New oscillator concept based on band edge degeneracy in lumped double‐ladder circuits

Abstract

An oscillator scheme based on the degenerate band edge (DBE) in a periodic, double-ladder resonant circuit made of lumped elements is proposed for the first time. The circuit exhibits a DBE in the dispersion diagram of its phase-frequency eigenstates and possesses unique resonance features associated with a high loaded Q-factor resonance, compared to a singleladder circuit. This oscillator is shown to have an oscillation threshold that is half that of a single LC ladder circuit having the same total quality factor, and thus is more robust than an LC oscillator in the presence of losses. Moreover, the double-ladder oscillators have a unique mode selection scheme that leads to stable single-frequency oscillations even when the load is varied. It is also shown that the output amplitude of the double-ladder oscillator is much less sensitive to the output loading compared to single-ladder oscillators. The authors show the analysis and design of such oscillators that potentially lead to enhancing the efficiency of RF components and sources.

Distributed Degenerate Band Edge Oscillator

“…The high quality factor of such DBE cavities and the concept of DBE resonance has been already explained in [19], [22]. Gain is modeled using the non-linear cubic I-V characteristic i(t) = −g m v(t) + ζv 3 (t) of the active device [23] which can be practically implemented in circuits with amplifying devices, such as CMOS transistors or op-amps, with positive feedback. Here −g m is the small-signal slope of the I-V curve in the negative resistance region, and ζ is the third-order nonlinearity constant that models the saturation characteristic of the device.…”

“…An important advantage of the proposed DBE oscillator is the robustness of the oscillation frequency against a large variation in the load. This advantage has been shown only for a DBE-based double ladder lumped-element circuit oscillator with only one active device [23]. Typically, the oscillation behavior is very sensitive to the output termination resistance variation resulting in a significant shift in oscillation frequency (e.g.…”

General Conditions to Realize Exceptional Points of Degeneracy in Two Uniform Coupled Transmission Lines

“…The first experimental demonstration of the existance of the DBE in periodic waveguides at radio frequency was shown in [18], and recently extended to periodic coupled microstrips [19]. Structures exhibiting DBEs have been proposed recently for a wide range of applications such as, for example, high quality factors photonic crystals [5], high power electron-beam devices [20]- [21], RF oscillators [22] and lasers [23].…”

Experimental Demonstration of Exceptional Points of Degeneracy in Linear Time Periodic Systems and Exceptional Sensitivity

“…An EPD of order two is simply the splitting point (or degenerate point) of two resonance frequencies and it emerges in systems when two or more eigenmodes coalesce into a single degenerate eigenmode, in both their eigenvalues and eigenvectors. The emergence of EPDs is associated with unique properties that promote several potential applications such as enhancing the gain of active systems [11], lowering the oscillation threshold or improving the performance of laser systems [12,13] or circuit oscillators [14], enhancing sensors' sensitivity [9,[15][16][17][18], etc. EPDs emerge in EM systems using various methods: by introducing gain and loss in the system based on the concept of parity-time (PT-) symmetry [13,[17][18][19][20][21], or by introducing periodicity (spatial or temporal periodicity) in waveguides [22][23][24][25].…”