High Speed Samplers and Digital Filters for VLBI

1

High Speed Samplers and Digital Filters for VLBI

Dick Ferris

AT Electronics Development Group

June 2003

2High Speed Samplers and Digital Filters for VLBI

Topics

Digital Filters can provide the identical, stable and linear-phase channel passbands required for an ideal interferometer....

Current Usage in VLBI

Polyphase Digital Filterbanks

The Geocentric DAS

The slow march of ADC technology


USB LSB

+

- jsinw.t

j

w. -w.

1

p/2

~ -p/2

64Msps

32MHz

IF

I+jQ

LPF

USB

cosw.t

- jw.t e

32MHz

LSB

-p/2 w.

w.

w.

- + +

16MHz, 8, 4, 2...

500..1000MHz

Eg. 1 K4 System (CRL ~1993)


w. -w.

¯ M

32Msps

IF

BPF

B=16MHz

w.=8,24,..104

B=8, 4, 2, 1MHz

0..112MHz

w.

w.

w.

w.

16* 1MHz Bands

8* 2MHz Bands

4* 4MHz Bands

3* 8MHz Bands

Eg. 2 X_FILT (ATNF 1994)


Eg. 3 LBA DAS BandSplitter (ATNF 1997)

-

0..192MHz

Fo=Fs/ 4

¯ M

Fs=128Msps IF

LPF

B=64MHz

Fo=32, 96, 160MHz -Fo Fo

I+jQ

USB

LSB

Q I

~

-p/2

+ + +

HT

¯ M

USB LSB

-

¯ M

+ + +

HT

¯ M

USB LSB

-j

n(+1) -1 n -1

B=16MHz,... 1MHz


Eg. 3 LBA DAS BandSplitter (ATNF 1997)

0..192MHz

Fs=128Msps IF

LPF

B=64MHz Fo=32, 96, 160MHz

-Fo Fo

I+jQ

Analytic Q I

¯M

HT

¯M

n(+1) -1

n -1 T

-M/2 z

Fo -Fo

B=32, 16..., 1MHz

Fo

Fo

Fo


Eg. 3 LBA DAS FineTuner (ATNF 1997)

-

¯M

+ + +

¯M

USB LSB

-j

~- jsinw.t

cosw.t

IF

p/2

0..16MHz

0..16MHzFo

- M/2 z

Q I

¯M ¯M

T ~

- jsinw.t

cosw.t

IF

p/2

0..16MHz

0..16MHzFo

B=16MHz,... 62.5kHz

Fo

Fo

Fo

B=16MHz,... 62.5kHz

Fo

Fo

Fo

LBA DAS Summary

Input 'virtual' LO at 32, 96 & 160MHz, 64MHz bandwidth

Fine tuner 1Hz resolution over 16MHz

LO-centred single passbands (64MHz), 32,…62.5kHz

LO-contiguous dual passbands 16MHz,…62.5kHz

Flip all passbands, separate duals

40dB sideband separation, 40dB stopbands

8-bit ADC, 10-28 bits internal

2-bit requantiser servos, 12dB range + 12dB AGC


w. -w. I F

BPF

w.

w.

w.

w. 16* 32MHz Bands

8* 64MHz Bands

4* 128MHz Bands

2* 256MHz Bands

¯ M

1024Msps

512MHz

B=256,128,..,16MHz

Eg. 4 VERA (NAO 2001)


1

0 1

The Filterbank Alternative

2

1/M

M-10

wk=2pk/M

-jwkne

n=mM+

= e-j2pk(mM+)/M

= e-j2pk/M

=WM-k

WM= e j2p/M

IF

x(n)

x(n)

x(n)

-jwM-1ne

x(n)

M

M

M

M

X1(m)

Xk(m)

XM-1(m)

X0(m)

-jwkne

-jw1ne

-jw0ne

B

Fs=B

eg. B=1GHz

M=1000


p0(m)

p(m)

p1(m)

pM-1(m)

x(n) WM-

k

p0(m)

p(m)

p1(m)

pM-1(m)

x0(m)

WM-

WM-k(M-

1)

x1(m)

WM-k

x(m)

WM-k

xM-1(m)

x(n)

p0(m)

p(m)

p1(m)

pM-1(m)

x0(m)

x1(m)

x(m)

xM-1(m)

x(n)

y0(m)

y1(m)

y(m)

yM-1(m)

WM-

WM-k(M-

1)

WM-k

WM-k

Xk(m)= y(m)WM-k

p0(m)

p(m)

p1(m)

pM-1(m)

x1(m)

x(m)

xM-1(m)

x(n)

y1(m)

y(m)

yM-1(m)

x1(m)

xk(m)

xM-1(m)

0

1

M-1

DFTasFFT

x0(m) y0(m) x0(m)

Transforming the Filter

WM-k

=n MOD M

x(n) M

Xk(m)

y(n)= h(i) x'(n-i)

h(n)

x'(n)


1GHz

4k channels

1GHz

4k channels

Subband Analysis

Standard

Zoom

n*Zoom

n*Zoom^n


Conventional Channelisation


Filterbank Channelisation


DAS<->Correlator Tasking

Schedule+DataBase+Clock

Control Process

Pointing

Tuning

(Digitisation)

Delay Tracking

Channelisation

Phase Tracking

(Re) quantisation

Correlation


PCFS

Pointing

Tuning

(Digitisation)

Channelisation

2-bit quantisation

Data Transport >>>>>>>>


CorrCon

Data Transport

Delay Tracking

Phase Tracking

Channelisation

Correlation (Complex XMULT and Int)


PCFS

Pointing

Tuning

Digitisation

Delay Tracking

Channelisation

2-bit quantisation



CorrCon

Data Transport

Phase Tracking

Channelisation



PCFS

Pointing

Tuning

Digitisation

Delay Tracking

Channelisation

Phase Tracking

2-bit quantisation



CorrCon

Data Transport

Channelisation



PCFS

Pointing

Tuning

Digitisation

Delay Tracking

Channelisation I

Channelisation II

Phase Tracking

2-bit quantisation



CorrControl

Data Transport


15

2GHz

4k channels

4k channels

Multiple Zoom (>2 possible)Multiple Zoom (>2 possible)

2GHz

4k channels

4k channels

Com pound ZoomCompound Zoom

2GHz

4k channels

Simple ZoomSimple Zoom

2GHz

4k channels

Basic ConfigurationBasic Configuration

FFT

FFT

FIR

FIR

FilterbankFringe

Rotators CorrelatorsDMUX

A 2GHz bandwidth polyphase digital filterbank with 4096 channels ... ... will fit into four XC2V6000 FPGAs

FPGA hardware may be completely reprogrammed to

produce many different filterbank configurations, as

different observations may

require.

RF, IF and Baseband Signal Path

Filterbank Architecture

A Wideband Upgrade for the Australia Telescope Compact Array

Luneburg Lens Phased Array Luneburg Lens Phased Array6 * 22m antenna AT Compact Array


commercialexperimental/military

0

2

4

6

8

10

12

14

16

18

20

22

1E+4 1E+5 1E+6 1E+7 1E+8 1E+9 1E+10 1E+11

Sample Rate (Samples/s)

Sta

ted

Re

so

luti

on

(B

its

)Analog-to-Digital Converters:

COTS / non-COTS

from Bob Walden HRL 1999


Wavelength-DivisionDemultiplexer

Detectors and LPFs

A/D

A/D

A/D

MultiwavelengthOptical PulseSource

1 2 N....

BASE STATION

Electro-opticModulator

Receiving Element

Antenna 1

A/D

N

2

1

..

1 x K

To K Antennas

DownconversionFringe RotationCorrelationetc

DSP

Antenna 2

Antenna K

From K Antennas

The short optical pulses sample the RF at the antenna

Succesive wavelength codedsamples are separated by afilter and digitised in parallel

High repititon rate, low jitterpulse source locked tostation reference clock

1 2 N....

A Sub-Array Incorporating Impulse Sampling

and Photonic A/D Conversion

from Paul Roberts ATEDG 2002


Summary

Digital Filters can provide the identical, stable and linear-phase channel passbands required for an ideal interferometer....

Current Usage in VLBI

Polyphase Digital Filterbanks

The Geocentric DAS

The slow march of ADC technology



Digital Filter Basics

Two-point running mean: y(n)=(x(n)+x(n-1))/2 >> LPF

First order differences: y(n)=(x(n)-x(n-1))/2 >> HPF

FIR filter as generalised N-point running mean (convolution)

y(n)= h(i) x(n-i) 0<=i<N

h(n) is impulse response h(n) H(f)

Even part: he(n)=(h(n)+h(N-1-n))/2; a(i)=2he((N-1)/2-i)

Odd part: ho(n)=(h(n)- h(N-1-n))/2; b(i)=2ho((N-1)/2-i)

H(f)=a(0)/2+(a(i) cos2pif + j b(i) sin2pif) Fs=1, N odd

he(n) He(f); zero/linear phase, zero/constant group delay

ho(n) Ho(f); quadrature phase Why


Why choose Digital?

Completely deterministic; no component selection or tweaking

‘Easy’ design, exact modelling, precise performance

Amplitude & phase characteristics as stable as sampling clock

Wider, flatter passbands, perfectly matched between systems

Nil dispersion/group delay distortion across the passband

Reduced closure errors >> better calibration

One sampler, multiple passbands; avoids ‘platforming’

One hardware platform; many modes, functions

Cost effective for high performance multichannel systems– Ex


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Documents

High Speed Samplers and Digital Filters for VLBI