# A Survey of Analog-to-Digital Converters for Operation under Radiation Environments
## 4 Data Analysis
### Frequency and Resolution  
Nyquist sampling rate and input bandwidth were selected as reference frequencies to establish a common playground for the whole _selection_. The choice of the latter is in detriment of some ADCs with a passband wider than their Nyquist input bandwidth; however, the best SNDR is usually obtained within the Nyquist input bandwidth, which justifies its choice.  
Figure 2 depicts the ENOB of each _selection_'s member versus its Nyquist sampling rate \(f_{s}\)-Their ceiling is 20.5 bits up to 1 kHz, decaying 1.5 bits per decade from this point (dashed line with interleaved crosses in Figure 2). Unfortunately, no TID data could be found in the literature for specimens supporting that ceiling (AD7984 and ADS5483). We have hence considered a more accurate envelope; it has the same slope from 10 kHz, but shifted 1 bit down (dashed line in Figure 2). The ceiling of the _the state of the art_ is 20 bits up to 10 kHz and decays from this point 1.5 bits per decade. Comparing both envelopes, it can be said that radiation hardening does not affect the maximum achievable ENOB up to 1 kHz; nevertheless, ENOB is punished with 2 bits above 10 kHz. For both the _selection_ and the _state of the art_, ENOB decays 1.5 bits per decade above 10 kHz. Furthermore, if data of the _state of the art_ after 2008 were not considered, both envelopes would be overlapped. In other words, for a given \(f_{s}\), the best scientific ADCs back in 2008 already achieved the ENOB that the best available radenv-ADCs do nowadays.  
In addition to the intrinsic limitations of ADCs--quantization noise, input-referred circuit noise, aperture uncertainty and comparators ambiguity --, radenv-ADCs are also limited in speed by the qualified packaging technologies [63]. This explains the sparsely populated area in Figure 2 for radenv-ADCs above 1 GHz and 10 bits compared to the _the state of the art_. Furthermore, our study has limited the collected data to single core solutions, while ADCs operating above 1 GHz are usually implemented with time-interleaved multi-core architectures.  
Figure 3 plots the Nyquist input bandwidth against maximum SNDR for the _selection_'s members. It also includes the performance of an ideal sampler with sinusoidal input for two jitter cases of its sampling clock: solid and dashed lines represent 0.1 and 1 ps\({}_{rms}\) cases respectively. For a given ENOB, _selection_'s members with the highest bandwidth perform as ideal samplers with a sampling aperture uncertainty close to 1 ps\({}_{rms}\). Jitter becomes more critical for bandwidths close to 100 MHz and above, for which the most performing _selection_'s members exceed the 1 ps\({}_{rms}\) line but without surpassing the  
Figure 3: Nyquist input bandwidth against signal-to-noise and distortion ratio.  
Figure 2: Effective Number of Bits against Nyquist sampling rate.  
0.1 ps\({}_{rms}\) one. A practical conclusion at system level is that hi-rel TID tolerant oscillators shall provide a sampling clock better than 0.1 ps\({}_{rms}\) to avoid jitter limiting the performance of new radenv-ADC designs; this requirement can also be extended to PLLs in SoC implementations. Note indeed that this is a best case figure based on the comparison with a simplified mathematical model; jitter can be more harmful in the actual performance of an ADC depending on implementation particularities of each design. Jitter requirements for the _state of the art_ are just above the 0.1 ps\({}_{rms}\) line (less than one order of magnitude above the _selection_'s). In fact, for the _state of the art_, jitter becomes more critical for bandwidths close to 1 GHz and above, for which the most performing members exceed the 0.1 ps\({}_{rms}\) line. In addition, if data after 2012 of the _state of the art_ were not considered, its envelope in Figure 3 would be similar to the one of the _selection_. In other words, for a given SNDR, best scientific ADCs back in 2012 already achieved the input bandwidth that the best available radenv-ADCs do nowadays.