With the continuous reduction of integrated circuit processing size and increasing integration density, power supply noise seriously threatens further improvement of high-speed digital system performance, which can cause jitter, latency, and even system malfunction. Power supply noise is strongly related to the design quality of the power distribution network and the activity of transient currents. In this paper, a method for estimating the worst-case voltage supply based on the ramp time of the transient current is proposed. At the same time, the worst-case current activity can also be obtained which can be used to guide the core or field programmable gate array (FPGA) design for a given power distribution network. The ramp current is first encoded and divided into segments. Then, two dynamic matrices are used to track the worst-case accumulated voltage noise and worst-case current activities. The proposed method is compared with state-of-the-art approaches showing consistent advantages in estimating the worst-case power supply noise. Its accuracy is also validated by comparing the simulated and measured data.

With the increase in nonlinear effects of high-speed links, the higher order multiple edge response (MER) method is widely used to accurately evaluate high-speed link performance by computing the statistical eye diagram at the price of massive edge responses. The computational complexity of the MER algorithm exponentially increases with the order. In this article, the estimation method for the minimum order of the MER method is proposed based on the last time of nonlinearity in high-speed links. The edge responses are divided into nonlinear and linear sections according to the minimum order of MER. To further improve the computational efficiency of the convolution operation of higher order MERs, a hybrid method is proposed that combines the double edge response (DER) method and statistical data of the edge response. The DER convolution is used to obtain the probability density distribution in the linear section, and the probability density distribution in the nonlinear section is obtained by the statistics of the rising and falling edge responses with different leading bits, which can greatly reduce the computation time. The accuracy and efficiency of the proposed method are verified by comparison with the higher order MER method.

A fast and accurate statistical eye diagram estimation method for high-speed nonlinear links is proposed in this article. Probability density functions (PDFs) of output responses are derived based on multiple edge responses (MERs). According to the property that the influence of nonlinearity will not propagate for a long time in high-speed links, a new scheme for calculating the PDFs of responses is presented, in which the convolution process is divided into nonlinear section, transition section, and linear section. Convolutions via high-order of MERs are only used for the nonlinear section, low-order of MERs are used for the transition section, and double edge responses are used for the linear section. The new scheme can drastically reduce the amount of computation. The proposed method is verified by comparing the probability density distributions of the statistical eye diagram, the bathtub curves, and the simulation time with that of the traditional total MER-based statistical eye diagram. Results show that the simulation speed of the proposed method has been improved by more than ten times, and the accuracy is almost the same as the traditional statistical eye diagram for nonlinear links. This method provides an efficient and accurate solution for estimating the statistical and BER eye diagrams for serious nonlinear links.

As the clock frequency of a chip increases, the on-chip decoupling capacitor must be placed closer to the load to be effective. A method of efficiently defining the location of capacitor placement to meet specified noise limits is presented. Based on a single RL line model for the power distribution system, charging radius of the decoupling capacitor is calculated under the constraint of the target noise but not the constraint of being fully charged. Under the constraints of the length of the charging path and the target noise, discharging radius of the decoupling capacitor is figured out. The conversion coefficient that converts the radii of a decoupling capacitor in a single RL line model into the equivalent one in a meshed model is presented based on the expression that can exactly compute the impedance between any two points on an infinite meshed network. In this paper, it is shown that the conversion coefficient is a constant when the radius of the decoupling capacitor is taken as the per unit length of the meshed model.