Outline. Design Considerations for Continuous-Time Bandpass ADCs. An ADC Figure-of-Merit? An ADC Figure-of-Merit? DR-P Trade-Off: Part 2

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1 Design onsiderations for ontinuous-time Bandpass ADs ichard Schreier Oct 5 ANALOG DEVIES Outline An AD Figure-of-Merit Overview of Bandpass ADs 3 A High-Q Active- esonator IDA Design onsiderations Thermal noise Switching dynamics An AD Figure-of-Merit? Is an AD which has SN = db over BW = MHz fundamentally better or worse than an AD which has SN = 9 db over the same bandwidth, if AD consumes W while AD consumes mw? An AD Figure-of-Merit? More generially, what is the fundamental trade-off between Bandwidth (BW), Dynamic ange (D) and ower consumption ()? 3 D- Trade-Off: art To increase D at the expense of, parallel two ADs and average: Input AD AD.5 Averaging reduces noise by a factor of : D += 3 db Assuming the ADs noises are uncorrelated Output But uses twice the power: += 3 db D- Trade-Off: art To reduce at the expense of D, cut the AD in half May not be practical if the AD is already small, but if it can be done, = 3 db & D = 3 db For an AD of some BW, x db in D costs x db in, or D (in db) log () = const 5 6

2 Q: Is This Trade-Off Optimal? A: Yes, because it is bi-directional The fact that you can (in principle) go both ways for any AD means that no other tradeoff can exist for ADs that are optimal. onsider a (supposedly) optimal AD that can get more than 3 db increase in D for a doubling of Double, then cut that AD in half. The resulting AD has the same as the original, but more D. D- Trade-Off: art b an increase D by 3 db by reducing T by a factor of : Input AD Temp = T/ Output Temp = T But this also costs twice the power Ideal efrigerator 7 8 What About BW? educing BW by a factor of increases D by 3 db but leaves alone Assuming the noise is white (distortion is not dominant) and that digital filtering takes no power. Time-interleaving two ADs doubles BW and doubles, but leaves D unchanged I/Q processing does the same. Assumes that interleaving is perfect (can be calibrated). esulting FOM Use a db scale: ( BW ) FOM = ( D) db + log- For a given FOM, factors of in BW or are equivalent to a 3-dB change in D Should really include T, but since T is usually 3K, omit it Steyaert et al. like FOM = kt D BW - 9 FOM (db) State-of-the-Art FOM Architecture Front [],[] [3] [] [5] BW (Hz) Technology Front [6] [7] [8] [9] [] eferences [] Y. Yang, A. hokhawala, M. Alexander, J. Melanson, and D. Hester, A db 68 mw chopperstabilized stereo multi-bit audio A/D converter, ISS Digest of Technical apers, pp. 6-65, Feb. 3. [] L. Yao, M. Steyaert and W. Sansen, V 88dB khz Σ modulator in 9nm MOS, ISS Digest of Technical apers, pp. 8-8, February. [3] S. abii, and B. A. Wooley, A.8-V digital-audio sigma delta modulator in.8µm MOS, IEEE Journal of Solid-State ircuits, vol. 3, no. 6, pp , June 997. [] K. Vleugels, S. abii, and B. A. Wooley, A.5-V sigma delta modulator for broadband communications applications, IEEE Journal of Solid-State ircuits, vol. 36, no., pp , Dec.. [5]. H. M van Veldhoven, A tri-mode continuous-time Σ modulator with switched-capacitor feedback DA for a GSMEDGE/DMA/UMTS receiver, ISS Digest of Technical apers, pp. 6-6, Feb. 3. [6] M. Moyal, M. Groepl, H. Werker, G. Mitteregger and J. Schambacher, A 7/9mW/channel MOS dual analog front-end I for VDSL with integrated.5/.5dbm line drivers, ISS Digest of Technical apers, pp. 6-7, Feb. 3. [7].. Grace,. J. Hurst and S. H. Lewis, A b 8MS/s pipelined AD with bootstrapped digital calibration, ISS Digest of Technical apers, pp. 6-6, Feb.. [8] B. Hernes, A. Briskemyr, T. N. Andersen, F. Telstø, T. E. Bonnerud and Ø. Moldsvor, A.V MS/s b pipeline AD implemented in.3µm Digital MOS, ISS Digest of Technical apers, pp , Feb.. [9] G. Geelen and E. aulus, An 8b 6MS/s mw MOS folding A/D converter using an amplifier preset technique, ISS Digest of Technical apers, pp. 5-55, Feb.. []. Taft,. Menkus, M.. Tursi, O. Hidri, V. ons, A.8V.6GS/s 8b self-calibrating folding AD with 7.6 ENOB at Nyquist frequency, ISS Digest of Technical apers, pp. 5-53, Feb..

3 A Bandpass Σ AD System Bandpass NTF IF (or F) Input desired signal B Σ AD shaped noise Quadrature Digital Mixer complex data signal shifted to dc f s f s f s f s Decimation Filter To DS baseband data f B Gain (db) 6 High f.5.5 Normalized Frequency AD outputs noise-shaped data DS translates signal to baseband and removes out-of-band noise NTF attenuates quantization noise in the band of interest 3 U L L Generic Σ AD Y Y = L, where U + L V V = GU + HE V = Y + E H = -, G = L L H inverse relations: L = - /H, L = G/H oles of L are the zeros of H E AD DA oarse AD and DA V 5 U A Bandpass Σ AD Lots of f esonator Loop Filter esonator Q Quantizer Quantization noise is suppressed at frequencies where the loop gain is large Need high-q resonances to get deep nulls V 6 Active- esonator Amplifier Gain and hase Finite gain degrades Q hase lag enhances Q Analysis shows φ = 5º yields high Q, independent of amplifier gain + Amenable to integration; eadily tuned over several octaves Amplifier drives and δ = µ ( + j)ω µ = A φ=arg(µ) 7 8

4 A ircuit With φ = f esulting High-Q esonator - Amplifier load yields f Finite gm shifts the pole frequency, but does not degrade Q! 9 Finite Bandwidth & Non-zero Switch esistance Switch resistance degrades Q Finite gm bandwidth enhances Q sw ancellation occurs if = - + s ω p ω sw = ω p urrent-mode DA (IDA) B B B B Excellent spectral performance 8 dbc IMD to 3 MHz [Schofield et al., ISS 3] I A I B I Diff =(I A I B )/ IDA SN/ower Limit Assume square-law operation i.e. = K ( V ). I FS The power of a 3-dBFS signal is S = (.5( I FS ) ) = K ( V ) 6 While the noise in bandwidth B is = ( ktbk V ) 3 N S - N = 3I FS V 6kTB IDA SN/ower Limit (cont d) S - N = 3I FS V 6kTB DA SN is proportional to the power allocated to its current sources For example, to get SN = db with B = 5 MHz and V = 3 mv requires (at least) I FS =5mA 3

5 DATA IN IOUT Switching Dynamics Actual Ideal Model of Dynamic Nonlinearity v [,] z linear processing w w w w EO (Actual Ideal) non-linear processing v x v - e 5 6 Model Equations Zero error if the rise and fall waveforms are perfectly complementary w w w e = 3 w w w w where w,w,w and w are the output waveforms in response to,, and data inputs. e =.5[ ( w + w ) ( w + w )] 7 8 DA Example Simulated Single-Ended W * D G 3V w w w Simulated Waveforms (normalized to ) w 3 G IA IB w w Model Waveforms (normalized to ) w 3V MOS for low noise Symmetric drive for symmetric switching 3. e Error Waveform (normalized to ) -. 3 Time (ns) 9 3

6 db 8 9 Fourier Transform of E 5 MHz Frequency (MHz) 3 dbfs/nbw Example Spectra in Model 33-level v sequence; f = f s /3; no MS 6 8 x: 6 dbfs x convolves with e to yield nonlinear component of the output NBW=5.9X Normalized Frequency v: 9 dbfs 3 E.g. SFD alculation The signal level is 9 dbfs db = dbfs The spur level (in the absence of any differential cancellation) will be 6 dbfs db = 7 dbfs Thus, the SFD will be 96 db Need only db of differential cancellation to reach SFD = db alculating the impact of element dynamics on SN is done similarly 33 onclusions 3 db is a factor of (in BW, D, or ). An active- resonator can achieve high Q despite several circuit nonidealities. 3 urrent-mode DAs can have nearperfect spectral performance up to several tens of MHz. 3 35