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

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

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 $\alpha$ -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 $\left | \alpha \right | = \left \{ 0, 1, 2 \right \}$ .

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

$G = \dfrac{1}{\alpha_B}\times 20\times\log{F}$

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

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

A strict mapping between F and G requires $M =0, M_0 = 1.76$ , but $M_0$ 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 $\alpha$ 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

$P_{tot}$	Total power dissipation
$P_{on-chip}$	On-chip power dissipation
$P_{core}$	ADC-core power dissipation
$P_{a}$	Analog power dissipation

Frequency – f

$f_{clk}$	Clock frequency
$f_{s}$	Nyquist sampling rate
$BW$	Signal bandwidth
$2\times BW$	Twice the signal bandwidth
$ERBW$	Effective resolution bandwidth
$2\times ERBW$	Twice the ERBW
$\min {\left \{ 2\times ERBW, f_{s} \right \}}$	Twice the ERBW clipped to Nyquist sampling rate
$f_{in}$	Input signal frequency
$f_{g} = \sqrt{2\times f_{in}\times f_{s}}$	Geometric mean frequency
$f_{a} = \dfrac{2\times f_{in} + f_{s}}{2}$	Arithmetic mean frequency

Voltage – V

$V_{DD}$	Supply voltage
$V_{DD, max}$	Largest supply voltage, if more than one
$V_{DD, min}$	Lowest supply voltage, if more than one
$V_{DDA}$	Analog supply voltage
$V_{DDD}$	Digital supply voltage
$V_{FS}$	Full-scale voltage range

Area – A

$A_{tot}$	Total chip area (including pads)
$A_{core}$	Core area (excluding pads)
$A_{a}$	Analog area
$A_{d}$	Digital area

Length – L

$L_{min}$

Minimum CMOS channel length (“CMOS node”)

Resolution – B

$N$	Nominal resolution
$ENOB$	Effective number-of-bits
$SNR-bits$	ENOB calculated from SNR only

Dynamic performance – X [dB]

$DR$	Dynamic range
$SFDR$	Spurious-free dynamic range
$THD$	Total harmonic distortion
$SNR$	Signal-to-noise ratio
$SNDR$	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 $F_{J1}$ 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]

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A generic ADC FOM