CN105608237B - Rapid waveform prediction method for post-simulation stage of circuit layout - Google Patents
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Abstract
The method belongs to the field of integrated circuits, and relates to a rapid waveform prediction method for a circuit layout in a post-simulation stage. Based on the fact that the simulation waveforms before and after the layout have strong correlation, firstly, according to the simulation waveforms before and after the layout of the circuit and the simulation waveforms after the layout for a short period of time, a mathematical model is established by means of a system identification technology to describe the relation between the simulation waveforms before and after the layout, then the simulation waveforms before the layout are used as system input, and the simulation waveforms after the whole layout are predicted through the output of the system. By applying the method, the extremely strong correlation of the front simulation waveform and the rear simulation waveform of the layout can be fully utilized, and the whole rear simulation waveform is predicted by using the front simulation waveform of the layout and the rear simulation waveform of the layout for a short time, so that the time for obtaining the rear simulation waveform of the circuit is greatly shortened, and a corresponding test method is provided to ensure that the predicted waveform has high reliability.
Description
Technical Field
The method belongs to the field of integrated circuits, relates to a layout post-simulation waveform prediction method based on system identification, and particularly relates to a rapid waveform prediction method in a circuit layout post-simulation stage.
Technical Field
The prior art discloses that in the design process of Analog Mixed Signal (AMS) circuits, post-layout simulation is an extremely important and computationally intensive part, and after parasitic parameters are extracted, the number of nodes and devices in the post-AMS simulation circuit netlist is increased by at least ten times compared with the pre-simulation circuit. Therefore, the post-simulation process of the AMS circuit is often time-consuming and requires the development of an efficient and fast waveform simulation method.
Model reduction (MOR) is considered a viable approach to solve this problem in post-simulation processes [1-4 ]. The MOR technology generates a relatively accurate reduced-order model for the interconnection line, thereby reducing the time and hardware cost in the post-simulation process of the layout. Among the various degradation methods proposed in the past, methods such as PACT [1] and TICER [4] based on the elimination principle have been successfully applied to post-layout simulation procedures and commercial tools for AMS circuits.
Research shows that simulation data of the front stage and the back stage of the layout are from the same circuit, so that the simulation data have strong correlation, and the possibility of accelerating the back simulation by means of the front simulation information is provided. For example, in recent years, the Bayesian model-based hybrid method (BMF) has been rapidly developed and used in the research of "accelerating the post-simulation yield analysis based on pre-simulation data" [5], thereby greatly reducing the number of samples required in the post-simulation yield analysis.
Transient analysis is one of the most critical steps in the design and verification process of AMS circuits and can help designers to better diagnose and optimize circuits. For a well-designed circuit, transient simulation waveforms of front-and-back simulation of a layout are also strongly correlated, for example, two sub-graphs in fig. 1 illustrate the change of circuit nodes of the same part of circuit in the front-and-back simulation stages of the layout, and nodes such as N1, N3 and N5 in the right sub-graph are added into the simulation circuit after the layout, so that the node N of the front simulation circuit is replaced. If the circuit is well designed, the waveforms at nodes N1-N9 should be similar to those at node N and not exactly the same due to the effects of parasitic parameters. Therefore, it is feasible to predict the post-imitation waveform by the pre-imitation waveform, and the problem has not been studied yet.
System Identification (System Identification) is a method for describing a certain System by constructing a mathematical model based on observed data, and is widely applied to a plurality of fields such as industrial processes [7], automatic control [8] and neural networks [9 ]. Because the front simulation waveform and the rear simulation waveform of the layout have strong correlation, the front simulation waveform and the rear simulation waveform can be respectively used as the input and the output of a system. All the front imitation data and part of the rear imitation data are used as observation data, a mathematical model is obtained through a system identification technology to describe the relation, and therefore the rear imitation waveform output by the system is predicted by means of the front imitation waveform input into the system.
References relevant to the present invention are:
[1].Sheehan B N.TICER:Realizable reduction of extracted RC circuits[C]//Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design.IEEE Press,1999:200-203.
[2].Odabasioglu A,Celik M,Pileggi L T.PRIMA:passive reduced-orderinterconnect macromodeling algorithm[C]//Proceedings of the 1997 IEEE/ACMinternational conference on Computer-aided design.IEEE Computer Society,1997:58-65.
[3].Freund R W.SPRIM:structure-preserving reduced-order interconnectmacromodeling[C]//Proceedings of the 2004 IEEE/ACM International conferenceon Computer-aided design.IEEE Computer Society,2004:80-87.
[4].Kerns K J,Yang A T.Stable and efficient reduction of large,multiport RC networks by pole analysis via congruence transformations[J].Computer-Aided Design of Integrated Circuits and Systems,IEEE Transactionson,1997,16(7):734-744.
[5].Gu C,Chiprout E,Li X.Efficient moment estimation with extremelysmall sample size via bayesian inference for analog/mixed-signal validation[C]//Design Automation Conference(DAC),2013 50th ACM/EDAC/IEEE.IEEE,2013:1-7.
[6].Ljung L.System identification[M].
Boston,1998.
[7].Favoreel W,De Moor B,Van Overschee P.Subspace state space systemidentification for industrial processes[J].Journal of Process Control,2000,10(2):149-155.
[8].Ichikawa S,Tomita M,Doki S,et al.Sensorless control of permanent-magnet synchronous motors using online parameter identification based onsystem identification theory[J].Industrial Electronics,IEEE Transactions on,2006,53(2):363-372.
[9].Chu S R,Shoureshi R,Tenorio M.Neural networks for systemidentification[J].Control Systems Magazine,IEEE,1990,10(3):31-35.
[10].Andersson L,
U,Johansson K H,et al.A manual for systemidentification[J].Laboratory Exercises in System Identification.KF Sigma iLund AB.Department of Automatic Control,Lund Institute of Technology,Box,1998,118.
[11].National-Instrument.Selecting a Model Structure in the SystemIdentication Process.http://www.ni.com/white-paper/4028/en/,2010.
[12].Mathworks.Identifying Transfer Function Models.http://www.mathworks.cn/cn/help/ident/ug/identifyingtransfer-function-models.h tml,2013.
[13].Aarts R.System identification and parameter estimation[J].1998.
[14].Ding F,Chen T.Identification of Hammerstein nonlinear ARMAXsystems[J].Automatica,2005,41(9):1479-1489.
[15].Mathworks.Compare outputs with measured data.http://www.mathworks.cn/cn/help/ident/ref/compare.html,2013.。
disclosure of Invention
The invention aims to provide a method for quickly predicting circuit waveforms in a post-layout simulation stage based on a system identification technology. The waveform prediction method can fully utilize the strong correlation of the front simulation waveform and the rear simulation waveform of the layout, only uses the front simulation waveform and the rear simulation waveform for a short time to predict all the rear simulation waveforms, can obviously shorten the time for obtaining the rear simulation waveforms of the circuit, and provides a corresponding test method to ensure that the predicted waveforms have strong reliability.
In order to achieve the purpose, the technical content of the invention is as follows: a method for predicting a rapid waveform in a post-simulation stage of a circuit layout is provided, a framework of the method can be described with reference to FIG. 4, and the method comprises the following steps:
step 1: completing the pre-domain simulation and the post-simulation of a short time segment of the circuit, and taking the post-simulation waveform of the short time segment and a corresponding short pre-simulation waveform as observation data, as shown by two small rectangular dotted line boxes in FIG. 4;
step 2: performing system identification by analyzing observation data, and establishing a relation of a mathematical model describing a front simulation waveform and a rear simulation waveform of a layout;
step 2-1: selecting proper models to form a candidate model set,
the method specifically selects four model structures which are an ARX model, an impact response model, a transmission function model and a Hammerstein-Wiener model, wherein the ARX model belongs to a nonlinear model, the rest three models belong to linear models, the ARX model belongs to a dynamic model in a time domain, the impact response model belongs to a static model in the time domain, and the transmission function model belongs to a dynamic model in a frequency domain. The mathematical representations of the above four models are as follows:
ARX model:
A(q)y(k)＝B(q)u(k)+e(k)，
wherein:
A(q)＝1+a1q-1+…+anaq-na
B(q)＝b1q-1+…+bnbq-nb，
y (k), u (k) and e (k) are respectively the input, output and measurement noise of the system at the k-th time point, and e (k) can be ignored as the observation data is directly from the system simulation and not the actual measurement; the polynomials A (q) and B (q) use the delay operator q to express the delay of one unit, e.g. for the signal q in the time domain-1u (k) denotes u (k-1), so another equivalent representation of the ARX model is:
in the process of determining the model parameters, the difference between the predicted calculation value and the actual value is minimized by a least square method and the like, so that the parameters { a ] are estimated1,…,anaAnd { b }and1,…,bnb}；
The impact response model:
wherein g isnTo be aThe first N conventional impulse response coefficients can be obtained by substituting the first N inputs u (k) and the outputs y (k) into the above equation;
frequency domain transfer function model:
by means of the laplace transform, the transfer function of the system has the following form [12] in the s-domain:
wherein, Y(s), U(s) and E(s) respectively represent Laplace transform of system output, input and measurement error, and E(s) can be ignored in the same way as ARX model. num(s) and den(s) represent numerator and denominator polynomials describing the input-output relationship, the roots of which are the poles and zeros of the system and can be obtained by frequency response experiments and other methods;
Hammerstein-Wiener model:
the structural block diagram of the model is shown in FIG. 2, wherein
w(k)＝f(u(k)),x(k)＝(B(q)/F(q))w(k),y(k)＝h(x(k))。
f is a non-linear function that maps the input data u (k) to an intermediate linear system; b (q)/F (q) is a linear function characterizing the internal linear module; h is a non-linear function that maps the output of the internal module to the external output;
step 2-2: determining parameter values for individual models from observation data
For linear systems, the framework of fig. 3 is used for general description, and in this general model, the essence of the system is a function g (Φ) of input values and past output values, and when a series of parameters θ in the function are determined, the system is determined;
for example, for the ARX model, if represented in the generalized form of FIG. 3, then:
g(φ)＝θ1φ1+θ2φ2+…+θn+mφn+m，
wherein,
φ＝[φ1φ2…φnφn+1…φn+m]T＝[u(t-1)…u(t-n)-y(t-1)…-y(t-m)]T。
using waveforms corresponding to the previous short period of time of the before-and-after simulation circuit of the layout as reference data for parameter estimation, and the goal of the parameter estimation is to find the optimal parameter set
Make the model predict the result
And the error of the actual backward simulation waveform y at the previous part time point {0,1, …, s } is minimum, namely
Wherein:
this process can be solved by the least squares method;
similarly, for the nonlinear model, the error between the predicted result and the actual simulated waveform at the previous part of time point is minimized in each iteration process by adopting an iterative solution method, so that the value of the model parameter is determined. A specific parameter determination method is set forth in reference [14 ];
and (2) substeps 2-3: model verification, selecting the best model from the candidate model set and verifying the reliability of the prediction result
After the parameters of the alternative model are determined, the validity of the model needs to be verified, the front and back simulated waveforms corresponding to a short period of time point are continuously used as verification data, a fit rate (fit level) function is defined as an index of the validity of the model, and the expression is as follows:
wherein
The method is a result of model prediction in a short period of time, y is an actual post-simulation waveform in a short period of time, the fitting rate is 100% and 0% respectively represents that the model completely does not predict correct information;
after calculating the fitting rates of all the alternative models, selecting the model with the highest fitting rate, and if the fitting rate is within an acceptable range, predicting the simulated waveform after the residual time period by using the model.
And step 3: the identified system predicts a post-imitation waveform for the remaining time period,
as shown in the larger rectangular dashed box in fig. 4, the simulated waveform before the layout of the remaining time period is used as the input of the identified system, and the output is the predicted simulated waveform after the remaining time period, as shown in the elliptical dashed box in fig. 4.
The rapid waveform prediction method for the post-simulation stage of the circuit layout has the following advantages:
1. the correlation of the front simulation and the back simulation of the layout is fully utilized, and the time and the hardware pressure of the back simulation of the layout are greatly reduced.
2. The method provides various alternative models of linearity and nonlinearity, dynamic and static states, time domain and frequency domain and an effective model verification method, ensures that the correlation of front and back simulation waveforms can be effectively described by one model under most conditions, and performs reliable prediction.
Drawings
FIG. 1 is a portion of a sense amplifier used to illustrate the differences and connections between the front and back simulation circuits of a layout;
FIG. 2 is a block diagram of the Hammerstein-Wiener model;
FIG. 3 is a generalized structure description diagram of a system model;
FIG. 4 is a flow chart of the present waveform prediction method;
FIG. 5 is a schematic diagram of waveforms of a sense amplifier circuit node BL in a simulation stage before and after a layout;
FIG. 6 is a comparison of a post-simulated actual waveform of the sense amplifier circuit node BL and a predicted waveform using the present prediction method;
FIG. 7 is a waveform diagram of an output node of a power amplifier circuit at a simulation stage before and after layout;
FIG. 8 is a comparison of a post-simulated actual waveform at an output node of a power amplifier circuit and a predicted waveform using the present prediction method;
FIG. 9 is a schematic diagram of waveforms of intermediate nodes of a ring oscillator circuit at a simulation stage before and after layout;
FIG. 10 is a comparison of a post-simulated actual waveform at an intermediate node of a ring oscillator circuit and a predicted waveform using the present prediction method.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, three specific examples are provided below.
A small voltage difference is applied to the differential inputs BL and BL _ of the amplifier, and the front and back simulation waveforms at the node BL are shown in fig. 5, from which the similarity and difference of the back simulation waveforms can be seen. The target of waveform prediction is to accurately predict a rear imitation waveform by means of the front imitation waveform.
The whole section of waveform comprises 1000 time sampling points, front and rear simulated waveforms of the first 250 time points are selected for system identification, wherein the waveforms of the first 200 time points are used for determining model parameters, and the waveforms of the remaining 50 time points are used for model verification. The waveforms at 750 time points after post-simulation are predicted.
Table 1:
the prediction situations and the time consumption of three alternative linear models are listed in table 1, and the frequency domain transfer function model is selected as the prediction model of the post-simulation waveform because the frequency domain transfer function model obtains the highest verification data fitting rate. Finally, 93.4% of predicted fitting rate is obtained, and the predicted waveform and the actual simulated waveform are shown in FIG. 6. Therefore, the trend of the rear simulation waveform of the rear three quarters is well predicted through all the front simulation waveforms and the rear simulation waveform of the front one quarter.
The front and back simulation waveforms of the output node are shown in fig. 7, from which the similarity and difference of the back surface simulation waveforms can be seen. The target of waveform prediction is to accurately predict a rear imitation waveform by means of the front imitation waveform.
The whole section of waveform comprises 1000 time sampling points, front and back simulated waveforms of the first 200 time points are selected for system identification, wherein the waveforms of the first 100 time points are used for determining model parameters, and the waveforms of the remaining 100 time points are used for model verification. The waveforms at 800 time points after post-simulation are predicted.
Table 2:
the prediction cases and the time consumption of three alternative linear models are listed in table 2, and the ARX model is selected as the prediction model of the post-simulation waveform because the highest fitting rate of the verification data is obtained. Finally, a prediction fitting rate of 98.79% is obtained, and a predicted waveform and an actual simulated waveform are shown in fig. 8. Therefore, the trend of the rear simulation waveform of the rear fifth is well predicted through all the front simulation waveforms and the rear simulation waveform of the front fifth.
Example 3 is a ring oscillator circuit using a 32nm process. This example is presented to illustrate the predictive effectiveness of a nonlinear model.
The front and back simulation waveforms of one of the middle nodes are shown in fig. 9, and it can be seen that the difference of the front and back simulation waveforms is more complex, which is represented by the fact that the front and back simulation waveforms are not pure delay or change in amplitude, but are extended in period. At this time, the linear model cannot describe the relatively complex front-back simulated waveform relationship, so that the nonlinear Hammerstein-Wiener model is adopted for prediction.
The whole section of waveform comprises 500 time sampling points, front and rear simulated waveforms of the first 200 time points are selected for system identification, wherein the waveforms of the first 150 time points are used for determining model parameters, and the waveforms of the remaining 50 time points are used for model verification. The waveforms at 300 time points after post-simulation are predicted.
In the process of model verification, the Hammerstein-Wiener model obtains 91.07% of fitting rate, so that the Hammerstein-Wiener model can be considered to have the capability of predicting the waveform more accurately, 78.95% of predicted fitting rate is finally obtained, and the predicted waveform and the actual simulated waveform are shown in FIG. 10. It can be seen that the cycle extension is accurately predicted, only the detail difference in amplitude exists, and the trend of the rear simulation waveform three fifths later is well predicted by the whole front simulation waveform and the front two fifths later simulation waveform.
The embodiment shows that the rapid waveform prediction method in the post-simulation stage of the circuit layout can fully utilize the correlation of the pre-simulation and the post-simulation of the layout, greatly reduce the time and the hardware pressure of the post-simulation of the layout, has strong reliability, and is a high-efficiency and practical rapid waveform prediction method.
Claims (1)
1. A quick waveform prediction method for a circuit layout post-simulation stage is characterized by comprising the following steps:
step 1: completing the pre-domain simulation and the post-domain simulation of the circuit for a period of time, and taking the post-simulation waveform of the period of time and the corresponding pre-simulation waveform as observation data;
step 2: performing system identification by analyzing observation data, and establishing a relation of a mathematical model describing a front simulation waveform and a rear simulation waveform of a layout; the step 2 comprises the following steps:
step 2-1: selecting proper models to form a candidate model set,
a black box model is adopted for system identification, namely, no prior knowledge of the system is assumed, system parameters are adjustable, and actual physical meanings are not considered; the model is selected from an ARX model, an impact response model, a transfer function model and a Hammerstein-Wiener model;
the system comprises an ARX model, an impact response model and a transmission function model, wherein the ARX model, the impact response model and the transmission function model belong to linear models; the Hammerstein-Wiener model belongs to a nonlinear model, and is shown as follows:
ARX model:
A(q)y(k)＝B(q)u(k)+e(k)，
wherein:
A(q)＝1+a1q-1+…+anaq-na
B(q)＝b1q-1+…+bnbq-nb
y (k), u (k) and e (k) are respectively the output, input and measurement noise of the system at the k-th time point, and e (k) can be ignored as the observation data is directly from the system simulation and not the actual measurement; the polynomials A (q) and B (q) use the delay operator q to represent a unit delay, where for a signal q in the time domain-1u (k) denotes u (k-1), so another equivalent representation of the ARX model is:
in the process of determining the model parameters, the difference between the predicted calculation value and the actual value is minimized by a least square method and the like, so that the parameters { a ] are estimated1,…,anaAnd { b }and1,…,bnb}；
The impact response model:
wherein g isnThe first N impulse response coefficients of the system can be obtained by substituting the first N inputs u (k) and the output y (k) into the above formula to construct a linear equation set;
frequency domain transfer function model:
by means of the laplace transform, the transfer function of the system has the following form in the s-domain:
y(s), U(s) and E(s) respectively represent Laplace transformation of system output y, input u and measurement errors, E(s), num(s) and den(s) can be omitted in the same way as an ARX model, numerators and denominator polynomials for describing input-output relations are represented, roots of the numerators and the denominators are poles and zeros of the system, and the numerators and the zeros can be obtained through frequency response experiments and other methods;
Hammerstein-Wiener model:
in the structure of the model, in the structure,
w(k)＝f(u(k)),x(k)＝(B(q)/F(q))w(k),y(k)＝h(x(k))，
f is a non-linear function that maps the input data u (k) to an intermediate linear system;
b (q)/F (q) is a linear function characterizing the internal linear module; h is a non-linear function that maps the output of the internal module to the external output;
step 2-2: the parameter values for each model are determined by observing the data,
wherein, for linear systems, a general description is adopted, in which the essence of the system is a function g (phi) of input values and past output values, and when a series of parameters theta in the function are determined, the system is determined;
wherein, for the ARX model, if expressed in a generalized form, it is:
g(φ)＝θ1φ1+θ2φ2+…+θn+mφn+m，
wherein,
φ＝[φ1φ2…φnφn+1…φn+m]T＝[u(t-1)…u(t-n)-y(t-1)…-y(t-m)]T；
using waveforms corresponding to a period of time before and after the simulation circuit of the layout as reference data for parameter estimationThe goal of parameter estimation is to find the optimal set of parameters
Make the model predict the result
And the error of the actual backward simulation waveform y at the previous part time point {0,1, …, s } is minimum, namely
Wherein:
the process is solved by a least square method;
for the nonlinear model, the error between the predicted result and the actual post-imitation waveform at the previous part of time point is minimized in each iteration process by adopting an iteration solving method, so that the value of the model parameter is determined;
and (2) substeps 2-3: model verification, selecting the best model from the candidate model set and verifying the reliability of the prediction result,
after the parameters of the alternative model are determined, the effectiveness of the model is verified, the front and the back simulated waveforms corresponding to a period of time point are continuously used as verification data, a fit rate (fit level) function is defined as an index of the effectiveness of the model, and the expression is as follows:
After the fitting rates of all the alternative models are calculated, selecting the model with the highest fitting rate, and if the fitting rate is acceptable, predicting the simulated waveform after the residual time period by using the model;
and step 3: and predicting the rear simulated waveform of the residual time period through the recognized system, taking the simulated waveform before the layout of the residual time period as the input of the recognized system, and obtaining the output of the simulated waveform which is the predicted rear simulated waveform of the residual time period.
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