A Novel Analysis of Periodic Structures Based on Loaded Transmission Lines

Periodically loaded transmission lines are characterized by a frequency response with regular pass and stopbands. Interestingly, each of the passbands exhibits a peculiar comb-alike behavior, in which again, nested (or internal) pass and stopbands can be identified. In this work, we focus our attention on the effect that changing the characteristics of the periodic load (which is a varactor capacitance in our case) has in this peculiar response of the structure, providing a novel and detailed analysis of such bands. The control of the response of the structure when changing the properties of the load allows to adjust the transmission characteristics of the circuit once it is fabricated. To this purpose, we derive the design equations of the periodically loaded structures, obtaining the expressions which govern the position and number of the transmission peaks, i.e., the points where $|S_{21}|=1$ for both cases, the frequency sweep and the capacitance sweep. We experimentally validate our analysis by fabricating a periodic structure with five unit cells and compare the measurements against both theoretical results and circuit simulations to an excellent agreement. The present analysis paves the way towards further exploitation of these kind of structures for the design of different microwave applications such as tunable filters or phase shifters.