The (ideal) ADC transitions take place at_lsB above zero and thereafter every LSB, until 1_ LSB below analog full scale. Since the analog input to an adC can take any value, but the digital output is quantized, there may be a difference of up to LSB between the actual analog input and the exact value of the digital output This is known as the quantization error or quantization uncertainty. In AC (sampling)applications, this quantization error gives rise to quantization noise. If we apply a fixed input to an ideal AdC, we will always obtain the same output, and the resolution will be limited by the quantization error. Suppose, however, that we add some ac (dither)to the fixed signal, take a large number of samples, and prepare a histogram of the results. We will obtain something like the result in Figure 3. 5. If we calculate the mean value of a large number of samples, we will find that we can measure the fixed signal with greater resolution than that of the AdC we are using This procedure is known as oUer-sampling. OVERSAMPLING WITH DITHER ADDED TO INPUT N AND N.1 Figure 3.5 The AC(dither) that we add may be a sine-wave, a tri-wave, or Gaussian noise(but not a square wave) and, with some types of sampling AdCs(including Sigma-Delta ADCs), an external dither signal is unnecessary, since the adC generates its own Analysis of the effects of differing dither waveforms and amplitudes is complex and for the purposes of this section, unnecessary. what we do need to know is that with the simple over-sampling described here, the number of samples must be doubled for each bit of increase in effective resolutio If, instead of a fixed DC signal, the signal that we are over-sampling is an ac signal then it is not necessary to add a dither signal to it in order to over-sample, since the signal is moving anyway (If the ac signal is a single tone harmonically related to the sampling frequency, dither may be necessary, but this is a special case.) Let us consider the technique of over-sampling with an analysis in the frequency domain. Where a dC conversion has a quantization error of up to_LSB, a sampled data system has quantization noise. As we have already seen, a perfect classica5 The (ideal) ADC transitions take place at _ LSB above zero and thereafter every LSB, until 1_ LSB below analog full scale. Since the analog input to an ADC can take any value, but the digital output is quantized, there may be a difference of up to _ LSB between the actual analog input and the exact value of the digital output. This is known as the quantization error or quantization uncertainty. In AC (sampling) applications, this quantization error gives rise to quantization noise. If we apply a fixed input to an ideal ADC, we will always obtain the same output, and the resolution will be limited by the quantization error. Suppose, however, that we add some AC (dither) to the fixed signal, take a large number of samples, and prepare a histogram of the results. We will obtain something like the result in Figure 3.5. If we calculate the mean value of a large number of samples, we will find that we can measure the fixed signal with greater resolution than that of the ADC we are using. This procedure is known as over-sampling. OVERSAMPLING WITH DITHER ADDED TO INPUT Figure 3.5 The AC (dither) that we add may be a sine-wave, a tri-wave, or Gaussian noise (but not a square wave) and, with some types of sampling ADCs (including Sigma-Delta ADCs), an external dither signal is unnecessary, since the ADC generates its own. Analysis of the effects of differing dither waveforms and amplitudes is complex and, for the purposes of this section, unnecessary. What we do need to know is that with the simple over-sampling described here, the number of samples must be doubled for each _bit of increase in effective resolution. If, instead of a fixed DC signal, the signal that we are over-sampling is an AC signal, then it is not necessary to add a dither signal to it in order to over-sample, since the signal is moving anyway. (If the AC signal is a single tone harmonically related to the sampling frequency, dither may be necessary, but this is a special case.) Let us consider the technique of over-sampling with an analysis in the frequency domain. Where a DC conversion has a quantization error of up to _ LSB, a sampled data system has quantization noise. As we have already seen, a perfect classical