# Dithering in Analog-to-digital Conversion

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2 3. How Adding Noise Can Make Things Better At first glance, it might seem to be questionable that adding noise could improve the dynamic range of a signal. Many attempts to explain this phenomenon was done by using some abstract examples or analogies to illustrate in a simple way how dithering can enhance a signal. Here we have chosen a numerical analogy. We might consider the famous Π figure. This gives a decimal figure with an infinite number of digits: If one wants to keep the same precision of this value, one should keep an infinite number of digits, which would require an infinite resolution. In the real world, this is not possible and there are at least three different methods to optimize the accuracy of this figure. The first method would be to truncate the figure to its first three decimals, leading to 3.141, but then all the information contained in the other digits is definitely lost. The second method would be to round the value but then a decision should be made between and and in both cases, the result is not correct and will be conveying the same error at each attempt (arbitrary result). Finally, a trade-off can be reached by adding a random figure to the last digit that cannot be taken into account: X = 314Z Where Z could be a two with the same statistical probability: it might be sometimes one or some other times two. On average, the fourth digit which cannot be taken into account because of lack of accuracy is contained in the averaged figure. On 1 attempts, the probability to have is half and the probability to have is also half, which gives on average : ( )/1 = The decision to make the third digit a one or a two is non-deterministic, on the contrary to the two first methods where it is arbitrary. Of course, when you consider Π changing from to at every new attempt, there is some kind of blur around the figure, which can be associated to the noise which is added in dithering. Dithering adds a little noise but allows for a significant reduction in distortion. The following sections describe primarily why dither can be of benefit in analog-to-digital conversion and secondly it gives more details on the effects of dithering in analog-to-digital conversion. 2

4 5. What Are the Effects of Adding Dither to High-speed ADCs The advantage of adding dither is to smooth the spectrum of the signal out, this impacts directly the SFDR performance of the ADC and the experiments show that an improvement of about 5 db can be achieved by adding dither to the ADC input. Figure 5-1. Signal Spectrum with No Dither (Fs = 1.7 Gsps and Fin = 71 MHz, 5 dbm) Fundamental = 17/2-71 = 14 MHz SFDR = - 57 dbc H5 H8 H2 H Figure 5-2. Signal Spectrum with 17 dbm Added Dither Noise (Fs = 1.7 Gsps Fin = 71 MHz, 5 dbm) Fundamental = 17/2-71 = 14 MHz SFDR = -63 dbc H2 H

5 In Figure 5-1 on page 4 and Figure 5-2 on page 4 illustrated above, we see the two main effects of adding dither noise to the ADC input: The spectrum with dither shows a noise floor below 85 db while the spectrum without dither has a noise floor below 9 db. Most of the harmonics in the spectrum with dither have been smoothed out (except for H2 and H3, whose level has however decreased significantly). In this particular case (Fs = 1.7 Gsps Fin = 71 MHz, Pin = 5 dbm, Pdither = 17 dbm), the SFDR increases by 6 db compared to the SFDR without dither and the spectrum has been cleaned out from most of the harmonics and spurious components. However, the spectrum shows a cone under each tone (under the fundamental and H2), which is due to the saturation of the analog input due to the addition of dither noise. To avoid this saturation and therefore this kind of spectral shape, it is necessary to reduce the dither noise level, as shown in Figure 5-3 but then the SFDR will not be optimum. Figure 5-3. Signal Spectrum with 25 dbm Added Dither Noise (Fs = 1.7 Gsps, Fin = 71 MHz, 5 dbm) Fundamental = 17/2-71 = 14 MHz SFDR = dbc H2 H

6 Figure 5-4. Signal Spectrum with No Dither Noise (Fs = 1.7 Gsps Fin = 71 MHz, dbm) Fundamental = 17/2-71 = 14 MHz SFDR = -44 dbc H Figure 5-5. Signal Spectrum with 17 dbm Added Dither Noise (Fs = 1.7 Gsps Fin = 71 MHz, dbm) Fundamental = 17/2-71 = 14 MHz SFDR = -52 dbc H As shown in Figure 5-4 and Figure 5-5, the effect of dither on the spectrum is clear: all the spurs (dependent and independent) have been cleaned out except for H2 which remains and defines the SFDR parameter. In this particular case (Fs = 1.7 Gsps Fin = 71 MHz, Pin = dbm, Pdither = 17 dbm), the SFDR increases by 8 db. 6

7 Again, the analog input saturates, leading to this spectral shape with the cones under each tone but again also, adding dither is a question of compromise between the spectral purity to be achieved and the increase in signal-to-noise ratio. Figure 5-6. Signal Spectrum with No Dither Noise (Fs = 1.7 Gsps Fin = 71 MHz, 45 dbm) Figure 5-7. Signal Spectrum with 17 dbm Added Dither (Fs = 1.7 Gsps Fin = 71 MHz, 45 dbm) In Figure 5-6 and Figure 5-7, the dither has no additional effect on the performance of the ADC: the SFDR and SNR of the signal with and without dither are equivalent. 7

10 Figure dbrms, DC to 5 MHz Out-of-band Dither Curve V1 [T1] V2 [T2] V3 [T3] 5.17 dbm.12 KHz 5.75 dbm 3.4 MHz 7.8 MHz dbm Start Hz 1 MHz Stop 1 MHz Going back to audio signals, the noise is added to the part of the spectrum where it will affect the listening the least which, is the high frequencies. The noise-shaping technique used on the 1-bit 2.2 Gsps ADC can be qualified as very basic technique (low pass filtered noise). Other very sophisticated noise shaping techniques have indeed been devised, mainly by audio engineers, who were the first to work on this topic. High-order filters are then used to shape very accurately noise to match the exact portion of the spectrum where the ear is sensitive. One known noise-shaping curves for audio signals is given below (by Steinberg): Figure 6-2. Noise-shaping Curve Integrated into WaveLab Audio System (By Steinberg) VU HZ

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