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2006.12.14 A. Matsuzawa, Titech 1
Mixed signal systems and integrated circuits
Akira Matsuzawa
Tokyo Institute of Technology
http://www.ssc.pe.titech.ac.jp
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2006.12.14 A. Matsuzawa, Titech 2
Over sampling ADC and DAC 2
• Higher order system• Stability
– Stability compensation
• Saturation of integrator– Scaling
• Multi-stage Sigma-delta modulation• Circuit design
– kT/C noise– OP amp. gain– DAC and DEM
• Recent important developments
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2006.12.14 A. Matsuzawa, Titech 3
111
−− z 111
−− z 1−z...
Quantizer
Q
( ) ( ) ( ) ( )
( ) )z(Ez)z(X)z(Y
QYzz.....Y
zzY
zzX
zY
k
kkk
1
1
1
11
1
1
1
1
1
11111
−
−
−
−−
−
−
−
−
−+=
∴
+−
−−−
−−
−−
=
111
−− z
3rd-- >10 steps 4 th ---- >30
In OutH
Higher order sigma-delta modulation
Cascade connection of the integrators
The feed back loop becomes unstabledue to large phase delay and system gain,when the order is larger than 2.
Increase the resolution of the quantizerfor stabilization
Higher order sigma-delta modulator falls into unstable state easily.
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2006.12.14 A. Matsuzawa, Titech 4
System stability
Quantizer has a gain of k
System expression of quantizer
A gain of 1bit quantizer can be taken zero to infinity!
Small kLarge k
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2006.12.14 A. Matsuzawa, Titech 5
System model for stability analysis
1
1
n
1i
n
ij
1inii
n
1ii
ni
STF
z1z)z(IallyConvention
)z(Iak1
a)z(Ik)z(H
−
−
= =
+−
=
−=
⋅+
⋅⋅=
∑∏
∏
Gain of quantizer
1bit quantizer
Considering gains of integrator and quantizer.
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2006.12.14 A. Matsuzawa, Titech 6
Stability in z function
MNazazazbzbzbzb
zAzBzH N
NN
MM
MM ≥
++++++++
== −−
−− ,
........
)()()(
011
1
011
1
Real single pole: ( )npcp →
Complex pole : ( ) ( )θσσ +Ω→Ω∠±→± ncjba n cos,
Plural poles : ( ) ( )( ) ( ) ( ) ( )θσ +Ω++++→ ninncnpinncnpi nn cos.....,..... 11
Stable: [ ] Nipnnh i ....,,,,),( 2110 =<⇒∞→→
Meta stable: 1p:plural,1p:Singlen0,c]n[h <≤⇒∞<≤≤
Unstable: ( ) 1p:plural,1pglesinn,]n[h ≥>⇒∞→∞→
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2006.12.14 A. Matsuzawa, Titech 7
Stability and pole position
System is stable, if the poles locate on inside of the unit circle.
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2006.12.14 A. Matsuzawa, Titech 8
Stability of 1st order sigma-delta modulator
1st order system is stable.
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2006.12.14 A. Matsuzawa, Titech 9
Stability of 2nd order sigma-delta modulator
Split at K=1
UnstableStable
Stable when a1 is less than unity
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2006.12.14 A. Matsuzawa, Titech 10
Stability of 3rd order sigma-delta modulator
Unstable when k is smaller than the certain value.
UnstableUnstable
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2006.12.14 A. Matsuzawa, Titech 11
Actual 4th order Sigma-delta ADC
+X +
( )( ) ( ) ( ) ( ) 4
1311
2221
3131
441
41
11111
−−−−−−−−
−
+−+−+−+−
−
zazzazzazzazzNTF :
1
1
1 −
−
− zz
a2a1
+1
1
1 −
−
− zz
1
1
1 −
−
− zz
nQ Y+
a3 a4
1
1
1 −
−
− zz
Needs adjustment of coefficients for system stabilization.
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2006.12.14 A. Matsuzawa, Titech 12
Feed forward type
( ) ( )
( ) ( )
( ) ( )N
kikk
ii
ikk
ii
k
N
k
ii
i
QAzXa
A
zaY
zazzA
QYzXazaY
1
0
1
1
1
1
11
10
11
11
11
1
−
−−
=
−−
=
−−
−
=−
−+
−=
−+−≡
+−⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−=
∑
∑
∑
( )N
k
kkc
QazXaY
aAffz1
0
1
1
1−
−
−+≅∴
≅∴<<≅ )(
Feed forward technique is also used for system stabilization.
Quantizer
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2006.12.14 A. Matsuzawa, Titech 13
SNR at stable condition
M
SNR is degraded when the system becomes stable.In particular, it is heavily degraded at low over sampling rate.
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2006.12.14 A. Matsuzawa, Titech 14
Local resonator
)()(:
zFzHNTF
+11
Pole s of H(z) become zeroes of NTF
Quantizer
Local resonators are used to make NTF zeroes.
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2006.12.14 A. Matsuzawa, Titech 15
Zero distribution
1=zDistribute the zeroes on the
Noi
se le
vel (
dB)
Frequency
Poles can’t be changed so much because of stability. Deep notches in pass band
Distribute the zeroes can reduce in-band noise.
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2006.12.14 A. Matsuzawa, Titech 16
Effect of zero distribution
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2006.12.14 A. Matsuzawa, Titech 17
MASH (Multi-stage noise shaping)
111
−− z+
1−z
Q1
+
+
11 −− z
111
−− z+
1−z
Q2
+
+
11 −− z
111
−− z+
1−z
Q3
X
-Q1
-Q2
1st
quantization noise
YY1
Y2
Y3
2nd
quantization noise
( )( )( ) 3
123
21
12
11
1
11
1
QZQYQZQY
QZXY
−
−
−
−+−=
−+−=
−+=
( ) ( )( ) 3
31
321
21
1
1
11
QZXY
YZYZYY−
−−
−+=∴
−+−+=
Feed forwarded multi-stage noise shaping architecture is free from instability,however requires good matching.
Realizing the stable 3rd order sigma delta modulation.
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2006.12.14 A. Matsuzawa, Titech 18
Design issue: signal saturation at integrator
a1z-1
1
+Node1 a1
z-1f1
+1f1
f1
1f1
Node1
Scaling
Systematic Approach for Scaling Coefficients of DiscreteSystematic Approach for Scaling Coefficients of Discrete--Time and ContinuousTime and Continuous--Time SigmaTime Sigma--Delta ModulatorsDelta ModulatorsN. Beilleau, H. Aboushady, M. M. Lou¨erat Universit´e Paris VI, Laboratoire LIP6/ASIM
Signal saturation at integrator degrades SNR so much.
We should reduce the output signal swings of integrators by adjusting gain coefficients.
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2006.12.14 A. Matsuzawa, Titech 19
MatLab simulation for Scaling
f = [MAXmax3 MAXmax4 MAXmax5 MAXmax6 MAXmax7] / Targethalfswinga5 = [ a5(1)/f(1) a5(2)*f(1)/f(2) a5(3)*f(2)/f(3) a5(4)*f(3)/f(4) a5(5)*f(4)/f(5) ]lfb5 = [ lfb5(1)*f(3)/f(1) lfb5(2)*f(5)/f(3) ]w = [ w(1)*f(1) w(2)*f(2) w(3)*f(3) w(4)*f(4) w(5)*f(5) ]
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2006.12.14 A. Matsuzawa, Titech 20
Scaling effect
a5 = 0.8106 0.3861 0.2236 0.1280 0.0401lfb5 = 0.0177 0.8412w = 1.0 1.0 1.0 1.0 1.0
a5 = 0.2996 0.3219 0.2811 0.2417 0.1565lfb5 = 0.0169 0.1141w = 2.7054 3.2444 2.5804 1.3670 0.3500
After ScalingBefore Scaling
We can reduce signal swings by scaling
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2006.12.14 A. Matsuzawa, Titech 21
1bit
Scaling effect
After ScalingBefore Scaling
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2006.12.14 A. Matsuzawa, Titech 22
5bit
Scaling effect
After ScalingBefore Scaling
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2006.12.14 A. Matsuzawa, Titech 23
Scaling effect
After ScalingBefore Scaling
SNR is heavily damaged!
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2006.12.14 A. Matsuzawa, Titech 24
SCF integrator
Comparator
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2006.12.14 A. Matsuzawa, Titech 25
kT/C Noise effects
1st integrator
5order 1bit 3order 3bit
2nd integrator
3rd integrator
4th and 5th integrator
1st integrator
2nd integrator
3rd integrator
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2006.12.14 A. Matsuzawa, Titech 26
kT/C Noise effects
Int. 1 Int. 2 Int. 3 Int. 4
DAC
In Out
Pn1 Pn2 Pn3 Pn4
724
6
4N523
4
3N322
2
2N1Ntot_N MA7P
MA5P
MA3P
M1PP πππ
+++=
egratorintth'iuntilGain:Ai
Impacts of kT/C noises on each stage reduces along with increase of integrator number.
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2006.12.14 A. Matsuzawa, Titech 27
op-amp gain
― 5-order 1-bit― 3-order 3-bit― 2-2 MASH 1-bit
40dB for single loop,60dB for MASH are needed.
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2006.12.14 A. Matsuzawa, Titech 28
Mismatch effect of DAC
Higher SNR needs smaller mismatch for DAC, even though sigma-delta method is used.
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2006.12.14 A. Matsuzawa, Titech 29
Dynamic Element Matching (DEM)
ThermometerType
decoderShuffler
Unit Element
Unit Element
Unit Element
+
DigitalInput
2B unity elements
2B
B
AnalogOutput
•Randomization•Clocked Averaging (CLA)•Individual Level Averaging (ILA)•Data Weighted Averaging (DWA)
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2006.12.14 A. Matsuzawa, Titech 30
Data Weighted Averaging
+VDACー
+VDACー
+VDACー
010、100、011
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2006.12.14 A. Matsuzawa, Titech 31
DEM Comparison
Y.Geerts and M. Steyaert, “Guidelines for implementation of CMOS multibitoversampling modulators”, ESPRIT project: SYSCONV Work Package 2,http://www.imse.cnm.es/esd-msd/deliverables.html
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2006.12.14 A. Matsuzawa, Titech 32
Continuous time ΣΔADC
L. Breems and J.H. Huijsing,”Continuous-time sigma-delta modulation for A/D conversion in radio Receivers”Kluwer
We can make sigma delta ADC with CT filter.
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2006.12.14 A. Matsuzawa, Titech 33
Effect of clock jitter
DAC Pulse
Ts
TΔσ
2281
Tbwit Mf
SNRΔ
≈σlim_
SNR=85dB, M=32, fbw=1.25MHz, 2.8psfbw=12.5MHz, 0.028ps
SNR of CT ΣΔADC is very sensitive to the clock jitter.In contrast, DT type is not so.
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2006.12.14 A. Matsuzawa, Titech 34
High dynamic range design
P. Balmelli, et al., ISSCC 2004
Sigma delta method with multi-bit quantizer and dynamic element matching technique realized 25MS/s, 80dB ADC.
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2006.12.14 A. Matsuzawa, Titech 35
Add new functionSigma-delta ADC can change the performance by changing over sampling ratio and filter characteristics. High DR and narrow BW
Low DR and wide BW Compatible:
T. Burger and Q. Huang, ISSCC 2001
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2006.12.14 A. Matsuzawa, Titech 36
Add new function
K. Philips, ISSCC 2003
Complex band-pass sigma-delta
gm-C filter5th order complex sigma-delta 1b, @64MHz
Delta-sigma ADC can use complex band-pass filter.Analog filter and VGA can be removed from IF stage.
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2006.12.14 A. Matsuzawa, Titech 37
LV and LP design
Low voltage OTA
Conventional SC integrator
2nd order, 16x over sampling ADC
Simple low voltage OTA enabled itT. Ueno, et al., ISSCC 2004
0.8V 1.5mW CT sigma-delta modulator attained 50dB at 2MHz in.
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2006.12.14 A. Matsuzawa, Titech 38
References
• J.C. Candy and G.C. Tems, “Oversampling Delta-Sigma Converters,” IEEE Press, 1992.
• S. R. Norsworthy, R. Schreier, and G. C. Tems, “Delta-Sigma data Converters: Theory, Design, and Simulation,” IEEE Press.
• R. Schreier, and G. C. Tems, “Understanding Delta-Sigma Data Converters,” IEEE Press.
• Y. Geerts, M. Steyaert, and W. sansen,” Design of Multi-Bit Delta-Sigma A/D Converters,” Kuluwer.
• Rudy van de Plassche, “ CMOS Integrated Analog to Digital and Digital to Analog Converters,” Kluwer.
• F. Medeiro, A. Perez-Verdu and A. Rodriguez-Vazquez, “Top-Down Design of High-Performance Sigma-Delta Modulators,”, Kluwer.
• C. Toumanzou, G. Moschytz, and B. Bilbert, “Trade-offs in Analog Circuit Design,”Kluwer.
• 岩田 「CMOSアナログ回路設計技術」 トリケップス