Envelope-Domain Analysis and Modeling of Super-Regenerative Oscillators

An envelope-domain methodology for the numerical modeling of super-regenerative oscillators (SROs) is presented. The main advantage is its generality of application to transistor-based oscillators with arbitrary topology. Initially, a stability analysis of the nonoscillatory steady-state solution, forced by the quench signal, is performed. It is based on the calculation of a linear-time-variant (LTV) transfer function, obtained by linearizing the circuit envelope-domain equations about the nonoscillatory 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 an SRO at 2.7 GHz, which has been manufactured and measured.