An Interconnect Line Model Reduction Method Based on Time-Domain Trapezoidal Difference

A technology of model reduction and interconnection lines, which is applied in special data processing applications, instruments, electrical digital data processing, etc., can solve the problems of high complexity and difficulty in reducing the order of large-scale system models, and achieve high order reduction accuracy, The effect of ensuring accuracy and reducing computational complexity

Active Publication Date: 2017-06-20
FUDAN UNIV
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Problems solved by technology

However, these time-domain model reduction methods are too complex to solve the orthogonal polynomial expansion system, and it is difficult to reduce the model for large-scale systems.

Method used

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  • An Interconnect Line Model Reduction Method Based on Time-Domain Trapezoidal Difference
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  • An Interconnect Line Model Reduction Method Based on Time-Domain Trapezoidal Difference

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Embodiment 1

[0038] The implementation steps of the method for reducing the order of the interconnection line model based on the difference of the time-domain trapezoidal method in the present invention are as follows: figure 1 shown.

[0039] Step 1: Read the characteristic data and input stimulus of the interconnect circuit. The characteristic data of the interconnection circuit includes the parasitic network netlist of resistance, capacitance and inductance obtained by extracting the parasitic parameters of the interconnection line;

[0040] Step 2: Use the improved node voltage method to establish the time domain equation (1) of the interconnect circuit:

[0041]

[0042] where x∈R N×1 Represents the state variable composed of unknown node voltage and branch current, where N is the number of unknown variables in the equation, and represents the order of the original system; y represents the output voltage or current; C, G∈R N×N , where C represents the contribution of capacitance...

Embodiment 2

[0066] This embodiment adopts a bus circuit, the order of which is 12738, and the input is a pulse signal of 1 GHz. In this embodiment, the order of the circuit is reduced to 30, 50, and 70 respectively, and one of the output signals is observed in the time domain, so as to measure the accuracy of different order reduction methods. We take the HSPICE simulation results as the exact results of the original system output. Define the relative error rel_err as follows:

[0067]

[0068] where y and y% denote the outputs of the original system and the reduced-order system, respectively.

[0069] mistake! Reference source not found. The reduction time and accuracy of different model reduction methods are shown. It can be seen from Table 1 that the reduction time of the model reduction method proposed in this paper based on the difference of time-domain trapezoidal method is equivalent to that of the existing frequency-domain model reduction method, and far lower than the exis...

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Abstract

The invention belongs to the field of integrated circuits, and relates to an interconnection line model reduction method based on time-domain trapezoidal method difference. The method comprises the steps as follows: reading performance data of an interconnection circuit, utilizing an improved node voltage method to build a corresponding time-domain equation; utilizing a trapezoidal method to discretize the time-domain equation of the interconnection circuit and obtain a nonhomogeneous recurrence relation; using a nonhomogeneous Arnoldi algorithm to construct a projection matrix, and then using the projection matrix to perform contragradient transformation on the time-domain equation of the interconnection circuit to obtain a reduction system; and finally, using the trapezoidal method to discretize the reduction system to obtain time-domain output. By virtue of the method, the matching of state variables between the reduction system after the time-domain trapezoidal method difference and the original system is ensured; the time-domain reduction precision is ensured; and the numerical stability during the reduction process and the passivity of the reduction system are ensured. Compared with the original time-domain model reduction method, the computing complexity is greatly reduced; and the method has higher precision in time-domain compared with a frequency-domain reduction method.

Description

technical field [0001] The invention belongs to the field of integrated circuits, and relates to a method for reducing the order of an interconnection line model based on time-domain trapezoidal method difference, in particular to a method for reducing the order of a model that can quickly simulate an interconnection line circuit. [0002] technical background [0003] With the rapid development of integrated circuit technology, the operating frequency of integrated circuits has reached several GHz, the number of monolithic integrated circuit transistors has reached hundreds of millions, and the feature size has entered 22 nanometers. Interconnect delay has surpassed device delay to become the main factor determining the performance of integrated circuits. [0004] The scale of interconnection system can reach tens of thousands to hundreds of thousands. It is very time-consuming or even impossible to directly analyze such a large-scale circuit. The complexity of interconnect...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
Inventor 曾璇杨帆侯丽敏
Owner FUDAN UNIV
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