In bandlimited QPSK and QAM transmission systems, phase jitter occurs in the output of a carrier recovery circuit that uses a fourth-power multiplier. To analyze the phase jitter, an exact expression was derived for the autocorrelation function and power spectral density for the case in which bandlimited Gaussian noise and a QPSK or QAM signal with random modulation and arbitrary waveform are simultaneously applied to the fourth-power multiplier. Using this expression, the rms phase jitter of the recovered carrier in root-cosine-rolloff transmission systems for QPSK, 16QAM, 64QAM and 256QAM was calculated. It was shown that the conventional theories for rectangular waveforms are special cases of our theory.

This paper presents a fully integrated voltage boost converter consisting of a charge pump (CP) and maximum power point tracking (MPPT) controller for ultra-low power energy harvesting. The converter is based on a conventional CP circuit and can deliver a wide range of load current by using nMOS and pMOS driver circuits for highly efficient charge transfer operation. The MPPT controller we propose dissipates nano-watt power to extract maximum power regardless of the harvester's power generation conditions and load current. The measurement results demonstrated that the circuit converted a 0.49-V input to a 1.46-V output with 73% power conversion efficiency when the output power was 348µW. The circuit can operate at an extremely low input voltage of 0.21V.