| On-chip inductors and transformers play a crucial role in radio frequency integrated circuits (RFICs). For gigahertz circuitry, these components are usually realized using bond-wires or planar on-chip spirals. Although bond wires exhibit higher quality factors (Q) than on-chip spirals, their use is constrained by the limited range of realizable inductances, large production fluctuations and large parasitic (bondpad) capacitances. On the other hand, spiral inductors exhibit good matching and are therefore attractive for commonly used differential architectures. Furthermore, they permit a large range of inductances to be realized. However, they possess smaller Q values and are more difficult to model.; In this dissertation, we develop a current sheet theory based on fundamental electromagnetic principles that yields simple, accurate inductance expressions for a variety of geometries, including planar spirals that are square, hexagonal, octagonal or circular. When compared to field solver simulations and measurements over a wide design space, these expressions exhibit typical errors of 2–3%, making them ideal for use in circuit synthesis and optimization. When combined with a commonly used lumped π model, these expressions allow the engineer to explore trade-offs quickly and easily.; These current sheet based expressions eliminate the need for using segmented summation methods (such as the Greenhouse approach) to evaluate the inductance of spirals. Thus, the design and optimization of on-chip spiral inductors and transformers can now be performed in a standard circuit design environment (such as SPICE). Field solvers (which are difficult to integrate into a circuit design environment) are now only needed to verify the final design.; Using these newly developed inductance expressions, this thesis explores how on-chip inductors should be optimized for various circuit applications. In particular, a new design methodology is presented for enhancing the bandwidth of broadband amplifiers using optimized area efficient, on-chip spirals. This method is applied in the implementation of a CMOS gigabit ethernet transimpedance preamplifier to boost the bandwidth by ≈40%.; This dissertation also develops a general methodology for computing the mutual inductance and mutual coupling coefficient of various on-chip spiral transformers. Furthermore, this work provides lumped, analytical transformer models that show good agreement with measurements. |
