Guang-Xiao Luo

Modeling of arbitrary power-ground planes with slot by using integral equation and transmission line method

A coupled integral equation equivalent circuit (IEEC) and transmission line (TML) method is used to model the gapped power-ground planes. The integral equation equivalent circuit method can model an arbitrary shaped power-ground pair with much less time than usual commercial software. However, in gaped planes, there is strong coupling between the two sides of narrow slot, so the coupling effects should be taken into account in the modeling. In this model, the segmental lumped circuits of coupled microstrip lines are integrated to the equivalent circuit, which is deprived by the integral equation equivalent circuit method for arbitrary shaped power-ground (PG) planes. The proposed method has been examined by using he commercial simulator HFSS through several examples.

PDN Impedance Modeling for Multiple Through Vias Array in Doped Silicon

The power distribution network (PDN) impedance of 3-D-through silicon vias (TSVs) interposer layer is modeled by considering the metal-oxide-semiconductor (MOS) structure effects. The Lambert W function is proposed to simulate the change of depletion width with the bias voltage in the static field, and the high-frequency MOS capacitance is obtained while considering the charges at the semiconductor-insulator interface. Furthermore, based on the depletion width and the insulating dielectric layer assumption, the electrical model of power-ground TSVs pair is presented by combining the MOS capacitance with TSVs parasitic RLGC (resistance-inductance-capacitance-conductance). Finally, the PDN impedance characteristics of the 3-D-IC integrated system with multiple TSVs are performed by using the proposed multitransmission line and model reduction methods, and the importance of the capacitance is presented.

A New Hybrid Field-Circuit Approach to Model the Power–Ground Planes With Narrow Slots

Narrow slots are often employed in printed circuit board and electronic package designs to isolate the power noise coupling. In this paper, an equivalent circuit method is proposed to analyze the power and signal integrity of gapped power-ground (PG) planes. With this method, the whole gapped PG planes are divided into two regions: one is a parallel-plane structure, and another is a slot structure. An integral-equation equivalent circuit method is used to model the arbitrarily shaped parallel-plane structure. Meanwhile, the transmission-line method is used to model the slot structure. Finally, the whole modeling of gapped PG planes can be obtained by integrating the aforementioned two equivalent networks. Numerical examples reveal that this circuit approach is efficient and accurate, in comparing with the available methods.

Modelling of planar EBG structure by using equivalent circuit method

A novel method based on equivalent circuit is presented to model and analyze the EBG(Electromagnetic Band Gap) structure of power planes. The planar EBG structure is divided into cells and connecting parts, the equivalent circuit is developed by combining the integral equation multi-port networks and the micro-strip transmission lines. The stop bandgap of the EBG structure is obtained by the circuit simulation. The proposed method is validated by both measurement and full-wave simulation, where the proposed EBG structure shows the stop bandgap at 0.7-3 GHz with less than -50 dB insertion loss.

Full RLGC model extraction of Through Silicon Via (TSV) with charge distribution effects

The analytical model based on Poisson–Boltzmann equation in a cylindrical coordinate system is developed for simulating the electrical parameters of the three-dimensional Through Silicon Via (TSV) interconnection. Considering the effects of bias voltage, the accurate charge distribution and the high-frequency capacitance in the depletion layer of the semiconductor is obtained. Moreover, the resistance and inductance parameters of TSV are extracted by using the partial element equivalent circuit method. Finally, the full resistance–inductance–capacitance–conductance electrical model of TSV interconnection is presented first time with the semiconductor behaviour, and the transmission characteristics of signal-ground TSV structure are studied.

Analytical extraction of via-via inductance by using SMM for power-ground planes

In this paper, the via-via inductance between power-ground plane in printed circuit board is extracted analytically by using the scattering matrix method(SMM). A gap voltage source is used to excited the higher order modes between parallel plates, by solving the linear scattering matrix equation, the scattered wave coefficient is obtained, furthermore, the admittance parameter between two vias is calculated, and the analytical inductance formula with frequency dependence is obtained and validated by quasi-static numerical method.

EMI and EMC analysis of arbitrarily shaped power-ground planes

The radiation from a power-ground planes structure in high-speed printed circuit boards due to high switching noise current is investigated in this paper. A 2D contour integral method is used to characterize the radiation from the power-ground planes. The contour integral method can model an arbitrarily shaped power-ground planes pair more efficient than 3D numerical methods. By combining the noise current source with the [Z] matrix of power-ground planes, the edge voltage and electric field are obtained. Based on the field equivalent principle, the equivalent magnetic current around the edges of power-ground planes is obtained. Thereafter, the radiated intensity is calculated by equivalent magnetic current and free-space Green function.