On low-pass reconstruction and stochastic modeling of PWM signals

pulse width modulation (PWM);oversampling;low-pass reconstruction;natural sampling;uniform sampling;blurring effect

Sevuktekin, Noyan Cem ; Singer ; Andrew C.

关键词: pulse width modulation (PWM);    oversampling;    low-pass reconstruction;    natural sampling;    uniform sampling;    blurring effect;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/88162/SEVUKTEKIN-THESIS-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis.