High-resolution digital quadrature detection

Abstract

We illustrate the principles of digital quadrature detection and call attention to its various benefits (ghost-free spectra and high immunity to low-frequency interference) and its intrinsic capability of generating data sets with different aliasing behaviors. A function describing the filtering efficiency is introduced, and the digital filters of our detector are compared with their analog counterparts of conventional nuclear magnetic resonance spectrometers. With an appropriate analog-to-digital converter (ADC), our digital detector has a dynamic range which is essentially limited by the analog noise, and increases when the spectral bandwidth is reduced. These nearly ideal performances are achieved through dithering, which randomizes the quantization error and oversampling, which reduces the quantization noise in the band of interest. We introduce a ‘‘figure of merit’’ for AD converters which estimates the noise performances of ADCs, and allows to compare products which achieve different compromises between speed and accuracy. The distortions due to the nonlinearities of the ADCs are analyzed through simulations. We find that the majority of the spurious signals (i.e., the errors other than noise) occur outside the band of interest, and are disposed through digital filtering. An unexpected result of the simulation is that, in some circumstances (e.g., large-scale narrowband dithering), an increase in the number of bits of the ADC may actually reduce the distortion-free dynamic range. In Sec. VIII we analyze practical problems like the role of the aperture jitter and the selection of the sampling frequency.