Tech Talk #3 — Antenna Temperature and Flux Density

by Richard Flagg, WCCRO

Using a calibrated noise source like the RF2080 and the Calibration Wizard in Radio-Skypipe 2 observers can establish the vertical scale of SkyPipe to measure antenna temperature referenced to the antenna terminals. Antenna temperature is a way of expressing the power captured by the antenna. Power and temperature are related by P=kTB, where P is power, k is Boltzmann’s constant, T is temperature, and B is the receiver bandwidth. For a given temperature, the wider the receiver bandwidth the higher will be the observed power. Antenna temperature is a measurement taken on the “observer side” of the antenna structure.

If we are interested in the amount of power in the incident wave striking the antenna then we talk about flux density. This is the true measure of signal strength from a cosmic source. The units of flux density are a little daunting at first glance – they are watts per square meter per unit of bandwidth.

Imagine an electromagnetic wavefront – and consider just 1 square meter of that wavefront. Now measure the power in that 1 square meter with your “receiver” using a bandwidth of 1 Hertz. What you measure is flux density – the unit of flux density is the Jansky (Jy). Of course if you collected power from more than 1 square meter and used a receiver with a bandwidth greater than 1 Hertz, then you would collect more energy. Think of it like a bucket in a rain storm – the bigger the throat of the bucket the more water you collect.

Your antenna is a bucket for electromagnetic waves. The bigger the aperture of the antenna the more energy it extracts from the incident wavefront. The antenna actually acts like a passive amplifier. An antenna with a bigger aperture has more gain than a smaller one. Note that the effective area speaks to the area of the wavefront intercepted by the antenna and this may be different than the physical area of the antenna.

So our antenna stands between our measurement of antenna temperature and the flux density of the incident wave. If we know the effective area of our antenna in terms of square meters of capture area, and we know the bandwidth of our receiver then we can make an antenna temperature measurement (at the observer side of the antenna) and convert it into flux density on the “space” side of our antenna. A big antenna with lots of aperture and a receiver with a wide bandwidth will capture more energy but when we express it in terms of flux density we must normalize our measurement to 1 square meter and 1 Hertz of bandwidth. Having done this we have a standard method of expressing how strong a cosmic signal is when it reaches our antenna.

By way of an example let’s assume we measure an antenna temperature of 500,000 K (degrees Kelvin) for a strong Jovian burst. Assume the receiver bandwidth is 7 kHz and the effective antenna aperture is 150 square meters. (typical values for the JOVE radio telescope)

From P=kTB we have (1.38x10-23 Joules/Kelvin)x(5x105 Kelvin)x(7x103 Hz) = 4.8 x 10-14 watts.

This is the power collected in the 7 kHz bandwidth of the receiver. To find the power in a 1 Hertz bandwidth we divide by the receiver bandwidth obtaining 6.9x10-18 watts per hertz.

This power was collected by our antenna intercepting 150 square meters of the wavefront – but we are interested in the power in a single square meter – so we must divide by our antenna aperture obtaining 4.6 x 10-20 watts/square meter/hertz.

The final step is to express this number in Jy. By definition 1 Jy equals 1x10-26 watts per square meter per hertz. So our final calculation of (4.6x10-20)/(1x10-26) yields the flux density of our burst which is 4.6 million Jy.

By the way — this is a huge flux density. Radio astronomers using big dishes in the microwave region frequently detect sources with flux densities less than a hundredth of a Jansky.