Design of a Self-Oscillating PWM Signal Generator With a Double Integration Loop

An asynchronous pulse width modulator for DC‐DC buck converter

“…Asynchronous pulse width modulator is a type of modulator that converts analog input signal to bi‐level digital signal, As shown in Figure , its structure is simple and composed a loop filter and a hysteretic block. Also, the APWM is known as a self‐oscillating or a hysteretic modulator, due to an internal oscillating behavior (limit‐cycle oscillation) and non‐linear hysteretic block . Unlike the conventional pulse width modulator (CPWM) that are mainly targeted to be utilized in the switching circuits with low carrier frequencies (i.e., several hundred kilohertz), the APWM is utilized to achieve high‐frequency operation to generate high precision single‐bit signals .…”

“…Therefore, due to the noise‐shaping feature it reduces or suppresses the spurious tones in the output spectrum . A side advantage of APWM is that this architecture provides a low‐cost implementation by eliminating high‐quality carrier generator (sawtooth signal) . In addition to, due to the absence of the external sampling signal (e.g., the clock signal in the SDM), the APWM output signal is modulated as a continuous time signal without producing the quantization noise .…”

“…For example, they can be employed in inverter circuits, active filters, class‐D amplifiers, Universal Mobile Transmitter Systems (UMTS), ADSL/VDSL line drivers, etc. Unfortunately, the precise mathematical analysis of the APWMs is a demanding task due to the nonlinearity of the system . In other words, the nonlinearity and the ambiguity in the delay of the hysteretic comparator make it difficult to deduce a linearized model for the closed‐loop analysis.…”

“…The describing function ( DF ) and the Fourier series analysis are the two popular methods to analyze and model the nonlinear system such as the hysteretic APWMs. However, the DF representation depends on the primary component of the nonlinear block and its input signal amplitude . It is worth to mention that, at higher order hysteretic based modulator (i.e., second order), the stability of a limit cycle state can be determined graphically using the describing function .…”

“…However, the DF representation depends on the primary component of the nonlinear block and its input signal amplitude . It is worth to mention that, at higher order hysteretic based modulator (i.e., second order), the stability of a limit cycle state can be determined graphically using the describing function . However, at higher order hysteretic based modulator the system with stable limit cycles cannot be easily identified as being stable or not.…”