A resistor generates a weak radio frequency noise voltage across its terminals due to the random motion of free electrons within the resistor. If we heat the resistor up with a blowtorch (don't try this at home kids) the noise signal will increase in amplitude because of the increased thermal motion of those free electrons. If the resistor is connected to the antenna terminals of a receiver the noise power delivered to the receiver is:
P = kTB
P = power in Watts
k = Boltzmann's Constant = 1.38×10-23 Joules per °K
B = receiver bandwidth in Hz
T = resistor temperature in °K
This equation is strictly valid only if the resistor value is matched to the receiver antenna input impedance for the Jove receiver this would require a 50 ohm resistor.
Let's calculate how much power is delivered to the receiver; given that the resistor is at 50,000 °K, and the bandwidth of the receiver is 6 kHz. (6000 hertz).
P = (1.38×10-23)(5×104)(6×103) = 4.14×10-15 Watts
At a radio-quiet receiving site this is about the amount of power from the galactic background delivered to the receiver by the Jove antenna (assuming there is no attenuation between the antenna terminals and the receiver).
Because of this relationship between the noise generated by a resistor and the noise delivered from an antenna, it is convenient to describe the antenna signal in terms of antenna temperature. In theory we could replace the antenna with a resistor and vary the temperature of the resistor until its noise power matches the noise power from the cosmic radio source. When the noise power levels match we note the temperature of the resistor. This value of temperature is called antenna temperature.
Instead of using a hot physical resistor we use a calibrated noise source — a device that generates a known amount of noise. While the measurement is usually made with the calibrator connected directly to the receiver, the actual antenna temperature should be referenced back to the antenna terminals — taking into account attenuation in the coax cable and other devices such a power combiner.