Application of the AWE method with the 3-D TVFEM to model spectral responses of passive microwave components

Zhang, X.-M.; Lee, J.-F.

doi:10.1109/22.734573

Cited by 43 publications

(18 citation statements)

References 11 publications

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“…where is a column vector of coefficients that define the FE approximation to , superscript denotes transpose, and is the global finite-element stiffness matrix associated with (1): (4) Further, using the adjoint variable method, it is shown in [1] that the derivative of the scattering parameters with respect to any design variable can be found using (5) (This formula assumes that the geometries of ports and do not change as varies, which is usually the case.) No derivatives of with respect to are needed, and no adjoint problems have to be solved.…”

Section: Fe Scattering-matrix Adjoint Methods (Fesam)mentioning

confidence: 99%

Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices

Webb

2002

IEEE Trans. Magn.

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The finite-element method is an established computational tool for analyzing three-dimensional microwave devices. It can also provide, at little additional cost, the sensitivities of the device's scattering parameters to changes in design variables. This paper describes a method for computing these sensitivities over a whole range of frequencies in an efficient way, by solving at just one frequency and employing a Padé expansion in the complex frequency. The sensitivity of the reflection coefficient of a piece of empty waveguide to change in its length is computed with the new approach, and there is excellent agreement with the exact values available in this case. The insertion loss of a partial-height metallic post in a waveguide is also computed. The sensitivity to change in the post height found with the new method closely matches values obtained by direct analysis of the perturbed post at a number of discrete frequencies.

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Section: Fe Scattering-matrix Adjoint Methods (Fesam)mentioning

confidence: 99%

Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices

Webb

2002

IEEE Trans. Magn.

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“…In other words, it will be shown that (11) and (19) are equivalent. To prove this, it su$ces to show that the elimination of b from (14) leads to an equation for e that is identical to (5). This, in turn, requires the proof of the following equality,…”

Section: Modified Algorithmmentioning

confidence: 97%

“…One of the applications is to use a model order reduction method, called asymptotic waveform evaluation (AWE), for the fast generation of the broadband response of an electromagnetic component or sub-system [4,5]. However, AWE su!ers the numerical instability and has been replaced by Krylov sub-space method in circuit community [1].…”

Section: Introductionmentioning

confidence: 99%

Finite element‐based model order reduction of electromagnetic devices

Zhu¹,

Cangellaris²

2002

Int J Numerical Modelling

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SUMMARYIn this paper an e$cient algorithm is presented for the development of compact and passive macro-models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of "nite elements. The proposed methodology is founded on a new "nite element formulation that casts Maxwell's curl equations in a state-space form. Such state-space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the "nite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation e$ciency can be avoided by a proper selection of the "nite element expansion functions used for the discretization of the electromagnetic "elds. More speci"cally, it is shown that the proper selection of expansion functions renders the state-space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector "nite elements. This equivalence is then used to e!ect Krylov-based model order reduction directly from the "nite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macromodelling algorithm is demonstrated through its application to a variety of microwave passive components.

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“…(2), the scattering parameters are needed at all the frequencies f 1 ; f 2 ; : : : ; f N f . This is achieved by asymptotic waveform evaluation (AWE; Zhang & Lee, 1998). One extra problem is solved for each higher derivative of fE .q/ g, with respect to frequency, at frequency f a .…”

Section: Cfementioning

confidence: 99%

Adaptive Optimization of Microwave Devices over a Frequency Band

Nair¹,

Webb²

2010

Electromagnetics

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Traditional optimization using the finite element method keeps the accuracy of the finite element analysis roughly constant throughout the optimization. Adaptive optimization uses adaptive finite element analysis and increases the accuracy as the optimization proceeds, since a coarse solution is adequate early on, but more accuracy is needed as the optimum is approached. Here, adaptive optimization is extended to cost functions that depend on the performance of the device over a range of frequencies, which changes the criterion used to terminate the adaption. Results are presented for rectangular waveguide components: an E-plane bend, an impedance transformer, and a magic-T.

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Application of the AWE method with the 3-D TVFEM to model spectral responses of passive microwave components

Cited by 43 publications

References 11 publications

Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices

Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices

Finite element‐based model order reduction of electromagnetic devices

Adaptive Optimization of Microwave Devices over a Frequency Band

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