Sebastian Hoyoshttp://ece.tamu.edu/~hoyos/
Several of these slides were provided by
Dr. Jose Silva-Martinez and Dr. Jun Zhou
Fundamentals of Data Conversion: Part I.1
• Fundamentals of Analog-to-Digital Converters
• Introduction
• Sampling and Quantization
• Quantization noise and distortion
• INL and DNL
• Technological related issues
• Sample and Hold
• Switching issues
• S/H Accuracy
• Active S/H
• Switch around S/H
Outline
The Smartphone market
• Global smartphone market projected to growAnticipated global unit sales to approach 400 millions in 2013
(market research report from Forward Concepts Co)Projected revenue in 2012: $32.2 billion
(source: In-Stat Group)
GSM
WCDMA
FM
WiMax & 802.20
GPS
Bluetooth
WiFi
Multi-standard Wireless Systems• Multiple services
• Reuse circuits as much as possible• Power• Area• Competitiveness
• Smaller Cell phone,stronger function,longer battery duration
• Use of digital (analog unfriendly) nanometric tecnologies
Exponential growth in mobile computing and broadband wireless Major need for high dynamic range, wide-bandwidth, low power ADCs.
Multi-standard Wireless Systems
Bandwidth requirements for higher connectivity
Bluetooth, 802.11band 802.11g
Frequency (GHz)
Spec
turm
802.11a
5.42.4
UMTS
2
DECT
1.91.0
GSM
IS-95
DTV
0.05 0.8
> 45 dB
Higher flexibility on operational frequency and bandwidth, higher blocker rejection, higher dynamic range
Receiver Architectures:
Super-heterodyne, Low-IF, Direct Conversion, High-IF, Digital Radio
What is an Analog-to-Digital Converter (ADC)?Analog
Continuous with no apparent discontinuities
The way we interpret our surroundings: sound, light, temperature … etc
Digital01001011001010010101010101010100101001010010100101010010010010010110011001010100100101001001010
Discrete with limited range; based on binary numbers with limited number of bits.
The way we mathematically represent and process our world using electronic “brain” power
ADC
R. Walden, 1999
x(t)
Sampling
δ(t-nTS)
x(nTS)
Quantization
x(nTS)+q(nTS)
Decoding111110101
010001000
765
210
N bits
How does an ADC work?Analog Digital
Continuous with no apparent discontinuities
The way we interpret our surroundings: sound, light, temperature … etc
10010100101001010010011001011001010
01001011001010010101010101010100101001010010100101010010010010010110011001010100100101001001010
ADC Discrete with limited range; based on binary numbers with limited number of bits.
The way we mathematically represent and process our world using electronic “brain” power
How does an ADC work?
x(t)
Sampling
δ(t-nTS)
x(nTS)
Quantization
x(nTS)+q(nTS)
Decoding111110101
010001000
765
210
N bits
x(t)
t
x(n)
nTS
Analog Digital
10010100101001010010011001011001010
ADC
δ(n)
nTS
x(n)
nTS
2N Levels separated by 1LSB, 1LSB = VFS
* / 2N
* VFS = full scale range, Vmax-Vmin
Quantization noise
ADCs are indispensable, but now need to handle smaller signals at higher speeds with similar or higher resolutions.
ADCs: Yesterday vs. TodayExample: Digital photography (8-12b ADCs)
2000
CCD/CMOS Image Array
Balance Control
DSP(black level
compensation , encoding ...etc)
AMP ADC
0.5-0.8µm CMOS with 5V supply (moderate gate density and speed in DSPs)
2M pixel CCD sensor (low pixel scanning speed) Some pre-ADC analog conditioning ~ 2.5mV / LSB
2009
DSP(balance control, black level
compensation, image stabilization, exposure levels, noise reduction, lens shading
correction, encoding...etc)
AMP
CCD/CMOS Image Array
ADC
90nm-180nm CMOS with 1.2-1.8V supplies (high gate density and speed in DSPs)
12M pixel CCD sensor (high pixel scanning speed) Minimal pre-ADC analog conditioning ~ 0.5mV / LSB
Faster DSPs capable of performing numerous complex functions are developed thanks to advanced CMOS technologies
ADCs are becoming the bottleneck for advancement, and new design techniques need to be developed.
ADCs: Tomorrow?ADC IEEE literature survey: 2006-2008
Pipeline ADC is currently most published architecture Pipeline ADC is breaking the trend set by Sigma-Delta and Flash ADCs
Pipeline ADC is expected to be a key ADC architecture in future applications
2468
101214161820
0.1 1 10 100 1000 10000Signal Bandwidth (MHz)
Res
olut
ion
(bits
)
0.01
Sigma-DeltaPipelinedFlash
The development of new design techniques for high speed, low voltage and low power Pipeline ADCs is crucial to stay on the future applications roadmap
15M?20M?
From 1080P to 4K (2160P)?
4G?HDTV?
Tomorrow
Pipeline ADC ApplicationsToday
Pipeline ADC is breaking the trend set by Sigma-Delta and Flash ADCs, and driven by consumer electronics
Design Challenges of Pipeline ADCs in Advanced CMOS Technologies (Summary)
High Speed Low Voltage Low Power
DSP(balance control, black level
compensation, image stabilization, exposure levels, noise reduction, lens shading
correction, encoding...etc)
AMP
CCD/CMOS Image Array
ADC
With the added speed of new generations of DSPs, the ADC is becoming the bottleneck for overall system speed
in addition to increased speed, the DSP ability to perform more complex tasks will require higher ADC resolutions
Reduction of Device size allows for denser integration, but device reliability dictate lower supply voltages
Reduced supplies means reduced signal range, which requires a higher ADC accuracy for the same number of bits
Many applications are portable and operated from a battery
As a potentially power hungry component, the ADC power needs to be reduced to help prolong battery life
Digital Camera Example
Super-heterodyne Receiver
BPF LNA BPFVGA
LO2LO1
Digital Output
RF(0.45-5 GHz)
High IF(100-200 MHz)
Antenna
LPF Baseband ADC
Baseband(< 20 MHz)
Invented by Armstrong in 1918 Hardware specific radio architectureExtensive filtering to relax ADC specsSuitable for narrow-band applications
Design issues for multi-standard solutions
Excessive power at the front-end (Linearity issues)Extensive down conversions: LO and mixers increase both
noise and power consumptionExtensive filtering: Area, Power and Noise issuesNot fully compatible for the Telecoms roadmap
Limited by flicker noise
Not flexible
Hardware intensiveBPF LNA BPFVGA
LO2LO1
Digital Output
RF(0.45-5 GHz)
High IF(100-200 MHz)
Antenna
LPF Baseband ADC
Baseband(< 20 MHz)
Current Multi-standard designs
BPF LNA BPFVGA
LO2LO1
RF(1-2 GHz)
IF(100-200 MHz)
Antenna
RFSwitch
Receiver for standard 1
BPF LNA BPFVGA
LO2LO1
RF(1-2 GHz)
IF(100-200 MHz)
Receiver for standard 2
Minimum sharing of blocks
Area and powerconsumption overhead
Not Flexible at all
Limited number of standards can be accommodated
Introduction to Analog-to-Digital Converters
• Analog-to-Digital Converters (ADC) are necessary to convert real world signals (which are analog in nature) to their digital equivalents for easy processing.
• Common applications for ADCs are communication systems, TV receivers, Digital Oscilloscopes, Audio applications..
Analog
Efficient radio transceiver: Direct Conversion
Direct conversion + broadband ADC (1 receiver per service) Lowpass filter is required (~ 50-100 mW) 13-14 bits 80 MHz Lowpass ADC (500 mW from ADI) Bank of receivers, filters and ADCs
Antenna
RFsignal
Software Platform
DSP
or
FPGAs
LNA & VGA
16-Channel Multiband Digital Receiver
RF Filter 1 ADC 1IF Filter 180 MHz
4-channel digital
receiver
4-channel digital
receiver
ADC 2IF Filter 24-
channel digital
receiver
4-channel digital
receiver
Antenna
RFsignal
LNA & VGARF Filter 2
Optional
Mixer
Mixer
Frequency Synthesizer
Recent Approaches to Broadband Receivers Sample rate, downsampling and filteringR. Crochiere and L. Rabiner, Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice Hall,
1983.
Sampling with built-in anti-aliasing Y. S. Poberezhskiy et.al. “Sampling and signal reconstruction circuits performing internal
antialiasing filtering and their influence on the design of digital receivers and transmitters,” TCASI, Jan. 2004.
A discrete-time RF sampling receiverR. B. Staszewski, et. al. “All-digital TX frequency synthesizer and discrete-time receiver for
Bluetooth radio in 130-nm CMOS,” IEEE J. Solid-State Circuits, Dec. 2004.
SDR receiverAbidi, “The path to software-defined radio receiver”, IEEE JSSC, May 2007
Frequency-domain-sampling receiversS. Hoyos and B. M. Sadler, “Ultra-wideband analog to digital conversion via signal expansion,” IEEE
Transactions on Vehicular Technology, Sept. 2006.
A. Abidi, “The path to software-defined radio receiver”, IEEE JSSC, May 2007
Direct conversion with tunable LO in the freq. range 800 MHz to 6 GHz.
Cascade of sincN filters followed by decimation to achieve the initializing needed.
Good for narrowband signals as a single ADC can handle the bandwidth. But SDR should also be good for wideband and ultra-wideband signals. Need parallel ADC to sample at a fraction of Nyquist rate. Parallelization of the front-end will be needed if want to keep the ADC sampling rate down.
UCLA SDR receiver
x A/D
A/Dx
jj( 1m+
∫( 1m+
∫1
Tc
0R
Frequency-Domain ADC Based on Fourier Coefficients
Mixers and integrators. Lower frequency sample and
hold requirements.
No signal reconstruction. Parallel digital processing.
Optimal bit allocation minimizes quantization error. Some samples may
not be quantized at all.
F0 F1 FN-1F2
1R2R
1NR −
S. Hoyos and B. M. Sadler, “Ultra-wideband analog to digital conversion via signal expansion,” IEEE Transactions on Vehicular Technology, Sept. 2006.
Dout
Antenna
LNA & VGARF Filter BP-Σ∆-ADC RF
signalVin
Software radio transceiver: Design Issues
Makes it sense to have a multi-standard solution based on this architecture?
Bandwidth required? Dynamic range required? DTV SNRsignal=25 dB; Blockers > 45 dB; Crest factor > 20 dB LNA+VGA+ADC Dynamic Range over 90 dB (practical ?) Can you use tracking filters? (back to the past)
Ultimate goal: Reality or Dream
Antenna
RF signalDSP
Filter+
LNA
T/R switch
Linear RF Power
amplifierDAC
Reconfigurableprograms
ADC
Concept introduced in 1991Modulation/demodulation waveforms in software Flexible multi-standard software architecture
1
2
3
LNA
RF Filter
RF
Anti-Aliasing
Filter
A/D
SCF, GmCOP-RC
Anti-Aliasing
Filter
A/D
Dig. Filter
DSP
DSPRF
RF Filter
RF Filter
A/D
Dig. Filter
DSPG
Dig. Mod.RF
IF or BB
DR
DR
BB
How much RF processing should be done before the ADC? The front-end must be scalable and configurable to fit multiple standards
Roadmap for high-resolution Receivers
The single-chip Transceiver Paradigm25
Critical Analog components must be minimized
• Modern technologies:“Digital intensive” System-on-Chip (SOC) environmentScaling of transistor dimensions in digital CMOS
technologiesIncreased intra-die variability from device scalingDefect densities increase in newer technologiesYields decrease as SOC chip sizes increaseYield impact on analog specifications leads to
process corner-based overdesignto allow for analog parameter variations Increased test cost
M. Onabajo, 2011
Fast CMOS ADC’s: State of the art
Freq (GHz)
Spec
turm
5.42.421.91.00.05 0.8
16
14
12
10
8
6
4
10 MS/s 100MS/s 1GS/s 10GS/s 100GS/s
Flash
Pipeline Interleaved
Sampling rate
Resolution
Trends:Extensive use of parallelism
Time interleavedReduced supply voltages make analog
more challengingHeadroom for amplifiersLittle room for cascodingPoor devices if VDS is further reduced
Use techniques that take advantage of digital trendsDigital circuitry is “cheap and fast”Tendency is Digitally Assisted Analog
Circuits
Research Goal
Pipeline
Calibrated Pipeline
BP Sigma-delta
R. Walden, 1999
LTE
Where we were in 99? Where we are?
A Little bit of History
A Little bit of History
Jitter and noise limitations on ENOB
Classic FoM to compare ADCs
Recent Σ∆ modulators
Bandwidth (Nyquist) vs. SNDR
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
1.E+10
1.E+11
10 20 30 40 50 60 70 80 90 100 110 120
BW
[Hz]
SNDR [dB]
ISSCC 1997-2009VLSI 1997-2009ISSCC 2009Jitter=1psrmsJitter=100fsrms
B. Murmann, "ADC Performance Survey 1997-2010, http://www.stanford.edu/~murmann/adcsurvey.html.
Energy per conversion at Nyquist rate
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
10 20 30 40 50 60 70 80 90 100 110 120
P/f s
[pJ]
SNDR [dB]
ISSCC 2010ISSCC 1997-2009VLSI 1997-2009FOM=100fJ/conv-stepFOM=10fJ/conv-step
B. Murmann, "ADC Performance Survey 1997-2010, http://www.stanford.edu/~murmann/adcsurvey.html.
The quantized signal presents a finite number of output values that are associated with digital codes
Data Converters: The main issue
What the problem is?
The quantized signal presents a finite number of output values that are associated with digital codes
Issues: Sampling, Holding and conversion
Properties of the Fourier Series
Properties of the Fourier Series
Modulation properties
Convolution in time
Relevant properties of the Fourier Series
Product in time
Relevant properties of the Fourier Series
Additional properties of the Fourier Series
Define the problem: Sampling Operation
Sampling Operation: Nyquist Rate
According to the sampling theorem: If no alias issues, then
Ideal sampling does not add distortion but replicas of the original spectrum
Signal Sampling Theorem
Time domain sampling
Frequency Spectrum
Signal Sampling employing a train of pulsesTime domain sampling with pulses
Spectrum
Alias issue if undersampling
Under-sampling of a broadband signal
The sampling and Held operations generate alias frequency components and (sinc) signal distortion, respectively
Error is an odd function (no even harmonic distortions, why?)
Quantization generates harmonic distortioncomponents when sinusoidal input signals are used
S/H and Quantization errors
Freq Freq
Error signal
Quantized signal
( ) ( ) ( )tErrortStS qin +=
Distortion due to quantization errors
ADC metrics: Quantization error• Signal is sampled at given instants• Signal is encoded to a limited number of codes resulting in quantization noise
(random signals) and distortion (periodic signals)
What the fundamental problem is?Mapping an infinite resolution analog signal into a digital but finite resolution representation
Quantization noise for Random (Ramp) input signal
( ) dB.N./
/P
/APP
SQNRN
noisenoise
signalideal 761026
12222
2
22
+=∆⋅∆
===
The maximum Signal-to-Quantization Noise ratio (SQNR) for an N-bit ADC:
02.676.1)dB(SNDRENOB −
=
• For an ADC with a measured SNDR, the effective number of bits is defined as:
ADC metrics: SQNR
The dynamic range of a system is equal to the signal to noise ratio measured over a bandwidth equal to half of the sampling (Nyquist) frequency
Then,
Is the total while the quantization noise density (quantization noise measured in a bandwidth of 1 Hz)
s
2
s
2
22
f6q
f2densityNoise
12q
==
=
σ
σ
Quantization noise density
fs/2-fs/2
Incommensurate fs and fin Sampling frequency fs is fixed.
Input frequency fin is chosen to satisfy (a) integernumber of cycles C and (b) N / C = fs / fin isincommensurate. An easy way is to make N a power of 2 and C a prime number. Additionally to guarantee thatthe input frequency falls on a DFT freq. bin use fin = fs/2-kfs/N, where k is an integer. Then checkinconmesurate requirement.
Windowing lifts the need to have an integer numberof cycles. Good for measurements.
Pick N depending on noise floor requirements: TheDFT noise floor is 10*log10(N/2) below the noise floor. Then DFT noise floor = -SNR_0dFS -10*log10(N/2).
Practical Limitations
Digital to Analog Converters
Practical Definitions
Practical Limitations
Practical Limitations
Quite critical issue! Usually not a major issue
Practical Limitations: Offset error
Practical Limitations
Usually not a major issue Quite critical issue!
Practical Limitations: Gain error
Practical Limitations: Differential Error
Practical Limitations
Practical Limitations: Integral error
Practical Limitations
Practical Limitations: Absolute Accuracy
Analog to Digital Converters
Usually the effects of
the systematic offsets
can be minimized
through calibration or
accounted in digital
domain
Digital to Analog Converters
Practical Limitations
Practical Limitations
Practical Limitations
DNL must be smaller or equal to 1 LSB
Practical Limitations
Offset Voltages
Practical Limitations