Backend electronics for Backend electronics for radioastronomyradioastronomy

G. Comoretto

Data processing of a Data processing of a radioastronomic signalradioastronomic signal

Receiver (front-end) Separates the two polarizations Amplifies the signal by ~108 Limits the band to a few GHz Translates the sky frequency to a more manageable

range The resulting signal is then processed by a back end

Electric field E(t)

Power density S(f)to backend

Data processing of a Data processing of a radioastronomic signalradioastronomic signal

Measure S as a function of time, frequency, polarization status, baseline Total power Polarimetry Spectroscopy Interferometry Pulsar (search and timing)

Record the instantaneous field E(t) for further processing

VLBI/ Remote interferometry Radio science

Composite of the above (e.g. spectropolarimetric interferometry)

Signal conversionSignal conversion

IF output may be too wide Difficulties of building wideband backends Necessity of having several spectral points across

the IF bandwidth (e.g. for Faraday rotation) Interest in a specific spectral region (e.g. line

spectroscopy) Necessity to avoid contaminated portion of the IF

band Baseband converters (BBC): select a portion of the IF

bandwidth and convert it to frequencies near zero

Each BBC followed by a specific backend (total power, polarimeter, spectrometer, VLBI channel....)

Simplest observable: total integrated flux over the receiver bandwidth

Filter: selects the frequency band of interest Square law detector: diode (simpler, wideband) or

analog multiplier (more accurate, expensive, band limited)

Integrator: sets integration time: time resolution vs. ADC speed

ADC: converts to digital. Integrator & ADC are often implemented as a voltage-to-frequency converter & counter

Total powerTotal power

Sensitivity:

= integration time f = bandwidth or frequency resolution S = total (receiver dominated) noise

For modern receivers, 1/f gain noise dominant for t > 1-10 s

need for accurate calibration & noise subtraction Added mark Correlating receiver On-the fly mapping Wobbling optics

Total powerTotal power

PolarimetryPolarimetry

Dual polarization receiver: vertical/horizontal or left/right

Cross products give remaining Stokes parameters

Instrumental polarization: 30dB = 0.1%

Bandwidth limited by avaliable analog multipliers

Need for coarse spectroscopic resolution (Faraday rotation)

SpectroscopySpectroscopy Acousto-optic spectrometer:

signal converted to acoustic waves in a crystal diffraction pattern of a laser beam focussed on a CCD amplitude of diffracted light proportional to S(f)

Large bandwidth, limited (1000 points) resolution Rough, compact design All parameters (band, resolution) determined by

physical design => not adjustable

AOS Array for Herschel - HiFiAOS Array for Herschel - HiFi

LiNb cell with 4 acoustic channels Instantaneous band: 4x1.1 GHz (4 – 8 GHz) Resolution : 1 MHz

Spectroscopy – Digital Spectroscopy – Digital correlatorcorrelator

Digital spectrometers: Bandwidth determined by sampling frequency

Max BW technologically limited, currently to few 100MHz Reducing sampling frequency decreases BW = > increased

resolution Autocorrelation spectrometers (XF)

Compute autocorrelation function: Fourier transform to obtain S(f) Frequency resolution:

Signal quantized to few bits (typ. 2) Complexity proportional to N. of spectral points

Spectroscopy – FFT Spectroscopy – FFT spectrometerspectrometer

FFT spectrometers: Compute spectrum of finite segment of data

Square to obtain power and integrate in time

Complexity proportional to log2(N) => N large Requires multi-bit (typ. 16-18 bit) arithmetic Easy to implement in modern, fast FPGA, with HW

multipliers Slower than correlator, but keeping pace Polarimetric capabilities with almost no extra cost

Spectroscopy – FFT Spectroscopy – FFT spectrometerspectrometer

Poly-phase structure: multiply (longer) data segment with windowing function => very good control of filter shape

Very high dynamic range (106-109) => RFI control

InterferometryInterferometry

Visibility function: <E1(t)*E2(t+)> Computed at distant or remote location: need for

physical transport of the radio signal Directly connected interferometers Connected interferometers with digital samplers

at the antennas and digital data link E-VLBI: time-tagged data over fast commercial

(IP) link Conventional VLBI: data recorded on magnetic

media Accurate phase and timing control

InterferometryInterferometry Visibility computed on dedicated correlator or FFT

processor Conventional correlator scales as (number of antennas)2

FFT (FX) scales as N Must compensate varying geometric delay:

Varying sampler clock Memory based buffer, delay by integer samples Phase correction in the frequency domain

Due to frequency conversion, varying delay causes “fringe frequency” in the correlation

ALMA correlator (1 quadrant)

Digital vs. Analog BackendDigital vs. Analog Backend All backend functions can be performed on a digital

signal representation Current programmable logic devices allow to implement

complex functions on a single chip Digital system advantages:

predictable performances – easy calibration high rejection of unwanted signals - RFI Better performances, filter shapes etc. Easy interface with digital equipments

Example of a general-purpose full digital backend

Digital vs. Software Digital vs. Software BackendBackend

Software backends (e.g. SW correlator) becoming possible e.g Blue Chip IBM supercomputer viable as LOFAR

correlator Most Radio Science processing done on software

Computing requirements scale as a power of the BW Dedicated programmable logic still convenient 1 FPGA: 50-500 MegaOPS, ~16 FPGA/board MarkIV correlator (in FX architecture): 1.7 TeraOPS EVLA Correlator: 240 TeraOPS

Digital Backend: ExamplesDigital Backend: Examples

ALMA Digital filterbank:

2 GHz IF input 32x62.5 MHz

independently tunable BBC

General purpose board, can be configured to implement 16 FFT spectropolarimeters @ 125 MHz BW each

Digital Backend: ExamplesDigital Backend: Examples

VLBI dBBC:

1 GHz IF input 250 MHz output bandwidth Directly interfaces with E-VLBI

BEE2 Berkeley system

1 GHz IF input General purpose board, with library of

predefined components System design and validation using MATLAB