General method for calculating time-domain transient response of arbitrary circuit

Abstract

The application provides a general calculation method for time-domain transient response of an arbitrary circuit, and belongs to the field of circuit analysis and signal processing. The method comprises the following steps: firstly, an arbitrary circuit containing elements of any type is expressed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit, and direct current operating point analysis and alternating current linear or nonlinear steady-state sweep analysis are performed on the circuit to obtain complex amplitude values of each node voltage and branch current in the circuit at each frequency point in a sweep range; then, complex amplitude values of voltage of a certain node or current of a certain branch are arranged in order of sweep frequency from small to large to obtain a frequency-domain transfer function sequence of the node voltage or the branch current, and inverse discrete Fourier transform is performed on the sequence to obtain an impulse response of the node voltage or the branch current; and finally, actual excitation signals of the circuit are convoluted with the impulse response to obtain a transient response of the node voltage or the branch current.

Description

Technical Field

[0001] This invention belongs to the field of circuit analysis and signal processing, and more specifically, relates to a general method for calculating the time-domain transient response of any circuit. Background Technology

[0002] Calculating transient response is a crucial step in the analysis and design of circuit systems, especially when dealing with complex lumped-parameter and distributed-parameter circuits. Lumped-parameter circuits consist of lumped components such as independent voltage / current sources, controlled voltage / current sources, resistors, capacitors, and inductors. Distributed-parameter circuits include planar or three-dimensional circuits, including microwave transmission lines and their discontinuous structures; their component characteristics change with frequency, and their expressions or models can only be established in the frequency domain. Transient response describes the transition process of a circuit from one steady state to another, playing a key role in ensuring the normal operation and function of the circuit.

[0003] In existing technologies, the calculation of transient response typically relies on a series of mathematical analyses and computational methods, such as Laplace transform, Fourier analysis, and numerical integration techniques. These methods work well for simple lumped parameter circuits, but they become unsuitable or computationally prohibitive when dealing with complex multiport circuits, especially those containing frequency-varying distributed parameter elements.

[0004] The conventional transient analysis method is called SPICE transient analysis. Based on Kirchhoff's voltage and current laws, it establishes a system of time-domain equations (algebraic or ordinary differential equations) for the circuit. This requires that the components in the circuit be lumped-parameter components, and that their parameters do not change with frequency. Examples include linear or nonlinear resistors, inductors, capacitors, independent voltage / current sources, and controlled voltage / current sources. The system of time-domain equations is then solved step-by-step using numerical integration. Therefore, SPICE transient analysis cannot handle linear or nonlinear circuits containing transmission lines or their discontinuous structures forming frequency-varying components, multi-port S-parameter matrix components, or other dispersive lossy components. Summary of the Invention

[0005] To address the limitations of conventional transient analysis methods in handling circuits containing frequency-varying components, this invention incorporates convolution operations into the AC steady-state response calculation method, forming a universal calculation method capable of handling the transient response of circuit systems containing any type of components.

[0006] When all components in the circuit to be analyzed are linear components, the method includes the following steps:

[0007] Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit. The circuit to be analyzed may contain any lumped parameter linear element, distributed parameter linear element, multi-port linear network element, and excitation voltage source or excitation current source s(t) of arbitrary waveform;

[0008] Step 2 involves performing DC operating point analysis and AC small-signal sweep frequency analysis on the equivalent circuit described above. This yields the complex amplitude values ​​of each node voltage and branch current within the sweep frequency range of 0 to N·Δω at various frequency points n·Δω, where n = 0, 1, 2, ..., N. AC small-signal sweep frequency analysis is a type of AC linear steady-state response analysis. During the sweep frequency analysis, all excitation sources in the circuit are set as sinusoidal voltage or current sources with unit amplitude, their frequencies being the sweep frequency values, and Δω being the angular frequency step size of the sweep frequency analysis.

[0009] Step 3: Arrange the complex amplitude values ​​of a node voltage or a branch current obtained from the above frequency sweep analysis according to the frequency sweep sequence to obtain the frequency domain transfer function sequence H(ω) of the node voltage or branch current: H(0), H(Δω), H(2Δω), ..., H(n·Δω), ..., H(N·Δω);

[0010] Step 4: Perform discrete inverse Fourier transform on the frequency domain transfer function sequence H(ω) to obtain the impulse response h(t) of the node voltage (or branch current);

[0011] Step 5: Convolve the waveform function s(t) of the actual excitation voltage source or excitation current source of the circuit to be analyzed with the impulse response h(t) obtained in step 4 to obtain the transient response y(t) of the node voltage or branch current.

[0012] Furthermore, the angular frequency step size Δω in the steady-state response analysis of swept-frequency AC determines the frequency resolution of the transient response, while the time resolution of the transient response y(t) is... The sampling frequency of y(t) is Therefore, the waveform function s(t) of the actual excitation signal of the circuit to be analyzed must also be expressed in terms of f. s After sampling, perform convolution calculations as described in step 5 above.

[0013] Furthermore, if the circuit to be analyzed contains components composed of uniform transmission lines, the component can be represented as a frequency-varying lumped parameter equivalent circuit model containing impedance and admittance components that vary with frequency for AC steady-state response analysis. Alternatively, its impedance matrix, admittance matrix, or cascade matrix can be obtained from its scattering parameter matrix and then substituted into the circuit to be analyzed to establish a set of algebraic equations for AC steady-state response analysis of the circuit.

[0014] Furthermore, if the circuit to be analyzed contains a multi-port microwave network composed of transmission lines and their non-uniform structures, the scattering parameter matrix of these microwave networks can be extracted using a three-dimensional electromagnetic field numerical calculation method or measured using a vector network analyzer, and thus represented as a multi-port SnP element. Then, the scattering parameter matrix of this SnP element is converted into an impedance matrix, admittance matrix, or cascade matrix, and then substituted into the circuit to be analyzed to establish a set of algebraic equations for the AC steady-state response analysis of the circuit.

[0015] For example, the multi-port S-parameter matrix of an actual microwave circuit layout or three-dimensional structure can be calculated using the method of moments or the finite element method. The specific process for frequency domain steady-state response analysis is as follows:

[0016] (1) Based on the characteristic impedance Z0 of the network port, the scattering parameter matrix corresponding to the SnP element is converted into an impedance matrix or admittance matrix. The impedance matrix equation of the multi-port network is as follows:

[0017]

[0018] in, These represent the port voltage column vector, port current column vector, and network impedance matrix of the multiport network, respectively.

[0019] (2) Based on the termination element at each port of the multi-port network, determine the equations satisfied by the port voltage and port current at each port. For example, the port voltage and port current at port i. The termination circuit equations that are satisfied are:

[0020]

[0021] in, Z represents the electromotive force of the external voltage source connected to the i-th port. Li This indicates the internal resistance of the external voltage source. If no external voltage source is connected to this port, then... Therefore, the termination circuit equations for a multiport network are:

[0022]

[0023] Right now:

[0024] (3) Substituting the above equation into the impedance matrix equation of the multiport network, we get:

[0025]

[0026] From this, the complex amplitude of the current or voltage at each port can be obtained:

[0027]

[0028]

[0029] Where, matrix [Y] = [Z] -1 Let be the admittance matrix of the multiport network, and [1] denote the identity matrix.

[0030] (4) Calculate the port voltage (or port current) at each frequency point n·Δω, n=0,1,2,...,N within the sweep frequency range 0~N·Δω using the above formula. Arrange the complex amplitude values ​​of the port voltage (or port current) in the order of the sweep frequency to obtain the frequency domain transfer function sequence H(ω) of the port voltage (or port current): H(0), H(Δω), H(2Δω), ..., H(n·Δω), ..., H(N·Δω). Perform a discrete inverse Fourier transform on it to obtain the impulse response h(t) of the port voltage or port current.

[0031] (5) The actual excitation signal s(t) is sampled at a frequency of Sampling is performed, and the convolution of the sampled sequence with h(t) is calculated to obtain the transient response of the port voltage (or port current).

[0032] For cases where multiple multiport networks are arbitrarily cascaded, the voltage and current of each port can be calculated using termination conditions and block circuit matrices.

[0033] When only the i-th port among the N ports of a multi-port network is connected to an external excitation source s i (t), where the internal resistance of the excitation source is Z. Li (t), and when the other ports are only terminated with loads, the following formula is used to calculate: Port current at time

[0034]

[0035] Then, the impulse response h(t) of the current (or port voltage) at each port is calculated using the inverse discrete Fourier transform. Finally, the convolution of s(t) and h(t) is calculated. This gives us the transient response of the port.

[0036] When multiple ports out of N ports have external excitation sources s i (t), the internal resistance of the excitation source is Z Li When (t), i = 1, 2, ..., N, then calculate the excitation source E connected only to the i-th port. i Port frequency domain response The impulse response h of the current or voltage at each port is obtained using the inverse discrete Fourier transform. (i)(t), and then calculate the transient response of the current or voltage at each port. Finally, the total transient response y(t) of the port current or voltage when all excitation sources are present is obtained by linear superposition:

[0037]

[0038] Among them, symbols This represents the convolution operation.

[0039] When the circuit to be analyzed contains nonlinear elements, the method includes the following steps:

[0040] Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit. The circuit to be analyzed may contain any lumped parameter linear element, distributed parameter linear element, multi-port linear network element, lumped parameter nonlinear element, and excitation voltage source or excitation current source s(t) of arbitrary waveform, etc. The lumped parameter nonlinear element is represented as a time-domain nonlinear volt-ampere characteristic function (VI function), or a time-domain nonlinear charge-voltage characteristic function (QV function), or a time-domain nonlinear flux linkage-current characteristic function (Ψ-I function), or a time-domain nonlinear transresistance characteristic function (RI function);

[0041] Step 2: Perform DC operating point analysis and sweep-frequency single-frequency harmonic balance analysis on the above equivalent circuit to obtain the DC complex amplitude H(0) and the m-th harmonic complex amplitude H at each frequency point n·Δω, n=0,1,2,...,N within the sweep-frequency range 0~N·Δω. n (m·n·Δω), m=1,2,...。 During the sweep frequency analysis, all excitation sources in the circuit are set as sinusoidal voltage sources or sinusoidal current sources with unit amplitude, and their frequencies are the sweep frequency values. Δω is the angular frequency step size of the sweep frequency analysis.

[0042] Step 3: Calculate the complex amplitude H of the voltage at a certain node or the current in a certain branch obtained from the above frequency-sweeping single-frequency harmonic balance analysis at the m-th harmonic of the fundamental frequency n·Δω. n (m·n·Δω), m=1,2,... are arranged in order of sweep frequency to obtain the frequency domain transfer function sequence H of the node voltage or branch current in the m-th harmonic band. m (ω): H(0), H1(m·Δω), H2(m·2Δω),…,H n (m·n·Δω), ..., H N (m·N·Δω), where m=1,2,...;

[0043] Step 4, perform a frequency domain transfer function sequence H m(ω) is used to perform a discrete inverse Fourier transform to obtain the impulse response h of the node voltage (or branch current) in the m-th harmonic frequency band. m (t);

[0044] Step 5: Compare the waveform function s(t) of the actual excitation voltage source or excitation current source of the circuit to be analyzed with the impulse response h obtained in step 4. m (t) By performing convolution operations, the transient response y of the node voltage or branch current in the m-th harmonic frequency band can be obtained. m (t).

[0045] Furthermore, the angular frequency step size Δω in the swept-frequency single-frequency harmonic balance analysis determines the transient response y of the m-th harmonic band. m The frequency resolution of (t) is m·Δω, while y m The time resolution of (t) is y m The sampling frequency of (t) is Therefore, the actual excitation signal s(t) of the circuit to be analyzed must also be expressed in terms of f. s The sampled data is used in step 5 to calculate the transient response y of the m-th harmonic frequency band. m (t).

[0046] Furthermore, if the circuit to be analyzed is a nonlinear circuit with multi-frequency signal excitation such as a frequency converter, containing a single-frequency local oscillator voltage source or current source, and single-frequency or bandpass modulation excitation sources of different frequencies, then the sweep-frequency single-frequency harmonic balance analysis in step 2 must be changed to a sweep-frequency dual-frequency or multi-frequency intermodulation wave balance analysis. The complex amplitudes of the fundamental, harmonic and intermodulation wave frequencies of the voltage at each node or the current in each branch of the circuit at each sweep frequency point are calculated, and the impulse response at the fundamental, harmonic and intermodulation wave frequency bands is calculated accordingly. Finally, the transient response of the circuit to be analyzed at the fundamental, harmonic or intermodulation wave frequency bands is calculated by convolving with the actual bandpass excitation signal s(t).

[0047] Furthermore, if the frequency response S of the reflection coefficient of the i-th port of the multi-port circuit to be analyzed is known... ii (f) Then, the time-domain reflection coefficient waveform Γ(t) of the port is calculated using the inverse discrete Fourier transform, and the input impedance waveform of the port can be calculated from this.

[0048]

[0049] The general calculation method for the time-domain transient response of any circuit in this invention has the following characteristics:

[0050] (1) It can handle circuits containing arbitrary lumped parameter linear elements, lumped parameter nonlinear elements, distributed parameter linear elements, multi-port network linear elements and excitation voltage sources or excitation current sources with arbitrary waveforms, and has extremely strong versatility.

[0051] (2) This method, based on frequency domain steady-state response calculation, discrete Fourier transform, and convolution operation, eliminates the limitation of conventional SPICE time-domain numerical integration transient response calculation methods, which can only handle linear or nonlinear circuits composed of lumped parameter elements. Furthermore, the calculation process is stable and reliable, avoiding the poor solution accuracy or even integration divergence and non-convergence issues often caused by poor selection of the integration step size in SPICE transient response calculations. In addition, for solving long-range transient response requirements of circuits, the computational load is significantly reduced compared to the SPICE transient response calculation method.

[0052] (3) It can be used for transmission channel transient characteristic simulation, signal integrity analysis, DDR high-speed data / clock simulation and field-circuit joint simulation combined with the method of moments or the finite element method. The method of moments or the finite element method is used to extract the equivalent network parameters of two-dimensional or three-dimensional structures such as circuit layout or planar / three-dimensional circuits, such as the scattering parameter matrix, and has strong applicability. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0054] Figure 1 This is a flowchart of a general calculation method for the time-domain transient response of any circuit provided by the present invention;

[0055] Figure 2 This invention provides a multi-port circuit with termination elements;

[0056] Figure 3 The present invention provides a reflective amplifier circuit containing distributed parameter elements, lumped parameter elements, and tunnel diodes;

[0057] Figure 4 This is the seven-port equivalent circuit diagram of the reflection amplifier circuit provided by the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0059] This invention provides a general method for calculating the time-domain transient response of any circuit. When all components in the circuit to be analyzed are linear, the method includes the following steps:

[0060] Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit. The circuit to be analyzed may contain any lumped parameter linear element, distributed parameter linear element, multi-port linear network element, and excitation voltage source or excitation current source s(t) of arbitrary waveform;

[0061] Step 2: Perform DC operating point analysis and AC small-signal sweep frequency analysis on the above equivalent circuit to obtain the complex amplitude values ​​of each node voltage and branch current in the circuit at each frequency point n·Δω, n=0,1,2,...,N within the sweep frequency range 0~N·Δω. AC small-signal sweep frequency analysis belongs to AC linear steady-state response analysis. During the sweep frequency analysis, all excitation sources in the circuit are set as sinusoidal voltage sources or sinusoidal current sources with unit amplitude, their frequencies being the sweep frequency values, and Δω being the angular frequency step size of the sweep frequency analysis.

[0062] Step 3: Arrange the complex amplitude values ​​of a node voltage or a branch current obtained from the above frequency sweep analysis according to the frequency sweep sequence to obtain the frequency domain transfer function sequence H(ω) of the node voltage or branch current: H(0), H(Δω), H(2Δω), ..., H(n·Δω), ..., H(N·Δω);

[0063] Step 4: Perform a discrete inverse Fourier transform on the frequency domain transfer function sequence H(ω) to obtain the impulse response h(t) of the node voltage (or branch current);

[0064] Step 5: Convolve the waveform function s(t) of the actual excitation voltage source or excitation current source of the circuit to be analyzed with the impulse response h(t) obtained in Step 4 to obtain the transient response y(t) of the node voltage or branch current.

[0065] When the circuit to be analyzed contains nonlinear elements, the method includes the following steps:

[0066] Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit. The circuit to be analyzed may contain any lumped parameter linear element, distributed parameter linear element, multi-port linear network element, lumped parameter nonlinear element, and excitation voltage source or excitation current source s(t) of arbitrary waveform, etc. The lumped parameter nonlinear element is represented as a time-domain nonlinear volt-ampere characteristic function (VI function), or a time-domain nonlinear charge-voltage characteristic function (QV function), or a time-domain nonlinear flux linkage-current characteristic function (Ψ-I function), or a time-domain nonlinear transresistance characteristic function (RI function);

[0067] Step 2: Perform DC operating point analysis and sweep-frequency single-frequency harmonic balance analysis on the above equivalent circuit to obtain the DC complex amplitude H(0) and the m-th harmonic complex amplitude H at each frequency point n·Δω, n=0,1,2,...,N within the sweep-frequency range 0~N·Δω. n (m·n·Δω), m=1,2,...。 During the sweep frequency analysis, all excitation sources in the circuit are set as sinusoidal voltage sources or sinusoidal current sources with unit amplitude, and their frequencies are the sweep frequency values. Δω is the angular frequency step size of the sweep frequency analysis.

[0068] Step 3: Calculate the complex amplitude H of the voltage at a certain node or the current in a certain branch obtained from the above frequency-sweeping single-frequency harmonic balance analysis at the m-th harmonic of the fundamental frequency n·Δω. n (m·n·Δω), m=1,2,... are arranged in order of sweep frequency to obtain the frequency domain transfer function sequence H of the node voltage or branch current in the m-th harmonic band. m (ω): H(0), H1(m·Δω), H2(m·2Δω),…,H n (m·n·Δω), ..., H N (m·N·Δω), where m=1,2,...;

[0069] Step 4, perform a frequency domain transfer function sequence H m (ω) is used to perform a discrete inverse Fourier transform to obtain the impulse response h of the node voltage (or branch current) in the m-th harmonic frequency band. m (t);

[0070] Step 5: Compare the waveform function s(t) of the actual excitation voltage source or excitation current source of the circuit to be analyzed with the impulse response h obtained in Step 4. m (t) By performing convolution operations, the transient response y of the node voltage or branch current in the m-th harmonic frequency band can be obtained. m (t).

[0071] Example:

[0072] Figure 1 This is a flowchart of a general calculation method for the time-domain transient response of any circuit provided by the present invention. Figure 2 This invention provides a multi-port circuit with termination elements. Figure 3 Taking the reflective amplifier circuit containing distributed parameter linear elements, lumped parameter linear elements, and a tunnel diode linearized at the DC bias point as an example, calculate its transient response. The specific calculation steps are as follows:

[0073] Step 1: The reflective amplifier circuit includes distributed parameter elements, namely microstrip lines TL1, TL2, TL3, TL4, and TL5; linear non-frequency-varying lumped parameter elements capacitors, namely C1, C2, L1, and L2; a non-linear tunnel diode TD; and an excitation voltage source Vs. The equivalent circuit transformation of this reflective amplifier circuit is as follows: the PCB microstrip circuit pattern composed only of distributed parameter elements microstrip lines (TL1, TL2, TL3, TL4, and TL5) is equivalent to a seven-port linear network. The linear non-frequency-varying lumped parameter elements C1, C2, L1, and L2, the frequency-varying tunnel diode TD linearized at the DC bias point, and the excitation voltage source Vs are used as the termination elements for each port of the above seven-port linear network, such as... Figure 4 As shown. The scattering parameter matrix S of the above seven-port microstrip circuit pattern is extracted using the method of moments in the frequency range of 0 GHz to 3 GHz. 7×7 (ω), represented as:

[0074]

[0075] Where 0≤ω≤2πf T Frequency interval Δω=2π·Δf, f T The GHz is 3GHz, and the Δf is 0.01GHz.

[0076] The scattering parameter matrix S is calculated according to the following formula. 7×7 (ω) is converted into the impedance matrix Z 7×7 (ω):

[0077] [z 7×7 (ω)]=([1]+[S 7×7 (ω)])([1]-[S 7×7 (ω)]) -1 ;

[0078]

[0079] Among them, [z 7×7 [ω] is the normalized impedance matrix, which is converted to a non-normalized impedance matrix [Z]. 7×7 (ω)]:

[0080] [Z 7×7(ω)]=[Z C (ω)][z 7×7 (ω)][Z C (ω)];

[0081] in, [Z C [ω] is the characteristic impedance matrix of the port transmission lines of the seven-port network:

[0082]

[0083] Z Ci Let represent the characteristic impedance of the transmission line at port i. The impedance matrix equation for this seven-port network is:

[0084]

[0085] Step 2: Convert the reflection amplifier circuit to be analyzed into a seven-port equivalent circuit including termination elements. The termination circuit equations for each port are as follows:

[0086]

[0087] in, Z represents the electromotive force of the external voltage source at the i-th port. Li This represents the external impedance at the i-th port. (Corresponding to...) Figure 4 The matrix expression for the above formula is:

[0088]

[0089] in, Z is the electromotive force of the excitation voltage source connected to port 1. S For its internal resistance, Z TD (ω) represents the impedance of the tunnel diode after linearization at the DC bias point, and its value varies only with frequency.

[0090] Substituting the above termination circuit equations into the impedance matrix equations of the seven-port network, we obtain the complex amplitudes of the currents at each port:

[0091]

[0092] Step 3: Arrange the complex amplitude values ​​of the current at each port in order of the sweep frequency to obtain the sampling point sequence H of the frequency domain transfer function of each port current. i (ω) is represented as follows:

[0093] H i (ω):[H i (0),H i (Δω),H i (2Δω),...,Hi [(300Δω)]i=1,2...,7

[0094] Step 4, sample the frequency domain transfer function's sampling point sequence H. i Performing a discrete inverse Fourier transform on (ω) yields the impulse response h of the current at each port. i (t), i = 1, 2, ..., 7.

[0095] Step 5, apply the electromotive force V of the actual excitation voltage source. S (t) at sampling frequency Perform sampling, and compare the sampled sequence with h i Convolution operations are performed on (t), i = 1, 2, ..., 7, to obtain the transient response y of the current at each port. i (t), i = 1, 2, ..., 7, is represented as follows:

[0096]

[0097] The above description is merely a preferred embodiment of the present invention, but the present invention should not be limited to the content disclosed in this embodiment and the accompanying drawings. Therefore, any equivalent or modified versions made without departing from the spirit of the present invention fall within the scope of protection of the present invention.

Claims

1. A general method for calculating the time-domain transient response of any circuit, characterized in that, Includes the following steps: Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit; the circuit to be analyzed includes arbitrary lumped parameter linear elements, distributed parameter linear elements, multi-port linear network elements, and excitation voltage sources or excitation current sources of arbitrary waveforms; Step 2: Perform DC operating point analysis and AC small signal sweep frequency analysis on the equivalent circuit to obtain the complex amplitude values ​​of each node voltage or branch current in the circuit to be analyzed at each frequency point n·Δω, n=0,1,2,...,N within the sweep frequency range 0~N·Δω; AC small-signal sweep frequency analysis belongs to AC linear steady-state response analysis. During the sweep frequency analysis, all excitation sources in the circuit to be analyzed are set as sinusoidal voltage sources or sinusoidal current sources with unit amplitude. The frequency of the excitation source is the sweep frequency value, and Δω is the angular frequency step size of the sweep frequency analysis. Step 3: Arrange the complex amplitude values ​​of the target node voltage or target branch current obtained from the frequency sweep analysis according to the sweep frequency order to obtain the frequency domain transfer function sequence H(ω) of the target node voltage or target branch current: H(0), H(Δω), H(2Δω), ..., H(n·Δω), ... and H(N·Δω); the target node voltage is any node voltage in the circuit to be analyzed, and the target branch current is any branch current in the circuit to be analyzed; Step 4: Perform discrete inverse Fourier transform on the frequency domain transfer function sequence H(ω) to obtain the impulse response h(t) of the target node voltage or the target branch current; Step 5: Perform convolution operation between the waveform function s(t) of the actual excitation voltage source or the actual excitation current source in the circuit to be analyzed and the impulse response h(t) obtained in step 4 to obtain the transient response y(t) of the target node voltage or the target branch current.

2. The general calculation method for the time-domain transient response of any circuit according to claim 1, characterized in that, The angular frequency step size Δω in the steady-state response analysis of swept-frequency AC determines the angular frequency resolution of the transient response, while the time resolution of the transient response y(t) is... The sampling frequency of y(t) is Accordingly, the waveform function s(t) of the actual excitation signal of the circuit to be analyzed is f s Sampling is performed for use in step 5 to compute the convolution.

3. The general calculation method for the time-domain transient response of any circuit according to claim 1, characterized in that, Also includes: If the circuit to be analyzed contains elements composed of uniform transmission lines, the elements composed of uniform transmission lines are represented as frequency-dependent lumped parameter equivalent circuit models containing impedance and admittance that vary with frequency for AC steady-state response analysis. Alternatively, the impedance matrix, admittance matrix, or cascade matrix can be obtained from the scattering parameter matrix of the elements composed of uniform transmission lines, and then substituted into the circuit to be analyzed to establish a system of algebraic equations for AC steady-state response analysis of the circuit.

4. The general calculation method for the time-domain transient response of any circuit according to claim 1, characterized in that, Also includes: If the circuit to be analyzed contains a multi-port microwave network composed of transmission lines and transmission line inhomogeneities, then for the multi-port microwave network, the scattering parameter matrix is ​​extracted using a three-dimensional electromagnetic field numerical calculation method or measured using a vector network analyzer, and represented as a multi-port SnP element. Then, the scattering parameter matrix of the SnP element is converted into an impedance matrix, admittance matrix, or cascade matrix, and then substituted into the circuit to be analyzed to establish a set of algebraic equations for the AC steady-state response analysis of the circuit.

5. The general calculation method for the time-domain transient response of any circuit according to claim 1, characterized in that, Also includes: If the frequency response S of the reflection coefficient of the i-th port of the multi-port circuit to be analyzed is known, ii (f) Then, the time-domain reflection coefficient waveform Γ(t) of the i-th port is calculated using the inverse discrete Fourier transform, and then the time-domain waveform of the input impedance of the i-th port is calculated: The characteristic impedance of the network port is Z0.

6. A general method for calculating the time-domain transient response of any circuit, characterized in that, Includes the following steps: Step 1: Represent the circuit to be analyzed as a frequency-dependent lumped parameter equivalent circuit or a behavioral model equivalent circuit; the circuit to be analyzed includes arbitrary lumped parameter linear elements, distributed parameter linear elements, multi-port linear network elements, lumped parameter nonlinear elements, and excitation voltage sources or excitation current sources of arbitrary waveforms; the lumped parameter nonlinear elements are represented as time-domain nonlinear volt-ampere characteristic functions, or time-domain nonlinear charge-voltage characteristic functions, or time-domain nonlinear flux linkage-current characteristic functions, or time-domain nonlinear transresistance characteristic functions; Step 2: Perform DC operating point analysis and sweep-frequency single-frequency harmonic balance analysis on the equivalent circuit to obtain the DC complex amplitude H(0) and the m-th harmonic complex amplitude H at each frequency point n·Δω, n=0,1,2,...,N within the sweep-frequency range 0~N·Δω of the circuit under analysis. n (m·n·Δω), m=1,2,...;During the frequency sweep analysis, all excitation sources in the circuit to be analyzed are set as sinusoidal voltage sources or sinusoidal current sources with unit amplitude. The frequency of the excitation source is the frequency value of each frequency sweep, and Δω is the angular frequency step size of the frequency sweep analysis. Step 3: Calculate the complex amplitude H of the target node voltage or target branch current obtained from the frequency sweep single-frequency harmonic balance analysis at the m-th harmonic of the fundamental frequency n·Δω. n (m·n·Δω), m=1,2,... are arranged in order of frequency sweep frequency to obtain the frequency domain transfer function sequence H of the target node voltage or target branch current in the m-th harmonic band. m (ω): H(0), H1(m·Δω), H2(m·2Δω),…,H n (m·n·Δω), ... and H N (m·N·Δω), where m=1,2,...; the target node voltage is any node voltage in the circuit to be analyzed, and the target branch current is any branch current in the circuit to be analyzed; Step 4, perform a frequency domain transfer function sequence H m (ω) is used to perform a discrete inverse Fourier transform to obtain the impulse response h of the target node voltage or target branch current in the m-th harmonic frequency band. m (t); Step 5: Compare the waveform function s(t) of the actual excitation voltage source or actual excitation current source in the circuit to be analyzed with the impulse response h obtained in Step 4. m (t) Perform convolution operation to obtain the transient response y of the target node voltage or target branch current in the m-th harmonic frequency band. m (t).

7. The general calculation method for the time-domain transient response of any circuit according to claim 6, characterized in that, The angular frequency step size Δω in swept-frequency single-frequency harmonic balance analysis determines the transient response y of the m-th harmonic band. m The angular frequency resolution of (t) is m·Δω, while y m The time resolution of (t) is y m The sampling frequency of (t) is Accordingly, the waveform function s(t) of the actual excitation signal of the circuit to be analyzed is f s Sampling is performed for calculating the transient response y of the m-th harmonic band in step 5. m (t).

8. The general calculation method for the time-domain transient response of any circuit according to claim 6, characterized in that, Also includes: If the frequency response S of the reflection coefficient of the i-th port of the multi-port circuit to be analyzed is known, ii (f) Then, the time-domain reflection coefficient waveform Γ(t) of the i-th port is calculated using the inverse discrete Fourier transform, and then the time-domain waveform of the input impedance of the i-th port is calculated: The characteristic impedance of the network port is Z0.

9. The general calculation method for the time-domain transient response of any circuit according to claim 6, characterized in that, Also includes: If the circuit to be analyzed is a nonlinear circuit with multi-frequency signal excitation such as a frequency converter, containing a single-frequency local oscillator voltage source or current source, and single-frequency excitation sources or bandpass modulation excitation sources of different frequencies, then the sweep-frequency single-frequency harmonic balance analysis in step 2 must be changed to a sweep-frequency dual-frequency or multi-frequency intermodulation wave balance analysis. The complex amplitudes of the fundamental, harmonic and intermodulation wave frequencies of each node voltage or branch current in the circuit to be analyzed at each sweep frequency point are calculated, and then the impulse response at the fundamental, harmonic and intermodulation wave frequency bands is calculated. Finally, the transient response of the circuit to be analyzed at the fundamental, harmonic or intermodulation wave frequency bands is calculated by convolving with the actual bandpass excitation signal s(t).

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