Astronomy 302

Measuring Receiver Noise Figures

Spring 2000

Abstract: One of the most important characteristics of a radio receiver system is its sensitivity, that is, its ability to detect a signal of a certain intensity. The amount of inherent system noise (due to atmosphere, telescope optics and alignment, and receiver optics and electronics) is the fundamental quantity that dictates the sensitivity of a radio telescope; i.e. how much integration time it will take to detect a signal of a certain strength. In this laboratory experiment, you will measure the effective noise power of the 1.4 GHz hydrogen-line feed horn and amplifier system used on the 12-foot Student Radio Telescope, to be relocated on Steward Observatory's new 6th floor.

Introduction: In optical astronomy, the intensity of light from an astronomical source is usually defined in terms of a frequency-integrated specific intensity, in units of watts$\cdot$m^-2 (MKS) or ergs$\cdot$s$^{-1}\cdot$cm^-2 (CGS). At radio wavelengths, a more convenient unit of evaluating intensity is the equivalent blackbody temperature that corresponds to that intensity of light at that frequency. Plotting several blackbody curves at once, it is readily apparent that at a particular frequency, a certain intensity uniquely maps to a particular blackbody at a certain temperature:

Figure 1: Equivalence of frequency-evaluated ``classical intensity'' and ``blackbody equivalent temperature''

This notation may seem initially cumbersome, but one rapidly finds it to be a vastly better match to the techniques of radio astronomy than the classical definition of specific intensity. For example, optically thick broad-band submillimeter and infrared dust emission emits with a characteristic blackbody spectrum; the measured antenna temperature of the dust emission therefore relates directly to the physical temperature of the dust. Similarly, saturated emission lines coming from atoms and molecules in a molecular cloud emit with a maximum intensity that corresponds to the kinetic temperature of the molecular cloud under the assumption of thermodynamical equilibrium. Also, when measuring the blackbody temperature of a known object, such as the Moon or a planet, the ratio of the observed antenna temperature to the expected antenna temperature yields the telescope/receiver beam efficiency, an important figure of merit for radio telescopes.

The amount of on-source integration time needed to integrate to a desired RMS (root-mean-square, or 1-$\sigma$) noise level may be written in terms of a system equivalent noise temperature, commonly written as T$_{\rm sys}$:

$$t = \frac{T_{\rm sys}^2}{B \cdot \sigma_{\rm RMS}^2}$$

Clearly, the necessary on-source integration time to reach a certain RMS noise temperature $\sigma_{\rm RMS}$ and with bandwidth B, depends critically upon T$_{\rm sys}$. What comprises T$_{\rm sys}$ and how do we reduce it? The system noise temperature when looking at blank sky can be decomposed into the following:

$$T_{sys} \sim T_{\rm RX} + (1 - \alpha \cdot e^{-\tau}) T_{\rm H}$$

where $T_{\rm H}$ is the temperature of a hot load (usually a eccosorb vane at ambient room temperature inserted into the beam), $\tau$ is the atmospheric opacity at the observed zenith angle, $\alpha$ is the hot spillover efficiency (the fraction of power not falling on ``hot'' objects, like spilling over past the primary mirror edge and looking at the ground, etc...), and T$_{\rm RX}$ is the receiver equivalent-noise temperature.

How do we measure T$_{\rm RX}$? We provide a calibration between equivalent blackbody temperature and receiver voltage by putting two objects of differing, known temperatures into the beam. The ``hot load'' is usually a piece of eccosorb at room temperature inserted into the beam, and the ``cold load'' is a piece of eccosorb dipped in liquid nitrogen. The relation needed to compute T$_{\rm RX}$ is:

$$T_{\rm RX} = \frac{T_{hot} - {\rm Y} \cdot T_{cold}}{{\rm Y} - 1}$$

$${\rm Y} = \frac{P_n + P_{hot}}{P_n + P_{cold}} \sim \frac{P_{hot}}{P_{cold}}$$

where P is a measure of the total power observed while observing the hot and cold loads, and P_n is a measure of the intrinsic receiver equivalent noise power.

Experimental Apparatus:

The following hardware is needed to perform this experiment:

1.

Feed horn, feed line and amplifier: The Student Radio Telescope (SRT) uses a circular feed horn in place of a subreflector, tuned approximately to the frequency of the 1.42 GHz hydrogen spin-flip transition. Since atomic hydrogen is so pervasive in interstellar space, this line is of critical importance to the study of the distribution of matter both in our own Milky Way, and out to the realms of distant galaxies. Deep inside the feed horn, a pick-off wire conducts the received signal to an amplifier, which relays the signal via coaxial cable to a 1-2 GHz receiver system and analysis computer.

2.

Total Power Box: The output of the amplifier is transmitted via coaxial cable to a device which integrates the intensity of radio-wave radiation over the entire bandpass receivable by the feedhorn/amplifier system. The result is a single number that represents the relative total collected power.

3.

Frequency Analyzer: The output of the amplifier is then sent to a frequency (spectrum) analyzer, which provides a real-time frequency spectrum (signal intensity versus frequency) of the collected signal.

4.

Signal Generator: Although we do not have the luxury of the assembled 12-foot Student Radio Telescope this year, we can simulate the 1.4 GHz hydrogen line in the laboratory. A signal generator can be used to radiate a sharp 1.4 GHz signal throughout the room, which can be detected as a change in the total collected power and as a sharp ``spectral feature'' in the spectrum shown by the frequency analyzer.

Figure 2: The experimental setup, consisting of the 1.4 GHz hydrogen-line feed horn and attached amplifier, signal generator, total power box, and frequency analyzer.

Tasks:

You will measure the noise temperature of the SRT's feed horn and amplifier system, by inserting a hot load and cold load in front of the feed horn system and measuring the resulting total power in each case. You will then use the signal generator to simulate detecting the 1.42 GHz hydrogen recombination line. Guidelines for the writeup are specified in last week's lab, as both experiments will be submitted on February 7th. You can choose to write each exercise up separately, or combine them as you see fit. I will not impose a formal structure for the lab report so long as it is written in a readable, organized and thorough fashion. The goal of the lab report should be to communicate what you did and what you learned so that I could repeat the experiment based based upon your descriptions.

Pay close attention to the following things when performing the lab:

1.

How are the various experimental components interconnected? What does each component do and roughly how does it work? How did you use them?

2.

When using the spectrum analyzer, why are dB's used instead of linear units? How did you measure the exact frequency of the ``simulated'' emission line? What is the instantaneous bandwidth of the feedhorn/amplifier combination? How did you measure it?

3.

You may have noticed sharp noisy features in the spectral bandpass. We could determine that they were simply noise features by covering the entrance to the feed horn with our hands (or, in other cases, turning off the signal generator) and watching the noise spikes disappear. But at the telescope, we will usually not have this luxury - and there might be no way of knowing if a feature in the bandpas is simply an intrinsic noise spike in the bandpass or a real astronomical signal. Can you think of an observational technique that might eliminate this uncertainty? Hint: Think of how we reduced the observational noise in the Gaussian Beam Optics Lab...

4.

Are there differences in the receiver noise temperature between the two groups? What contributed to the difference? Which measurement is more reliable and why? Does the "worse" measurement yield an upper limit on the noise temperature, or a lower limit, or is it not useful at all?

5.

Let's assume the system temperature is completely dominated by the receiver noise temperature (Note: In submillimeter astronomy, sky noise is the dominant factor, NOT receiver noise). With the instantaneous bandwidth that you have measured in this lab, how much on-source integration time would it take to integrate down to an RMS noise temperature of 10 milliKelvin?