Radio Telescope Recievers

Question 1

An antenna

Answer 1

turns the EM wave into voltage V(t). V(t) has a ~ ‘white’ spectrum with a power/Hz of KTa.

Question 2

Pre-Amplifier

Answer 2

boosts V(t) by ~X1000 so μVrms from antenna => ~mV signal now strong enough to not be degraded or lost in further processing.

Question 3

Filter

Answer 3

to restrict the range in frequencies and define the bandwidth

the filter also helps cut out interference from other signals

Question 4

tMixer

Answer 4

High frequency signals are difficult to control => shift to a lower ‘intermediate frequency’ by mixing the signal with a ‘local oscillator’ signal.

Question 5

Square-Law Detector

Answer 5

we are interested in the power of the signal, not the voltage, power ∝ V^2 need to square V(t). A suitable diode is able to do this

Question 6

Integrator

Answer 6

Averages the fluctuating output of the detector to determine its mean level accuracy

Question 7

Telescope diagram

Answer 7

See notes

Antenna -> pre amplifier -> filter -> mixer -> square-law detector -> integrator

Question 8

drift-scan of the source

Answer 8

diagram see notes

Question 9

Sensitivity

Answer 9

how weak a source can we detect

Question 10

The signal is

Answer 10

band limited noise

Question 11

Self-Noise

Answer 11

uncertainty in the mean level due to the naturally fluctuating nature of the signal

Question 12

After a time τ, number of independent measurements N is

Answer 12

N = τ/coherence time ≈ Δvτ

Question 13

SNR ≈ 1 √N = √Δvτ

is only true if

Answer 13

there is no other source of noise

Question 14

In a real system the amplifier introduces additional noise so

Answer 14

that it looks like the antenna temperature is T_LNA even when it is zero.

Question 15

Can distinguish Tsource from the rest by

Answer 15

Chopping or Beam-Switching on and off the source.

If nothing else changes in the switching then

Tsource = Ton - Toff

Question 16

System Temperature

Answer 16

Tsys = Tsource + Tbackground +…+ T_LNA + Telectronics

Question 17

For nearly all sources at all frequencies

Answer 17

Tsource &laquo_space;Tsys

Question 18

Derivation of the two equations are of radio astronomy

Answer 18

SNR = Tsource/Tsys √Δvτ

kTsource = 1/2 SAe

=> Tsource = SAe/2k

SNR = SAe/2kTsys √Δvτ

Smin = 2kTsys/Ae√Δvτ

Question 19

The equations of radio astronomy

Answer 19

SNR = SAe/2kTsys √Δvτ

Smin = 2kTsys/Ae√Δvτ

Question 20

SNR =

Answer 20

S/Sys √Δvτ

Question 21

sensitivity formula

Answer 21

sensitivity = Ag η/Tsys