The Figure-Of-Merit (FOM)

Table 5-1 shows the comparisons of sigma-delta modulators for the audio applications. The range of paper survey is below 1mW and above 60dB of SNR. It is difficulty to compare power efficiency. In general, the figure-of-merit (FOM) is a criterion for the power efficiency of sigma-delta modulators. The FOM is defined as

P DR f kT FOM 4 ⋅ ^B⋅

= (5.1)

where k is Boltzmann’s constant, T is the absolute temperature, f_B is the signal bandwidth, and P is the power consumption. Although the signal bandwidth and power consumption are considered in FOM, the supply voltage is not taken into account [29]. To make a fair comparison, Table 5-2 shows the FOM comparisons for the sigma-delta modulators in Table 5-1. This work achieves the highest FOM except [29] with 90nm process. The area is not included into FOM and it is difficulty to compare due to different capacitor processes (poly-to-poly, metal-to-metal, and so on) and structures. In general, the area is dominated by capacitors for sigma-delta

Table 5-1 The comparison of sigma-delta modulator for the audio application.

Name & Year V_DD SNDR SNR DR BW Power Process

Tille, 2004 [28] 1.8V 72dB 77dB - 8kHz 1mW 0.25µ m CMOS Yao, 2004 [29] 1.0V 81dB 85dB 88dB 20kHz 140µ W 90nm CMOS Nielsen,2004 [30] 1.8V 62dB - 67dB 3.6kHz 108µ W 0.35 µ m CMOS Safarian, 2003 [31] 2.5V - 83dB 86dB 4kHz 125µ W 0.25 µ m CMOS Gerfers, 2003 [32] 1.5V 70dB 73dB 80dB 25kHz 135µ W 0.5 µ m CMOS

Hu, 2003 [33] 0.9V - 74dB - 10kHz 38µ W 0.18 µ m CMOS

Samid, 2003 [34] 1.5V 60dB 62dB - 50kHz 50µ W 0.5 µ m CMOS Sauerbrey, 2002 [35] 0.7V 67dB 70dB 75dB 8kHz 80µ W 0.18 µ m CMOS Qunying, 2001 [36]* 1.2V 63dB 75dB 75dB 3.4kHz 38µ W 0.35 µ m CMOS Gerfers, 2001 [37] 1.5V 65dB - 75dB 25kHz 230µ W 0.5 µ m CMOS Dessouky, 2000 [38] 1.0V 85dB 87dB 88dB 25kHz 950µ W 0.35 µ m CMOS Peluso, 1998 [39] 0.9V 62dB 76dB 77dB 16kHz 40µ W 0.5 µ m CMOS Peluso, 1997 [19] 1.5V 66dB - 74dB 3.4kHz 100µ W 0.7 µ m CMOS vanderZwan, 1996 [40] 2.2V - - 80dB 3.4kHz 200µ W 0.5 µ m CMOS This Work 1.0V 69dB 75.7dB 76.6dB 20kHz 40µ W 0.18 µ m CMOS

* Only simulation results.

Table 5-2 The FOM comparison.

Name & Year ^V_DD DR BW Power Area Process FOM

Yao, 2004 [29] 1.0V 88dB 20kHz 140µW 0.18mm ² 90nm CMOS 1493e-6 Gerfers, 2003 [32] 1.5V 80dB 25kHz 135µW - 0.5µ m CMOS 306.8e-6 Sauerbrey, 2002 [35] 0.7V 75dB 8kHz 80µW 0.082mm² 0.18µ m CMOS 52.39e-6 Qunying, 2001 [36]* 1.2V 75dB 3.4kHz 38µW - 0.35µ m CMOS 46.88e-6 Gerfers, 2001 [37] 1.5V 75dB 25kHz 230µW 1.2mm ² 0.5µ m CMOS 56.95e-6 Dessouky, 2000 [38] 1.0V 88dB 25kHz 950µW 0.63mm ² 0.35µ m CMOS 275.1e-6 Peluso, 1998 [39] 0.9V 77dB 16kHz 40µW 0.85mm ² 0.5µ m CMOS 332.2e-6 Peluso, 1997 [19] 1.5V 74dB 3.4kHz 100µW 0.5mm ² 0.7µ m CMOS 14.15e-6 This Work 1.0V 76.6dB 20kHz 40µW 0.54mm² 0.18µ m CMOS 378.7e-6

* Only simulation results.

5.2 Conclusions

The sigma-delta modulators have been proposed to achieve the high resolution A/D converters. This thesis presents the simple switched-capacitor structure with inverters to implement a 40µW third-order sigma-delta modulator with single-loop architecture. In Table 5-1, almost all the lower power modulators are single-loop due to less circuit blocks and component matching requirements. Also, the switched-capacitor circuits provide more accurate integrators and higher power efficiency. Moreover, the inverter opamp consumes less chip area and power consumption than the general opamp structures. Therefore, this thesis achieves a peak SNDR of 69.01dB, SNR of 75.74dB, and DR of 76.61dB at a sampling rate 2M Hz and a signal bandwidth of 20k Hz under single 1.0V supply voltage.

However, there are problems in this architecture, offset and clock feed-through due to inverter opamp and single ended integrators. The clock feed-through noise is still lager in proposed single-end integrators with dummy switches than differential-end integrators.

Although the SNDR in the proposed sigma-delta modulator is only 69.01dB, it is high enough for the hearing aids applications [21]. Only 40µW power consumption extends battery life longer. The chip area is also reduced by using inverter opamp.

Therefore, the proposed sigma-delta modulator is suitable for hearing aids and other similar audio applications.

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