Transcript Lecture 1 By Tom Wilson Lecture 1 page 1 history Maxwell: Equations Hertz: Reality Marconi: Practical wireless Fessenden, Armstrong: Voices on wireless, Heterodyne De Forrest: Amplifiers Jansky: Cosmic radio.

Lecture 1
By Tom Wilson
Lecture 1 page 1
history
Maxwell: Equations
Hertz: Reality
Marconi: Practical wireless
Fessenden, Armstrong: Voices on wireless,
Heterodyne
De Forrest: Amplifiers
Jansky: Cosmic radio sources
Radio Astronomy: Pawsey, Bolton, Oort, Ryle…
1963-8: Quasars, Molecular Clouds, Pulsars…
The 20.5 MHz Sky (Jansky)
Lecture 1 page 2
Galactic Continuum Sources
Sn in Jy is 10-26 W m-2 Hz-1 (intensity integrated over the source)
Lecture 1, page 3
M82 in the radio, mm, sub-mm
and FIR ranges
Atomic
Lines,
Molecular Lines
Free-Free
(Bremstrahlung)
& Synchrotron
Continuum
Emission
Dust continuum
Lecture 1, page 4
Opacity of the Atmosphere
ionosphere
mm and sub-mm range
2  h  n 3 
Bn (T ) 
c2 
Peak
Intensity
 T
5

 =2n2/c2 . kT

 1
1
e
hn
kT
Lecture1 page 5
Peak of black body:
    T

     2.8978
 mm   K 
 n MAX 
 T

58
.
789



 
 GHz 
 K
T=3K, =1 mm
T=10K, =0.3 mm
Lecture 1, page 6
Rayleigh-Jeans:
I
2 kT

2
Sn 
In Jy,
Sn
or
10-26 Wm-2 Hz-1
 2.65

2 kTMB
2
2 kTMB
 In d 

TMB  0 (')
 (cm)
2
 

2

2
 2.65
TMB  0 2 (')
2 cm
Cassiopeia A
At 100 MHz, Sn= 3 104 Jy, s=4’ (source size),  = 3 m = 300 cm
Sn  2.65

TMB  0 (')
 (cm)
3  10  2.65  T
4

2
2
16
 9  10 
4
7.5  108 K  T ( source)
Lecture 1, page 7
Three Types of Radio Sources
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 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 Sn increases with frequency
squared.
Lecture 1, page 8
Development
Radiative Transfer
Receivers
Receiver Calibration
Atmosphere
Lecture1 page 9
One Dimensional Radiative Transfer
Suppose absorption,  n , and emission, n in 1 dimension :
dIn
 n  In  n
dx
Assume n and n are constants w.r.t. s. Then
Integrating

 n s
e
at s  0 , In  In (0) . So
Kirchhoff ’s law:
n
 Bn (T )
n

e
n s
n  n  s
In 
e
 const
n
const  In (0) 
when
 dIn

n s



I



e

n
n
n
 ds

n
n
Bn (T ) is the Planck Function
In  In (0)  e  n s  Bn (T )1  e  n s 
2  h  n3
Bn (T ) 
c2

1

hn
 kT
e 



1
In  In (0)  e  n s  Bn (T )1  e  n s 
2n 2 
Bn (T )  2  T 
c

2
2n

In  2  TB 
c


2n 2
In (0)  2  T0 
c

Lecture1 page 10
Radio: h  n  k  T , for T=10K, n   200GHz
Then:
 n  s  n
Radio Range
(Definition)
2n2
Bn (T ) 
kT
c2
Emission
from
Atmosphere
TB (n )  T  1  e n   T0  e  n
(Rayleigh-Jeans)
Absorption
of
Source
(all for a frequency n )
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,
Source
(e.g. MOON)
 TB  TB (n )  TB (n ' ) , so
atmosphere
 TB  T  T0   1  e   n 
If T=T0, see no emission or absorption
(could be species with T=T0=2.73 K)
Lecture1 page 11
Types of Receivers
Fractional Resolution
Lecture1 page 12
Analog Coherent Receiver Block Diagram
Time
Frequencyn, 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?
Lecture 1, page 13
Hot-cold load measurements
(to determine receiver noise contribution)
Absorber at
a
given
temperature
Input to
receiver
Lecture 1, page 14
Hot and Cold Load Calibration
Ratio of
Ph to Pl
is defined
as ‘y’
Lecture1 page15
Suppose you have y=2, 2.5, or 3. What is the receiver noise?
Lecture1 page16
Basic Elements of Coherent Receivers
•
•
•
•
Mixers (HEB, SIS, Schottky)
Amplifiers (Mostly for n  100GHz )
Attenuators (Adjust power levels)
Circulators, Filters
TS 2
T
 S3
G1 G1  G2
G1: Gain of the stage 1, in cm range, G1 is larger than 103 typically,
Noise temperature of an amplifier chain:
TS  TS 1 
so that TS1 dominates
Sometimes (as in mm or sub mm), stage 1 has loss, then L 
For example, 3 dB loss in common 100.3 =2, so
(divided by
Gain of element 1)
TS1  mixer

TS  TS1  2  TS 2  ....TS 2  low noise amplifier
( LNA) with 5K

=T +10K
S1
1
G
Lecture 1, page 17
Current Receiver Noise Temperatures
Tmin=hn/k
for coherent
receivers
Lecture 1, page 18
Noise
Lecture 1 page 19
(See problem 4-14 in
‘Tools Problems’)
(See problem 4-14
in ‘Tools Problems’
for a derivation)
RECEIVERS
Fundamental Relation:
Time
 TRMS
TSYS
 TRMS 
1 sec
1
n
TSYS
n 
1 hour
16 hours
64 hours
0.016
n
0.004
n
0.002
n
• For broadband measurements, try to keep TSYS small, but also
good to have n large (bolometers)
•
For very narrow spectral lines, coherent receivers have n as
small as you want. For example one can have n = 10-9 n0
•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
Lecture 1, page 20
Systematic Effects increase Noise
RMS
(See 4-27 in ‘Tools Problems’)
Lecture 1, page 21
Dicke Switching to Cancel
Systematic Effects
But switching against a reference will increase the random noise
Lecture 1, page 22
Effect of Mixing in Frequency Space
Difference
Frequency
L.O.
frequency
Signal
Frequency
Lecture 1, page 23
Double Sideband Mixers
111 GHz
Lecture 1, page 24
(See 4-24 in ‘Tools Problems’)
Lecture 1, page 25
Heterodyne receivers at the HHT
Lecture1 page 26
BACKENDS
Want to have S(n).
Output of front end is V(t).
Problem is how to get S(n) from V(t) in the best way. The most
Common solutions in Radio Astronomy are:
• Filter bank
• Autocorrelator
• “Cobra”
• AOS
• Chirp transform spectrometer
Lecture1, page 27
Wiener-Kinchin
Lecture 1, page 30
F.T.
n
tt
R( ) 
( )2
 A(t )  B(t   )  dt
F.T.
(Must be careful with limits in integral of periodic functions)
Lecture 1, page 31
Graphical Correlation
(Problem 4-11 in ‘Tools Problems’.
Correlations are useful in many different areas)
Lecture 1, page 32
Time behavior of input
Frequency behavior
Sampling
function in
time
Sampling
function in
frequency
undersampled
Sufficiently
sampled
(see 4-12 in ‘Tools Problems’)
R( ) 

Lecture 1, page 29
A(t )  B(t   )  dt
Autocorrelator
Current
Sample
(A)
Delayed
Sample
(B)
The correlation of A with B; examples are the
correlation of two sine waves or two squares
Lecture 1, page 33
Filter Bank Spectrometers
Lecture1 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:
TRMS 
A  TSYS
A  NEP

n  2  k  n  
Lecture 1, page 35
0.8 mm Bolometer Passband
Lecture 1, page 36
19 channel Bolometer at the HHT