A generic ADC FOM

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 PfVALDB, 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]