# Non-Magnetic Circulator Based on a Time-Varying Phase Modulator
###### Abstract  
Non-reciprocal devices are key elements in modern wireless communication systems. The circulator devices can simultaneously save spectrum resources and antennas. A traditional circulator is made of ferrite materials with an external magnetic bias field, and its bulk and incompatibility with CMOS technology can hardly satisfy the miniaturization and integration of modern high-speed communication systems. In recent years, there have been many outstanding achievements in the study of non-magnetic circulators, among which, the method of producing non-reciprocity by temporal modulation is considered the most likely to have a transformative influence on the industry. By varying one of the parameters of the system with time, the time inversion symmetry of the system can be broken so that the non-reciprocal devices can be formed by applying appropriate topological structures without the use of magnetic materials. In the paper, a new concept of a time-varying phase modulator (TVPM) is proposed to achieve a relatively simple method to break the symmetry of time inversion. Two different time-varying phase modulators and buffering units can be integrated to form a gyrator, with which a circulator can be formed. This paper provides a relatively simple design idea and shows the circuit design and implementation method as well as the numerical analysis and simulation results. The simulation results show that the insertion loss of the circulator at the center frequency is \(-1.7\) dB and the isolation is \(-18\) dB. The proposed non-magnetic circulator shows potential applicability in related 5G and pre-6G systems. circulator; gyrator; non-reciprocal; non-magnetic; high-speed communication +
Footnote †: journal: Applied  
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Footnote 1: email: _Applied_  
Footnote †: journal: Applied  
Temporal modulation involves varying one of the parameters of the system with time, which breaks the symmetry of time inversion. The transmission path is changed using a single-pole double-throw switch [4]. The phase of the transmitted signal was changed by using varactors in [11] to change the conductivity of the transmission line, which modulates the phase of the transmitted signal. The frequency as well as the phase of the transmitted signal can be modulated and demodulated by [13] using two mixers on the left and right terminals. All of these methods allow for a change in one of the variables in the structure to break the time-reversal symmetry. However, there is no topology to be concluded with the varied structures. Among the other published methods on time-varying modulations, many similarities can be found. As the N-Path filter [15] shown in Figure 1a, the transmitted carrier waves with different phases can be shifted in propagating and opposite directions based on controlling the switch on/off at different times (Figure 1a). The switching transmission line [16] is the spatiotemporal conductivity modulation, by which the phase reference point can be altered, which can be used to change the carrier wave phase. The transmission line also makes the carrier undergo different phase changes in propagating and opposite directions, resulting in non-reciprocity (Figure 1b). The structure of realizing an optical isolator with a series phase modulator in Reference [17] is similar to the mentioned one above. The sine wave is used as an exciting phase modulator. A delay unit is added to cancel the phase of the transmission wave in a certain direction for realizing one-way transmission (Figure 1c). By summarizing the above three kinds of non-reciprocity circuits, a systematic structure can be extracted to achieve non-reciprocity. As shown in Figure 1d, periodic time-varying modulators are placed on both sides, while buffer stages are placed in the middle stage. The appropriate combination can construct a non-reciprocal circuit. Compared with the traditional circulator composed of ferrite materials, the circulator based on the time-varying modulation method is compatible with CMOS technology.