antennasgbtaylor/astr423/lectures/07_antennas.pdf2 g. taylor, astr 423 at unm outline •fourier...

Astronomy 423 at UNMRadio Astronomy

AntennasGreg TaylorUniversity of New Mexico

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G. Taylor, Astr 423 at UNM

Outline

• Fourier Transforms • Interferometer block diagram• Antenna fundamentals• Types of antennas• Antenna performance parameters• Receivers• Dipole Antennas

stationary time series

indefinitely long

but

statistical properties don’t vary with time

time, minutes

assume that we are dealing with a fragment of an indefinitely long time series

timeseries,d

duration, Tlength, N

one quantity that might be stationary is …

“Power”

0

T

0

T

Power

mean-squared amplitude of time series

How is power related topower spectral density ?

write Fourier Series asd=Gm

weremare the Fourier coefficients

now use

now use

coefficients of sines and cosines

coefficients of complex exponentials

Fourier Transformequals 2/T

so, if we define the power spectral density of a stationary time series as

the integral of the p.s.d. is the power in the time series

Example: Atmospheric CO2(after removing anthropogenic trend)

0 5 10 15 20 25 30 35 40 45 50-4

-2

0

2

4

time, years

CO2,

ppm

0 1 2 3 4 50

1

2

3

frequency, cycles per year

log1

0 ps

d of

CO

2

0 0.5 1 1.5 2 2.5 3-3

-2

-1

0

1

2

3

4

time, years

CO2,

ppm

enlargement

0 0.5 1 1.5 2 2.5 3-3

-2

-1

0

1

2

3

4

time, years

CO2,

ppm

enlargement

period of 1 year

0 5 10 15 20 25 30 35 40 45 50-4

-2

0

2

4

time, years

CO

2, p

pm

0 1 2 3 4 50

1

2

3

frequency, cycles per year

log1

0 ps

d of

CO

2

power spectral density

frequency,cyclesperyear

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

frequency, cycles per year

powe

r

cumulative power

power in time series

Fourier Transforms 18

G. Taylor, Astr 423 at UNM

Fourier Transforms 19

G. Taylor, Astr 423 at UNM

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G. Taylor, Astr 423 at UNM

Mixer

Software

Square law detector

Bandpass filter, IF amplifier

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G. Taylor, Astr 423 at UNM

E.g., pre-upgrade VLA observing

at 4.8 GHz (C band) Interferometer Block Diagram

Antenna

Front End

IF

Back End

Correlator

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G. Taylor, Astr 423 at UNM

• Antenna amplitude pattern causes amplitude to vary across the source.

• Antenna phase pattern causes phase to vary across the source.

• Polarization properties of the antenna modify the apparentpolarization of the source.

• Antenna pointing errors can cause time varying amplitude andphase errors.

• Variation in noise pickup from the ground can cause timevariable amplitude errors.

• Deformations of the antenna surface can cause amplitude andphase errors, especially at short wavelengths.

Importance of the Antenna Elements

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G. Taylor, Astr 423 at UNM

Wavelength > 1 m (approx) Wire AntennasDipole

Ae = Gl2/4p Yagi

Helixor arrays of these

Wavelength < 1 m (approx) Reflector antennas

Wavelength = 1 m (approx) Hybrid antennas (wire reflectors or feeds)

Feed

General Antenna Types

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G. Taylor, Astr 423 at UNM

Effective collecting area A(n,q,f) m2

On-axis response Ae = hAh = aperture efficiency

Normalized pattern(primary beam)A(n,q,f) = A(n,q,f)/Ae

Beam solid angle WA= ∫∫ A(n,q,f) dWall sky

Ae WA = l2

Basic Antenna Formulas

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G. Taylor, Astr 423 at UNM

f(u,v) = complex aperture field distributionu,v = aperture coordinates (wavelengths)

F(l,m) = complex far-field voltage patternl = sinqcosf , m = sinqsinf

F(l,m) = ∫∫aperturef(u,v)exp(2pi(ul+vm)dudvf(u,v) = ∫∫hemisphereF(l,m)exp(-2pi(ul+vm)dldm

For VLA: q3dB = 1.02/D, First null = 1.22/D, D = reflector diameter in wavelengths

Aperture-Beam Fourier Transform Relationship

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G. Taylor, Astr 423 at UNM

The Standard Parabolic Antenna Response

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Primary Antenna Key Features

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G. Taylor, Astr 423 at UNM

+ Beam does not rotate + Lower cost+ Better tracking accuracy + Better gravity performance- Higher cost - Beam rotates on the sky- Poorer gravity performance- Non-intersecting axis

Types of Antenna Mount

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G. Taylor, Astr 423 at UNM

Parallactic angle

Beam Rotation on the Sky

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G. Taylor, Astr 423 at UNM

Prime focus Cassegrain focus(GMRT) (AT)

Offset CassegrainNaysmith

(VLA) (OVRO)

Beam Waveguide Dual Offset(NRO)(ATA)

Reflector Types

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G. Taylor, Astr 423 at UNM

Prime focus Cassegrain focus(GMRT) (AT)

Offset CassegrainNaysmith

(VLA) (OVRO)

Beam Waveguide Dual Offset(NRO) (ATA)

Reflector Types

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G. Taylor, Astr 423 at UNM

Effelsberg 100-m telescope near Bonn, Germany

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G. Taylor, Astr 423 at UNM

DualOffset

Unblocked Aperture(GBT)

Reflector Types

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VLA and EVLA Feed System Design

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Example Feed Horn

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G. Taylor, Astr 423 at UNM

8 x 9Array for2-7 GHz

IvashinaEt al.

Focal Plane Arrays

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G. Taylor, Astr 423 at UNM

Aperture EfficiencyA0 = hA, h = hsf * hbl * hs * ht * hmisc

hsf = reflector surface efficiencyhbl = blockage efficiencyhs = feed spillover efficiencyht = feed illumination efficiencyhmisc= diffraction, phase, match, loss

hsf = exp(-(4ps/l)2)e.g., s = l/16 , hsf = 0.5

rms error s

Antenna Performance Parameters

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G. Taylor, Astr 423 at UNM

Primary Beam

l=sin(q), D = antenna diameter in contours:-3,-6,-10,-15,-20,-25,wavelengths -30,-35,-40 dBdB = 10log(power ratio) = 20log(voltage ratio)For VLA: q3dB = 1.02/D, First null = 1.22/D

pDl

Antenna Performance Parameters

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G. Taylor, Astr 423 at UNM

Pointing AccuracyDq = rms pointing error

Often Dq < q3dB /10 acceptableBecause A(q3dB /10) ~ 0.97BUT, at half power point in beamA(q3dB /2 ± q3dB /10)/A(q3dB /2) = ±0.3

For best VLA pointing use Reference Pointing. Dq = 3 arcsec = q3dB /17 @ 50 GHz

Dq

q3dB

Primary beam A(q)

Antenna Performance Parameters

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G. Taylor, Astr 423 at UNM

Subreflector mount

Quadrupod

El encoder

Reflector structure

Alidade structure

Rail flatness

Az encoder

Foundation

Antenna Pointing Design

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G. Taylor, Astr 423 at UNM

Surface: s = 25 µmPointing: Dq = 0.6 arcsec

Carbon fiber and invar reflector structure

Pointing metrology structureinside alidade

ALMA 12m Antenna

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G. Taylor, Astr 423 at UNM

Polarization

Antenna can modify the apparent polarization properties of the source:• Symmetry of the optics• Quality of feed polarization splitter• Circularity of feed radiation patterns• Reflections in the optics• Curvature of the reflectors

Antenna Performance Parameters

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G. Taylor, Astr 423 at UNM

Cross polarized Cross polarizedaperture distribution primary beam

VLA 4.8 GHzcross polarizedprimary beam

Off-Axis Cross Polarization

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G. Taylor, Astr 423 at UNM

VLA 4.8 GHz

Far field pattern amplitudePhase not shown

Aperture field distributionamplitude.Phase not shown

Antenna Holography

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Other Concerns

• Pointing errors, especially at high frequencies• Gain curves• Atmospheric opacity corrections• Ionospheric effects: scintillation, isoplanatic patch size

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G. Taylor, Astr 423 at UNM

Practical concerns continued• Opacity corrections and tipping scans

– Can measure the total power detected as a function of elevation, which has contributions

Tsys = T0 + Tatm(1-et0a) + Tspill(a)and solve for t0.– Or, make use of the fact that there is a good correlation between

the surface weather and t0 measured at the VLA (Butler 2002):

and apply this opacity correction using FILLM in AIPS

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G. Taylor, Astr 423 at UNM

Noise Temperature

Pin = kBT Dn ,kB = Boltzman’s constant

When observing a radio source Ttotal = TA + Tsys

Tsys = system noise when not looking at a discrete radio source

TA = source antenna temperatureTA = hAS/(2kB) S = source flux (Jy)

SEFD = system equivalent flux density SEFD = Tsys/K (Jy)

ReceiverGain GB/W Dn

Matched load Temp T (oK)

Pout=G*PinPin

Rayleigh-Jeans approximation

Band (GHz) h Tsys SEFD

1-2 .50 21 236

2-4 .62 27 245

4-8 .60 28 262

8-12 .56 31 311

12-18 .54 37 385

18-26 .51 55 606

26-40 .39 58 836

40-50 .34 78 1290

VLA Sensitivities

Receivers

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G. Taylor, Astr 423 at UNM

Hertz Dipole

Ae = Gl2/4p G=1.5 for Hertz DipoleG = 2.5 at 20 MHz for LWAG = 4.0 at 60 MHz for LWA

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G. Taylor, Astr 423 at UNM

LWA Antenna

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G. Taylor, Astr 423 at UNM

20 MHz 3D

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E and H-Plane Antenna Pattern

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G. Taylor, Astr 423 at UNM

Further Reading

http://www.nrao.edu/whatisra/mechanisms.shtmlhttp://www.nrao.edu/whatisra/www.nrao.edu

Synthesis Imaging in Radio Astronomy ASP Vol 180, eds Taylor, Carilli & Perley