Frequency‐dependent expressions for inductance and resistance of microstrip line on silicon substrate

Abstract

A new closed‐form expression to calculate frequency‐dependent distributed inductance and the associated distributed series resistance of microstrip lines on a lossy silicon substrate (CMOS technology) are presented. The proposed analytic model for series impedance is based on a self‐consistent field method and the vector magnetic potential equation. It is shown that the calculated frequency‐dependent distributed inductance and the associated resistance are in good agreement with the results obtained from rigorous full wave solutions and CAD‐oriented equivalent‐circuit modeling approach. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 349–352, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10318

The attenuation and slow‐wave characteristics of an inverted embedded (IEM) metal‐insulator semiconductor (MIS) microstrip line

“…Here, the procedure to determine these distributed capacitances in Eqs. (1c)-(1e) involves combining the equations in [1][2][3] with the Kirschning-Jansen equations [4]. Under such circumstances, the high-frequency effects on the distributed parameters can be treated appropriately.…”

“…On the other hand, it should be noted that the series resistance R IEM ( f ) can be determined by the closed-form equation given in [2]. At high frequencies, the shunt capacitance C IEM ( f ) and conductance G IEM ( f ) need to be modified in order to take the high-frequency effects into account.…”

“…In Figure 2, the line with solid dots ( si ϭ 0.2 and 10 S/m) indicates that when calculating ␣( f ) the series resistance R IEM ( f ) is extracted by the closed-form equation given in [2], where R IEM ( f ) also depends on the value of si . Whereas in [1], the series resistance R IEM ( f ) has no relation to si , which is denoted by the line with empty dots in Figure 2 ( si ϭ 10 S/m).…”

“…In Figures 3(a) and 3(b), the attenuation constant ␣( f ) and SWF are also calculated based on the extracted distributed parameters, where the series resistance R IEM ( f ) is determined by the closed-form equation in [1] (lines with empty dots) and [2] (lines with solid dots).…”

“…For this configuration, we want to explore the effects of different geometric and physical parameters, including strip width, thickness, and embedding depth, as well as silicon conductivity, on the mode-attenuation constant and slowwave factor (SWF). The mathematical treatment is based on the analytical model proposed in [1,2] for characterizing the per-unitlength series resistance and inductance, shunt capacitance, and conductance. However, some modifications have been made to take into account of the frequency-dependent characteristics of these distributed parameters.…”