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Decimation Filtering For Complex SigmaDelta Analog to Digital Conversion in A
Low-IF Receiver
Anjana GhoshSERC, Indian Institute of Science
BangaloreFebruary 2006
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Presentation Outline
Fundamentals of Receiver Operation
Salient features of ADC
Decimation Filtering for Low Pass ADC Existing literature on decimation for
bandpass modulators
Proposed architecture
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Receiver Architectures: A HeterodyneReceiver
if
Frequency Downconversion
HighFrequency
Filter
cosct
LNALowPassFilter
A/D to Demodulator
Receiver Block Diagram
c-c 0-
imagesignal
High FrequencyFilter
c +ifc -if-c -if -c +if
0-if if
LO Signal
desiredsignal
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Low IF ReceiverLO Signal
c-c DC-
desiredsignal
image signal
c + ifc - if-c -if -c + if
if-
if DC
-
RF
Stage
cosct
sinct
Analog to Digital
Conversion
Digital Filtering,Baseband
Downconversion ,
Demodulation
X
Y
A
B
Frequency Downconversion
Receiver Block Diagram
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ADC Sample rate : Effect on AnalogAntialias Filter (AAF)
fN/2-fN/2
fN/2-fN/2 fOS/2-fOS/2
AAF in Nyquist
rate ADC
AAF in
OversampledADC
Decimation
FilterAnalog AAF
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ADC Quantization Noise
fN/2-fN/2
fos/2-fos/2
fos/2-fos/2
Nyquist Rate
Converter
Oversampled
Converter
Oversampled Lowpass
Converter
0
0
0
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Decimation Digital Filter for ADC
Purpose of decimation filters : Antialiasfiltering followed by sample rate reduction
Multistage Decimation preferred to single
stage Popular structure consists of a Cascaded
Integrator comb followed by one or two
FIR stages
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CIC Filter
Moving Average Filter
Z transform
11
01
1 )()(M
iM
inxny
))1(
)1(1()(1 11
1
z
z
MzH
M
)1(.
sin
sin)(
1
11
11
11 MfTjetTM
TfMfH
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Order of the CIC Filter For A Low Pass
ADC For a modulator of order l, a CIC of order l+1 is
suitable for antialias filtering in the first stage ofdecimation
This CIC can be used to reduce the sample rate to aslow as 4 times the Nyquist sampling rate with negligibleSNR degradation (
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CIC Structure (Second Order)
REG REG
REG-
REG-
fs1/M1i/p o/p
1
1-z-1
1
1-z-1
1-z
-M1 1-z
-M1
1
M12
fs1/M1
1
1-z-1
1
1-z-1
1-z
-11-z
-1
1
M12
fs1/M1
1-z-M
1
M1 (1-z-1
)
1-z-M
1
M1 (1-z-1
)
fs1/M1
1
M12
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Efficient Polyphase Decomposition ofComb Filter
k
M
i
izzH
1
0
1
1
)(
)()( )1()1(1
1
1
1
z
z
M
M
zH
kN
i
k
i
i
kM
i
ii
N
zzzzH
1
0
212
0
1
0
1)(1
k
i
MM
i
zzH
12log
0
22
1
1)(
E0(z)
E1(z)
P
P
E0(z)
E1(z)
2
2
z-1
z-1
E0(z)
E1(z)
2
2
z-1
y(n)x(n)
EP-1(z)P
z-1
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Modified SINC
-
M1=4 CIC
Angle
Rotation of
Zeros
Zeros of
Rotated
Sinc Filter
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Noise Transfer Function(NTF) and
Signal Transfer Function(STF)
fos/2-fos/2Bandpass 0
NTFSTF
fos/2-fos/2
Complex
Bandpass 0
NTFSTF
fos/2-fos/2Lowpass
0
NTFSTF
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Complex Downconversion &
Decimation
e-jot
I/P
Complexlow passfilter
Complex
fos/2-fos/2
Signal Before
Downconversion 0
fos/2-fos/2
Signal After
Downconversion 0
fos/2-fos/2 -fIF
fIF-fIF
0
Complex
Sinusoidal
Downconverter
Followed by
Complex LPF
signal
quantizationnoise
e-j
0t
-2fIF
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Decimation structure for Band pass &Complex modulator
cos0T = 1,1/2,0,- 1/2,-1,..
I/PLow pass
filter Real O/P
-sin0T = 0,-1/2,-1,- 1/2,0,..
Low passfilter
o=/4
Complex O/P
cos0T
ReLow passfilter
sin0T
Low passfilter
-sin0T
cos0T
Im
Bandpass Complex
Existing Art : Downconversion of IF signal to Baseband followed by
Standard Low Pass Decimation Digital Filter
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New Decimation Filter Architecture :Motivation
Accepted approach imposes restrictionson the choice of in order to takeadvantage of the optimization in the mixing
process
Compatability with the existing GPSengine
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New Architecture : Block Diagram
RFStage
cosct
sinct
Anti alias Filter
and Complex
Bandpass Modulator
Digital
Baseband
X
Y
DigitalDecimation
Filters
A
B
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Low IF Receiver : Signal Spectrum
c-c 0-
desiredsignal
image signalband
c-c 0-
1/2
c
-c 0-
j/2
-j/2
RF
C (cosct)
S (sinct)
if-if 0
-
1/2A=IP*C
if-if0
-
j/2B=IP*S
-j/2
if
-if
0
-
1IF
c + ifc - if-c -if -c + if
RF Stage cos
ct
sinct
A
B
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Use of Complex Digital Filters
c-c 0-
desiredsignal
image signalband
IP
if-if 0-
1/2A=IP*cosct
if-if 0-
j/2B=IP*Sinct
-j/2
c + ifc - if-c -if -c + if
if-if0 -
P=X+jY
X=A*
Y=B*
if-if 0-
Q=X-jY Noise TransferFunction
Noise TransferFunction DF1 Transfer
Function
DF2 TransferFunction
if-if 0-
OP 1
RF Stage
cosct
sinct
AAnti aliasFilter and
ComplexSigmaDeltaModulator
OPj
-j
DF1 (ComplexDigital Filter)
X
Y
P
QDF2 (ComplexDigital Filter)
C l Di i l Fil R l Fil F
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Complex Digital Filters : Real Filters From
Complex Filters
HDF1(z)= HRE(z) - j.HIM(z) ;
HDF2(z)= HRE(z) + j.HIM(z) ;
OP = P(z).HDF1(z) + Q(z).HDF2(z) ;
=>OP = [X(z) +j.Y(z)].[HRE(z) - j.HIM(z)] + [X(z)-j.Y(z)].[HRE(z) + j.HIM(z)]
=> OP= 2.[X(z). HRE(z) + Y(z). HIM(z)]
Thus the Complex Digital Filtering can be accomplished by using two real filters corresponding to
the real and imaginary parts of the transfer function of the individual complex filters.
if-if 0-
if-if 0 -
DF1 Transfer
Function
DF2 Transfer
Function
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Complex Digital Filters: Implementation
Real Filter Implementation of Digital Filtering, at Low IF.
Advantage: Number of Computations reduced from eight to two
RFAmpandFilter
90o
AntialiasFilter andComplexSigmaDeltaModulator
cosct
sinct
real
imaginary
IP
A
B
S
C
OP
HRE(z)
X
Y
HIM(z)
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Decimation Filter : Requirements
antialias filtering and reduction of thesample rate by 16
attenuation of remaining out of bandcomponents in the signal
generation of a real two sided signalcentered aroundwif
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Multistage Decimation FilterStructure
COMPLEX FILTER
AAF14
AAF22
REAL
PART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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ADC Output FFT
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AAF1: Fourth Order Comb
Passband (3-5MHz) droop = 0.33dB
Stopband Attenuation : 83.1dB
Aliasing Bands: 59MHz to 69MHz,123MHz to 128MHz on either side
COMPLEX FILTER
AAF14
AAF22
REAL
PART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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AAF2: 11 Tap HalfBand
Passband (3-5MHz) Ripple =0.0027dB/-0.0054dB
Stopband Attenuation : 75.8 dB
Aliasing Bands: 27MHz to 32MHz oneither side
COMPLEX FILTER
AAF14
AAF22
REALPART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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Image Reject Filter
Passband (3-5MHz) Ripple =0.0027dB/-0.0054dB
Stopband Attenuation : 75.8dB
Aliasing Bands: 27MHz to32MHz on either side
COMPLEX FILTER
AAF14
AAF22
REALPART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX ADCMIXER
O/PAAF1
4AAF2
2IMAGINARY
PART2
4fs 2fs
I
QOP
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Image Reject Filter : StopbandCOMPLEX FILTER
AAF14
AAF22
REAL
PART2
4fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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Image Reject Filter : Ripple, PhaseResponse
Passband Droop = 0.94dB Phase Response
COMPLEX FILTER
AAF14
AAF22
REAL
PART2
4fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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Droop Correction filterCOMPLEX FILTER
AAF14
AAF22
REALPART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX
ADCMIXERO/P
AAF14
AAF22
IMAGINARYPART
2
4fs 2fs
I
QOP
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Net Transfer FunctionCOMPLEX FILTER
AAF14
AAF22
REALPART
24fs 2fs16fs
16fs
fs
fs
DROOPCORRECTION
FILTER
COMPLEX ADCMIXER
O/PAAF1
4AAF2
2IMAGINARY
PART2
4fs 2fs
I
QOP
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Decimation Filter Structure
Sigma
Delta
Modulator
4rth order Comb 11 tap Half Band
49 tap
FIR
I
13 tap Image Reject
4 2 2O/P
256 M samples/s
4rth order Comb 11 tap Half Band 13 tap Image Reject
4 2 2
Q
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FFT of Silicon Data For A Single Tone Input
ADC O/P
Digital Filter O/P
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Optimized Architecture : Scope
Sigma
Delta
Modulator
4rth order Comb 11 tap Half Band
49 tap
FIR
I
13 tap Image Reject
4 2 2O/P
256 M samples/s
4rth order Comb 11 tap Half Band 13 tap Image Reject
4 2 2
Q
Low Pass ComplexBand Pass
Band PassLow Pass
Scope for optimization :Complex Bandpass?
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Alternate Architecture : Block Diagram
-
OP
HRE(z)
HIM(z)
HAAFRE
HAAFIM
HAAFIM
HAAFRE
Complex
SigmaDelta
ADC
X
Y
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Alternate Architecture I:Decimate By 16
STAGE 1 STAGE 2 STAGE 3
Hc1R(13 taps)
Hc1I(13 taps)
Hc1I(13 ta s)
Hc1R(13 taps)
X
Y
Hc2R(5 taps)
Hc2I(5 taps)
Hc2I(5 ta s)
Hc2R(5 taps)
4
4 Hc3R(5 taps)
Hc3I(5 taps)
Hc3I(5 taps)
Hc3R(5 taps)
2
2
2
2
OP_Q
OP_I
- - -
48444321
4
)1()1(116
1)(
zzzzzzH
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Shifted 4th Order Comb : Stage 1
13 tap , 15 bit coefficient quantization ; performs decimation by 4
Passband = 3MHz to 5 MHz
Aliasing bands = 67MHz to 69MHz, -59MHz to -61 MHz, -123MHz to -
125MHz
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Shifted 4th Order Comb :Stage 2
5tap , 11 bit coefficient quantization;performs decimation by 2
Passband = 3MHz to 5 MHz
Aliasing bands = 35MHz to 37MHz, -27MHz to -29 MHz
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Shifted 4th Order Comb :Stage 3
5 tap, 11 bit coefficient quantization; Performs decimation by 2
Passband = 3MHz to 5 MHz
Aliasing bands = 19MHz to 21MHz, -11MHz to -13 MHz
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Image Reject Filter
5 tap, 15 bit coefficient quantization
Passband = 3MHz to 5 MHz
Aliasing bands = 19MHz to 21MHz, -11MHz to -13 MHz
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Optimized Architecture
AAF & Decimation ImageReject
ComplexAAF
Stage14
X
Y
Droopcorrection(48 taps)
IRR(5 taps)
IRIM(5 taps)
OP
ComplexAAF
Stage22
ComplexAAF
Stage32
Complex
Sigma
Delta
ADC
Multiplier lesspolyphase
implementation
CSD coded; multiplier less polyphase implementation
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Comparison of Transfer Function :Original Architecture and Architecture I
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Comparison of Transfer Function :Original Architecture and Architecture I
Comparison of ImageRejection
Comparison of Passband
Ripple
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STAGE 1 STAGE 2 STAGE 3
4thorderComb
(13 taps)
4rthorderComb
(13 taps)
X
Y
Hc2R(5 taps)
Hc2I(5 taps)
Hc2I(5 taps)
Hc2R(5 taps)
4
4 Hc3R(5 taps)
Hc3I(5 taps)
Hc3I(5 taps)
Hc3R(5 taps)
2
2
2
2
OP_Q
OP_I- -
Optimized Architecture II
Low Pass COMB Shifted COMB
D i i Fil S i
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Decimation Filter Stages inArchitecture II
C i f h Th
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Comparison of the ThreeArchitectures
Design Parameter Original Architecture Alternate Architecture I Alternate Architecture II
Stage 1 AAFFilter TypeNumber of tapsCoefficient QuantizationData QuantizationArea
Real Filter4th order comb13Ideal101160
Complex Filter4th order shifted comb1315 bits16 bits3409.5
Real Filter4th order comb13Ideal10 bits971.75
Stage2 AAFFilter TypeNumber of TapsCoefficient QuantizationData QuantizationArea
Real FilterHalfband1115 bits13 bits3154.5
Complex Filter4th order shifted comb511 bits16 bits4460.75
Complex Filter4th order shifted comb511 bits15 bits3147.75
Stage 3 AAFFilter TypeNumber of TapsCoefficient QuantizationData Quantization
Area
None Complex Filter4th order shifted comb511bits15 bits
4657.75
Complex Filter4th order shifted comb511 bits15 bits
4437.25Image RejectFilter TypeNumber of TapsCoefficient QuantizationData QuantizationArea
Complex FilterShifted Modified Comb1315 bits14 bits11702
Complex FilterShifted Modified Comb515 bits14 bits2208.5
Complex FilterShifted Modified Comb515 bits14 bits2209.25
Total area 16037.25 14736.5 10766
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Summary
Architecture and design of decimationdigital filtering of the output of a complex modulator for low IF receivers is
proposed. Two optimized implementations with
variations of the same basic architecture
are proposed
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Reference
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Brian Paul Brandt, Oversampled Analog to Digital Conversion, Doctoral Thesis, Stanford University, Electrical Engineering Department, Stanford, California, October1991
Letizia Lo Presti, Efficient Modified-Sinc Filters For Sigma Delta A/D Converters,IEEE Transaction on Circuits and Systems-II:Analog and Digital SignalProcessing,Vol 47,No 11,November 2000
Richard Schreier and W Martin Snelgrove,Decimation For Bandpass Sigma Delta Analog to Digital Conversion, IEEE International Symposium on Circuits andSystems,1990, 1-3 May, Pages 1801-1804 Vol 3
Stephen Andrew Jantzi, Quadrature Bandpass Delta Sigma Modulation for Digital Radio, PhD Thesis, Dept of Electrical and Computer Engineering,University of Toronto Ashok Swaminathan,A Single-IF Receiver Architecture Using a Complex Sigma-Delta Modulator, ME thesis, Dept of Electronics, Ottawa-Carleton Institute for Electrical
Engineering, Carleton University,Ottawa,Canada Stephen A Jantzi, Kenneth W Martin, Adel S Sedra, Quadrature Bandpass DS Modulation For Digital Radio, IEEE Journal Of Solid State Circuits, Vol 32,No 12,
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and Systems, Volume: 1 , 14-17 Aug. 2001 Yonghong Gao, Lihong Jia, Hannu Tenhunen, A Fifth Order Comb Decimation Filter For Multi-standard Transceiver Applications, IEEE International Symposium on
Circuits and Systems, May 28-31,2000,Geneva , Switzerland Brian A White, Mohamed I Elmasry, Low Power Design of Decimation Filters For A Digital IF Receiver, IEEE Transactions On Very Large Scale Integration (VLSI)
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Yonghong Gao, Lihong Jia, Hannu Tenhunen, An Improved Architecture and Implementation of Cascaded Integrator Comb Decimation Filters,IEEE Pacific RimConference on Communications, Computers and Signal Processing, 1999
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Ken Martin, Complex Signal Processing is Not Complex, Conference on European Solid-State Circuits, 2003, 16-18 Sept James C Candy, Decimation for Sigma Delta Modulation, IEEE Transactions On Communications, Volume COM 34,No1,January 1986 Alan V Oppenheim , Ronald W Schafer, Discrete Time Signal Processing, Prentice Hall Signal Processing Series Ghosh Anjana, BG Chandrashekar , Venkatraman Srinivasan and Nandy S K, Decimation For Complex Sigma Delta Analog to Digital Conversion In A Low-IF GPS
Receiver,10th International Symposium On Integrated Circuits, Devices & Systems, September 2004
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