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

Abstract

Abstract-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 (Σ∆) modulation combined with polar quantisation. This paper analyses the behaviour of the resulting non-uniform polar quantisation and predicts the signal to noise ratio (SNR) performance of both Cartesian and polar filtered Σ∆ 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 bandpass Σ∆ scheme. Their complexity grows linearly with the number of quantisation points.

Baseband tuning of Cartesian delta–sigma RF upconverters

“…The width and position of the pulse train are updated after K periods of the RF carrier ( K ≥ 1 ) giving a fixed relationship between the ΔΣ sample frequency, f s , and the nominal carrier frequency f c : K = f c / f s . See [4] for further details. In the simulations, the ΔΣ filters are second order (MOD 2) [1], the nominal carrier frequency f c = 512 MHz, K = 1 and N = 32.…”

“…In this Letter, we describe a method of tuning which is particularly suitable for schemes with high-resolution polar quantisers, such as the waveform PWM-mode Cartesian ΔΣ [2][3][4]. The proposed scheme recovers much of the dynamic range over the operating band.…”

ΣΔ modulator for digital wireless architecture: A review

“…The proposed quantiser used an even quantisation technique where the three-level-waveform at the output is based on pulses with an even number of clock period� 18,21,22]. The quanti sed amplitudes, R, of the RF signal are calculated by changing the pulse widths in increments of two clock periods.…”