EVLA Memo. 88 Quantization Noise

In receiving systems in which the analog signal voltage is sampled and quantized to allow further processing in digital form, the difference between the analog samples and their digital representation gives rise to a component of random quantization noise. The power spectrum of the quantization noise is close to being uniformly level across the receiver passband, even for large variation in the shape of the input spectrum. Thus in cases where the gain of the analog system varies across the passband, the addition of the quantization noise causes a variation in signal-to-noise ratio (SNR). This effect limits the allowable variation of analog gain and is particularly important in wideband receiving systems. The memorandum examines the definition of quantization noise and its relationship to quantization efficiency. Numerical simulation is used to determine the spectrum of quantization noise for a number of commonly used quantization schemes, with Nyquist and higher sampling rates. Examples are given of the limiting values of gain variation within the passband. These are modeled as slopes and sinusoidal ripples and are applicable to the EVLA and ALMA systems. Equations for precise calculation of quantization efficiency based on evaluation of the quantization noise are derived in Appendix A.