Analysis of Non-Uniform Polar Quantisers in a Sigma Delta Transmitter Architecture

The drive signals for radio frequency switch mode amplifiers can be directly generated by digital circuits using pulsewidth modulation and pulse position modulation. The quantisation noise that occurs when the pulsewidths are quantised to the timing grid can be shaped using sigma delta (ΣΔ) modulation combined with polar quantisation. This paper analyses the behavior of the resulting non-uniform polar quantisation and predicts the signal to noise ratio (SNR) performance of both Cartesian and polar filtered ΣΔ architectures. Practical measurements and simulations support the analysis. Orthogonal frequency division multiplexing and wideband code division multiple access signals are shown to have an increasing SNR with signal strength of 0.5 dB/dB at low signal levels, and 1 dB/dB at medium signal levels prior to entering the overload region. The schemes trade-off improved quantiser fidelity for higher oversampling requirements. They have reduced transitions, better coding efficiency and generally outperform the traditional band-pass ΣΔ scheme. Their complexity grows linearly with the number of quantisation points.