Probabilistic power flow analysis based on arbitrary polynomial chaos expansion for networks with uncertain renewable sources

The ball grid array (BGA) structure is the interconnection between package to printed circuit board and the discontinuity from BGA affects the performance for the whole link path in the high-speed digital system. So, it is important to accurately model the BGA structures. In current methods, the current distribution of conductors is treated as isotropic. However, the pitch size of solder balls is comparable to the diameter. The current is no longer uniformly distributed. In this paper, a fast modal-based approach is developed to accurately and efficiently capture the proximity effect. Image theory is also applied in the proposed approach to reduce the computational domain from 3-D structure to 2-D. The matrix reduction approach is applied to obtain the physical loop inductance. The lumped capacitance is obtained in [1] . A $\pi $ topology equivalent circuit model for the BGA structure is built. Good agreement between the equivalent circuit model and full-wave simulation can be achieved up to 40 GHz.

Analytical Equivalent Circuit Modeling for BGA in High-Speed Package

The variability of crosstalk due to changes in differential and ground via configurations is studied in this paper. The polynomial-chaos method and the response surface method are adopted to mathematically model the variability. One goal of the work is to exploit the obtained models to locate the optimal response that both meets the performance requirement and remains robust to geometry variations due to manufacturing tolerances. Both methods correlate well with simulations and show great capabilities in practical applications for optimization and sensitivity analysis. The other goal of the work is to compare the two methods in terms of mathematical theories, sampling schemes, postprocessing, accuracy, efficiency, and limitations. Details of the comparison is given through this paper and a summary table is included in Section V .

Variability Analysis of Crosstalk Among Differential Vias Using Polynomial-Chaos and Response Surface Methods

Compared to 4-port de-embedding, 8-port de-embedding is much more challenging due to the presence of crosstalk terms in both the differential mode and the common mode. Using the 2nd order mixed-mode concept, this work proposes an 8-port smart fixture de-embedding (SFD) method. The proposed method neglects modal conversion terms by requiring balanced and symmetrical designs. Analysis showed that this approximation generally has negligible impact on the de-embedded differential results with careful test fixture design.

Differential S-Parameter De-embedding for 8-Port Network

Multilayer printed circuit boards are widely used for the development of modern computing equipment. Often, in multi-layer printed circuit boards, electromagnetic compatibility problems arise. This leads to a distortion of information signals in interconnects. One of the reasons for the distortion of information signals in a multilayer printed circuit board is the resonant effects in interconnects. Resonant effects in interconnects can occur due to the presence of cutouts in the ground layer or power layer of board. These cutouts are present to connect any elements, connectors, etc. A tool is proposed in the work and simulation models for the analysis of resonance effects are developed. The distortion of information signals due to resonance effects in interconnects in the presence of cutouts in the ground layer is simulated. Comparison of the results of numerical modeling with experimental data indicates sufficient accuracy of the developed models.

Research of Resonant Effects in Interconnects of Multilayer PCB of Computing Equipment

The variability of the worst-case crosstalk among differential vias in response to the change of the relative locations of the ground and the differential vias are studied in this work. The polynomial-chaos (PC) and the design of experiments (DoE) methods are applied to construct the statistical models. Both methods work well. But the DoE method is preferred in our case since it takes fewer simulations.

Variability analysis of crosstalk among pairs of differential vias using polynomial-chaos and design of experiments methods

In electric vehicles, the pulse width modulation scheme is widely used in three-phase motor drive systems for its high performance. However, the fast switching of semiconductor devices may induce excessively high dv/dt and di/dt, which can cause electromagnetic interference (EMI) issues, making it difficult to satisfy electromagnetic compatibility standards. In this paper, the current conducted emission test for a three-phase motor drive system is performed based on CISPR 25 component-level testing setup for AM radio frequency band, which is from 530 kHz to 1.8 MHz. Under these conditions, common-mode (CM) noise generation mechanisms of the motor drive system are identified through measurements. It is found that the dominant mechanism is the mode conversion from differential mode (DM) switching current of the three-phase PWM inverter to CM current through the cable harness due to the imbalances in the PCB structure and EMI filter network which are at the dc input side of the three-phase inverter. Based on this finding, ground (GND) bridges are added between the digital signal and power GND nets to reduce the CM noise. The GND bridge effect on the reduction of CM noise in AM band is experimentally verified and further studied using circuit simulations.

Ground Bridge Effect on Reduction of Conducted Emission from Three-Phase Motor Drive System

A differential via structure with four varying factors are defined in this paper. The Monte Carlo (MC), stochastic collocation (SC) and design of experiments (DoE) methods are employed to quantify the drilling uncertainties in the abovementioned via structure. A comparison of the results shows that the SC method is more robust and can more efficiently and accurately estimate the mean and the standard deviation of the responses, compared to the DoE method.

Studying the effect of drilling uncertainty on signal propagation through vias

The mobile industry processor interface (MIPI) standards defines industry specification for design of mobile devices such as smartphone, tables, laptop and hybrid devices. Such standard plays a critical role in the Internet of Things (IoT), 5G mobile devices, as well as autopilot automobiles. MIPI specification has comprehensive requirements on the data storage, data transfer, display, camera, memory, power, etc on the transmitter and receiver. In the testing phase, the transmitter and receiver may not be easily directly measured. Herein, a fast transmitter and receiver eye diagrams calculation methodology is necessary to predict the RX and TX performances of those devices. The calculated RX and TX eye diagrams are evaluated by using the D-PHY protocol to identify the quality of the signals. An in-house MIPI tool is built to directly display the calculated eye diagrams as well as the MIPI D-PHY report in the PC. The validations are performed by using both simulation and measurement examples.

Srinath Penugonda

Papers

Variability Analysis of Crosstalk Among Differential Vias Using Polynomial-Chaos and Response Surface Methods

Variability analysis of crosstalk among pairs of differential vias using polynomial-chaos and design of experiments methods

Ground Bridge Effect on Reduction of Conducted Emission from Three-Phase Motor Drive System

Studying the effect of drilling uncertainty on signal propagation through vias

Fast Transmitter and Receiver Eye Diagrams Acquisition in the MIPI D-PHY Interface