The design of integrated systems requires the knowledge of the values of the effective permittivity of the substrate. Designing antenna using computer-aided design tools is a long process that necessitates doing iterative steps to find the correct dimensions that meet specific requirements at a certain operating frequency. The objective of this work is to propose an analytic model to reduce the time required for the design. By using electromagnetic simulation, the effect of the relative permittivity and the height of the substrate on the final effective permittivity have been studied. An analytic model that helps the designer in estimating the value of the effective permittivity has been proposed.

A novel topology for millimeter-wave-integrated transformers is proposed. The windings are stacked and secondaries are designed with different trace widths and different diameters from that of the primary, in order to obtain relatively high-inductance transformation ratios. Measurement and simulation results of 65 nm Complementary Metal Oxide Semiconductor (CMOS) and 130 nm combination of Bipolar and CMOS (BiCMOS) transformers present the impact of this structure on the inductances, quality factor, coupling coefficient, and minimum insertion loss. Within certain limits on the trace widths, it is shown that the proposed topology not only increases the transformation ratio but also improves its overall performance.

In order to perform an accurate design, in particular in non-linear circuit, the equivalent circuit of inductors must be precisely described in a wide frequency band. Many models have been proposed to describe the behavior of inductors on lossy substrate. They consist of a great number of elements, often suggested by physical phenomena. Most of them cannot be extracted from measurements. In this paper, we propose a model composed only of elements that can be analytically extracted from measurement results.