A methodology for extracting high-frequency IC interconnect transmission parameters directly from S-parameter measurements has been demonstrated using on-chip test structures. The methodology consists of: (1) building on-chip interconnect structures for microwave test, (2) characterizing and subtracting measurement system parasitics, (3) extracting the transmission line impedance and propagation constant (attenuation constant and phase constant) from the calibrated data, and (4) extracting the Telegrapher's Equation transmission parameters (R, L, C, and G). Additional on-chip calibration permits subtraction of pad parasitic effects. This methodology is demonstrated over a 45-MHz to 20-GHz frequency range using an example 1-cm-long, 4- mu m-wide IC interconnect built in an advanced BiCMOS technology. Variations in interconnect impedance and capacitance indicate two signal propagation modes. Significant substrate-based loss is measured at microwave frequencies. >

S-parameter-based IC interconnect transmission line characterization

This paper presents a new technique for the passivity enforcement of linear time-invariant multiport systems in state-space form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system input-output transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on first-order perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that first-order perturbation is applicable. Several examples illustrate and validate the procedure.

Passivity enforcement via perturbation of Hamiltonian matrices

The density-matrix theory of semiconductor lasers with relaxation broadening model is finally established by introducing theoretical dipole moment into previously developed treatments. The dipole moment is given theoretically by the k . p method and is calculated for various semiconductor materials. As a result, gain and gain-suppression for a variety of crystals covering wide wavelength region are calculated. It is found that the linear gain is larger for longer wavelength lasers and that the gain-suppression is much larger for longer wavelength lasers, which results in that single-mode operation is more stable in long-wavelength lasers than in shorter-wavelength lasers, in good agreement with the experiments.

Density-matrix theory of semiconductor lasers with relaxation broadening model - Gain and gain-suppression in semiconductor lasers

We report recent device characterization results for a fully packaged widely tunable digital supermode (DS) distributed Bragg reflector (DBR) laser which has been monolithically integrated with a semiconductor optical amplifier. This new device gives all of the wide tunability and high side-mode suppression ratio performance previously reported for the DS-DBR laser with the added feature of output powers in excess of 14 dBm in fiber. In addition to output power and basic tuning behavior, we report on linewidth and relative intensity noise measurements for this device in order to investigate the noise characteristics of this laser.

Widely tunable DS-DBR laser with monolithically integrated SOA: design and performance

This paper presents an attempt to formulate a high-level description of the optimal transmission line simulation method. To formulate the optimal approach, most significant aspects of the problem are identified, and alternative approaches in each of the aspects are analyzed and compared to find the combination that results in the maximum efficiency, accuracy and applicability for the transient analysis of digital circuits. The practical implementation of the optimal method for uniform multiconductor lossy frequency-dependent lines characterized by samples of their responses is outlined. It is shown on an extensive set of runtime data that, based on the optimal approach, the accurate line modeling in a circuit simulator is as efficient as the simple replacement of interconnects with lumped resistors.

Optimal transient simulation of transmission lines

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficiency.

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Analysis of crosstalk and field coupling to lossy MTLs in a SPICE environment

This paper addresses the development of computational models of digital integrated circuit input and output buffers via the identification of nonlinear parametric models. The obtained models run in standard circuit simulation environments, offer improved accuracy and good numerical efficiency, and do not disclose information on the structure of the modeled devices. The paper reviews the basics of the parametric identification approach and illustrates its most recent extensions to handle temperature and supply voltage variations as well as power supply ports and tristate devices.

Mpilog, Macromodeling via Parametric Identification of Logic Gates

Crosstalk, propagation delay, pulse distortion in multiconductor buses for high-speed GaAs logic circuits are analyzed. A simple but accurate quasi-TEM model of the bus is developed, and a critical analysis is carried out both on the accuracy of different approximate lumped and distributed models and on the impact of such approximations on the time-domain response. Results on the behavior of multiconductor buses in the presence of realistic input waveforms, are presented and design criteria are obtained. >

Modeling of multiconductor buses and analysis of crosstalk, propagation delay and pulse distortion in high speed GaAs logic circuits

Three-section distributed Bragg reflector (DBR) tunable lasers emitting in the 1.55 mu m region are studied through a theoretical model which takes into account thermal effects and exploits an accurate calculation of the optical parameters. Static modal competition is discussed for transverse and longitudinal modes in operation at and above threshold. The static tuning characteristics are presented; a saturation of the wavelength shift is found for control current densities of approximately=20 kA-cm/sup -2/ due to Auger recombination processes and heating effects. The dependence of the tuning ranges on the section lengths, waveguide thickness results, and some design criteria are derived. >

Analysis and design criteria of three-section DBR tunable lasers

This paper addresses the modeling of differential drivers and receivers for the analog simulation of high-speed interconnection systems. The proposed models are based on mathematical expressions, whose parameters can be estimated from the transient responses of the modeled devices. The advantages of this macromodeling approach are: improved accuracy with respect to models based on simplified equivalent circuits of devices; improved numerical efficiency with respect to detailed transistor-level models of devices; hiding of the internal structure of devices; straightforward circuit interpretation; or implementations in analog mixed-signal simulators. The proposed methodology is demonstrated on example devices and is applied to the prediction of transient waveforms and eye diagrams of a typical low-voltage differential signaling (LVDS) data link.

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Ivano Adolfo Maio

Papers

Analysis of crosstalk and field coupling to lossy MTLs in a SPICE environment

Mpilog, Macromodeling via Parametric Identification of Logic Gates

Modeling of multiconductor buses and analysis of crosstalk, propagation delay and pulse distortion in high speed GaAs logic circuits

Analysis and design criteria of three-section DBR tunable lasers

Parametric macromodels of differential drivers and receivers