Hochschule Kempten      
Fakultät Elektrotechnik      
Interface Electronics       Fachgebiet Elektronik, Prof. Vollrath      

Interface Electronics

14 Figure of Merit

Prof. Dr. Jörg Vollrath

13 Sigma Delta ADC

Review and Overview

Data converter performance parameters

ISSC 2008 [1]VLSI 2012 [2] VLSI 2013 [3]ISSC 2014 [4]
Technology [nm]9040 32 SOI40 LP
Resolution56 67
Power supply [V]11.1 0.851.1
Sampling Frequency [GS/s]1.753 52.2
Power Consumption [mW]2.211 8.527.4
SNDR @Nyquist [dB]27.633.1 30.937.4
FoMw [fJ/conv step]64.599.3 59.4210
FoMs [dB]143.5144.4 145.6143.3
Core area [mm2]0.01650.021 0.020.052
CalibrationOff chipForeground Off chipNo need

[1] B. Verbruggen, et al., “A 2.2mW 5b 1.75GS/s Folding Flash ADC in 90nm Digital CMOS,” ISSCC Dig. Tech. Papers, pp. 252-253, Feb. 2008.
[2] Y.-S Shu, “A 6b 3GS/s 11mW Fully Dynamic ADC in 40nm CMOS with Reduced Number of comparators,” Symp. VLSI Circuits, pp. 26-27, June 2012.VLSI 2012
[3] V. H. -C. Chen and L. Pileggi, “An 8.5mW 5GS/s 6b Flash ADC with Dynamic Offset Calibration in 32nm CMOS SOI,” Symp. VLSI Circuits , pp. 264-265, June 2013.
[4] M. Miyahara, et. al., "22.6 A 2.2GS/s 7b 27.4mW time-based folding-flash ADC with resistively averaged voltage-to-time amplifiers," 2014 ISSCC, San Francisco, CA, 2014, pp. 388-389.

Data converter performance parameters


Video: https://www.youtube.com/watch?v=dlD0Jz3d594
A figure of merit (FoM) is a useful tool for comparing the conversion efficiency of A/D converters. This presentation reviews the make-up and composition of the most popular FoMs quantifying the tradeoff between ADC speed, resolution and power dissipation. In addition, it investigates the pertaining asymptotes and trends over time. The obtained information allows us to quantify past progress rates and lets us speculate about the future.

ADC Figure of Merit


\( FOM_{1} = \frac{Power}{f_{S} \cdot 2^{ENOB}} [fJ/conversion step] \)

\( ENOB = \frac{SNDR-1.76}{6.02} \)

Ref: R.H. Walden, "Analog-to-digital converter survey and analysis," IEEE J. Selected Areas Comm., April 1999


\( FOM_{2} = SNR + 10log\left( \frac{f_{S}}{2 P}\right) [dB]\)

R. Schreier and G.C.Termes, Understanding Delta-Sigma Data-Converters, Wiley 2005

\( FOM_{3} = SNDR + 10log\frac{f_{S}}{2 Power} [dB]\)

A.M.A. Ali et al., "A 16-bit 250MS/s IF Sampling Pipelined ADC with background calibration, JSSC, Dec2010


Fundamental Limit

Class-B Amplifier, sample and hold C, Brickwall LPF at fsample/2

\( SNR = \frac{\frac{1}{2} \left( \frac{V_{FS}}{2}\right)^2 }{\frac{kT}{C}} \frac{f_S}{f_{snyq}} = \frac{1}{8} \frac{C}{kT} V_{FS}^{2} \frac{f_S}{f_{snyq}} \)
Pmin = I · V = Q · fsample · VDD = C · VFS · fS · VFS


\( E_{min} = \frac{P_{min}}{f_{synyq}} = 8 k T \cdot SNR \)
Energy over SNR, energy per bit.

Ref: Hosticka, Proc. IEEE 1985; Vitoz, ISCAS 1990

\( FOM_{2} = SNR + 10log\left( \frac{f_{S}}{2 P}\right) = SNR + 10log\left( \frac{1}{E_{min}}\right) = 10 log\left( \frac{1}{8kT}\right) = 198 dB\)

Summary of Interface Electronics


Overview Interface Electronics