# The mother of all ADC FOM

– “We all love figures-of-merit – that’s why there are so many of them.”

ADC measurement

Well … in reality there are only one or two that have reached canonical status, while the rest have found marginal use independently of their qualities (or possible lack thereof). Nevertheless, they are out there, and to bring some order in the flora and also to prepare the way for future analog-to-digital converter (ADC) FOM proposals and a better discussion of the topic, I will follow in the footsteps of another Swede – Carl Linnaeus – and try to develop some classification of the FOM species. In order to do that, I’d like to introduce you to “The Mother of All FOM” (TMAF):

$F = K \times{P}^{\alpha_P}\times{f}^{\alpha_f}\times{V}^{\alpha_V}\times{A}^{\alpha_A}\times{L}^{\alpha_L}\times{D}^{\alpha_D}\times{2}^{\alpha_B B}$

TMAF is a generic FOM expression that is explained in more detail on the page ‘A generic ADC FOM’ [1], which also explains the mapping between the linear form F (above) and the logarithmic form G

$G = X_{dB}+M_0+M+ \dfrac{20}{\alpha_B}\times[\alpha_P\times\log{P}+\alpha_f\times\log{f}+...\\ +\alpha_V\times\log{V}+\alpha_A\times\log{A}+\alpha_L\times\log{L}+\alpha_D\times\log{D}]$

A long list of generic sub-expressions (FOM classes) are found on the page named ‘Generic ADC FOM classes’ [2], together with examples of explicit FOM expressions found in the literature. Here, I’ll just give one example by looking at the generic sub-expression for the “A-class” FOM (for lack of better nomenclature):

$F_{A} = \dfrac{P}{2^{B} f}$

With $B = ENOB$, and $f = f_s$, we get the expression for the “ISSCC FOM”, the most commonly used ADC FOM today:

$F_{A1} = \dfrac{P}{2^{ENOB} f_{s}}$

By setting $B = ENOB @ DC$, and $f = \min \left \{ 2\times ERBW, f_{s}\right \}$, we get the inverted expression for the “ITRS FOM”, which is used e.g., in [3]

$F_{A2} = \dfrac{P}{2^{ENOB @ DC} \min{\left\{2\times ERBW, f_{s}\right\}}}$

Read more in [1], and see more examples in [2]. The introduction of a generic FOM and generic FOM classes allows the similarities and differences between figures of merit to be analyzed in a more systematic way. It’s a first attempt to define a common language and classification so we can actually compare and discuss the strengths and weaknesses of different FOM – a discussion that I believe is much needed.

Why?

Stay tuned, and you will find out …

# References

[1] B. E. Jonsson, “A generic ADC FOM”, Converter Passion blog, On-line, https://converterpassion.wordpress.com/a-generic-adc-fom/, Jan., 2011.

[2] B. E. Jonsson, “Generic ADC FOM classes”, Converter Passion blog, On-line, https://converterpassion.wordpress.com/generic-adc-fom-classes/, Jan., 2011.

[3] System drivers, International Technology Review for Semiconductors, 2009 Update, On-line, http://www.itrs.net

### 2 responses to “The mother of all ADC FOM”

1. God afton! Härligt att se att du är igång med bloggen och att det inneburit så mycket positivt för dig. Otroligt!!!! Det var så roligt att ha “lilla frun” här och få rå om henne så länge…nästa gång måste du komma med. Hälsa alla

2. @Cinna: Thank’s a lot, and all the best for your blog too! You’re an inspiration for both of us, no doubt. Next time in Stockholm, I could perhaps come and help you count the vases to see how close you are to the 1000. You’re getting there …