OVERVIEW

Microwave circuits had traditionally been built using the distributed approach in which impedance-matching and resonator networks were constructed by stub- loaded transmission lines or waveguide cavities. With the invention of integrated circuits (ICs), however, the distributed approach became a big obstacle in the path to the integration of passive microwave circuits with active components, directly affecting the cost, volume, and weight of the circuits. Lumped elements (i.e., capacitors, inductors, resistors, and so forth) would provide a unique solution to these problems because they could be manufactured directly on the same substrate with active circuits using photolithographic techniques. Prompted with these requirements, work on microwave lumped elements was reported as early as 1967, when the authors demonstrated spiral inductors and metal-insulator-metal (MIM) capacitors at frequencies up to 2 GHz with Q-factors around 50 ^[1]. In the following years, more applications of lumped elements for MMICs were reported ^{[2] [7]}.

Despite the clear advantages in terms of integration, perhaps the biggest two problems with using lumped elements in microwave frequencies have been the lack of accurate modeling tools and relatively low Q-factors compared to their distributed counterparts because of the associated metallization and dielectric losses. Unlike waveguide and coaxial circuits, where closed-form analytical solutions can be obtained in many cases, it is quite difficult to get accurate analytical models for lumped elements because of their intricate construction. The first models created for lumped elements were based on quasi-static approximations and semiempirical formulations ^{[8] [12]}.