Analysis of wire-bonded multiconductor transmission line-based phase-shifting sections

The theoretical analysis of wire-bonded multiconductor transmission lines (MTL) for synthesizing phase shifters is accomplished and generalized in order to extend the traditional theory where 3-dB quarter-wavelength directional couplers are usually employed. In this paper, it is demonstrated that this kind of reflection phase shifters, where the coupled and direct ports are terminated with reactive loads, can be designed for any coupling level. Therefore, analytical design equations are derived to compute both the insertion and return losses as well as the operating frequency band as a function of the coupling factor of the MTL. Furthermore, two general equivalent circuits as a function of the number of strips are derived for two particular arrangements, when both coupled and direct ports are open- or short-circuited. These simple equivalent circuits provide some insight into the physical behavior of the MTL and are expedient to the design of filtering structures and and phase shifters. Finally, the validity of the developed theory is assessed by means of measurements. Two critical- and over-coupling open-circuited and short-circuited wire-bonded MTLs and a broadband balun with an operating fractional bandwidth higher than 92% and excellent output isolation are designed, manufactured, and measured.