CN106934123A - A kind of circuit transient response computational methods based on recursive convolution - Google Patents

Abstract

A kind of circuit transient response computational methods based on recursive convolution, including step：(1) breakdown of transfer function H (s) is obtained, and determines the expression formula of excitation function h (t)；(2) based on input voltage V_in(t₀) and transfer function H (s) breakdown, carry out initial time t₀State variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton Raphson iteration；(3) based on last moment t_n‑1State variable V_out,i,j(t_n‑1) and current time t_nInput voltage V_in(t_n), carry out current time t_nState variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton Raphson iteration；(4) step (3) is repeated, until emulation end time.Circuit transient response computational methods based on recursive convolution of the invention, the basic thought calculated using recursive convolution, the characteristics of emulation with reference to transient circuit, sub-circuit or element to giving input voltage and transmission function, in circuit simulation, there is provided a kind of method of quick calculating output voltage.

Description

A kind of circuit transient response computational methods based on recursive convolution

Technical field

The present invention relates to simulation technology field, more particularly to a kind of circuit transient response meter based on recursive convolution Calculation method.

Background technology

In circuit simulation, Laplace conversion is a kind of wide variety of Integral Transformation Method.Become with Laplace and brought Description non-linear element or LTI circuit obtained by equation it is more simpler in form than the linear differential equation of time domain, It is directly perceived and be easy to computing.The voltage or current transformation changed commanders in time domain are become to frequency domain by Laplace, transmission function is then used Various computings and the operation on frequency domain are further realized, the result on frequency domain is obtained, this result is converted finally by convolution For the result in time domain is exported.

Fig. 1 is the flow chart of Laplace conversion process circuit signal in the prior art, X (s) and Y (s) difference table in Fig. 1 Show the input signal and output signal on frequency domain, H (s) represents transfer function.H (s) has the form of rational fraction, because All of linear circuit system can be represented with ODE：

Laplace conversion is carried out to ODE above, and assumes zero initial condition, obtain following formula：

a_nsⁿY(s)+a_n-1s^n-1Y(s)+…+a₀Y (s)=b_ms^mX(s)+b_m-1s^m-1X(s)+…+b₀X(s)

Therefore, Y (s)=H (s) X (s), wherein,

Fig. 2 is a kind of transfer process figure of H (s) expression formulas of ball bearing made in the prior art.

Due to, the product on frequency domain is equal to the convolution in time domain, therefore, the differential equation can be write as the shape of convolution in time domain Formula：

Wherein, h (t) is the excitation function in time domain, and computing formula is：H (t)=L^-1(H(s))。

When convolution is calculated, traditional convolution method has a main difficulty：In order to obtain moment t convolution and, it is necessary to from Zero moment is integrated to moment t, and convolutional calculation must carry out reflexed, movement, multiplication, addition, and these operate and cause convolution fortune It is extremely complex, it is difficult to stand so as to cause simulated time to be made us.Shen Lin and Ernest S.Kuh are in document 《Transient Simulation of Lossy Interconnect based on the recursive convolution formulation》(it is published in " EEE Transactions on Circuits＆Systems " periodical the 39th Volume o. 11th) in propose a kind of recursive convolution algorithm, this algorithm make use of a period of time when the convolution at current time is calculated The convolution results at quarter, so as to avoid this defect, improve computational efficiency.

And recursive convolution algorithm only considers first order pole situation, although, white for army building and Lin Zhenghui is in document《Multi-chip module is mutual The even recursive convolution method analysis of transient response》Many limit feelings are considered in (being published in " microelectronics " periodical the 5th phase of volume 30) Shape, and recursion result is given, but the method comparison is complicated, and it is less practical in large-scale circuit simulation.

Therefore, proposing a kind of new circuit transient response computational methods based on recursive convolution, numerical computations can be combined Technology, it is succinct, efficient, practical for the less feature of time step in circuit Transient, and convolution is quickly calculated, As problem demanding prompt solution.

The content of the invention

In order to solve the deficiency of prior art presence, it is an object of the invention to provide a kind of circuit based on recursive convolution Transient response computational methods, can combine numerical computation technology, for the less feature of time step in circuit Transient, letter Clean, efficient, practicality, and quickly calculate convolution.

To achieve the above object, the circuit transient response computational methods based on recursive convolution that the present invention is provided, including with Lower step：

(1) breakdown of transfer function H (s) is obtained, and determines the expression formula of excitation function h (t)；(2) based on input electricity Pressure V_in(t₀) and transfer function H (s) breakdown, carry out initial time t₀State variable V_out,i,j(t₀) and output voltage V_out (t₀) Newton-Raphson iteration；(3) based on last moment t_n-1State variable V_out,i,j(t_n-1) and current time t_n's Input voltage V_in(t_n), carry out current time t_nState variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton- Raphson iteration；(4) step (3) is repeated, until emulation end time.

Further, the breakdown of transfer function H (s) is described in step (1)：

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

Further, the expression formula of excitation function h (t) is described in step (1)：

Wherein,p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

Further, the formula of Newton-Raphson iteration is described in step (2)：

Subscript (k) represents the Newton-Raphson iteration of kth time,

Parameter H_ijDefined formula be：

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

Further, described in step (2) in Newton-Raphson iterative process, the initial time t₀State become Amount V_out,i,j(t₀) on input voltage V_in(t₀) derivativeAnd the initial time t₀Output voltage V_out (t₀) on input voltage V_in(t₀) derivativeDefined formula be：

Parameter H_ijDefined formula be：

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

Further, the formula of Newton-Raphson iteration is described in step (3)：

Subscript (k) represents the Newton-Raphson iteration of kth time,

Wherein, V_out,i,j(t_n-1) it is last moment t_n-1Newton-Raphson iteration in state in final step become Amount, Δ t_nIt is last moment t_n-1And current time t_nTime step,p_iIt is limit, k_ijIt is coefficient, n_iIt is pole Point p_iTuple, m is limit p_iSum.

Further, described in step (3) in Newton-Raphson iterative process, current time t_nNewton- The state variable of the kth step of Raphson iterationOn input voltageDerivativeAnd output VoltageOn input voltageDerivativeDefined formula：

Subscript (k) represents the Newton-Raphson iteration of kth time,

Wherein, Δ t_nIt is last moment t_n-1And current time t_nTime step,p_iIt is limit, k_ijIt is Coefficient, n_iIt is limit p_iTuple, m is limit p_iSum.

Circuit transient response computational methods based on recursive convolution of the invention, the basic think of calculated using recursive convolution Think, the characteristics of emulation with reference to transient circuit, sub-circuit or element to giving input voltage and transmission function, in circuit simulation In, there is provided a kind of method of quick calculating output voltage.

Other features and advantages of the present invention will be illustrated in the following description, also, the partly change from specification Obtain it is clear that or being understood by implementing the present invention.

Brief description of the drawings

Accompanying drawing is used for providing a further understanding of the present invention, and constitutes a part for specification, and with it is of the invention Embodiment together, for explaining the present invention, is not construed as limiting the invention.In the accompanying drawings：

Fig. 1 is the flow chart of Laplace conversion process circuit signal in the prior art；

Fig. 2 is a kind of transfer process figure of H (s) expression formulas of ball bearing made in the prior art；

Fig. 3 is according to the circuit transient response computational methods flow chart based on recursive convolution of the invention.

Specific embodiment

The preferred embodiments of the present invention are illustrated below in conjunction with accompanying drawing, it will be appreciated that preferred reality described herein Apply example to be merely to illustrate and explain the present invention, be not intended to limit the present invention.

The thinking of the circuit transient response computational methods based on recursive convolution of the invention is：First, in circuit simulation The decomposition of rational fraction is done before starting to transfer function, key parameter is obtained；Secondly, set in circuit simulation initial time and be input into The computing formula of voltage and output voltage；Then, when circuit simulation is to subsequent time, according to input voltage and transfer function, Output voltage is calculated using the method for recursive convolution；Finally, repeat above method and calculate output voltage, until emulation terminates.

Circuit transient response computational methods based on recursive convolution of the invention, the flow for being applied to circuit Transient is worked as In, as a part of dynamic implement therein, some parameters (such as input voltage V_in(t_n)) from other portions of circuit Transient Separately win and take.It is of the invention to be based on due to generally using the nonlinear circuit simulation system of Newton-Raphson solutions by iterative method The circuit transient response computational methods of recursive convolution are through among each step of Newton-Raphson iteration.In addition, Need to calculate Jacobi matrixes in Newton-Raphson iteration, the present invention correspondingly gives calculating output voltage on input The method of the derivative of voltage.Circuit transient response computational methods based on recursive convolution of the invention, by C Plus Plus in electricity Realized in the emulation of road.

Fig. 3 be according to the circuit transient response computational methods flow chart based on recursive convolution of the invention, below with reference to Fig. 3, to being described in detail for the circuit transient response computational methods based on recursive convolution of the invention.

In step 301, the breakdown of transfer function H (s) is obtained, and determine the expression formula of excitation function h (t)；

Before circuit simulation starts, transfer function H (s) is processed, so as in obtaining subsequent step, recursive calculation institute The relevant parameter and the explicit expression of excitation function h (t) for needing.

Transfer function H (s) is generally represented in the form of rational fraction or zero pole point, when the expression formula of transfer function H (s) ForWhen, H (s) is decomposed into following form：

Wherein, p_iIt is limit (p_iIt is real number or conjugate complex number), k_ijIt is coefficient, n_iIt is limit p_iTuple (n_iFor just whole Number)；M is limit p_iSum (m also be positive integer).

Known parameters k_ij、p_i、n_i, m, just can uniquely determine the breakdown of H (s).

The computational methods of H (s) breakdowns comparative maturity, by the algorithm commonly used, obtains above-mentioned parameter.

Obtain the breakdown of H (s), you can obtain the expression formula of excitation function h (t)：

Wherein,

In this step, excitation function h (t) of acquisition, for subsequent step in, convolution is calculated using recursive method Among process.

In step 302, based on input voltage V_in(t₀) and transfer function H (s) breakdown, carry out initial time t₀Shape State variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton-Raphson iteration, corresponding iterative formula is：

Wherein, subscript (k) represents the Newton-Raphson iteration of kth time, correspondingly,

It is initial time t₀Newton-Raphson iteration kth step state variable,

It is initial time t₀Newton-Raphson iteration kth step output voltage,

It is initial time t₀Newton-Raphson iteration kth step input voltage；

Parameter H_ijObtained by H (s), defined formula is：

During above-mentioned iteration, the value of k is k=0,1,2 ..., and t₀It is usually taken to be t₀=0.

In above-mentioned iterative process, initial time t₀Input voltage V_in(t₀), state variable V_out,i,j(t₀) and output electricity Pressure V_out(t₀) be all updated in each step of Newton-Raphson iteration.

Need to calculate related derivative in Newton-Raphson iteration, initial time t is given below₀State variable V_out,i,j(t₀) on input voltage V_in(t₀) derivativeAnd initial time t₀Output voltage V_out(t₀) on Input voltage V_in(t₀) derivativeDefined formula：

DerivativeAndAll keep constant in each step of Newton-Raphson iteration.

In step 303, based on last moment t_n-1State variable V_out,i,j(t_n-1) and current time t_nInput voltage V_in(t_n), carry out current time t_nState variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton-Raphson change In generation, corresponding iterative formula is：

Wherein, subscript (k) represents the Newton-Raphson iteration of kth time, correspondingly,

It is current time t_nNewton-Raphson iteration kth step state variable,

It is current time t_nNewton-Raphson iteration kth step output voltage,

It is current time t_nNewton-Raphson iteration kth step input voltage；

V_out,i,j(t_n-1) it is last moment t_n-1Newton-Raphson iteration in state variable in final step；

Δt_nIt is last moment t_n-1And current time t_nTime step.

During iteration, state variable V_out,i,j(t_n-1) in V_out,i,j-1(t_n-1), in limit p_iTuple n_i≥2 When, participate in the calculating in formula (1)；As limit p_iTuple n_iWhen=1, j-1=0, now state variable V_out,i,j-1(t_n-1) nothing Need to be calculated.

Formula (1) is according to current time t of the invention_nNewton-Raphson iteration kth step state variableIterative formula, be calculate output voltage key, the derivation of formula (1) is given below：

Output voltage is with the relation formula of input voltage：V_out(t)=h (t) * V_in(t),

Wherein, the computing formula of excitation function h (t) is：

In order to make it easy to understand, in following derivations, casting out subscript (k)：

Formula (3) is according to convolution derivation formula of the invention, to each single item and V in h (t)_inT () does convolution, as a result It is designated as state variable V_out,i,j(t)。

In above-mentioned derivation, due to time step Δ t in circuit simulation_nUsual very little, therefore cast out Δ t in formula_n Second order term and higher order, also do not lose precision while simplifying and calculating.Therefore, the transient state for nonlinear circuit is imitated Very, Newton-Raphson iteration is performed a plurality of times in each time step to be simplified, computational efficiency can be improved.

Section 3 integration in formula (3) in final result items does numerical approximation, obtains

Further, formula (3) is converted into formula (4),

Launched by Taylor, obtain approximate expression：

Bring above-mentioned approximate expression into formula (4), that is, obtain formula (1).

Formula (1) is the recurrence Relation of calculating each component of output voltage (state variable).Formula (1) shows, when current The output voltage at quarter is only relevant with the state variable of last moment and the input voltage at current time.Also, from the shape of formula (1) As can be seen that the recurrence relation of formula (1) is relatively simple in formula, amount of calculation is smaller.

Need to calculate related derivative in Newton-Raphson iteration, current time t is given below_nNewton- The state variable of the kth step of Raphson iterationOn input voltageDerivativeAnd output VoltageOn input voltageDerivativeDefined formula：

In above-mentioned iterative process, current time t_nInput voltage V_in(t_n), state variable V_out,i,j(t_n), output electricity Pressure V_out(t_n), state variable V_out,i,j(t_n) on input voltage V_in(t_n) derivativeAnd output voltage V_out (t_n) on input voltage V_in(t_n) derivativeAll it is updated in each step of Newton-Raphson iteration.

In step 304, step 303 is repeated, until emulation end time.

Circuit transient response computational methods based on recursive convolution of the invention, are calculating the output voltage at current time When, the input voltage and the state variable of last moment at current time need to be only utilized, calculated on local temporal, therefore meter Calculation amount is smaller.Also, the recursion method form that the present invention is given is simple, and the data of required storage are less, with calculating higher Efficiency and stronger practicality.

One of ordinary skill in the art will appreciate that：The foregoing is only the preferred embodiments of the present invention, and without In the limitation present invention, although being described in detail to the present invention with reference to the foregoing embodiments, for those skilled in the art For, it can still be modified to the technical scheme that foregoing embodiments are recorded, or which part technical characteristic is entered Row equivalent.All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., all should include Within protection scope of the present invention.

Claims (7)

1. a kind of circuit transient response computational methods based on recursive convolution, it is characterised in that comprise the following steps：

(1) breakdown of transfer function H (s) is obtained, and determines the expression formula of excitation function h (t)；

(2) based on input voltage V_in(t₀) and transfer function H (s) breakdown, carry out initial time t₀State variable V_out,i,j (t₀) and output voltage V_out(t₀) Newton-Raphson iteration；

(3) based on last moment t_n-1State variable V_out,i,j(t_n-1) and current time t_nInput voltage V_in(t_n), enter the trade Preceding moment t_nState variable V_out,i,j(t₀) and output voltage V_out(t₀) Newton-Raphson iteration；

(4) step (3) is repeated, until emulation end time.

2. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (1) Described in the breakdown of transfer function H (s) be：

$H\left(s\right)=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}\frac{k_{ij}}{{(s-p_i)}^j}$

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

3. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (1) Described in the expression formula of excitation function h (t) be：

$h\left(t\right)=L^{-1}\left(H\right)=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}{\tilde{k}}_{ij}{t}^{j-1}{e}^{p_{i}t}$

Wherein,p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

4. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (2) Described in the formula of Newton-Raphson iteration be：

$V_{out,i,j}^{\left(k\right)}\left(t_0\right)=H_{ij}{V}_{in}^{\left(k\right)}\left(t_0\right)$

$V_{out}^{\left(k\right)}\left(t_0\right)=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}{V}_{out,i,j}^{\left(k\right)}\left(t_0\right)$

Subscript (k) represents the Newton-Raphson iteration of kth time,

Parameter H_ijDefined formula be：

$H_{ij}=\left\{\begin{array}{cc}\frac{k_{ij}}{{(-p_i)}^j}& (p_i\≠0)\\ 0& (p_i=0)\end{array}\right.$

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

5. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (2) Described in Newton-Raphson iterative process, the initial time t₀State variable V_out,i,j(t₀) on input voltage V_in(t₀) derivativeAnd the initial time t₀Output voltage V_out(t₀) on input voltage V_in(t₀) lead NumberDefined formula be：

$\frac{{\mathrm{dV}}_{out,i,j}\left(t_0\right)}{{\mathrm{dV}}_{in}\left(t_0\right)}=H_{ij}$

$\frac{{\mathrm{dV}}_{out}\left(t_0\right)}{{\mathrm{dV}}_{in}\left(t_0\right)}=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}{H}_{ij}$

Parameter H_ijDefined formula be：

$H_{ij}=\left\{\begin{array}{cc}\frac{k_{ij}}{{(-p_i)}^j}& (p_i\≠0)\\ 0& (p_i=0)\end{array}\right.$

Wherein, p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple；M is limit p_iSum.

6. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (3) Described in the formula of Newton-Raphson iteration be：

$V_{out,i,j}^{\left(k\right)}\left(t_n\right)=(1+p_i{\mathrm{\Δt}}_n)\[V_{out,i,j}\left(t_{n-1}\right)+(j-1){\mathrm{\Δt}}_n{V}_{out,i,j-1}\left(t_{n-1}\right)+{\left({\mathrm{\Δt}}_n\right)}^j{V}_{in}^{\left(k\right)}\left(t_n\right)\]$

$V_{out}^{\left(k\right)}\left(t_n\right)=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}{\tilde{k}}_{ij}{V}_{out,i,j}^{\left(k\right)}\left(t_n\right)$

Subscript (k) represents the Newton-Raphson iteration of kth time,

Wherein, V_out,i,j(t_n-1) it is last moment t_n-1Newton-Raphson iteration in state variable in final step, Δ t_nIt is last moment t_n-1And current time t_nTime step,p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_i's Tuple, m is limit p_iSum.

7. the circuit transient response computational methods of recursive convolution are based on according to claim 1, it is characterised in that step (3) Described in Newton-Raphson iterative process, current time t_nNewton-Raphson iteration kth step state become AmountOn input voltageDerivativeAnd output voltageOn input voltageDerivativeDefined formula：

$\frac{{\mathrm{dV}}_{out,i,j}^{\left(k\right)}\left(t_n\right)}{{\mathrm{dV}}_{in}^{\left(k\right)}\left(t_n\right)}=(1+p_i{\mathrm{\Δt}}_n){\left({\mathrm{\Δt}}_n\right)}^j$

$\frac{{\mathrm{dV}}_{out}^{\left(k\right)}\left(t_n\right)}{{\mathrm{dV}}_{in}^{\left(k\right)}\left(t_n\right)}=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{n_i}{\Σ}}{\tilde{k}}_{ij}\frac{{\mathrm{dV}}_{out,i,j}^{\left(k\right)}\left(t_n\right)}{{\mathrm{dV}}_{in}^{\left(k\right)}\left(t_n\right)}$

Subscript (k) represents the Newton-Raphson iteration of kth time,

Wherein, Δ t_nIt is last moment t_n-1And current time t_nTime step,p_iIt is limit, k_ijIt is coefficient, n_iIt is limit p_iTuple, m is limit p_iSum.