Lecture 1 By Tom Wilson

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…

The 20.5 MHz Sky (Jansky)

Galactic Continuum Sources Lecture 1 page 2 Galactic Continuum Sources Sn in Jy is 10-26 W m-2 Hz-1 (intensity integrated over the source)

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

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

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

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= 3 104 Jy, qs=4’ (source size), l = 3 m = 300 cm

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.

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

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

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

Fractional Resolution Lecture1 page 11 Types of Receivers Fractional Resolution

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?

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

Hot and Cold Load Calibration 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?

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 100.3 =2, so (divided by Gain of element 1) =TS1+10K

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

Lecture 1, page 18 Noise

(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

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

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

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

Double Sideband Mixers 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. t t n ( )2 F.T. (Must be careful with limits in integral of periodic functions)

Graphical Correlation 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’)

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

Filter Bank Spectrometers 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:

Lecture 1, page 35 0.8 mm Bolometer Passband

Lecture 1, page 36 19 channel Bolometer at the HHT