Envelope-Domain Analysis and Modeling of Super-Regenerative Oscillators

Abstract

Abstract-An envelope-domain methodology for the numerical modeling of super-regenerative oscillators (SRO) is presented. The main advantage is its generality of application to transistor-based oscillators with arbitrary topology. Initially, a stability analysis of the non-oscillatory steady-state solution, forced by the quench signal, is performed. It is based on the calculation of a linear timevariant (LTV) transfer function, obtained by linearizing the circuit envelope-domain equations about the non-oscillatory regime. Under moderate quench frequencies, it will be possible to estimate the SRO normalized envelope and sensitivity function from the detected dominant pair of complex-conjugate poles. In the general case, the SRO oscillatory response is modeled with a numerical method, valid under linear operation with respect to the input signal. This is based on the calculation of the LTV impulse response from a time-frequency transfer function obtained under a small-signal sinusoidal excitation. The LTV impulse response enables a straightforward determination of the sensitivity time interval and time distance to the envelope maximum. An integral expression, in terms of the LTV transfer function, will provide the SRO response to any small signal input, with any arbitrarily carrier frequency and modulation. The methodology has been successfully validated through its application to a SRO at 2.7 GHz, which has been manufactured and measured.

Analysis of Superregenerative Oscillators in Nonlinear Mode

“…where F is the vector containing the time-varying harmonic components (at k) of the resistive elements, Q is an analogous vector, corresponding to the reactive elements,   As explained in [27], this vector contains the low-frequency quench signal ( )…”

“…This nonlinear model of the SRO will be an extension to time variant systems of the single-kernel modified Volterra model proposed in [24]- [26]. It can also be considered as an extension of the time-variant model in [27] to nonlinear operation. In this extension, advantage is taken of the fact that the quench signal fully extinguishes the oscillation during a large fraction of each quench-signal period.…”

“…To obtain the above relationship, the frequency Ω is swept in the interval (ω min -ω p ) and (ω max -ω p ), and, at each Ω, an envelope-domain integration is performed [27] in the whole time interval considered in the input modulation. Once the set of functions H(V in,k ,t,ω) is available, the corresponding collection of impulse responses h(Vin,k,t,τ) are obtained in inhouse software.…”

“…The model is an extension to time variant systems of the single-kernel Volterra model in the envelope domain, presented in [24]- [26]. It can also be considered as an extension of the time-variant model in [27] to nonlinear operation. As will be shown, through a proper timing of the input-amplitude variations, the model is usable under any arbitrarily-modulated input signal, which is well suited for system level simulations.…”

Cyclostationary noise analysis of superregenerative oscillators

“…These properties enable an intuitive analysis of the cyclostationary process, which facilitates the calculation of both the output noise power spectral density (PSD) and the output noise power. The analysis presented here will make use of the numerical black-box model proposed in [6], which enables the determination of the SRO response to any arbitrarily modulated input signal. It is based on the calculation of an envelope-domain time-variant transfer function [7], relating the output and input of the SRO, and extracted from circuit-level envelope-transient simulations [8]- [9].…”