Emad Gad

Lateral performance of cold-formed steel-framed domestic structures

Abstract This paper presents key outcomes of an investigation in the performance of domestic structures with cold formed steel frames. The primary objective of this research project was to assess the performance and behaviour of these structures when subjected to earthquake loading. The research involved an extensive racking and dynamic testing program on both two- and three-dimensional framing configurations. A variety of construction details was tested to identify the critical components and assess the contributions from the non-structural components, particularly the plasterboard lining. It is concluded that the steel frames perform very well under earthquake loads. Non-structural components, such as plasterboard lining, make a significant contribution to the lateral bracing of the frames. The failure mechanisms and the load sharing between the various components are also identified and discussed.

Passive model reduction of multiport distributed interconnects

Signal integrity analysis has become imperative for high-speed designs. In this paper, we present a new technique to advance Krylov-space-based passive model-reduction algorithms to include distributed interconnects described by telegraphers equations. Interconnects can be lossy, coupled, and can include frequency-dependent parameters. In the proposed scheme, transmission-line subnetworks are treated with closed-form stamps obtained using matrix-exponential Pade, where the coefficients describing the model are computed a priori and analytically. In addition, a technique is given to guarantee that the contribution of these stamps to the modified nodal analysis formulation leads to a passive macromodel.

Efficient simulation of nonuniform transmission lines using integrated congruence transform

This paper presents a new algorithm based on integrated congruence transform for efficient simulation of nonuniform transmission lines. The proposed algorithm introduces the concept of model-order reduction (MOR) via implicit usage of the Hilbert-space moments in distributed networks. The key idea in the proposed algorithm is the development of an orthogonalization procedure that does not require the explicit computation of the Hilbert-space moments in order to find their spanning orthogonal basis. The proposed orthogonalization procedure can thus be used to compute an orthogonal basis for any set of elements that are related through a differential operator in a generalized Hilbert space, without the need to have these elements in an explicit form. The proposed algorithm also addresses the problem of MOR of nonuniform transmission lines, through defining a weighted inner product and norm mappings over the Hilbert space of the moments. Numerical examples demonstrate more accurate numerical approximation capabilities over using the moments explicitly.

Passivity verification in delay-based macromodels of electrical interconnects

This paper presents a new theory that addresses the issue of passivity in macromodels of electrical interconnects constructed based on the method of characteristics (MoC). The proposed approach develops a new algebraic test to check for passivity in macromodels generated using MoC. The theory behind the developed test is based on deriving the necessary and sufficient conditions for the loss of positive-realness in the admittance matrix of the developed macromodel. An algorithmic procedure is proposed to verify passivity of general macromodels derived from the MoC. The results presented in this paper can be employed to test for positive-realness in dynamical systems described by algebraic delay-differential equations with discrete commensurate delays.

Circuit reduction technique for finding the steady state solution of nonlinear circuits

Computing the steady state response of large nonlinear circuits is becoming a key simulation requirement due to the rapid market growth of RF silicon ICs. In this paper we describe a nonlinear circuit reduction algorithm for finding the steady state response. The proposed algorithm uses a congruent transformation-based technique to reduce the harmonic balance equations into a much smaller set of equations. The main feature of the reduced circuit is that it shares with the original one a certain number of the derivatives w.r.t. the RF input power. Steady state analysis is then done on the reduced circuit instead of the original circuit.

Decoupled Polynomial Chaos and Its Applications to Statistical Analysis of High-Speed Interconnects

This paper presents a new Hermite-based approach to circuit variability analysis using the polynomial-chaos (PC) paradigm. The new approach is aimed at limiting the growth of the computational cost with the increase in the number of random variables and the number of Hermite coefficients used to represent the circuit response in each random variable. The proposed method is based on deriving a closed form for the structure of the augmented matrices generated by the PC approach. It then develops an algorithm to decouple the large augmented matrices into independent matrices that can be factorized in parallel. Several numerical examples are presented to demonstrate the computational efficiency of the proposed method and its ability to handle the increasing dimension of random space.

Generalized Hermite Polynomial Chaos for Variability Analysis of Macromodels Embeddedin Nonlinear Circuits

This paper describes a new approach to extend the variability analysis based on the polynomial chaos (PC) technique to nonlinear circuits. The proposed approach enables interconnects and package modules whose macromodels have their variability characterized using the PC, to be used in general nonlinear circuits. This allows the PC variability analysis to be performed directly in the time domain. The numerical examples are presented to demonstrate the validity and accuracy of the proposed method.

A circuit reduction technique for finding the steady-state solution of nonlinear circuits

Computing the steady-state response of large nonlinear circuits is becoming a key simulation requirement due to the rapid market growth of RF silicon integrated circuits. In this paper, we describe a nonlinear circuit reduction algorithm for finding the steady-state response. The proposed algorithm uses a congruent transformation-based technique to reduce the harmonic-balance equations into a much smaller set of equations. The main feature of the reduced circuit is that it shares with the original one a certain number of the derivatives with respect to the RF input power, steady-state analysis is then carried out on the reduced circuit instead of the original circuit.

Passivity Verification in Delay-Based Macromodels of Multiconductor Electrical Interconnects

This paper presents a generalized theory of passivity verification in delay-based macromodels for multiconductor transmission line networks generated using the method of characteristics (MoCs). We demonstrate that the passivity in an MoC macro-model is equivalent to the nonnegative definiteness in the admittance matrices of two submodels. We then provide the necessary and sufficient conditions for each submodel to have a nonnegative definite admittance matrix. The presented theory develops an algebraic test to verify the passivity in MoC macromodels. Numerical results demonstrate the validity of the proposed theory.

Passive Order Reduction for RLC Circuits With Delay Elements

This paper describes a new algorithm to obtain reduced-order models for large networks with delay elements. The proposed algorithm can be used in situations where delay extraction-based modeling approaches have been used to model portions of interconnects with low losses, while other portions could be modeled with large networks of lumped components. It is shown that the reduced-order model is passive by construction.