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