Analytical Formulas for Tradeoff Among Channel Loss, Length, and Frequency of $RC$ - and $LC$ -Dominant Single-Ended Interconnects for Fast Equalized Link Tradeoff Estimation

This paper presents simple and intuitive closed-form formulas for tradeoff among channel loss, length, and frequency of single-ended interconnects to aid fast equalized link tradeoff estimation. Based on a transfer function model for single-ended interconnects, we derived two closed-form tradeoff formulas for RC- and LC-dominant interconnects. The formulas' accuracies and computation time improvements are verified by comparison with the SPICE simulation and the measurement results. According to our formulas, the loss is roughly a linear function of the product of the length and the square root of the frequency in RC-dominant interconnects. In LC-dominant interconnects, the channel loss due to skin effect is roughly proportional to the product of the length and the square root of the frequency, while the channel loss due to dielectric loss is approximately proportional to the product of the length and the frequency. From the channel loss of our formulas, an equalized eye size can be easily estimated. Therefore, designers can use our tradeoff formulas easily and quickly to estimate link-level tradeoff among the equalized eye size, the data rate, and the channel length in designing an equalized link through RC- and LC-dominant single-ended interconnects.