Characterization of Co-Planar Silicon Transmission Lines With and Without Slow-Wave Effect

Co-planar lines on silicon substrates with and without slow-wave effect are characterized using time-domain reflectometry (TDR) and vector network analyzer (VNA) measurements, and simulated using a proposed nonphysical resistance-inductance-conductance-capacitance (RLGC) model. The silicon co-planar lines are characterized based on comparison to package transmission lines. Co-planar silicon lines without slow-wave mode are modeled in the same way as package transmission lines, but co-planar lines with slow-wave mode are modeled in a different way from package transmission lines. Hence, a nonphysical RLGC model including slow-wave mode is proposed along with the extraction method from VNA measurements. Simulation results correlate well with time- and frequency-domain measurements for the co-planar silicon lines.     

Transient Simulation of Lossy Interconnects Based on a Dispersive Hybrid Phase-Pole Macromodel

A transient simulator for interconnect structures that are modeled by lossy transmission lines is outlined in this paper. Since frequency-dependent RLGC parameters must be employed to correctly model skin effects and dielectric losses for high-performance interconnects, we first study the behaviors of various lossy interconnects that are characterized by frequency-dependent line parameters (FDLPs). We then developed a frequency-domain dispersive hybrid phase-pole macromodel (DHPPM) for such lines, which consists of a constant RLGC propagation function multiplied by a residue series. The basic idea is to first extract the dominant physical phenomenology by using a propagation function in the frequency domain that is modeled by frequency-independent line parameters (FILPs). A rational function approximation is then used to account for the remaining effects of FDLP lines. By using a partial fraction expansion and analytically evaluating the required inverse Fourier transform integrals, the time-domain DHPPM can be decomposed as a sum of canonical transient responses for lines with FILP for various excitations (e.g., trapezoidal and unit step). These canonical transient responses are then expressed analytically as closed-form expressions involving incomplete Lipshitz-Hankel integrals of the first kind and Bessel functions. The closed-form expressions for these canonical responses are validated by comparing with simulation results from commercial tools like HSPICE. The DHPPM simulator can simulate transient results for various input waveforms on both single and coupled interconnect structures. Comparisons between the DHPPM results and the results produced by commercial simulation tools like HSPICE and a numerical inverse fast Fourier transform show that the DHPPM results are very accurate.     

基于硅氧化层的嵌入式传输线制造

在有损耗的硅衬底上试制了传输线(微带以及共面波导),并嵌入在CMOS Cu/SiO2互连层中.对传输线的几何尺寸与其特征阻抗、损耗以及衰减因子进行了研究.结果表明嵌入在硅氧化层中的微带和共面波导可以在有损耗的硅片上低损耗地实现,为在硅片上设计微波和毫米波电路提供了必要的无源器件.     

使用传输线理论的硅通孔电参数提取方法

针对三维集成电路中的关键技术硅通孔的电特性,使用传输线理论提取了其单位长度RL-GC参数。将硅通孔等效为传输线,利用HFSS仿真结果并结合传输线理论给出了具体的参数提取方法。计算结果表明,硅通孔单位长度RLGC 参数呈现较强的频变特性,当频率从1 MHz增加到20 GHz时,单位长度的电阻和导纳分别从0.45 mΩ/μm和2.5μS/μm增加到2.5 mΩ/μm和17μS/μm,而单位长度电感和电容分别从8.7 pH/μm和8.8 fF/μm减小至7.5 pH/μm和0.2 fF/μm。与传统的阻抗矩阵和导纳矩阵提取方法相比,该方法具有结果绝对收敛和适用频率高等诸多优点,可进一步应用于三维集成电路的仿真设计。     

Wideband and low return loss coplanar strip feed using intermediatemicrostrip

A wideband and low return loss coplanar strip feed has been achieved using an intermediate microstrip line between coax and coplanar strip lines. The measured and calculated return loss are below 13 dB up to 18 GHz. An extended calculation using TDR data shows the return loss below 10 dB up to 30 GHz. This coplanar strip feed is very practical for feeding wideband electro-optic devices which use coplanar strip as the electrodes     

Electromagnetic coupling of coplanar waveguides and microstriplines to highly lossy dielectric media

The spectral-domain technique is utilized to analyze the coupling characteristics of coplanar waveguides and microstrip lines coupled with multilayer lossy dielectric media. Numerical results illustrating the dispersion characteristics of coplanar and microstrip lines, as well as the various electric field components coupled to highly lossy dielectric media, are presented. It is shown that the presence of a superstrate of lossless dielectric between the coplanar waveguide and the lossy medium plays a key role in setting up an axial electric field component that facilitates leaky-wave-type coupling to the lossy medium. The thickness of the superstrate relative to the gap width in the coplanar waveguide is important in controlling the magnitude of this axial electric field component. The coupling characteristics of the microstrip and coplanar lines are compared, and results generally show improved coupling if coplanar waveguides are utilized. Values of the attenuation constant α are higher for coplanar waveguide than for microstrip line, and for both structures α decreases with frequency     

不等长非均匀有损耗传输线FDTD瞬态分析

以分析等长均匀无损耗多导体传输线的时域有限差分(FDTD)法为基础,在考虑传输线损耗的情况下,对不等长非均匀多导体传输线进行分析。首先,在考虑传输线损耗的情况下给出传输线上各点电压和电流的迭代计算公式;其次,利用该公式对不等长非均匀有损耗传输线模型进行数值计算和理论分析;最后,通过仿真实验,其结果表明所提计算方法是正确和有效的。该方法对不等长非均匀有损耗传输线的研究提供理论计算参考。     

A 7-dB 43-GHz CMOS Distributed Amplifier on High-Resistivity SOI Substrates

This paper presents designs and measurements of distributed amplifiers (DAs) processed on a 130-nm silicon-on-insulator CMOS technology on either standard-resistivity (10 Omegamiddotcm) or high-resistivity (>1 kOmegamiddotcm) substrates, and with either body-contacted (BC) or floating-body (FB) MOSFETs. Investigations have been carried out to assess the impact of active device performance and transmission line losses on circuit design by means of simulations, analytical calculations, and comparisons of the small-signal equivalent-circuit parameters. On standard-resistivity substrates, DAs with FB devices and lossy microstrip lines on thin film exhibit a measured gain of 7.1 dB and a unity-gain bandwidth (UGB) of 27 GHz for a dc power consumption of 57 mW. With the introduction of high-resistivity substrates, other DAs, with the same architecture and using lower loss coplanar waveguide lines, show a UGB of 51 GHz with FB devices and 47 GHz with BC devices. To the authors' knowledge, the designs presented in this paper achieve the best tradeoffs in terms of gain, bandwidth, and power consumption for CMOS-based circuits with comparable architecture.     

Characteristics of coplanar transmission lines on multilayersubstrates: modeling and experiments

Characteristics of coplanar transmission lines on multilayer substrates expressed in analytic formulas have been obtained using conformal mapping. The accuracy of these formulas has been verified experimentally on a variety of coplanar transmission lines using differential electro-optic (DEOS) sampling. For coplanar waveguides, the theory differs from the experiment by less than 3%; for coplanar striplines, the differences are less than 6%     

Electrical properties of coplanar transmission lines on lossless and lossy substrates

The characteristic impedance and the propagation constant of coplanar transmission lines on lossless and lossy substrates are given and compared with computed values within the frequency region 0?8 GHz. Al2O3 and n-Si substrates are used.     

An equivalent transmission-line model containing dispersion forhigh-speed digital lines-with an FDTD implementation

The increase in processor speeds in the last few years has created a growing need for the accurate characterization of waveform propagation on lossy printed-circuit-board (PCB) transmission lines. Due to the dispersive nature of pulse propagation on lossy transmission lines, approximations of the classic transmission-line model can fail in this application (i.e., lossless or DC losses approximations). This paper shows how an equivalent transmission-line model can be used to analyze dispersive transmission lines for high-speed digital applications. The equivalent-circuit elements of this transmission-line model incorporate the frequency dependence of the per unit length impedance and admittance caused by the finite conductivity of the conductors as well as the dielectric losses. We show that these equivalent circuit elements can be readily implemented into finite-difference time-domain (FDTD) transmission-line codes, and we present such a FDTD implementation. S-parameters and pulsed waveforms for a circular wire, coplanar waveguides (CPW) and microstrip lines are shown. Finally, we present approximate expressions for analytically obtaining the resistance and inductance per length of a microstrip line     

Compact model generation for on-chip transmission lines

An approach for the fast and accurate generation of compact distributed circuit models for on-chip transmission lines on lossy silicon substrates is presented. Using a novel ABCD matrix partitioning procedure, accurate distributed circuit models are extracted from scattering parameters obtained from measurements and calibrated full-wave electromagnetic simulations for a small set of transmission-line geometries spanning ranges of design parameter values. A feedforward artificial neural network is trained using the extracted results, and applied to generate accurate compact models for arbitrary values within the bounds of the training ranges. Consequently, the model generation time is greatly reduced compared to conventional approaches by exploiting the interpolation capabilities of the neural network. The compact model generator is fully compatible with HSPICE and SPECTRE-RF and is easily incorporated into parasitic-aware RF circuit design and optimization tools.     

Analytical analyses of v, elliptic, and circular-shaped microshieldtransmission lines

Several new types of monolithic coplanar transmission lines, v, elliptic, and circular-shaped microshield coplanar waveguide, have been proposed. The characteristic impedance expressions for those transmission lines have been derived using the conformal mapping method (CMM) under the assumption of the pure-TEM propagation and zero dispersion. In the analyses of the elliptic and the circular-shaped microshield coplanar lines, the methods using the graphical approximation and taking the geometric mean value of the upper and the lower bounds to the size of the line are put forward to calculate the characteristic impedance of this two kinds of microshield coplanar lines. The numerical results show the effects of the different shaped microshield walls on characteristic impedances     

Analysis and optimization of coplanar RLC lines for GSI global interconnection

Compact physical models are derived for the delay and crosstalk of on-chip coplanar transmission lines, which are used in state-of-the-art high-speed microprocessors. These lines are mainly used for long global interconnects that are relatively thick and wide and have prominent inductive effects. The models are then used to optimize the design of coplanar global interconnects.     

Guided-wave characteristics of periodic coplanar waveguides with inductive loading - unit-length transmission parameters

Periodic coplanar waveguides (CPWs) with inductive loading are thoroughly studied by resorting to unit-length transmission parameters, i.e., propagation constant and characteristic impedance, of an equivalent dispersive and/or lossy transmission line. The admittance-type method of moments (MoM) is at first formulated to full-wave modeling of a finite-cell periodic CPW with the two feeding lines and then the short-open-calibration procedure is carried out to deembed the two-port ABCD matrix of the core periodic CPW section. Thus, the above two parameters can be extracted from the MoM simulation to exhibit their guided-wave characteristics, i.e., slow-wave and bandstop behaviors. It is demonstrated for the first time that, within the bandstop or bandgap, the propagation constant must become complex with a nonzero attenuation constant, while the characteristic impedance appears purely imaginary. Three periodic CPW circuits with six finite cells are then characterized on a basis of the transmission-line theorem and the derived S-parameters are validated by Momentum simulation and RF measurement.     

The influence of finite conductor thickness and conductivity onfundamental and higher-order modes in miniature hybrid MIC's (MHMIC's)and MMIC's

The effect of finite metallization thickness and finite conductivity on the propagation characteristics of conductor-backed CPW on thin substrate is rigorously analyzed. A self-consistent approach is used together with the method of lines (MoL) to determine the propagation constant, losses and field distribution of the fundamental and first two higher-order modes in coplanar waveguides (CPWs) with finite metallization thickness and lossy backmetallization. The method used is general and can be applied to miniature MHMICs and MMICs including lossy semiconductor substrate. It is shown that the onset of higher-order modes limits the usable frequency range of conductor-backed CPWs. The analysis also includes microstrip transmission lines on thin substrate material. It is demonstrated that a resistive strip embedded into the microstrip ground plane may potentially be useful in the design of integrated planar attenuators     

Characterization and attenuation mechanism of CMOS-compatible micromachined edge-suspended coplanar waveguides on low-resistivity silicon substrate

This paper presents detailed characterization of a category of edge-suspended coplanar waveguides that were fabricated on low-resistivity silicon substrates using improved CMOS-compatible micromachining techniques. The edge-suspended structure is proposed to provide reduced substrate loss and strong mechanical support at the same time. It is revealed that, at radio or microwave frequencies, the electromagnetic waves are highly concentrated along the edges of the signal line. Removing the silicon underneath the edges of the signal line, along with the silicon between the signal and ground lines, can effectively reduce the substrate coupling and loss. The edge-suspended structure has been implemented by a combination of deep reactive ion etching and anisotropic wet etching. Compared to the conventional silicon-based coplanar waveguides, which show an insertion loss of 2.5dB/mm, the loss of edge-suspended coplanar waveguides with the same dimensions is reduced to as low as 0.5 dB/mm and a much reduced attenuation per wavelength (dB//spl lambda//sub g/) at 39 GHz. Most importantly, the edge-suspended coplanar waveguides feature strong mechanical support provided by the silicon remaining underneath the center of the signal line. The performance of the coplanar waveguides is evaluated by high-frequency measurement and full-wave electromagnetic (EM) simulation. In addition, the resistance, inductance, conductance, capacitance (RLGC) line parameters and the propagation constant of the coplanar waveguides (CPWs) were extracted and analyzed.     

Some measurement results for frequency-dependent inductance of ICinterconnects on a lossy silicon substrate

Frequency dependent measurements of scattering (S) parameters using a vector network analyzer (VNA) have been performed on IC interconnects on a lossy silicon substrate. The multiline calibration method has been used to perform the de-embedding of the line parameters, from which the line inductance is extracted. A highly accurate closed-form approximation for frequency-dependent impedance per unit length of a lossy silicon substrate for IC interconnects has been used to compare with the measurements performed     

Equivalent circuit representation of lossy coplanar waveguides

The study of the dispersion properties of planar transmission lines including metallic losses with the generalized transverse resonance method is formalized in building an equivalent network of the cross-section which specifies the relationships between the tangential components of the fields on each side of the interfaces. Virtual sources represent the trial quantities chosen to describe the problem. With twoport type boundary conditions, the trial quantities are not easily defined from physical considerations, but the virtual sources obey to specific rules. This purpose is illustrated in studying the attenuation in lossy suspended coplanar transmission lines.     

Dispersion of Picosecond Pulses in Coplanar Transmission Lines

The dispersion of coplanar-type transmission lines has been extended to the terahertz regime to examine the distortion of picosecond electrical pulses. Dispersion of coplanar waveguides is compared to equivalent microstrip lines. Agreement with available experimental data is demonstrated for coplanar strips, An approximate dispersion formula for coplanar waveguides is also reported for CAD applications.