Design of optimal coupled-resonator baluns in silicon IPD technology

Coupled-resonator baluns consist of a pair of LC resonators that are coupled by mutual inductance. They are usually designed using circuit optimization methods, but this optimization is highly constrained by limitations in the implementing technology and restrictions on size and cost. However, by tuning the capacitors in each resonator, acceptably good designs can be realized over a wide range of coupled inductor characteristics. It is usually straightforward to arrive at working designs for coupled-resonator baluns, but it is difficult to determine whether or not such designs are optimal. This problem can be solved by recognizing that the coupled-resonator balun circuit is identical to the two-pole coupled-resonator bandpass filter. The same analysis formalisms and optimization methods used in filter design can be applied to baluns. These methods are described, and several example designs are presented. In contrast to filters, however, baluns are not usually designed to exhibit frequency selectivity, and the most robust balun designs are the least selective (i.e. have the greatest bandwidth.) This results in different design characteristics. The characteristics of baluns designed according to bandpass filter prototypes are compared with example characteristics of a balun optimized to more typical criteria. Tabulated numerical optimization results are presented that can be used for the design of optimal baluns. The numerical results indicate that in optimal balun designs, both of the resonators have the same uncoupled external Q factor and resonant frequency.