1. Lecture 1
By Tom Wilson

2. history Maxwell: Equations Hertz: Reality Marconi: Practical wireless
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…

3. The 20.5 MHz Sky (Jansky)

5. Galactic Continuum Sources
Lecture 1 page 2
Galactic Continuum Sources
Sn in Jy is W m-2 Hz-1 (intensity integrated over the source)

6. M82 in the radio, mm, sub-mm and FIR ranges
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

7. Opacity of the Atmosphere
Lecture 1, page 4
Opacity of the Atmosphere
ionosphere
mm and sub-mm range

8. Lecture1 page 5 =2n2/c2 . kT Peak of black body: T=3K, l=1 mm

9. At 100 MHz, Sn= 3 104 Jy, qs=4’ (source size), l = 3 m = 300 cm
Lecture 1, page 6
Rayleigh-Jeans:
In Jy, or
10-26 Wm-2 Hz-1
Cassiopeia A
At 100 MHz, Sn= Jy, qs=4’ (source size), l = 3 m = 300 cm

10. Three Types of Radio Sources
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, l=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.

11. Development Radiative Transfer Receivers Receiver Calibration
Lecture 1, page 8
Development
Radiative Transfer
Receivers
Receiver Calibration
Atmosphere

12. One Dimensional Radiative Transfer
Lecture1 page 9
One Dimensional Radiative Transfer
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

13. Lecture1 page 10 Radio: , for T=10K, (Rayleigh-Jeans) Then:
Radio Range
Emission
from
Atmosphere
Absorption of
Source
(Definition)
(all for a frequency )
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)
atmosphere

14. Fractional Resolution
Lecture1 page 11
Types of Receivers
Fractional Resolution

15. Analog Coherent Receiver Block Diagram
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?

16. Hot-cold load measurements
Lecture 1, page 13
Hot-cold load measurements
(to determine receiver noise contribution)
Absorber at a
given temperature
Input to
receiver

17. Hot and Cold Load Calibration
Lecture 1, page 14
Hot and Cold Load Calibration
Ratio of
Ph to Pl
is defined
as ‘y’

18. Lecture1 page15
Suppose you have y=2, 2.5, or 3. What is the receiver noise?

19. Basic Elements of Coherent Receivers
Lecture1 page16
Basic Elements of Coherent Receivers
Mixers (HEB, SIS, Schottky)
Amplifiers (Mostly for )
Attenuators (Adjust power levels)
Circulators, Filters
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 =2, so
(divided by
Gain of element 1)
=TS1+10K

20. Current Receiver Noise Temperatures
Lecture 1, page 17
Current Receiver Noise Temperatures
Tmin=hn/k
for coherent
receivers

21. Lecture 1, page 18
Noise

22. (See problem 4-14 in ‘Tools Problems’ for a derivation)
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
1 sec
1 hour
16 hours
64 hours
For broadband measurements, try to keep TSYS small, but also good to have Dn large (bolometers)
For very narrow spectral lines, coherent receivers have Dn as small as you want. For example one can have Dn = 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

23. Systematic Effects increase Noise
Lecture 1, page 20
Systematic Effects increase Noise
RMS
(See 4-27 in ‘Tools Problems’)

24. Dicke Switching to Cancel Systematic Effects
Lecture 1, page 21
Dicke Switching to Cancel Systematic Effects
But switching against a reference will increase the random noise

25. Effect of Mixing in Frequency Space
Lecture 1, page 22
Effect of Mixing in Frequency Space
Difference
Frequency
L.O.
frequency
Signal
Frequency

26. Double Sideband Mixers
Lecture 1, page 23
Double Sideband Mixers
111 GHz

27. Lecture 1, page 24
(See 4-24 in ‘Tools Problems’)

28. Lecture 1, page 25
Heterodyne receivers at the HHT

29. 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

30. Lecture1, page 27
Wiener-Kinchin

31. Lecture 1, page 30
F.T. t t n
( )2
F.T.
(Must be careful with limits in integral of periodic functions)

32. Graphical Correlation
Lecture 1, page 31
Graphical Correlation
(Problem 4-11 in ‘Tools Problems’.
Correlations are useful in many different areas)

33. 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’)

34. Autocorrelator Lecture 1, page 29 Current Sample (A) Delayed Sample
(B)
The correlation of A with B; examples are the correlation of two sine waves or two squares

35. Filter Bank Spectrometers
Lecture 1, page 33
Filter Bank Spectrometers

36. 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 ≈ 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:

37. Lecture 1, page 35
0.8 mm Bolometer Passband

38. Lecture 1, page 36
19 channel Bolometer at the HHT