Engineering Documents

Document Type

Thesis or dissertation

Date of this Version

January 1996


Oversampled noise shaping analog to digital (A/D) converters, which are commonly known as delta-sigma (ΔΣ) converters, have the ability to convert relatively low bandwidth signals with very high resolution. Such converters achieve their high resolution by oversampling, as well as processing the signal and quantization noise with different transfer functions. The signal transfer function (STF) is typically a delay over the signal band while the noise transfer function (NTF) is designed to attenuate quantization noise in the signal band. A side effect of the NTF is an amplification of the noise outside the signal band. Thus, a digital filter subsequently attenuates the out-of-band quantization noise.

The focus of this thesis is the investigation of ΔΣ architectures that increase the bandwidth where high resolution conversion can be achieved. It uses parallel architectures exploiting frequency or time slicing to meet this objective. Frequency slicing involves quantizing different portions of the signal frequency spectrum using several quantizers in parallel and then combining the results of the quantizers to form an overall result. Time slicing involves quantizing various groups of time domain signal samples with different quantizers in parallel and then combining the results of the quantizers to form an overall output.

Several interesting observations can be made from this general perspective of frequency and time slicing. Although the representation of a signal are completely equivalent in time or frequency, the thesis shows that this is not the case for known frequency and time sliced A/D architectures. The performance of such systems under ideal conditions are compared for PCM as well as for ΔΣ A/D converters. A multi-band frequency sliced architecture for delta-sigma conversion is proposed and its performance is included in the above comparison. The architecture uses modulators which realize different NTFs for different portions of the signal band. Each band is converted in parallel. A bank of FIR filters attenuates the out of-band noise for each band and achieves perfect reconstruction of the signal component. A design procedure is provided for the design of the filter bank with reduced computational complexity. The use of complex NTFs in the multi-band ΔΣ architecture is also proposed. The peformance of real and complex NTFs is compared. Performance evaluations are made for ideal systems as well as systems suffering from circuit implementation imperfections such as finite opamp gain and mismatched capacitor ratios.


engineering, electrical



Date Posted: 22 November 2006