## Calibrating the Radio Telescope

**Hayley Skinner and Chris Holmes**

A 50 ohm resistor was attached to the receiver. This acted as a load on the receiver.

To record the temperature readings from the receiver for the cold load we submerged the resistor into liquid nitrogen. This was used as it has a known temperature of 77K. The temperature measured at the receiver was recorded onto the system.

In order to keep the temperature falling we gradually added the liquid nitrogen over a period of about five minutes.

Resistor once removed from liquid nitrogen.

The temperature recorded finally plateaued at 167K. From the plot (seen further down the page) it is clear that the resistor cools gradually until it reaches equilibrium. Along the way we can see two points where the temperature jumps suddenly. We believe the first point is due to a large dose of liquid nitrogen being added too quickly. The second we believe is due to a physical change in the resistor as it reaches a certain temperature.

Chris pouring liquid nitrogen into thermos flask in full safety gear.

We then removed the resistor from the liquid nitrogen and allowed the resistor to return to ambient temperature for the hot load. The room temperature was found using a thermometer, and was found to be 290K. The warming curve is not as accurate as the cooling curve. The temperature jumps unevenly over the duration of the warming. The major contribution to this was the need to remove moisture from the resistor by wiping it, to allow it to warm evenly. The final ambient temperature reached for the hot load was at 325K.

The calculations below show how to find the system temperature from these results.

The Planck blackbody equation is:

where *S(v) * is the power per unit frequency, *v* the frequency of radiation detected, *h* the Planck constant, *k * = the Boltzmann constant,* * the speed of light and T the temperature.

For the radiation being detected , therefore the exponential in the denominator can be expanded as and the power equation becomes:

This is the Rayleigh-Jeans approximation.

To calculate the temperature of the system, the following equations must be used:

Therefore an equation for the system temperature can be defined:

The Y-factor is calculated by looking at the readings taken at the two different temperatures. The two temperatures are as found on the maximum and minimum points of the temperature vs time graph produced by the telescope program. This can be seen below:

The blue line shows the cooling curve as the resistor was placed in liquid nitrogen. The red line is the warming curve as the resistor was allowed to warm back up to room temperature.

As mentioned before, this gives a value of 325K for the receiver when at hot temperature, HM, and a value of 167K for the cold temperature, CM.

Using the above Rayleigh-Jeans power approximation, the power ratio, or Y-factor, becomes:

This is very close to the manufacturer's value of 150K. This can be used to calibrate all the data received.

The gain of the system can also be found using:

### References

'Tools of Radio Astronomy' by Kristen Rohlfs, Springer-Verlag 1986, Pages 9-14

'Report on the hot/cold load test at the RPA on Jan 31, 2001', Shuleen Chau Martin, Erik Rosolowsky, Don Backer, http://astron.berkeley.edu/~ay203/2001/RPA/hotcold.01jan31