Transactions of The Japan Institute of Electronics Packaging Vol. 4, No. 1, 2011 [Technical Paper] A High-Signal-Integrity PCB Trace Composed of Multiple Segments for GHz VLSI Packaging: Its Prototyping and Performance Analysis Moritoshi Yasunaga*, Hiroki Shimada*, Shohei Akita*, Masami Ishiguro*, and Ikuo Yoshihara** *Graduate School of Systems and Information Engineering, University of Tsukuba, Japan, Ten-no-dai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan **Faculty of Engineering, Miyazaki University, Japan, Gakuen-kibanadai-nishi 1-1, Miyazaki, Miyazaki 889-2192, Japan (Received August 15, 2011; accepted November 4, 2011) Abstract High signal integrity (SI) is strongly required in PCB traces under GHz clock frequencies for the next generation of VLSI packaging. Unfortunately, however, conventional techniques based on characteristic impedance matching cannot work well with GHz digital signals. In order to overcome this problem, we have previously proposed a novel PCB trace struc- ture called “Segmental Transmission Line (STL).” In this paper, we design STLs for GHz bus-systems in which a high SI is indispensable, and demonstrate the high effectiveness of the STL showing the waveforms observed in the STL proto- types. Furthermore, the STL is analyzed in the frequency domain to demonstrate its mechanism of high robustness against frequency fluctuations. Keywords: Signal Integrity, Printed Circuit Board, PCB, Transmission Line, Impedance Matching, Genetic Algorithm 1. Introduction mimic the evolution process of living creatures, and their Waveform distortion is one of the most serious prob- foundations were already established in the early 1990’s. lems in PCB design for VLSI packaging in the GHz era. Since the late 1990’s, GAs have been widely applied to real The waveform distortion problem, also called the “Signal world problems and many successful results have been Integrity (SI) deterioration problem,” comes from the fact reported in the field of electronics as well as other fields that the PCB traces behave as transmission lines as their such as the aerospace industry, optical engineering, robot- lengths approach the wavelengths of the digital signals ics, etc. One typical application of a GA to the electronics propagating on them (e.g., the base wave length of a 1 field, for example, is “Place and Route Design in VLSIs,” in GHz digital signal in a PCB is about 15 cm). The transmis- which the wire-routings and circuit-placements are opti- sion line generates reflection waves, or noise, at character- mized in terms of their lengths and areas.[7] A GA can istic-impedance Z mismatched points, and the noise thus be regarded as a powerful design methodology for degrades the waveform dramatically. designs that have no deterministic algorithm under the In the GHz domain (more precisely, from about 500 huge search space of multiple parameters. MHz), however, conventional Z-matching designs will not On the other hand, there exists a strong constraint in a do their work gradually, and new techniques to counteract GA-based design also: the target design needs to be the waveform distortion have been urgently desired. In mapped onto a one-dimensional array of parameters (the order to overcome this difficulty, we have previously pro- one-dimensional array and parameter are called “chromo- posed a novel transmission line called “Segmental Trans- some” and “gene,” respectively), so that the key to success mission Line (STL),” which is designed based on genetic in a GA-based design depends on whether the target algorithms (GAs).[4] Furthermore, we have already design can be expressed with “chromosomes” and “genes” shown its fundamental effectiveness theoretically and or not. The STL introduced in this paper can be regarded experimentally.[1–3, 5, 6] as a one-dimensional array of characteristic impedances. GAs, which are search and optimization algorithms, Consequently, it can be easily expressed as a chromosome 44 Yasunaga et al.: A High-Signal-Integrity PCB Trace (2/8) with genes, and seems to be well-suited to a GA-based are generated at the interfaces between adjacent segments design. Zi and Zj. Figure 3 shows a bird’s-eye view and a cross-sec- In the first part of this paper, we describe the STL design tional view of the STL in the PCB. Characteristic imped- outline, and in the latter part we demonstrate its effective- ance, Z, is a function of trace width, W, trace thickness, T, ness for clock signals on the bus-system design with the and insulator thickness, D. In the STL, Z is thus controlled prototype evaluations. Signal distortion, or the SI degrada- by adjusting W. tion in the clock signals causes catastrophic malfunctions The adjustment of all Zi, however, results in a combina- in systems, so the STL was originally proposed for the torial explosion problem: for example, if there are 10 seg- clock distribution traces. Furthermore, in this paper, the ments (N = 10) and 100 characteristic impedance candi- STL designed for the clock signals is also applied to ran- dates from 21 Ω to 120- Ω at 1- Ω intervals, the resultant dom signals and its performances are analyzed in terms of search space reaches 10010, where no deterministic search the frequency domain. algorithm exists to find the optimized or semi-optimized set of Zi. We have thus proposed to apply genetic algo- 2. Segmental Transmission Line (STL) rithms (GAs)[4] to solve this combinatorial explosion Digital signals propagate in the PCB traces, or transmis- problem. The STL structure can be easily and well mapped sion lines, without distortions if no devices are connected onto the one-dimensional array of parameters as shown in to the traces (upper figure in Fig. 1). However, if some Fig. 4 (in this figure, the transmission line is divided into devices, e.g., VLSIs, are connected to the traces, their 10 segments, for example). Initially, a set of chromosomes, inputs, which can be regarded as load (stray) capacitances, which is called a “population,” is made up with characteris- cause characteristic-impedance mismatching and dramati- tic impedances randomly given to all genes, as shown in cally distort the signals (lower figure in Fig. 1). Fig. 5 (in the figure the population is composed of 5 chro- In the STL, a transmission line is divided into multiple mosomes). After the population is generated initially, the (N) segments of individual characteristic impedance Zi (i = three operations of “selection,” “crossover,” and “muta- 1, 2, ..., N) as shown in Fig. 2.[1–3, 5, 6] The values of Zi in tion” are applied to the population and the whole process is multiple segments are adjusted to achieve an ideal digital then repeated until the score of the chromosome is signifi- waveform at important points such as input points to the cantly improved. LSIs on the line by superposing reflection waves, which Fig. 3 Structure of STL in PCB. Fig. 1 Digital signal distortion. Fig. 2 Segmental transmission line (STL). Fig. 4 STL mapped onto chromosome in GA. 45 Transactions of The Japan Institute of Electronics Packaging Vol. 4, No. 1, 2011 Fig. 5 Initial population generation. Fig. 7 Fitness in STL design. Fig. 6 Score of chromosome. Fig. 8 Selection operation. The waveform of each chromosome is simulated using the SPICE circuit simulator as shown in Fig. 6, and each chromosome is scored according to the waveform: as shown in Fig. 7, the reciprocal of the difference area, Diff, between the ideal waveform, I(t), and the waveform, R(t), simulated by SPICE in the periodic signal (clock signals) is used as the score (fitness), so that the score increases as the waveform is improved, or approaches the ideal waveform. In the “selection” (Fig. 8), the population is updated for the next generation, where the chromosomes with lower scores are discarded and those with higher scores breed. (For example, in Fig. 8, chromosome 4 has Fig. 9 Crossover operation. the lowest score, “24,” and is discarded and chromosome 2 has the highest score, and is propagated, or copied.) In the “crossover” (Fig. 9), randomly selected pairs of chromosomes exchange parts of their genes at randomly chosen crossover points (in Fig. 9, chromosomes 1 and 2, and 2’ and 5 exchange their genes at crossover points C1 and C2, respectively). In the “mutation” (Fig. 10), some randomly chosen genes are changed to other values at a rather low probability. We have developed a program to design the STL, called “STL-Designer”. The configuration of STL-Designer is shown in Fig. 11. It consists mainly of a GA kernel pro- Fig. 10 Mutation operation. 46 Yasunaga et al.: A High-Signal-Integrity PCB Trace (4/8) Fig. 12 1 GHz DIMM model. Fig. 11 Configuration of STL Designer. mental wavelength in the 1 GHz digital signal on the PCB gram. The GA operations of “selection,” “crossover,” is approximately 15 cm, and the wavelengths of its har- “mutation,” and “fitness (score) evaluation” are repeated in monics, which mainly shape the rising and falling edges of this kernel program. In the fitness evaluation, a circuit net- the digital signal, are shorter than 15 cm, so that the 15 cm list, or circuit description file is output and fed to SPICE. long line (Fig. 12) can be regarded as a transmission line. SPICE outputs the waveform file and this is fed back to In the 250 MHz STL scale-up prototype for the 1 GHz STL-Designer and the fitness is calculated based on the DIMM (Fig. 12), the trace length, L, and the load capaci- waveform. During the GA-loop repetitions, some chromo- tor, CL, are designed at 60 cm and 15 pF, respectively, from somes evolve gradually and they finally achieve excellent the scale-up ratio of 4, which is the ratio of 250 MHz to 1 fitness.