# A Survey of Analog-to-Digital Converters for Operation under Radiation Environments
## 2 Performance Evaluation
### Proposed Figures of Merit  
A popular FOM to evaluate the efficiency of an ADC was proposed in [16]; it combines its power dissipation \(P\) together with its Nyquist sampling rate \(f_{s}\) and its effective number of quantization levels \(2^{ENOB}\) in the formula:  
\[\mathrm{FOM}_{W}=\frac{\mathrm{P}}{f_{s}\cdot 2^{ENOB}} \tag{1}\]  
where:  
\[\mathrm{ENOB}=\frac{\mathrm{SNDR}_{max}-10\cdot log_{10}(3/2)}{20\cdot log_{10} (2)} \tag{2}\]  
From Equation (1) it is deduced that the more efficient an ADC, the smaller its \(\mathrm{FOM}_{W}\). However, increasing wisely by design the power consumption of an ADC enhances its radiation tolerance.  
This assertion is based on the fact that higher biasing makes leakage currents due to TID and charge generated during transients less representative with regards to the affected internal analog signals; in addition, higher currents imply faster transient response and hence shorter recovery time from a SET. In fact, from a performance under radiation point of view:  
* The higher irradiated dose an ADC can stand without performance degradation, the robuster against radiation the ADC is.
* The more energized a particle shall be to cause an event in an ADC, the robuster against radiation the ADC is.
* The smaller the area an ADC has where a particle impact can affect its performance, the less sensitive to radiation the ADC is.  
These trade-offs flow into the FOMs that we propose in Equations (3) and (4), which aim to evaluate the efficiency of an ADC operating under radiation:  
\[\text{FOM}_{TID}=\frac{\text{TID}_{max}}{\text{FOM}_{W}} \tag{3}\]  
\[\text{FOM}_{SET}=\frac{\text{LET}_{th}}{\text{FOM}_{W}\cdot\sigma_{sat}} \tag{4}\]  
where \(\text{FOM}_{W}\) is given by Equation (1), \(\text{TID}_{max}\) is the maximum ionizing dose without performance degradation and the other two parameters, \(\text{LET}_{th}\) and \(\sigma_{sat}\), are the characteristic limits of the Weibull fit for a particular SET definition.  
Regarding units, \(\text{FOM}_{W}\) is given in joules per quantization level, \(\text{TID}_{max}\) in rads or Grays, \(\text{LET}_{th}\) in \(\text{MeV}\cdot\text{cm}^{2}/\text{mg}\), \(\sigma_{sat}\) in \(\text{cm}^{2}/\text{device}\) and both \(\text{FOM}_{TID}\) and \(\text{FOM}_{SET}\) in quantization levels per milligram (levels/mg). Note that some minor unit conversions are required to obtain the proper values of \(\text{FOM}_{TID}\) and \(\text{FOM}_{SET}\). It is deduced from Equation (3) that the more efficient an ADC is against TID, the bigger its \(\text{FOM}_{TID}\); comparably, a similar conclusion can be extracted from Equation (4): the more efficient an ADC is against SET, the bigger its \(\text{FOM}_{SET}\).  
Fine tuning of the proposed figures may be accomplished by the exponentiation of the parameters on the right side of Equations (3) and (4), depending on the importance that the analyst wants to give to each parameter. Following the general formula for ADCs' figures of merit presented in [14], the exponents of the bases \(\text{FOM}_{W}\), \(\text{TID}_{max}\), \(\text{LET}_{th}\) and \(\sigma_{sat}\) are respectively \(-1\), \(1\), \(1\) and \(-1\) in Equations (3) and (4). For example, \(\text{FOM}_{TID}\) can be customized having \(\text{TID}_{max}\) to the power of \(2\), if more emphasis to radiation performance is targeted evaluating the efficiency of the ADCs under analysis.  
Furthermore, as will be shown in Section 4.3, the proposed figures of merit can be used to estimate which design solutions are more efficient considering their performance under radiation.