Ying S. Cao

Distributive Radiation and Transfer Characterization Based on the PEEC Method

Power radiation and radiated coupling among different structures represent an important area for research study. The partial element equivalent circuit method (PEEC) is a powerful technique which bridges the gap between the electromagnetic and circuit theories. In this paper, we develop a new approach for PEEC to calculate the distributive power radiation and couplings. With this approach, formulations for both the radiated power and the transferred power can be evaluated. Further, the physical meanings of the power results are interpreted according to the conservation of energy law. We use electric dipoles, magnetic dipoles and patch antennas as well as coupled microstrip lines to benchmark the method. The approach can also be applied to EMC/EMI and other power dissipation computations.

An Equivalent Circuit Model for Graphene-Based Terahertz Antenna Using the PEEC Method

The electromagnetic (EM) characterization of graphene under general EM environments is becoming of interest in the engineering and scientific research fields. However, its numerical modeling process is extremely cost prohibitive due to the huge contrast between its thickness and other dimensions. In this work, for the first time, the EM features of graphene are characterized by a circuit model through the partial element equivalent circuit (PEEC) method. The atomically thick graphene is equivalently replaced by an impedance boundary condition. After incorporating the PEEC method, a novel surface conductivity circuit model is derived for graphene. A physical resistor and inductor are added into the conventional PEEC cell due to the dispersive conductivity property of graphene. The proposed novel method significantly reduces the memory and CPU time consumption for general graphene structures when compared with standard numerical finite element method (FEM) or finite difference (FD) methods, where 3-D meshing is unavoidable. This model also transforms the surface conductivity of graphene into a vivid circuit, and physical properties of the material can be conveniently obtained, such as radiation, scattering, and resistance properties, when compared with method of moments (MOM). In addition, the radiation and scattering calculation by MOM entail the cumbersome steps of defining a bounding surface and implementing a multidimensional integrand, while in PEEC, these complications are entirely bypassed by the concise vector-matrix-vector product (VMVP) formulas. To validate the introduced algorithm, various numerical examples are presented and compared with existing references.

Inductance Extraction for PCB Prelayout Power Integrity Using PMSR Method

Proper power integrity (PI) analysis is required for printed circuit board (PCB) power distribution network (PDN) design. Top-layer interconnect inductance for PI has always been a vital concern for high-speed industry. Developing a simple physics-based equivalent circuit model for critical structures is essential for understanding the physics of the system and for intelligent designs. In this paper, a physics-based model size reduction (PMSR) method is applied to get the equivalent circuit model for the above-ground geometries. The extracted physics-based models are also based on the partial element equivalent circuit (PEEC) method, and can be used in analyzing the structure in its parts. By applying PMSR method, a physics-based equivalent circuit model can be proposed and this circuit model is related to the geometric features of the design. In this way, PMSR method can provide an intuitive guideline in designing PCB and reducing above inductances, therefore, a low-ripple dc voltage can be delivered through PDN. Taking advantage of PEEC and PMSR methods, the top-layer inductances of three different geometries are calculated and the physics-based circuit models are obtained, respectively.

Physical interpretation of radiation and transfer characterization based on the PEEC method

The characterization of power radiation and coupling has been an important research subject. The partial element equivalent circuit method (PEEC) is a powerful tool in bridging the electromagnetic modeling together with a circuit solver. Even though PEEC was a convenient tool for many quasi-static applications, in this paper, we propose a new approach for PEEC to calculate the radiated and coupled power from the distributive point of view. Formulations for both radiated and transferred powers are proposed based on a full wave PEEC model. Distributive power can be evaluated with negligible additional computational cost in PEEC implementations. The physical meaning is interpreted according to the energy conservation law. Representative radiating units are employed as benchmarks. The proposed method can be applied in the diagnosis and optimization process for signal integrity, EMI, EMC, etc.

The Derived Equivalent Circuit Model for Magnetized Anisotropic Graphene

Due to the static magnetic field, the conductivity for graphene becomes a dispersive and anisotropic tensor, which complicates most modeling methodologies. In this communication, a novel equivalent circuit model is proposed for graphene with the magnetostatic bias based on the electric field integral equation. To characterize the anisotropic property of the biased graphene, the resistive part of the unit circuit is replaced by a resistor in series with current-controlled voltage sources (CCVSs). The CCVSs account for the off-diagonal parts of the surface conductivity tensor for the magnetized graphene. This proposed method is benchmarked with numerical examples. This communication also provides a new equivalent circuit model to deal with anisotropic materials.

Distributive radiation characterization based on the PEEC method

The intentional and unintentional radiations are of great importance to electromagnetic coupling and radiation problems in both high and low frequency regimes. However, conventional computational methods emphasize the port-to-port performance instead of the detailed radiation mechanism that is critical to designs and optimizations. In this paper, we employ the PEEC method to quantitively analyze, model, and illustrate how the energy is coupled and radiated. We also try to point out, based on calculations, which part is a greater contributor to the wanted or unwanted radiation. Employing the dynamic Greens function, the power terms associated with the inductive and capacitive components in the PEEC model can be explicitly extracted and categorized. Then the power relationship between multi-radiators and sub-segmentations of a single radiator can be analyzed clearly. How the partial elements contribute to radiation and transmission powers is also demonstrated at the end of the paper.

The derived equivalent circuit model for non-magnetized and magnetized graphene

In this work, for the first time the electromagnetic features of graphene are characterized by a circuit model derived instead of fitted from the electric field integral equation (EFIE). The atomically thick graphene is equivalently replaced by an impedance surface. When it is magnetized, the impedance surface is anisotropic with a tensor conductivity. Based on EFIE, the graphenes circuit model can be derived by the partial element equivalency circuit (PEEC) concept. The anisotropic resistivity is modeled using a serial resistor with current control voltage sources (CCVSs). From the derived circuit model, electromagnetic properties of graphene can be conveniently analyzed. This work also provides a new characterization method for dispersive and anisotropic materials.

Distributive Radiation Characterization Based on the PEEC Method

Summary form only given. The intentional and unintentional radiations are of great importance to wireless power transfer at the low frequency regime and antenna signal transportation at the higher frequency regime. Due to the rising speed of digital systems and thereby broad bandwidth of signal channels at all levels of electronic devices, it becomes more essential than ever to quantitively analyze, model, and illustrate how the energy is leaked out and which part is a greater contributor to the wanted or unwanted radiation. However, conventional computational methods seem to be not sufficient to answer these questions. They mostly focused on characterizing port based properties such as matching condition and insertion losses, or gave general efficiency description and radiation patterns. But it is not clear how the energy is radiated and coupled from different parts of the radiator. For computational electromagnetics algorithms, they blended all physical phenomena together and made the radiation property extraction and analysis not straightforward. In this work, we extend the partial element equivalent circuit (PEEC) method to distributive radiation analysis so that the radiation and coupling contributions from each segment of the whole radiator can be singled out. Instead of focusing on the conventional circuit modeling method of PEEC, we focus on distributive radiated power and transferred power calculation. To fully stick to the first principle without sacrificing reliability, dynamic Greens function is used throughout the proposed method, not only for the coupling term, but also for the self term. A great significance of this work is that it can help to provide eligible lossy model of antenna structures and meta surfaces more accurately, which avoids approximations and curve fitting methods frequently used in RF and microwave engineering designs to make the circuit model more physical. For example, we can benchmark the idea through the coupling and radiation mechanism of arbitrarily electrical radiators and magnetic radiators. The radiated power and coupled power between coupled structure will be systematically calculated and analyzed using the proposed method. It gives much more insights than the conventional radiation impedance concept. This work was supported in part by Hong Kong GRF 713011, GRF 712612, and NSFC 61271158.

Characterizing EMI radiation physics for edge-and broad-side coupled connectors

Electromagnetic radiation for a printed circuit board (PCB) midplane connector is studied in this paper. By applying integral-equation (IE) based method and characteristic mode (CM) analysis, the current is split into radiating and non-radiating ones. The radiated power from each part of the structure can be quantified using the radiating current. Therefore, the radiation hot spot can be identified for both edge-side coupled and broad-side coupled connectors. Furthermore, the radiation characteristics for these connectors are compared.

A novel z-directed embedded component for the reduction of voltage ripple on the power distribution network for PCBs

A new capacitor package and PCB embedding technique is introduced to significantly reduce the system power distribution network impedance at the pads of surface mounted integrated circuits. The capacitor is multi-layer ceramic capacitor (MLCC) that is a right cylindrical shape with via channels in the outer wall along the axis of the part. The capacitor called a Z-Directed component (ZDC) is then pressed into a hole in the PCB. The connections to the component are then made by the copper plating process similar to via hole construction. This new configuration dramatically improves the PDN performance of PCBs with fewer components than the conventional solution with SMD decoupling capacitors.