Texas A&M University 1 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Jose Silva-Martinez
Many of these slides were provided by
Dr. Sebastian Hoyos
January 2020
FUNDAMENTALS OF ANALOG TO DIGITAL CONVERTERS: PART I.1
Texas A&M University 2 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
• 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
Texas A&M University 3 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
R. Walden, 1999
Texas A&M University 4 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 5 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 6 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
How does an ADC work?x(t)
t
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
Texas A&M University 7 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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)
Yesterday: 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
Today: 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.
Texas A&M University 8 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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 ADCs is crucial to stay on the future applications roadmap
Pipeline ADC is breaking the trend set by Sigma-Delta and Flash ADCs, and driven by consumer electronics
Texas A&M University 9 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 10 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Super-heterodyne Receiver
Invented by Armstrong in 1918 Hardware specific radio architectureExtensive filtering to relax ADC specsSuitable for narrow-band applications
Texas A&M University 11 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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 consumption Extensive filtering: Area, Power and Noise issues Not fully compatible for the Telecoms roadmap
Limited by flicker noise
Not flexible
Hardware intensive
Texas A&M University 12 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 13 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 14 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 15 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
The single-chip Transceiver Paradigm15
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
Texas A&M University 16 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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)
Texas A&M University 17 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Ultimate goal: Reality or Dream
Concept introduced in 1991 Modulation/demodulation waveforms in software Flexible multi-standard software architecture
Texas A&M University 18 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
R. Walden, 1999
Texas A&M University 19 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
WiMAX
Where we were in 99? Where we are?
Texas A&M University 20 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 21 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
A Little bit of History
Texas A&M University 22 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
A Little bit of History
Texas A&M University 23 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Jitter and noise limitations on ENOB
Texas A&M University 24 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
The quantized signal presents a finite number of output values that are associated with digital codes
Data Converters: The main issue
Texas A&M University 25 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
What the problem is?
Texas A&M University 26 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
The quantized signal presents a finite number of output values that are associated with digital codes
Issues: Sampling, Holding and conversion
Texas A&M University 27 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Properties of the Fourier Series
Modulation properties
Convolution in time
Texas A&M University 28 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Relevant properties of the Fourier Series
Product in time
Texas A&M University 29 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Relevant properties of the Fourier Series
Texas A&M University 30 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Additional properties of the Fourier Series
Texas A&M University 31 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Define the problem: Sampling Operation
Texas A&M University 32 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 33 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Signal Sampling Theorem
Time domain sampling
Frequency Spectrum
Texas A&M University 34 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Signal Sampling employing a train of pulsesTime domain sampling with pulses
Spectrum
Texas A&M University 35 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 36 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Sampling
kscs
sk
s
FT
cs
ccs
kXT
jX
Tk
Tts
jSjXjX
nTttxtstxtx
1
2,221
T
ksc
Ts
n
nj
kXT
jX
znxeX
1
δ(t-nT)
xs(t)
t0 T 2T 3T 4T T
xc(t)·δ(t-nT)
Texas A&M University 37 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 38 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Notice in the afore equation that the delay due to exp(-jfT) has being ignored
In practice, this term corresponds to a signal delay of T/2 seconds!
Texas A&M University 39 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
The sampling and Held operations generate alias frequency components and (sinc) signal distortion, respectively
Quantization generates harmonic distortion components when sinusoidal input signals are used
S/H and Quantization errors
Texas A&M University 40 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Distortion due to S/H errors
tVtVtV error0PKd sinThe S/H signal can be expressed as:
The first part of this equation does not generate any distortion since it is a pure sine wave function
The error signal is input dependent and non-linear! Fundamental component is at the signal frequencyIt can be expanded in a Fourier series and then the harmonic components can be found
Texas A&M University 41 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Distortion due to quantization errors: Ramp
Nv1Nif1Nv2
v ininin
In general, the quantization error can be expressed as:
For the case of a ramp input signal, then Vin(t)=Kt, then
You may want to find the Fourier series that represent this sawtooth error function to find the harmonic distortion components.
NKt1Nif1N2
Ktt
or
NV1Nif1N2
tVt inin
Texas A&M University 42 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
The problem is more complex for a sine function, the quantization error can be expressed as a kind of frequency modulation function See Van dePlassche , pp. 14:
Interestingly, this complex expression can be simplified for n-bit converters, leading to a very simple result for the third order harmonic distortion
Distortion due to quantization errors: Sinusoidal input
oddispiffunctionBesselcomplexA
evenispif0A
pAv
p
p
1ppin
sin
1n2componentlfundamentaofPower
componentharmonicrd3ofPower3HD n51 .
Texas A&M University 43 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
For 10-Bit ADC, HD3 is in the range of -90.31 dB
HD3 reduces at a rate of -9dB per additional Bit
After 10 bits, this distortion can be easily ignored
Distortion due to quantization errors: Sinusoidal input
n5123HD
.
Texas A&M University 44 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Distortion due to quantization errors: Sinusoidal input
Notice that SNR is over 20dB more relevant than HD3 for n>=7
n223IM
For the case of intermodulation distortion using a couple of test tones, it is found
Texas A&M University 45 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Alias issue if undersampling
Texas A&M University 46 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 47 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Under-sampling of a broadband signal
Texas A&M University 48 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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 distortion components when sinusoidal input signals are used
S/H and Quantization errors
Freq Freq
Error signal
Quantized signal
tErrortStS qin
Texas A&M University 49 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Distortion due to quantization errors
Texas A&M University 50 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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)
Texas A&M University 51 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 52 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
What the fundamental problem is?Mapping an infinite resolution analog signal into a digital but finite resolution representation
Texas A&M University 53 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Quantization noise for Random (Ramp) input signal
Texas A&M University 54 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 55 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
Texas A&M University 56 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
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
f6
q
f
2densityNoise
12
q
Quantization noise density
fs/2-fs/2
Texas A&M University 57 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 58 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 59 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 60 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 61 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 62 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Digital to Analog Converters
Texas A&M University 63 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Definitions
Texas A&M University 64 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 65 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Quite critical issue! Usually not a major issue
Texas A&M University 66 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations: Offset error
Texas A&M University 67 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Usually not a major issue Quite critical issue!
Texas A&M University 68 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations: Gain error
Texas A&M University 69 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations: Differential Error
Texas A&M University 70 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 71 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations: Integral error
Texas A&M University 72 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 73 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations: Absolute Accuracy
Texas A&M University 74 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Analog to Digital Converters
Usually the effects
of the systematic
offsets can be
minimized through
calibration or
accounted in
digital domain
Texas A&M University 75 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Digital to Analog Converters
Texas A&M University 76 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 77 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 78 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
DNL must be smaller or equal to 1 LSB
Texas A&M University 79 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 80 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Offset Voltages
Texas A&M University 81 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Practical Limitations
Texas A&M University 82 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 83 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 84 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 85 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez
Texas A&M University 86 Spring, 2019
Fundamentals on ADCs: Part I Jose Silva-Martinez