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In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-based controllers, are analyzed estimating limit sets for the augmented state. Consequently, output chattering can be bounded. By using hybrid dynamical system theory, the control designer gains a deeper understanding of the effect of modulation in the closed-loop dynamics, avoiding the problems associated with the use averaged models. Experimental results validate the proposed method. [ABSTRACT FROM AUTHOR]

The growth of IoT applications requires DC-DC converters to have small printed circuit board (PCB) areas and high efficiency over a wide load range. A multi-mode operation of DC-DC converters, therefore, is often necessary to achieve this high efficiency over a wide load range. This paper introduces a tri-mode DC-DC buck converter for IoT applications. The tri-mode operation with PWM, PFM, and multiple-sawtooth PWM (MSPWM) modes helps to retain the high efficiency over the wide load range. The MSPWM mode also enhances a noise margin of the converter, ensuring a regular switching operation at an ultra-light load condition. With a load current prediction scheme, the proposed tri-mode converter requires neither additional load current sensor nor multiple mode controllers. In addition, a soft-start operation is employed to prevent an in-rush current. The proposed tri-mode buck converter has been fabricated through a 0.18- $\mu \text{m}$ CMOS process with a chip area of 0.97 mm $\times0.88$ mm. A load-dependent seamless mode transition is realized, and a maximum converter efficiency of 91% has been measured with a 7.4-MHz switching frequency. [ABSTRACT FROM AUTHOR]

It is essential to retain improved efficiency in a dc–dc converter over a wide load current range to extend the battery-life in portable devices. This requires a multi-mode controller, consisting of pulse-width-modulation (PWM) and pulse-frequency-modulation (PFM) schemes. However, existing approaches attempt to integrate structurally different controllers; thus it is difficult to achieve a seamless controller transition. While a digital platform offers controller configurations, it remains difficult to identify a suitable digital PWM/PFM technique and decide on its sampling mechanism to achieve stable behavior. This paper proposes a unified digital PWM/PFM scheme which shares a common digital PWM (DPWM) block and has the provisions for online controller configuration and automatic (switching) frequency adaptation. The proposed scheme retains improved efficiency over a wide operating range and inherently achieves seamless controller transitions. Further, a unified discrete-time framework is proposed for the analysis and design of the proposed multi-mode controller. Buck and boost converter prototypes are tested and the proposed controller is implemented using a field-programmable-gate-array device. [ABSTRACT FROM AUTHOR]

In this paper the stability and sensitivity function of three basic dc-dc converter with the consideration of circuit parasitics has been analyzed for analog and digital controller implementation. The steady state and small-signal analysis has been used to derive the mathematical expressions for uniformly sampled voltage-mode controlled converters. The effect of digital controller using the ratio of sampling to carrier frequency has been analyzed. The sampling frequency limits the voltage gain in the stepped manner and also affects the stability of the digitally controlled converter. The sensitivity function has been defined for voltage gain with respect to various system parameters. The maximum affected regions on duty ratio scale with corresponding parasitic variable have been discussed. The detailed stability analysis has been carried out for digitally implemented three basic dc-dc converters, i.e., buck, boost, and buck-boost circuits. The analytical results are verified with the simulations performed in PSCAD/EMTDC. An FPGA controller is considered as digital controller for the dc-dc converter and verification of the results through experiment. [ABSTRACT FROM PUBLISHER]

We propose a novel low-harmonics low-noise modulation scheme for switched-mode dc–dc converters. The proposed scheme is a hybrid of a randomized modulation scheme, namely, the randomized wrapped-around pulse position modulation scheme (RWAPPM), and a noise-shaper. The RWAPPM mitigates the switching-frequency harmonics in the input current, whereas the noise-shaper mitigates the low-frequency noise therein. We derive an analytical expression for the input current spectrum of the hybrid scheme. We benchmark the hybrid scheme against the conventional pulse width modulation scheme (PWM) and the RWAPPM without the noise-shaper. At 0.5 duty cycle, 3.3-V input voltage, 100-kHz average switching frequency, and with the second-order noise-shaper, the peak spectral power in the input current spectrum of the hybrid scheme is 18.1 dB lower than the PWM. Other randomized and spread-spectrum modulation schemes, in general, have undesirably higher input noise current than that of the PWM. However, the input noise current of the proposed hybrid scheme, obtained at ~73-mA rms (integrated over a 200-kHz bandwidth without an input filter), is comparable with that of the PWM, and is lower by ~16-mA rms compared with that of the RWAPPM without the noise-shaper. We also benchmark the hybrid scheme against other well known randomized and spread-spectrum modulation schemes. We further propose a novel pulse generator structure that embodies the hybrid scheme. We realize a dc–dc converter employing the pulse generator, and measure the converter to verify the derived expression and the characteristics of the hybrid scheme. We also measure the output voltage spectrum, the transient-response, and the operating range of the converter. [ABSTRACT FROM PUBLISHER]