-th pair of conjugate complex roots.

[0045] Further, the step of placing the calculated RLC elements corresponding to each root and coefficient into the corresponding circuit topology to construct the RLC circuit corresponding to the first polynomial further includes:

[0046] For each real root, place the resistor and capacitor in parallel corresponding to it into the circuit topology corresponding to the real root;

[0047] For each pair of conjugate complex roots, connect the corresponding first resistor in series with the inductor, and connect them in parallel with the second resistor and capacitor respectively, and place them into the circuit topology corresponding to the conjugate complex roots;

[0048] Connect the circuit topologies corresponding to all the conjugate complex roots and the circuit topologies corresponding to the real roots in series in turn to form the RLC circuit corresponding to the first polynomial.

[0049] To achieve the above object, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor is used to execute the computer program stored in the memory to implement the method for implementing a transfer function using an RLC circuit as described above.

[0050] To achieve the above object, the present invention also provides a computer-readable storage medium, in which at least one instruction is stored, and the instruction is loaded and executed by the processor to implement the method for implementing a transfer function using an RLC circuit as described above.

[0051] The method for implementing a transfer function using an RLC circuit provided by the present invention has the following beneficial effects compared with the prior art:

[0052] The present invention splits the transfer function of the simulation model order reduction into a first polynomial containing high-order frequency terms and a second polynomial containing a constant term and the sum of a rational proper fraction. The first polynomial and the second polynomial are respectively implemented using an RLC circuit, and then the two parts of the circuit are connected in parallel to implement the transfer function. This method supplements the circuit implementation process of the transfer function containing high-order frequency terms, so that more types of transfer functions can be circuit-characterized by an RLC.

[0053] Other features and advantages of the present invention will be described in the following specification, and, in part, will be obvious from the specification, or will be understood by implementing the present invention. Description of the Drawings

[0054] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention. In the drawings:

[0055] Figure 1Flowchart of a method for implementing a transfer function using an RLC circuit according to an embodiment of the present invention;

[0056] Figure 2 Schematic diagram of a circuit structure corresponding to a real root according to an embodiment of the present invention;

[0057] Figure 3 Schematic diagram of a circuit structure corresponding to a conjugate complex root according to an embodiment of the present invention;

[0058] Figure 4 Schematic diagram of an RLC circuit structure corresponding to the H1(s) term according to an embodiment of the present invention;

[0059] Figure 5 Schematic diagram of an RLC circuit structure corresponding to the H1(s) term according to another embodiment of the present invention;

[0060] Figure 6 Schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed implementation manners

[0061] The following describes the preferred embodiments of the present invention with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not used to limit the present invention.

[0062] The embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. On the contrary, these embodiments are provided to more thoroughly and completely understand the present invention. It should be understood that the drawings and embodiments of the present invention are only for exemplary purposes and are not used to limit the protection scope of the present invention.

[0063] The term "including" and its variations used herein are open-ended, that is, "including but not limited to". The term "based on" is "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". The relevant definitions of other terms will be given in the following description.

[0064] It should be noted that the concepts of "first", "second", etc. that may be mentioned in the present invention are only used to distinguish different devices, components or parts, and are not used to limit the order or interdependence of the functions performed by these devices, components or parts.

[0065] It should be noted that the modifications of "one" and "multiple" that may be mentioned in the present invention are illustrative rather than restrictive. Those skilled in the art should understand that unless otherwise clearly specified in the context, it should be understood as "one or more". "Multiple" should be understood as two or more.

[0066] Figure 1 FIG. is a flowchart of a method for implementing a transfer function using an RLC circuit according to an embodiment of the present invention. The embodiments of the present invention will be described in detail below with reference to Figure 1 the embodiments of the present invention will be described in detail.

[0067] In step 101, the transfer function H(s) of the reduced-order simulation model is split into an H1(s) term containing high-order frequency terms and an H2(s) term containing a constant term and the sum of rational proper fractions.

[0068] In the embodiments of the present invention, the transfer function between the input and output of one port is:

[0069]

[0070] Here, H(s) is the transfer function, which is the circuit admittance in this patent, that is, the input end is voltage and the output end is current. Admittance is the general term for conductance and susceptance. Like impedance, admittance is also a complex number, consisting of a real part (conductance) and an imaginary part (susceptance). s = j2πf, where f is the frequency. a i , i = 0,..., N are the coefficients and orders of the polynomial expansion. And c k and p k , k = 1,..., M are the residues and poles of the rational proper fraction.

[0071] This transfer function H(s) is split into two terms:

[0072] H(s) = H1(s) + H2(s) (4)

[0073] Where:

[0074]

[0075]

[0076] H1(s) contains high-order frequency terms (second order and above), and the coefficients a corresponding to each term i, where \(i = 0,\cdots,N\) are real numbers. \(H_2(s)\) contains a constant term and a sum of some rational proper fractions. Since \(H_2(s)\) can already be represented by an RLC circuit using existing methods (please refer to reference [1]), it will not be discussed further in this patent. This patent discusses how to implement the \(H_1(s)\) term using an RLC circuit. The two parts of the circuits \(H_1(s)\) and \(H_2(s)\) can be combined in parallel to form the final \(H(s)\).

[0077] In step 102, calculate the roots of the polynomial \(H_1(s)=0\).

[0078] In an embodiment of the present invention, \(H_1(s)\) is an \(N\)-th order polynomial in terms of the variable \(s\). When calculating the roots of the polynomial \(H_1(s)=0\), since the coefficients of \(H_1(s)\) are real numbers, the \(N\) roots obtained are either real numbers or conjugate complex roots. After obtaining the roots of the polynomial, \(H_1(s)\) can be written as:

[0079]

[0080] Here, \(N\) c is the number of pairs of conjugate complex roots, \(\alpha\) k and are the \(k\)-th pair of conjugate complex roots. From \(2N\) c + 1 to \(N\) are used to label the real roots, and the number of real roots is \(N - 2N\) c , \(\alpha\) l is the \(l\)-th real root. The total number of roots is \(N\). The set of all roots \(\alpha\) l , \(l = 2N\) c + 1,\(\cdots\), \(N\)}.

[0081] In step 103, calculate the coefficient set \(B\) according to \(H_1(s)\) and the set of roots \(R\).

[0082] In an embodiment of the present invention, each element in \(B\) has a one-to-one correspondence with each element in \(R\). For the \(n\)-th root, its corresponding coefficient can be calculated as:

[0083]

[0084] where \(H_1^{\prime}(s)\) is the polynomial obtained by differentiating \(H_1(s)\) with respect to \(s\), and \(H_1^{\prime}(\alpha\) n ) is the value of the differentiated polynomial at \(\alpha\) n , and \(\alpha\) n is the \(n\)-th root of \(H_1(s)=0\). The calculation here does not distinguish between real roots and complex roots, and can be calculated using the unified formula (8).

[0085] Specifically, for conjugate complex roots, their corresponding coefficients are also conjugate; for real roots, their corresponding coefficients are real. The coefficient set \(B\) is:

[0086]

[0087] Among them, β k and are the coefficients corresponding to the k-th pair of conjugate complex roots, and β l is the coefficient corresponding to the l-th real root.

[0088] In step 104, calculate the RLC components corresponding to each root and its corresponding coefficient.

[0089] In the embodiments of the present invention, the calculation of this process needs to process conjugate complex roots and real roots separately.

[0090] For the l-th real root, its corresponding root is α l and the coefficient is β l , corresponding to it with a resistor and a capacitor. The resistor and capacitor to be calculated are:

[0091]

[0092] For the k-th pair of complex conjugate roots, its corresponding roots are α k and The corresponding coefficients are β k and Corresponding to it with a total of four components: two resistors, an inductor, and a capacitor. The corresponding RLC can be calculated as:

[0093]

[0094]

[0095] Among them,

[0096] In step 105, construct the circuit topologies corresponding to the real roots and conjugate complex roots.

[0097] In the embodiments of the present invention, for real roots and conjugate complex roots, different circuit topologies are adopted, and the components corresponding to each root and coefficient calculated above are placed in their respective corresponding circuit topologies. The circuit topology corresponding to the real root is to connect the resistor and capacitor corresponding to the real root in parallel. For example, for the l-th real root, its corresponding circuit is the corresponding capacitor C l and resistor R l connected in parallel, as shown in Figure 2 , where For N - 2N c real roots, a total of N - 2N c such circuits are formed.

[0098] Figure 3Schematic diagram of the circuit topology structure corresponding to the conjugate complex root according to an embodiment of the present invention. Figure 3 As shown, the circuit topology corresponding to the kth pair of conjugate complex roots is to put its corresponding resistor R 1k and inductor L k After connecting in series, the corresponding resistor R 2k , capacitor C k Parallel. N c The conjugate complex roots can be constructed into N c A circuit like this.

[0099] In step 106, an RLC circuit corresponding to the item H1(s) and an RLC circuit corresponding to the item H2(s) are constructed.

[0100] In the embodiment of the present invention, the N obtained in step 105 based on the conjugate complex root is c circuits and N-2N constructed from real roots c The circuits are connected in series to form the RLC circuit corresponding to the H1(s) item, as shown in Figure 4 shown.

[0101] In the embodiment of the present invention, the RLC circuit corresponding to the item H2(s) is constructed according to reference [1].

[0102] The RLC circuit corresponding to the H1(s) term and the RLC circuit corresponding to the G2(s) term are connected in parallel to obtain an RLC circuit representing the transfer function H(s).

[0103] The present invention provides a method for implementing a transfer function using an RLC circuit. The method splits the reduced-order transfer function H(s) of a simulation model into an H1(s) term containing a high-order frequency term and an H2(s) term containing a constant term and the sum of rational proper fractions. The H1(s) and H2(s) terms are then implemented using RLC circuits, respectively. The H1(s) and H2(s) circuits are then connected in parallel to form the final H(s). The present invention focuses on implementing the H1(s) term using an RLC circuit, achieving RLC circuit equivalence for transfer functions containing high-order frequency terms, and thus enabling the transfer function reduction method to be used in a wider range of applications.

[0104] The following uses a specific expression of H1(s) as an example to describe the circuit implementation process using the method of the present invention. Assume:

[0105] H1(s)=2s 4 +s 3 -s 2 +0.5s

[0106] Execute step 102 to calculate the root of the polynomial H1(s) = 0, that is, calculate 2s 4 +s 3-s 2 The roots of +0.5s = 0. Calculated as follows:

[0107] α1 = 0.3174 - 0.3458j

[0108]

[0109] α3 = 0, α4 = -1.1348

[0110] Among them, α1 and are a pair of conjugate complex roots of the polynomial 2s 4 +s 3 -s 2 +0.5s = 0, and α3, α4 are real roots.

[0111] Execute step 103. Calculate the coefficient set B according to H1(s) and the set of roots R. According to formula (8), it can be calculated as follows:

[0112] β1 = -0.9011 + 0.5025j

[0113]

[0114] β3 = 2.0, β4 = -0.1977

[0115] In this way, the coefficient set β l , l = 3, 4} is formed.

[0116] Execute step 104. Calculate the resistors and capacitors corresponding to each root and coefficient. Among them, for the conjugate complex roots and its corresponding coefficient Use formula (10) to calculate as follows:

[0117] R 11 = 5.8657

[0118] R 21 = 14.4758

[0119] L1 = -11.4954

[0120] C1 = -0.5549

[0121] For the two real roots, use formula (9) to calculate as follows:

[0122] C3 = 0.5, R3 = ∞

[0123] C4 = -5.0572, R4 = -0.1743

[0124] Here, R3 = ∞ indicates that in the circuit corresponding to this real root, there is only a capacitor and no resistor. That is, the resistor path is an open circuit. Note that the calculated RLC here may be negative.

[0125] Execute steps 105 and 106 to construct the RLC circuit corresponding to the H1(s) term, that is, according to the resistors, inductors, and capacitors obtained from the above calculations, place them in the RLC circuits corresponding to the real roots and conjugate complex roots, and connect these circuits in series to form an RLC circuit representing H1(s) = 2s 4 + s 3 - s 2 + 0.5s, as Figure 5 shown. R 11 is connected in series with L1 and then in parallel with R 21 and C1 to form an RLC circuit corresponding to two conjugate complex roots. C3 is connected in series to the parallel combination of C4 and R4 to form a circuit corresponding to two real roots. Thus, these three parts of the circuits are connected in series in turn to form the RLC circuit corresponding to the H1(s) term, completing the process of implementing the H1(s) term in the transfer function using the RLC circuit.

[0126] In the embodiments of the present invention, in order to verify the correctness of the circuit, an AC analysis (alternating current analysis, mainly capable of calculating frequency-related characteristics) is performed on the circuit as Figure 5 shown. Calculate H1(s) at 1000 frequency points in the frequency range of 0 - 10. Its relative error is at the order of magnitude of 10 -12 , indicating the correctness of the circuit model.

[0127] In the embodiments of the present invention, an electronic device is also provided. Figure 6 For the structural schematic diagram of the electronic device according to the embodiments of the present invention, as Figure 6 shown, the electronic device of the present invention includes a processor 601 and a memory 602. Among them,

[0128] The memory 602 stores a computer program. When the computer program is read and executed by the processor 601, it executes the steps in the method embodiment of implementing the transfer function using the RLC circuit as described above.

[0129] In the embodiments of the present invention, a computer-readable storage medium is also provided. The computer-readable storage medium stores a computer program. Among them, the computer program is set to execute the steps in the method embodiment of implementing the transfer function using the RLC circuit as described above when running.

[0130] In this embodiment, the computer-readable storage medium may include, but is not limited to: various media such as USB flash drives, read-only memory (ROM), random access memory (RAM), external hard drives, magnetic disks, or optical discs that can store computer programs.

[0131] Those of ordinary skill in the art can understand that the foregoing are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for implementing a transfer function using an RLC circuit, characterized in that, Including: Splitting the transfer function for reducing the order of the simulation model into a first polynomial including high-order terms of frequency and a second polynomial including a constant term and the sum of a rational proper fraction; Calculating the roots where the first polynomial equals zero; Calculating the set of coefficients corresponding to all the roots according to the first polynomial and the set of all its roots; Calculating the values of the RLC elements corresponding to each root according to each root and its corresponding coefficient; Putting the calculated RLC elements into the circuit topologies corresponding to each root to construct the RLC circuit corresponding to the first polynomial; Constructing the RLC circuit corresponding to the second polynomial and paralleling the RLC circuit corresponding to the first polynomial with the RLC circuit corresponding to the second polynomial to implement the transfer function for reducing the order of the simulation model; The step of splitting the transfer function for reducing the order of the simulation model into a first polynomial including high-order terms of frequency and a second polynomial including a constant term and the sum of a rational proper fraction is carried out by using the following model: H(s) = H1(s) + H2(s) where \(H(s)\) is the transfer function, \(H_1(s)\) is the first polynomial containing high-order terms of frequency, \(H_2(s)\) is the second polynomial containing the constant term and the sum of rational proper fractions, \(a\) i , \(i = 0,\cdots,N\), are the coefficients and orders of the polynomial expansion, \(c\) k and \(p\) k , \(k = 1,\cdots,M\) are the residues and poles of the rational proper fraction, \(s = j2\pi f\), \(f\) is the frequency, and \(j\) is the imaginary unit; The step of putting the calculated RLC elements into the circuit topologies corresponding to each root to construct the RLC circuit corresponding to the first polynomial further includes: For each real root, putting the resistor and capacitor corresponding to it in parallel into the circuit topology corresponding to the real root; For each pair of conjugate complex roots, connecting the first resistor corresponding to it in series with the inductor and respectively connecting them in parallel with the second resistor and the capacitor, and putting them into the circuit topology corresponding to the conjugate complex roots; Connecting the circuit topologies corresponding to all the conjugate complex roots and the circuit topologies corresponding to the real roots in series in sequence to form the RLC circuit corresponding to the first polynomial.

2. The method for implementing a transfer function using an RLC circuit according to claim 1, wherein The first polynomial is expressed as follows: where N c is the number of pairs of conjugate complex roots, N is the total number of roots, α k and are a pair of conjugate complex roots, from 2N c +1 to N are used to label the real roots, N - 2N c is the number of real roots, α l is the l-th real root, s = j2πf, f is the frequency, and j is the imaginary unit.

3. The method for implementing a transfer function using an RLC circuit according to claim 1, characterized in that, The step of calculating the set of coefficients corresponding to all the roots according to the first polynomial and the set of all its roots further includes: For the nth root, calculating its corresponding coefficient according to the following formula Among them, H′1(s) is the polynomial obtained by differentiating the first polynomial with respect to s, and H′1(α n ) is the value of the polynomial after differentiating the first polynomial at α n . N is the total number of roots for which the first polynomial equals zero, α n is the n-th root for which the first polynomial equals zero, and β n is the coefficient corresponding to the n-th root of the first polynomial.

4. The method for implementing a transfer function using an RLC circuit according to claim 3, wherein The coefficient set is where B is a set of coefficients, β k and are the coefficients corresponding to the k-th pair of conjugate complex roots, β l is the coefficient corresponding to the l-th real root, N c is the number of pairs of conjugate complex roots, and N is the total number of roots.

5. The method for implementing a transfer function using an RLC circuit according to claim 1, characterized in that, The step of calculating the values of the RLC elements corresponding to each root according to each root and its corresponding coefficient further includes: For the real root and its corresponding coefficient, the corresponding RLC elements include a resistor and a capacitor, and calculating the values of the corresponding resistor and capacitor according to the following formula: Among them, C l , R l are the capacitance and resistance corresponding to the l-th real root, and α l , β l are the root and coefficient corresponding to the l-th real root.

6. The method for implementing a transfer function using an RLC circuit according to claim 1, characterized in that, The step of calculating the values of the RLC elements corresponding to each root according to each root and its corresponding coefficient further includes: For the conjugate complex root and its corresponding coefficient, the corresponding RLC elements include a first resistor, a second resistor, a capacitor and an inductor, and calculating the values of the first resistor, the second resistor, the capacitor and the inductor according to the following formula: Among them, C k , R 1k , R 2k , L k are the capacitance, the first resistor, the second resistor, and the inductor corresponding to the k-th pair of conjugate complex roots; β kr = Re(β k ), α kr = Re(α k ), k = 1, 2, …, N c ; N c is the number of pairs of conjugate complex roots; α k and are the k-th pair of conjugate complex roots; β k and are the coefficients corresponding to the k-th pair of conjugate complex roots.

7. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor is used to execute the computer program stored in the memory to implement the method for implementing a transfer function by using an RLC circuit according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, At least one instruction is stored in the storage medium, and the instruction is loaded and executed by the processor to implement the method for implementing a transfer function by using an RLC circuit according to any one of claims 1 to 6.

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