There are two mathematical forms commonly used for ADC figures-of-merit (FOM) – the *linear* form, and the equivalent *base-10 logarithmic* expression. As an example:

is the logarithmic equivalent of

and both are used in the literature. The mapping between the two is derived as follows: Assume that *B* is a performance measured in “bits”, and that *B* is determined by a performance (e.g., SNDR) as

Then

If a generic FOM [1] has the linear form

then we get the equivalent logarithmic form through the transformation

which yields

The scaling with gives the most natural expression for G, starting with an unscaled “dB-performance” term rather than a scaled one in case . For FOMs that does not include a “bits” or similar resolution-related performance, the scaling with is omitted.

A strict mapping between *F* and *G* requires , but is usually omitted and *M* is used to handle various scaling permutations.

# 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.

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