利用遞迴迴旋積分分析頻率相關之VLSI 傳輸線

Abstract

在現代的超大型積體電路(VLSI)中,積體電路包含大量的電路元件,其相互連結的金屬線便是實際的傳輸線(Transmission Line). 本論文介紹一種快速的離散時間分析法:遞迴迴旋積分(Recursive Convolution Integration);來分析非均勻耦合傳輸線的暫態模擬;其電容及電感參數皆為頻率相關.離散時間暫態摸擬是實行時變的特徵模式(Time-Verying Characteristic Model).其模式是由一般模式(Generalized Characteristic Model.)所轉換過來的. 這個模式是建構成二個不相交的時變阻抗網路,可表示成戴維寧或是諾頓型電路,而其電流/電壓源及端點的電流/電壓則成為遞迴迴旋積分輸入;而脈衝響應偶合傳輸線的阻抗函數(Immittance Function)和波型傳輸函數(Wave Propagation Function)則由Laguerre’s正交集來表示. 從實驗數據中可得知我們所使用的遞迴迴旋積分(Recursive Convolution Integration)比其它的演算法如波型鬆弛(waveform relaxation)及數值積分(numerical integration)來的更快. 而其結果跟實際的測量數據也只差了5%以內.

With the advent of Very Large Scale Integrated (VLSI) circuit technology, an integrated circuit (IC) nowadays consists of a very large number of circuit components interconnected by metal strips which in reality are transmission lines. In this thesis we present an efficient discrete-time method of simulating the transient response of nonuniform coupled transmission lines that are characterized with frequency-dependent parameters. The discrete-time transient simulation is carried out from a time-verying characteristic model converted from the generalized characteristic model. The time-varying characteristic model is constructed with two disjoint time-varying resistive networks connected with Norton/Thevanin’s current/voltage sources , which are generated by recursive convolution integration with the terminal currents/voltages and the Norton/Thevenin’s sources being the excitation and the impulse response functions are derived from the Laguerre’s orthonormal expansion of the characteristic immittance functions and the exponential wave propagation function of the coupled transmission line system. The experimental results show that our proposed algorithm has more timing improvements than other algorithm such as the waveform relaxation and numerical integration. The experimental results are practically identical and differ from the analytical solutions by less than 5%.