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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


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


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


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




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Image Reject Filter

5 tap, 15 bit coefficient quantization




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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



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

REFERENCES James C Candy and Gabor C Temes, Oversampling Methods for A/D and D/A Conversion,

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