FE8113 ”High Speed Data Converters”
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Transcript FE8113 ”High Speed Data Converters”
FE8113 ”High Speed
Data Converters”
Course outline
Focus on ADCs. Three main topics:
1: Architectures
2:
3:
”CMOS Integrated Analog-to-Digital and Digital-toAnalog Converters,” 2nd ed., Rudy van de
Plassche, Kluwer Academic Publishers, Ch. 1-3
Digital background calibration
Selected papers
State-of-the-art converters
Selected papers
Part 1: Architectures
First three chapters of van de Plassche’s
textbook
Ch.1:
The Converter as a black box
Ch.2: Specifications of converters
Ch.3: High-Speed A/D Converters
Chapter 1
The converter as a black box
Analog Input
S/H
Vin
Tclock
Digital output:
n 1
Va
Dout qe Bm 2m qe
Rref
m0
n 1
Dout Bm 2m
m 0
A/D
B[n-1:0]
Basic A/D converter function
Classification of signals
Continuous
Discrete
Continuous
Analog
Amplitude
Quantized
Discrete
Time
Amplitude
Sampled
Signal
Digital
A/D conversion:
Amplitude
Sampling
quantization
Quantization errors
Quantization error ε:
Mean squared error:
1/qs
qs
q
s
2
2
2
eqns
E 2
qs
2
P(ε)
-qs/2
qs/2
ε
S/N for sinewave input
(amplitude 2(n-1)qs):
2
fe d
2
q
1
2 d s
qs
12
qs
2
2 n qs
S / N 2 2 2n 1.5
2
eqns
S / N 6.02 n 1.76dB
Quantization errors
Nioise density:
qs2
qs2
e f
12 f qns 6 f s
2
qns
S / N ( f ) 2n1 3 f s
System with BW=fsig:
S / N system 2n 1 3
fs
f sig
Definition of dynamic range:
The dynamic range is equal to the signal-to-noise ratio measured
over a bandwith equal to half the sampling frequency
Oversampling of converters
Oversampling distributes the quantization
noise over a larger spectrum
S / N system
fs
6.02 n 1.25 10 log
dB
f
sig
However: Improvement in resolution is only
obtained if the linearity of the converter is at
least equal to the dynamic range obtained by
oversampling
Quantization error spectra
Error (LSB)
1/2
Input signal
-1/2
Sawtooth error signal, described by odd
harmonics:
qerror
1
y x
sin 2m x
m 1 m
Quantization error spectra
For a sinewave input,
the error signal will
get a kind of
frequency modulation:
Simplifying:
1
jp
y A sin Im
J p 2m A e
m
m1 p
y Ap sin p
p 1
where
2
J p 2m A
m
m 1
Ap p1 A
Ap 0
even p
p1 1
p=1
p1 0
p≠1
odd p
Amplitude dependence of
quantization components
?
Multiple signal distortion
Two input signals:
Cross-modulation:
x t At sin t a t sin t
y
p q odd 0
Apq sin p q
2
J p 2n A J p 2n a
n
n 1
Apq p1 q 0 A p 0 q1a
Quantization results in errors correlated with the signal
mostly as odd harmonics
This analysis allows for investigation of inter-modulation
and harmonic distortion
With resolutions above 10b these effects can practically be
ignored
Accurate dynamic range calculation
Fundamental signal
amplitude for an n-bit
converter (p=1):
Quantization error
calculated as sum of
power of all odd
harmonics:
Signal to noise ratio:
A1 2
n 1
2
J p 2m 2n1
m 1 m
2
J 2 q 1 2m 2n1
q 1 m 1 m
Aquantization
S / N n
2
A1
Aquantization
S / N n
2
J1 2m 2n 1
m 1 m
2n 1
2
n 1
m J 2 q 1 2m 2
q 1 m 1
2
Accurate dynamic range calculation
Number of bits n
S/N Accurate dB
S/N 6.02*n+1.76
1
6.31
7.78
2
13.30
13.80
3
19.52
19.82
4
25.59
25.84
5
31.65
31.86
6
37.70
37.88
7
43.76
43.90
8
49.82
49.92
9
55.87
55.94
10
61.93
61.96
Sampling time uncertainty
Assume full scale
sine wave input
Sampling
time error
must be within 1LSB
Vin A sin t
t
A
A cos t
A
2A
2n
2 n
t
fin cos 2 fint
Inserting for t=0
(worst-case):
tmax
2 n
fin
Sampling time uncertainty
Reduction of ENOB
Error
power due to
jitter:
Average power:
Including quantization
noise:
A2 qs2 22 n f sig2 2 cos 2 2 f sig t 2
A q 2
2
2
total
q
2
s
2 n 1
f t q 2
range:
2
2
2
s
2 n 1
t 2
2
Tsig
2
qs2
qs2
2
A 1 k 2j
12
12
where
Dynamic
2
sig
A2
t
k 2 2n 6
qs
Tsig
12
2
j
S
S
N
1.5 2n 2
N Nj N N Nj
log 1 k 2j
2log 2
Sampling clock time uncertainty
Ideal
sine wave
Vcl
e2noise
Vclock
Squaring circuit
delta tclock
Clock noise due to thermal noise over squaring amplifier
bandwith
With equivalent noise resistance Rn of squaring amplifier,
the noise is expressed as
en2 4kTRn f
Differentiating Vcl=Asin(ωt) we obtain the time
uncertainty (rms)
en
t
2 f cl A cos 2 f cl t
Sampling clock time uncertainty
Total time uncertainty, inserting at zero crossing
tcl
For a first-order system,
tcl
en
f cl A
f noise
2 kTRn f b
2
fb
, which yields
f cl A
In amplifier systems, ther is a general relation
between rise time at the output and bandwith
fb tr 0.35
Total clock time uncertainty from first order
squaring circuit:
0.7kTR
tcl
n
f cl A tr
Ch. 1.13-1.17
Design specific, supplementary reading
Ch
1.13 Nyquist filtering in A/D converter
systems
Ch 1.14 Combined analog and digital filter
Ch 1.15 Output filtering in D/A converter
systems
Ch 1.16 Dynamic range and alias filter order
Ch 1.17 Analog filter designs
Minimum required stop band
attenuation
If the ADC system has an internal bandwith greater than the overall
bandwith, quantization noise will fold down to the baseband
Example: SAR converters, where the comparator bandwith, fcomp, is N
times higher than the input bandwith
Due to the sampling of the input signal all frequencies that are in the
aliasing signal bands are folded back into the baseband of the
system
At which point the aliasing occurs depends on the architecture of the
ADC and the point in the system where the sampling is performed
A
Bandwith limitation
(comparator, amplifier ++)
Wide-band noise
fs/2
fs
2fs
3fs f
Minimum required stop band
attenuation
With fcomp denoting the internal bandwith, the number of unwanted
bands that fold back to the baseband is given by:
N fold
f comp
fs
2
fs
2
N fold 1 2
f comp
The ”noise” in the baseband now increases to
Stop-band rejection of low-pass filter must be increased by
This increase in stop-band rejection (Afoldback) is equal to
fs
N fold
Afoldback N fold 10 log N fold dB
Which gives the minimum required stop-band rejection Astopmin
f comp
Astop min 6.02 n 1.76 10 log 2
dB
f
s
This stopband rejection requirements yields an 3dB overall reduction
of dynamic range (S/N)
Discussion...