Analysis and Synthesis of Hysteresis Loops in an Oscillator Frequency Characteristic

A methodology for the analysis and synthesis of multiple hysteresis loops in the frequency characteristic of a voltage-controlled oscillator (VCO) is presented. This is achieved through the coupling of an oscillator inductance to multiple external (passive) resonators with resonant frequencies in the tuning range of the VCO. A possible application to the implementation of a compact chipless radio frequency identification (RFID) system is explored, using the oscillator as a reader and placing the external resonators in the tag. The system takes advantage of the high sensitivity to the tag resonances in the presence of hysteresis, which leads to vertical jumps in frequency versus the tuning voltage. A desired bit pattern would be encoded in the tag by enabling or disabling passive resonances at a sequence of frequencies. In the practical realization, the inductors in the oscillator and the external board are implemented through spiral inductors so that the resonators in the VCO and the tag have strong broadside coupling. The coupling effect is modeled through electromagnetic simulations, from which a linear admittance, representing the coupled subnetwork, is extracted. The multihysteresis oscillator characteristic can also be obtained experimentally through a new methodology able to stabilize the physically unstable sections without altering their steady-state values. Different demodulation methods for reading the tag are discussed.