Printed Circuit Design & Fab - October 2008 - (Page 33) ModElinG the EM numerical simulations. The code is based on the Finite Integration Technique (FIT), an integral method that can be implemented in either time domain or frequency domain. In this case, the frequency domain solver (with tetrahedral mesh) is used for two main reasons, the structure has relatively small dimensions and the evaluation of the attenuation factor due to conductor loss (α) is not available in time domain. In order to ensure a transversal electro-magnetic (TEM) structure of the field (essential condition for a meaningful interpretation of the S-parameters), lumped voltage sources are not suitable because they would excite higher-order modes. Because of this, the TEM excitation has been realized by considering waveguide ports. FiGurE 1b illustrates the field mode pattern distribution, the line impedance value and the attenuation factor alpha (α): the detected value of the line impedance is approximately 40 ohm while α = 40.98 [Neper/m]. Due to the non-deterministic nature of the surface roughness8,9 (different and complex geometries for the surface profile) there is always a certain level of approximation that will occur, therefore, different models should be developed depending on the surface profile type. A different approach to quantify conductor loss might be to measure the Q-factor of a quarter wavelength resonator10 or to directly measure the insertion loss of a transmission line, but the effectiveness of this method relies on the accuracy of the measurements and the availability of experimental samples. FiGurE 2 shows the different surface roughness profiles used to investigate the incidence on the transmission proper- ties of the considered stripline: A) cylindrical, B) triangular and C) rectangular profiles; the geometrical parameters are d, r, h =Figure 1 and a = 1 μm. The surface roughness is only field mode 0.5 μm – Test vehicle: stripline cross section view and modelled in the top portionimpedance, wavein order to reduce alpha va of the stripline impedance, beta and the aspect ratio for the full-wave simulation. The relation between conductor surfaces profile (surface roughness) and loss can be defined by EQuation 1. c Rs Np / m Z0 w EQuation (1) where Rs represents surface resistivity, Z0 is the impedance of the transmission line and w is the trace width. Surface resistance is a material property, partially governed by surface roughness, while Z0 and w are both design parameters. Conductive loss is directly proportional to the surface resistance though the skin effect, as signals travel at the conductor surface at different depths. Different techniques can be incorporated to generate a loss model that includes the surface roughness effect. A model can be generated by adjusting the classical skin effect conductor loss to a higher power than the square root of the frequency. Another approach is increasing the dielectric loss tangent (tanδ) of the dielectric material, due to the fact that for frequencies higher than 1 GHz, the difference among copper types is almost linear with respect to the frequency. Both of these approaches have some issues4. Hammerstad and Jensen proposed an empirical formula (EQuationS 2 and 3), derived from microstripline measurements, and used http://www.wssi.com/pcdm http://www.wssi.com/pcdm
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