Lecture 10- Radiometers
Random Noise
Natural signals all generated by random processes and have same basic form when incident on the receiver
In a radio receiver EF variations turned to random voltages Gaussian probability distribution
Signal voltages indistinguishable from therm agitation voltages in resistant components of the receiver
These voltages are "white noise"
because the power per unit bandwidth is independent of frequency (from Nyquist maths)
Only stable/measurable quantity at a single point in space is the average power or variance of the random variable
Basic Receiver
Random fluctuating electric field
Quasi-random voltage set by properties of the feed
Gain x Voltage set by amplifiers
Similar voltage set by the bandpass definin filter
Detected Power with fluctuations (maths)
Detected power smoothed over selected time period
Basic reciever components
Telescope antenna
Amplifier (gain G)
Bandpas filter
Square law detector
Integrator
Radio astronomy signals are very weak, so need huge amplification <100dB before they can be measured and quantified
Band-limited noise
Noise frequency spectrum restricted by a band-pass filter covering a range of frequencies
results in time series of random noise by with statistical structure imposed
Typical zero crossing times separated by 1/vrf and the amplitude modultion "envelope" exhibits a charcteristc "coherance time"
within this time the voltage is quasi sinusoidal and has quasi predictable phase
Extension to sum of random sine waves of the concept of "beats" ie. modulation resulting when two pure sine waves are added together
sum function in time has a modulation period
Key concepts
Radio astronomy signals need high degree of amplification
Noise voltage signals hae zero mean and fluctuate on rapid timescales (maths)
Need a steady non-zero signal so we measure power and average for long periods
Easiest way to measure power is to put amplified voltage into a semiconductor "square law detector" for small input signals
Square law detection
Maths and diagram
Peaks come from the envelope
multiplies a signal with itself
non linear process- input frequencies mix together to give new frequencies
input has gaussian stats, output has non gaussian stats
Central limit theorum: any large sample of independent random variables will exhibit a gaussian distribution
After square law detection
With random noise signals all we can do is observe the fluctuating power output of the receiver over a long enough time to obtain high enough accuracy
Increasing the receiver bandwidth also helps but reduction in level of fluctuation only goes as the square root of their product
Natural signals are very weak and hence long integration times often required for their detection
Radiometer equation maths
Detecting a weak source
Diagram
Schematic radio telescope record of the output power of a receiver after final averaging over a timescale seconds as the beam moves over a week source
On left and right the telescope only sees background brightness temperature
in central region beam is pointed at a weak source
because telescope is pointed a the source for time longer than tau avg the rise in mean temperature due to the source can be detected
Receiver temp:hot and cold lodes
Subject the system to known sources of input power which are comparable or larger than Trec, little or no integration needed to overcome output fluctuation
Echosorb, liquid nitrogen
Maths