Power systems for modern complementary metal-oxide-semiconductor (CMOS) technology are becoming harder to design. One design methodology is to identify a target impedance to be met across a broad frequency range and specify components to meet that impedance. The impedance versus frequency profiles of the power distribution system components including the voltage regulator module, bulk decoupling capacitors and high frequency ceramic capacitors are defined and reduced to simulation program with integrated circuit emphasis (SPICE) models. A sufficient number of capacitors are placed in parallel to meet the target impedance. Ceramic capacitor equivalent series resistance (ESR) and ESL are extremely important parameters in determining how many capacitors are required. SPICE models are then analyzed in the time domain to find the response to load transients.

Power distribution system design methodology and capacitor selection for modern CMOS technology

The decoupling of modern printed circuit boards introduces a very complex task. Powerful stochastic optimizers are usually used to determine values and positions of decoupling capacitors on the board. The number of capacitors used has to be determined a priori by the user which brings problems with convergence of the optimization process or can lead to a waste of resources when the noises are to be attenuated to a certain level. In this paper, an approach based on the combination of time-domain contour integral method and optimization with variable number of dimensions is introduced. The optimizer works with models having variable dimensions and searches for the optimal one. The approach is tested on two example power circuit boards with various noise attenuation limits and constraints on capacitor positions and values.

PCB Decoupling Optimization With Variable Number of Capacitors

This article considers fractional coupled networks with discrete and distributed delays, an algebraic criterion on global synchronization is derived by using fractional Razumikhin approach and matrix inequalities. Furthermore, two types of special fractional delayed networks are also investigated and several simple sufficient conditions on global synchronization are presented, respectively. Finally, two numerical examples are provided to demonstrate the validity of our theoretical results.

Global synchronization of fractional coupled networks with discrete and distributed delays

This paper considers both local and global synchronizations of fractional-order nonlinearly-coupled complex networks with time delay and unknown external disturbances. Here, neither delayed or non-delayed configuration matrices are necessarily irreducible or symmetric. Combined with the fractional order compare theorem and fractional order stability theory, some novel sufficient conditions are obtained that guarantee the realization of local and global asymptotic synchronization via adaptive control and pinning control. The network model and conclusion in this paper are more practical and general than those in the existing literature. The experimental results show the feasibility of our theoretical analysis.

Adaptive Synchronization of Fractional-Order Nonlinearly Coupled Complex Networks With Time Delay and External Disturbances

Miniaturized microwave cavities constructed by the parallel-plate waveguide (PPW) becomes one of the main propagation pathways of the radio-frequency interference (RFI) in 3-D integrated circuits. It is still challenging to suppress RFI in the practical cavities, where the space is extremely constrained. In this work, the working mechanism and design method of the noise suppression sheet (NSS) is quantitatively studied, serving as an efficient approach to suppress RFI within an electrically small size in these microwave cavities. The analysis is based on the dispersion relationship derivation of the NSS-loaded PPW structure. Both the derived formulas and the numerical study reveal that the imaginary part of the permeability, that is, $\mu _{i}$ , of the NSS plays a key role in increasing the reflection and attenuation loss, and thus obtaining a high RFI suppression level. Further study indicates even when the NSS’s profile is lower than 10% of the cavity’s height and the length is lower than $0.1\lambda _{0}$ , its suppression level up to 10 dB can be well accomplished, which is deemed difficult to achieve by using conventional methods. Moreover, this method is, respectively, applied in three practical engineering scenarios for the RFI suppression, that is, heatsink package above a chip, power distributed network (PDN), and flexible circuit. Good agreement is observed between the measurement results and the simulated ones, which confirmed the efficacy of our quantitatively developed NSS. The proposed method is promising for broad industrial applications, such as tiny chip packages, multi-channel systems, and flexible electronics.

Ultrathin, Electrically Small Noise Suppression Sheet for Microwave Cavities of 3-D Integrated Circuits: Design Methodology and Realization

In this paper, we propose a closed-form solution for the impedance calculation of grid power distribution network (PDN). Through the comparison of the equivalent circuit of the unit cell between the grid PDN and plane PDN, the complex three-dimensional (3-D) grid PDN is equivalent to a simple 2-D plane PDN with the same size. The impedance of this equivalent plane PDN can be calculated by the closed-form method. In order to further increase the accuracy of the proposed method, a modified modal function is proposed. And the original double series summation formula is reduced to a single series summation formula to accelerate the calculation. The proposed closed-form formula is scalable, and it can be used for grid PDNs with the sizes from micrometer to centimeter. To verify its accuracy, a micrometer grid PDN is calculated with the proposed closed-form formula up to 40 GHz, and a centimeter grid PDN is fabricated and measured for 10 MHz–1 GHz. The results obtained by the proposed method show good agreements with that obtained by 3-D full-wave simulation and measurement. Finally, the advantage of the proposed closed-form method for the analysis of the grid PDN modal voltage and current distributions and decoupling capacitor placement is demonstrated.

A Closed-Form Solution for the Impedance Calculation of Grid Power Distribution Network

For the package or on-chip power distribution network (PDN) design, plane metals are usually adopted. In this paper, we propose a closed-form grid metals solution to calculate the inductance of such grid PDN for the frequencies below its first antiresonant frequency. First, the grid PDN is equivalent to a plane PDN based on the equivalent circuit of their unit cells. Furthermore, the equivalent plane PDN is simplified as an RLCG lumped circuit, where ${L}$ is the inductance of the grid PDN. Finally, the inductance of the grid PDN is obtained by the mode analysis of the equivalent plane PDN with a modified modal function. The proposed method is scalable, which can calculate the grid PDNs with the size from micrometer to centimeter. To verify the proposed method, a centimeter grid PDN is fabricated. The inductance obtained by the proposed method has a good agreement with that obtained by measurement and 3-D full-wave simulation. The proposed method can also be expanded to the case that the grid PDN has load impedances. In comparison with the numerical methods, the proposed method can give a more easy-to-understand explanation of the new antiresonant frequency produced by the load impedance.

Inductance Extraction of Grid Power Distribution Network

The grid power distribution network (PDN) is an essential component in electronic packages to provide the dc power to circuits. In this paper, an integral equation hybrid method is proposed for the efficient calculation of the impedance of the complex grid PDN. First, the original 3-D grid PDN is reduced to a simple 2-D plane PDN. Both of them have the same input and mutual parasitic impedances. After that, this equivalent plane PDN is solved by using the 2-D integral equation method to consider its arbitrary shape. By comparing between the obtained impedances from the proposed method, full-wave method, and measurement, the accuracy and efficiency of the proposed method is verified. The proposed method provides a simple and useful electronics design automation tool for the power integrity analysis of complex circuits.

An Integral Equation Hybrid Method for the Impedance Calculation of the Grid Power Distribution Network With an Arbitrary Shape

In this paper, an efficient method is proposed to calculate the impedance of the grid power distribution network (PDN) with irregular shapes. Based on the analysis of the equivalent circuits of grid unit cell and plane unit cell, the irregular shaped grid PDN is simplified to a plane PDN with the same shape. The differences in the grid PDN and equivalent plane PDN are the material parameters of substrate and metal. The equivalent plane PDN has the equivalent conductivity, permeability, relative permittivity and loss tangent. Then, the equivalent plane PDN is efficiently calculated by the finite element method due to its simplified structure. The proposed method can be used to calculate the irregular shaped grid PDN of different sizes. An example is given to verify the effectiveness of the proposed method.

Wei-Ying Ding

Papers

A Closed-Form Solution for the Impedance Calculation of Grid Power Distribution Network

Inductance Extraction of Grid Power Distribution Network

An Integral Equation Hybrid Method for the Impedance Calculation of the Grid Power Distribution Network With an Arbitrary Shape

Impedance calculation of grid power distribution network with irregular shapes