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Many control techniques applied to converters with power factor correction use cascaded control. These techniques usually ignore the periodic output voltage oscillation by using compensators with low-pass characteristic. This strategy result in voltage closed loop with poor dynamic response. In order to reduce the time-response, designers have associated notch filters into the controller to increase the bandwidth without compromising the power factor correction. However, the linear time invariant approach is no longer valid for stability analysis of such systems. In this case, a better dynamic representation can be achieved by using linear time-periodic models. This paper presents a systematic methodology for stability analysis of continuous control systems using harmonic transfer functions.In this paper, this methodology is applied to analyze the stability of the single-phase half-bridge rectifier. Simulation results are presented to validate the proposed technique. I. IN TRODUCTIONStatic converters are nonlinear systems due to the switching effect. Many modeling techniques have been developed in order to obtain Linear Time Invariant (LTI) models of these systems. Most of these techniques, consider a small-signal model around an operating point. Such as average state space model [1] and pulse width modulation switch model [2]. However, these approaches do not consider the intrinsic frequency conversion, present in these converters.Analyzing single-phase half-bridge rectifier, it converts an input ac voltage signal with frequency W I into a dc voltage together with a sinusoidal component of frequency 2Wl. This behavior can be analyzed as modulation effect, whose nature may not be described by LTI models [3]. The control structure most widely used for this type of converter has basically two feedback loops: an inner current loop with fast dynamic response and an outer voltage loop, whose dynamics is slow. Most control designs techniques presents a current loop bandwidth at least ten times faster than the voltage dynamics. The voltage loop bandwidth is designed to ensure attenuation of the output oscillation frequency. Given these considerations, both loops may be considered decoupled, and controllers can be designed independently using LTI techniques. In this case, voltage and current models are derived from small-signals modeling techniques. However, the voltage loop dynamic response is slow.Aiming to improve the voltage loop dynamic response without compromising the input power factor, some designers have proposed to include notch filters to the direct control loop tuned to output ripple frequencies. Thus, the feedback swell effects are mitigated, making it possible to increase the bandwidth of the voltage loop. However, the system dynamic behavior may no longer be properly described by small-signal models, which invalidates the stability analysis based on these models.A better representation of the system is achieved with linear time-varying periodic (LTP) models, which can be used to analyze the stability of t...

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