We present and analyze a method of interpolation that improves the amplitude resolution of an analog-to-digital converter. The technique requires feedback around a quantizer that operates at high speed and digital accumulation of its quantized values to provide a PCM output. We show that use of appropriate weights in the accumulation has important advantages for providing finer resoution, less spectral distortion, and white quantization noise. The theoretical discussion is supplemented by the report of a practical converter designed especially to show up the strengths and weaknesses of the technique. This converter comprises a sigma-delta modulator operating at 8 MHz and an accumulation of the 1-bit code with triangularly distributed weights. 13-bit resolution at 8 kwords/s is realized by periodically dumping the accumulation to the output. We present a practical method for overcoming a thresholding action that distorts low-amplitude input signals.

In 1969 Iwersen [4] analyzed the quantizing noise (assuming no slope overload) associated with a delta modulator (\DeltaM) with step-size imbalance. In this concise paper we consider the effects of both step-size imbalance and quantizer threshold hysteresis on\DeltaMquantizing noise. The analysis is restricted to the important case of zero input signal. For this case we extend Iwersen's work to show that quantizer threshold hysteresis can significantly change the spectral shape of the idle channel noise. Our approach is to first construct two locus functions, one for the samples (of the steady-state noise waveform) taken at arbitrarily defined even sampling times and one for those taken at the odd sampling times. The noise waveform is then obtained as a superposition of interleaved samples of the even and odd loci. It is shown that the noise spectrum has a discrete tonal struture whose frequencies are independent of hysteresis and are determined solely by step imbalance as in Iwersen's analysis. Hysteresis changes the magnitude and phase of the discrete tones. We characterize the tone magnitude changes due to hysteresis and show that hysteresis can amplify, attenuate, or completely eliminate a tone. We present curves which specify the tone magnitude attenuation as a function of step imbalance ε, average step size σ, and hysteresish. We also calculate PT, the total noise power in the baseband up to half the sampling frequency. It is shown that for0 \leq h \leq \epsilon,P_{T} = \sigma^{2}/3independent ofhand ε ;forh > \epsilon, PTis an increasing function of\epsilon/\sigmaandh/\epsilon.