A truly generic *figure-of-merit* (FOM) for *analog-to-digital converter* (ADC) performance comparison would render a very complex expression indeed. But the vast majority of FOMs proposed in the literature – perhaps all of them – can be expressed with a generic figure-of-merit *F* written as

where *P* is a power measure, *f* is a frequency, *V* is a voltage, *A* is an area, *L* is a length, *D* is “any other parameter”, and *B* is a resolution-related performance expressed in “bits”, e.g., “SNR-bits”, effective number-of-bits (ENOB) or nominal resolution *N*. Examples of use is found in the parameter list below, and in [1].

The -parameters are introduced to make the expression more generic, although all FOMs proposed to this date (**Edit**: except for the FOM by *Vogels* et al. in [3]) have used .

ADC figures-of-merit are commonly written in their equivalent base-10 logarithmic form *G*, which yields from the transformation

A more detailed derivation is found in [2]. The generic log form FOM is

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

# Parameters

Each FOM is defined by a unique set of parameters. The parameters reveal the common and differentiating properties of each FOM, and therefore enables a more systematic treatment. Generic FOM classes are defined in [1], based on the combinations of values used. Below is a list of *P*, *f*, *V*, *A*, *L*, *D*, *B*, and *X*-parameters used in the literature, and some that are not (yet). Examples of their use are found in [1].

By exploring all combinations of parameters, a large number of proposed and yet un-proposed FOM permutations can be derived. The division into generic FOM classes allows simultaneous treatment of groups of FOM with similar properties, while the introduction of generic *P*, *f*, *V*, *A*, *L*, *D*, *B*, and *X*-parameters allows a discussion of the optimal choice of such parameters.

## Power – *P*

Total power dissipation | |

On-chip power dissipation | |

ADC-core power dissipation | |

Analog power dissipation |

## Frequency – *f*

Clock frequency | |

Nyquist sampling rate | |

Signal bandwidth | |

Twice the signal bandwidth | |

Effective resolution bandwidth | |

Twice the ERBW | |

Twice the ERBW clipped to Nyquist sampling rate | |

Input signal frequency | |

Geometric mean frequency | |

Arithmetic mean frequency |

## Voltage – *V*

Supply voltage | |

Largest supply voltage, if more than one | |

Lowest supply voltage, if more than one | |

Analog supply voltage | |

Digital supply voltage | |

Full-scale voltage range |

## Area – *A*

Total chip area (including pads) | |

Core area (excluding pads) | |

Analog area | |

Digital area |

## Length – *L*

Minimum CMOS channel length (“CMOS node”) |

## Resolution – *B*

Nominal resolution | |

Effective number-of-bits | |

ENOB calculated from SNR only |

## Dynamic performance – *X* [dB]

Dynamic range | |

Spurious-free dynamic range | |

Total harmonic distortion | |

Signal-to-noise ratio | |

Signal-to-noise-and-distortion ratio |

## Any other parameter – *D*

This is to make the generic FOM more future proof. Insert any type of parameter you feel is missing from the generic expressions for *F* and *G*.

# Comments

This page will be updated with new information, and the list of parameters may grow. The intention i not to list every minute variation of each parameter, but if you know of any parameter that should have been in the list, please let me know.

**Update**: Please note the addition of reference [3]. I was unaware of the contribution by *Vogels* and *Gielen* at the time of originally writing this page, but discovered it soon after. Their parameter-fitted proposed generic FOM is quite comparable to my proposal here, just without the area (*A*) and the catch-all parameter (*D*) thrown in to “future proof” it. The *Vogels-Gielen FOM* was included already in [4], but unfortunately it took me over a year to update this page to match. If you want to see the essential shape and form of their FOM formula, look for in [1].

# References

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

[2] B. E. Jonsson, “Linear-to-logarithmic FOM mapping”, *Converter Passion blog*, On-line, https://converterpassion.wordpress.com/linear-to-logarithmic-fom/, Jan., 2011.

[3] M. Vogels, and G. Gielen, “Architectural Selection of A/D Converters,” *Proc. of Des. Aut. Conf. (DAC)*, Anaheim, California, USA, pp. 974–977, June, 2003.

[4] B. E. Jonsson, “Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance,” *Proc. of 2011 IMEKO IWADC & IEEE ADC Forum*, Orvieto, Italy, pp. 1–6, June 2011. [PDF @ IMEKO]

Pingback: The mother of all ADC FOM | Converter Passion

Pingback: ADC FOM: What is a good figure-of-merit? | Converter Passion

Pingback: Going to Italy … Yes, Yes, Yes!! | Converter Passion