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High-efficiency linear radio frequency (RF) power amplifiers are needed for today's wireless communication systems. Switch mode techniques have the potential for high efficiency but require a pulse drive signal. The generation of pulse width modulated signals and pulse position modulated signals by sigma delta modulators can introduce unwanted spectral components. Third order and image components are the dominant distortions generated in the pulse position modulation circuit. The authors identify the cause of distortion and mathematically quantify its amplitude and frequency. In a single carrier environment, an increase in offset frequency increases the unwanted spectral components. Calculations, simulations and measurements show that offsets less than 1% of the carrier frequency are required to keep unwanted components 40'dB below the signal level. Simulations and measurements show that the effect on a multi-channel orthogonal frequency division multiplexing (OFDM) system is less detrimental. Nonetheless, unacceptable noise increases of up to 20 dB are observed in odd harmonic channels when the transmission is not centred on the nominal carrier frequency.