Title: Pseudonorms and theorems of Torelli type for birational equivalence
Description: All microwave and millimeter-wave systems are made of monolithic microwave integrated circuits (MMICs) which are placed together using bond wires and discrete transmission line components (such as filters and couplers) to form microwave integrated circuits and subsystems. Most of the problems encountered in microwave circuits, being at the MMIC level or at the hybrid circuit implementation level, are due to the presence of the underlying dielectric substrate. In this thesis, we propose the use of micromachining techniques to eliminate the dielectric substrate and to create a localized low-loss and low-$\rm\epsilon\sb{r}$ environment. The idea attacks the most basic point: How to build microwave planar circuits on very low dielectric constant substrates to eliminate dispersion and dielectric loss and to result in a TEM-wave, while still being compatible with standard silicon and GaAs processing techniques. The low-$\rm\epsilon\sb{r}$ environment is accomplished by depositing a 1-2$\mu$m-thick dielectric membrane layer on top of the dielectric substrate, then using micromachining techniques to locally remove the supporting silicon or GaAs substrate.

By using this technology, a membrane suspended 1-2 nH inductor has shown a resonant frequency of 60 GHz which is around three times higher than the same inductor built on a silicon substrate. This technology is also applied to the design of interdigitated resonators and filters which achieved conductor-loss limited performance at 15-40 GHz. A 20.3 GHz 16% bandwidth filter is presented and results in a measured port-to-port conductor-loss limited insertion loss of 1.7 dB. A Lange-coupler employing the membrane technology is also built and a $3.6\pm0.8$ dB port-to-port coupling bandwidth from 6.5 to 20 GHz is achieved while preserving a phase balance of $90\pm3$ degree. The micromachined interdigitated filter and Lange-coupler are used in a Ku-band single-sideband mixer. This SSB mixer achieves a 9.5 dB port-to-port conversion loss at 17 GHz with an image rejection of 30 dB for an IF of 1 GHz and above, requires no DC bias and 1-2 mW of LO power. This technology is fully compatible with the via-hole process in Silicon, SiGe, GaAs and InP MMICs, and can result in high performance millimeter-wave ICs suitable for high volume productions.