Fast Algorithm for Determining Eye-Diagram Characteristics of Lossy Transmission Lines Jeng-Hau Lin, Wei-Da Guo, Guang-Hwa Shiue, Chien-Min Lin, Tian-Wei Huang, and Ruey-Beei Wu Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan, 10617, R.O.C. Tel: +886-2-23635251 x 340 Fax: +886-2-23638247 E-mail: rbwu@ew.ee.ntu.edu.tw *Backend Technology Development Division, Taiwan Semiconductor Manufacturing Co., Ltd. Abstract A novel algorithm for fast and accurately determining the height and width of eye diagrams at the receiving ends of transmission lines is proposed. While the two parameters concerned in the conductive and dielectric losses in response to the impulse stimulus are derived, the transfer function associated with the propagation coefficient to represent the signaling mechanism on the eye diagram can be developed. A systematic flow is implemented to acquire the predictable eye diagrams in a good agreement with the analysis results by the time-domain circuit simulator for varying designed geometries. 1. Introduction The eye diagram at the receiving ends of transmission lines is the performance metric of signal integrity analyses for the high-speed interconnection. Design specifications are defined in an eye mask for the timing and voltage margins at the testing points on the channel to gauge the signaling tolerance in the time-domain simulation. Three analysis schemes, the full-wave simulation, macro-model, and signal processing, are usually used to generate the eye diagram in response to the input signal pattern of a pseudo-random bit sequence (PRBS) [1]. Although the shortest length of PRBS is with 127 bits, it is still time-consuming for the full-wave simulation. The procedure to construct a macro-model is also less comprehensible with the physical mechanism of lossy lines. In this paper, the relationship of mechanism between the lossy line and impulse response is thereof exploited. When transformiing the transfer function of frequency-dependant transmission lines to the time domain, two key characteristics of conductive and dielectric losses controlling the respondent behavior of impulse stimuli are investigated. By the convolution of PRBS patterns with various combinations of two designed parameters, the eye diagrams of different transmission-lines are acquired to measure the eye-opening signal integrity in a systematic flow. 2. Analysis Method A. Transfer Function For a microstrip structure as depicted in Fig. 1(a), its transmission-line model is known as a series of cells and each of them has the four equivalent elements as shown in Fig. l(b). The characteristic resistance (R) and conductance (G) vary with the frequency (w) are respectively given by R=Rj7 7 and G=Gd a), (1) where Rs = 4'2 /(Wvu) and Gd= C tan3. Considering the length of 'len' for a transmission-line with the propagation coefficient (i), its transfer fumction in a match case is given by H(w) - e J(R+ijwL)(G+jwC) - eAw -y (2) It is noted that the propagation coefficient can be approximated by [2] y' = J(R+ijWL)(G+ jcoC) T j iiT+kR ]+ G (3) and thus the transfer function is divided into three parts related to the time delay, conductive loss, and 1-4244-0883-0107/$25.00©20071EEE E1 119