Lecture 1Lecture 1

By Tom Wilson

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Lecture 1 page 1

The 20.5 MHz Sky (Jansky)

Galactic Continuum SourcesGalactic Continuum SourcesLecture 1 page 2

S in Jy is 10-26 W m-2 Hz-1 (intensity integrated over the source)

M82 in the radio, mm, sub-mm M82 in the radio, mm, sub-mm and FIR rangesand FIR ranges

Lecture 1, page 3

Dust continuum

Atomic Lines, Molecular Lines

Free-Free (Bremstrahlung)& SynchrotronContinuumEmission

Opacity of the Atmosphere

ionosphere

mm and sub-mm range

Lecture 1, page 4

Lecture1 page 5Lecture1 page 5

mm

T

K

GH z

T

KMAX

2 8 9 7 8

5 8 7 8 9

.

.

Peak of black body:Peak

In tensity

T 5

T=3K,=1 mmT=10K, =0.3 mm

B Th

ce

h

kT

( )

2 1

1

3

2=22/c2 . kT

S

T

cm

TMB MB

cm

2 6 5 2 6 50

2

20

2

2.( ' )

( ).

( ' )

IkT kT

S I dkT

MB

MB

2 2

2

2 2

2

Rayleigh-Jeans:

Cassiopeia A

At 100 MHz, SS= 3 10= 3 1044 Jy, Jy, s=4’ (source size), 4’ (source size), = 3 m = 300 cm

ST

cm

T

K T source

MB

2 6 5

3 1 0 2 6 51 6

9 1 0

7 5 1 0

0

2

2

44

8

.( ' )

( )

.

. ( )

In Jy,or 10-26 Wm-2 Hz-1

Lecture 1, page 6

Non-Thermal: Sources such as Cassiopeia A. At 3mm, find that Cas A has a peak temperature of about 0.8 K. Is this consistent with the flux density shown in the first plot?

Thermal: HII Regions such as Orion AThermal: HII Regions such as Orion A

= 5’ (FWHP) at 100 MHz,=300 cm, the flux density is 10 Jy. Find that

T=104 K

At 1.3 cm, find that T=24 K

True Black Bodies: Regions such as the Moon

Find that T=220 K (approximately). Note that SSincreases with frequency increases with frequency squared.squared.

Lecture 1, page 7

Three Types of Radio Sources

DevelopmentDevelopment

Radiative TransferRadiative Transfer

ReceiversReceivers

Receiver CalibrationReceiver Calibration

AtmosphereAtmosphere

Lecture 1, page 8

ss eI

ds

dIe

)(TB

e I e consts s

s 0 I I ( )0

B T ( ) B Th

ce

h

kT

( )

2 1

1

3

2

I

dx

dI

Lecture1 page 9Lecture1 page 9

One Dimensional Radiative Transfer

I I e B T e

B Tc

T

Ic

T

Ic

T

s s

B

( ) ( )

( )

( )

0 1

2

2

02

2

2

2

2

2

2 0

)0(Iconst

Suppose absorption, , and emission, in 1 dimension :

Assume and are constants w.r.t. s. Then

Integrating

at , . So

Kirchhoff ’s law: when is the Planck Function

Lecture1 page 10Lecture1 page 10

h k T

s T T e T eB ( ) 1 0

B Tc

kT

( )

2 2

2Radio: , for T=10K, (Rayleigh-Jeans) 2 0 0GH z

Then: Radio Range

(Definition) (all for a frequency )

atmosphere

Source

(e.g. MOON)

Receiver sees noise from Moon, plus noise fro atmosphere minus loss of source noise in atmosphere. Need calibration to relate receiver output to temperature. For spectral lines,

, so

If T=T0, see no emission or absorption

(could be species with T=T0=2.73 K)

T T TB B B ( ) ( ' )

T T T eB 0 1

Emission from Atmosphere

Absorption of Source

I I e B T e

B Tc

T

Ic

T

Ic

T

s s

B

( ) ( )

( )

( )

0 1

2

2

02

2

2

2

2

2

2 0

Lecture1 page 11Lecture1 page 11

Types of Receivers

Fractional R

esolution

Analog Coherent Receiver Block DiagramAnalog Coherent Receiver Block Diagram

Lecture1 page 12Lecture1 page 12

Time Frequency f

Total Amplification=1016

Suppose you measure Cas A with a dish of collecting area 50m2 at 100 MHz with a bandwidth of 10 MHz: what is the input power?

Hot-cold load measurementsHot-cold load measurements

Absorber at a given temperature

Input to receiver

(to determine receiver noise contribution)

Lecture 1, page 13

Hot and Cold Load CalibrationHot and Cold Load Calibration

Ratio ofPh to Pl

is definedas ‘y’

Lecture 1, page 14

Lecture1 page15Lecture1 page15

Suppose you have y=2, 2.5, or 3. What is the receiver noise?

Basic Elements of Coherent ReceiversBasic Elements of Coherent Receivers

• Mixers (HEB, SIS, Schottky)

• Amplifiers (Mostly for )

• Attenuators (Adjust power levels)

• Circulators, Filters

1 0 0GH z

Noise temperature of an amplifier chain:

G1: Gain of the stage 1, in cm range, G1 is larger than 103 typically,

so that TS1 dominates

Sometimes (as in mm or sub mm), stage 1 has loss, then

For example, 3 dB loss in common 100.3 =2, so

T TT

G

T

G GS SS S

12

1

3

1 2

LG

1

KwithLNA

amplifiernoiselowT

mixerT

TTT S

S

SSS

5)(

....2 2

1

21

=TS1+10K

Lecture1 page16Lecture1 page16

(divided by Gain of element 1)

Current Receiver Noise TemperaturesCurrent Receiver Noise Temperatures

Tmin=h/kfor coherentreceivers

Lecture 1, page 17

NoiseNoise

Lecture 1, page 18

Lecture 1 page 19Lecture 1 page 19

RECEIVERS

Fundamental Relation:

TimeTime 1 sec1 sec 1 hour1 hour 16 hours16 hours 64 hours64 hours

TT

RM SSYS

T

TRM S

SYS

1

0 0 1 6.

0 0 0 4.

0 0 0 2.

• For broadband measurements, try to keep TSYS small, but also good to have large (bolometers)

• For very narrow spectral lines, coherent receivers have as small as you want. For example one can have = 10-9 0

•For a 1/100 signal-to-noise ratio in 1 sec, have about 1-to-1 in 1 hour, 2.5-to-1 in 16 hours

(See problem 4-14 in ‘Tools Problems’

for a derivation)

(See problem 4-14 in ‘Tools Problems’)

Systematic Effects increase NoiseSystematic Effects increase Noise

RMS

Lecture 1, page 20

(See 4-27 in ‘Tools Problems’)

Dicke Switching to Cancel Dicke Switching to Cancel Systematic EffectsSystematic Effects

Lecture 1, page 21

But switching against a reference will increase the random noise

Effect of Mixing in Frequency SpaceEffect of Mixing in Frequency Space

L.O.frequency

Signal Frequency

DifferenceFrequency

Lecture 1, page 22

Double Sideband MixersDouble Sideband Mixers

Lecture 1, page 23

111 GHz

Lecture 1, page 24

(See 4-24 in ‘Tools Problems’)

Lecture 1, page 25

Heterodyne receivers at the HHT

Lecture1 page 26 Lecture1 page 26

BACKENDS

Want to have S().

Output of front end is V(t).

Problem is how to get S() from V(t) in the best way. The most

Common solutions in Radio Astronomy are:

• Filter bank

• Autocorrelator

• “Cobra”

• AOS

• Chirp transform spectrometer

Wiener-Kinchin Wiener-Kinchin

Lecture1, page 27

t t

F.T.

F.T.

R A t B t d t( ) ( ) ( ) ( )2

(Must be careful with limits in integral of periodic functions)

Lecture 1, page 30

Graphical CorrelationGraphical Correlation

(Problem 4-11 in ‘Tools Problems’.Correlations are useful in many different areas)

Lecture 1, page 31

Lecture 1, page 32Time behavior of input

Frequency behavior

Samplingfunction in time

Samplingfunction in frequency

undersampled

Sufficientlysampled

(see 4-12 in ‘Tools Problems’)

AutocorrelatorAutocorrelatorR A t B t d t( ) ( ) ( )

The correlation of A with B; examples are the correlation of two sine waves or two squares

DelayedSample(B)

Current Sample (A)

Lecture 1, page 29

Filter Bank SpectrometersFilter Bank Spectrometers

Lecture 1, page 33

Lecture1 page 34Lecture1 page 34

BOLOMETERS

These devices are temperature sensors, so

• Do not preserve phase

• Thus no quantum limit to system noise

• Wide bandwidths are easier to obtain

• No L.O. needed

• Thus multi-pixel cameras are ‘easier’ to build

•On earth, Bolometers are background limited; outer space is better & outer space with cooled telescopes better still!

•Today get NEP ≈ 10-16 watts Hz -1/2

•(Problem: Relate to flux density sensitivity of the 30-m)

For those who prefer ΔTRMS, one can use the following relation:

k

NEPATAT SYSRMS

2

0.8 mm Bolometer Passband0.8 mm Bolometer Passband

Lecture 1, page 35

Lecture 1, page 36

19 channel Bolometer at the HHT