In this work we consider the Colpitts oscillator as a paradigm for sinusoidal oscillation and we investigate its nonlinear dynamics. In particular, we carry out a two-parameter bifurcation analysis of a model of the oscillator. This analysis is conducted by combining numerical continuation techniques and normal form theory. First, we show that the birth of… (More)
Access to the full text of the published version may require a subscription. Abstract—A MASH digital delta–sigma modulator (DDSM) is analyzed mathematically. It incorporates first-order error feedback modulators (EFM) which include prime modulus quantizers to guarantee a minimum sequence length. The purpose of this analysis is to calculate the exact… (More)
— In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample… (More)
Access to the full text of the published version may require a subscription. Abstract—Two classes of techniques have been developed to whiten the quantization noise in digital delta–sigma modulators (DDSMs): deterministic and stochastic. In this two-part paper, a design methodology for reduced-complexity DDSMs is presented. The design methodology is based… (More)
Testing second-order delta–sigma modulator using pseudorandom pattern, " in Proc. Int. Self-testing second-order delta–sigma modulators using digital stimulus, " in Proc.
—A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state flow diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for… (More)