Small loop gain and low crossover frequency result in poor dynamic performance of a single-loop output voltage controlled boost converter in continuous conduction mode. Multi-loop current control can improve the dynamic performance, however, the cost, size and weight of the circuit will also be increased. Sensorless multi-loop control solves the problems, however, the difficulty of the closed-loop characteristics evaluation will be severely aggravated, because there are more parameters in the loops, meanwhile, different from the single-loop, the relationships between the loop gains and closed-loop characteristics including audio susceptibility and output impedance are generally indirect for the multi-loop. Therefore, in this paper, a novel robust H∞ synthesis approach in the time-domain is proposed to design a sensorless controller for boost converters, which need not solve any algebraic Riccati equation or linear matrix inequalities, and most importantly, provides an approach to parameterizing the controller by an adjustable parameter. The adjustable parameter behaves like a ‘knob’ on the dynamic performance, consequently, which makes the closed-loop characteristics evaluation straightforward. A boost converter is used to verify the proposed synthesis approach. Simulations show the great convenience of the closed-loop characteristics evaluation. Practical experiments confirm the simulations.

For a digitally controlled phase-locked loop (PLL), we evaluate the use of a clock-period comparator (CPC). In this PLL, only the frequency lock operation should be performed; however, the phase lock operation is also simultaneously achieved by performing the clock-period comparison when the phases of the reference signal and the output signal approach each other. Theoretically a lock-up operation was conducted. In addition, we succeeded in digitizing a voltage controlled oscillator (VCO) with a linear characteristic. We confirmed a phase lock operation with a slight loop characteristic through SPICE simulation.