Contents I. Introduction
Reciprocity is a general principle governing the fact that signal transmission between two points in space is identical in either direction regardless of the complexity of the intermediate channel. It applies to a broad range of materials, under the conditions that they are nongyrotropic, passive, linear, and time invariant [1]–[3]. Breaking any of these conditions allows the realization of nonreciprocal components, such as circulators, isolators, and gyrators, which have numerous applications in modern communication systems [4]–[10]. Recently, magnetless implementations of such components based on linear periodically time-varying circuits [11]–[38] have received significant attention, as they were shown to overcome the weight, size, and cost challenges of magnetic devices [39]–[43], while satisfying the requirements on all other essential metrics. In particular, [28] and [29] presented radio frequency (RF) circulators that can simultaneously achieve low transmission loss, excellent matching, large isolation, high power handling and linearity, low noise figure, and good harmonic response, all at a small form factor and low modulation frequency and amplitude. These circuits are also compatible with standard CMOS technologies, which permits further integration and cost reduction for large-scale production. Nevertheless, this remarkable performance was maintained over a relatively narrow fractional bandwidth (BW) of only a few percents. While this BW may be sufficient for a plethora of applications such as WiFi, RFID, and cellular communication, it is still highly desirable to increase it further for broadband scenarios, such as radar systems and future ultrawideband radios.
