A multi-scale (MS) approach combined to the generalized equivalent circuit (GEC) modeling is applied to compute the input impedance of pre-fractal structures with incorporated PIN diodes. Instead of treating the whole complex problem at once, the MS method splits the complex structure into a set of scale levels to be studied separately. The computation is done gradually from the lowest level. Each scale level is artificially excited by N modal sources to compute its input impedance matrix. The MS method is based on converting this input impedance matrix into an impedance operator to achieve the transition toward the subsequent level. The PIN diodes were easily integrated in the MS approach thanks to their surface impedance model. The main advantage of the MS-GEC method is the significant reduction of the problem's high aspect ratio since fine details are studied separately of the larger structure. Consequently, the manipulated matrices are well conditioned. Moreover, the reduced size of matrices manipulated at each level leads to less memory requirement and faster processing than the MoM. Values obtained with the MS-GEC approach converge to those given by the MoM method when a su±cient number of modal sources are used at each scale level. For frequencies between 1 GHz and 6.8 GHz, the agreement between the two methods is conspicuous.
Chiraz Larbi Aguili,
"Study of Fractal-Shaped Structures with PIN Diodes Using the Multi-Scale Method Combined to the Generalized Equivalent Circuit Modeling," Progress In Electromagnetics Research B,
Vol. 27, 213-233, 2011. doi:10.2528/PIERB10110105
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