This paper presents a time-domain analysis of an N-bit pulse-width-modulated digital-to-analog converter (PWM DAC) employing a first-order passive resistor-capacitor (RC) filter. Exact analytical expressions are derived for the output settling time in both rising and decreasing digital-code transition modes. The worst-case condition is identified, and the settling-time criterion is expressed as a function of the DAC resolution N, tolerance ε, and normalized filter parameter k = T/RC. The derived criterion is compared with a commonly used first-order RC settling approximation. For N = 8 and ε = 1/4, the proposed worst-case criterion gives a discrete settling interval of 823 PWM periods, whereas the literature-based estimate gives 355 periods. The analytical results are confirmed by numerical evaluation and LTspice transient simulations and are further supported by experimental measurements obtained using a microcontroller-based PWM generator and a passive RC filter. The results confirm the duty-cycle dependence of the steady-state ripple and demonstrate that the proposed criterion provides a conservative design rule for selecting PWM DAC parameters while balancing accuracy, ripple, and settling speed.

This paper presents a unified model of magnetoresistive angular position sensors, applicable to sensors based on the three major sensor technologies: Anisotropic Magnetoresistance, Giant Magnetoresistance, and Tunnel Magnetoresistance magnetoresistive elements. Theoretical models of the three different magnetoresistive elements, including manufacturing tolerances, have been derived first. The models are then employed to derive a realistic model of a magnetoresistive measurement bridge. In order to construct a model of a magnetoresistive magnetic field direction sensor, besides bridge models, a novel model of a free ferromagnetic layer has been developed. Finally, a unified magnetoresistive angular position sensor model has been obtained by combining the magnetic field direction sensor and a simple model of a permanent magnet. The experimental results confirmed the validity of the proposed model.