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Ask Dr. SETI ®

Chapter 6: Technology

Total Power Radiometry

Dear Dr. SETI:
Good news! I now have a nice power meter, an HP 436A with an HP 8484 power sensor, a 20 foot bolometer cable, and a 30 dB reference attenuator. It all works great. Question - The 8484A can be used down to 0.1nW. What power level would I expect to see if I connected it right on the horn feed and pointed the antenna at the sun? This would help me debug the system (I don't have a working noise source as of yet).

Jim (a California Argonaut)

The Doctor Responds:
First off, Jim, congratulations on your surplus test equipment acquisitions. This power measurement system will prove very useful as you continue to improve your Project Argus station.

The measurement which you propose is formally called Total Power Radiometry. Radiometers are perhaps the oldest kinds of radio telescopes; they work by measuring the total power recovered when pointing an antenna at various noise sources (including the Sun). But, they usually involve far more equipment than merely an antenna, a feedhorn, and a laboratory power meter, no matter how sensitive. Your system will probably not detect the Sun without a whole lot of additional gain. To find out why, let's run the numbers:

The noise power available at your antenna can be quantified by Boltzmann's Law:

Pn = kTB


Pn represents noise power, in Watts,
k is Boltzmann's Constant, 1.38 * 10-23 m2 kg s-2 K-1
(otherwise known as Watts/Kelvin),
T is the physical temperature, in Kelvins, of the thermal black body being observed, and
B is the bandwidth, in Hertz, of the power detector or selective circuit preceeding it.

OK, so the sensitivity of your power meter is 0.1 nW, or 100 pW. Let us assume that the Sun is a true blackbody radiator, with a surface temperature of 5780 K (this is a fairly good first order approximation), and that your antenna captures nothing but solar flux (a not-so-good first order approximation, as we shall see shortly). If your L-band feedhorn were flat from, say, 1200 to 1700 MHz, with zero response outside of this band (that is, a perfect bandpass filter -- which it isn't), and you hooked up your power sensor to its Type N connector, then the bandwidth preceeding the detector would be exactly 500 MHz. From the above equation, Pn comes out to 4 * 10-11 W, or 40 picoWatts, or about 2 1/2 times weaker than the detector's threshold.

But wait, it gets worse. The Sun subtends about a 0.5 degree angle in the sky, as viewed from Earth. But the beamwidth of your small dish is perhaps 5 degrees, or ten times as wide as the Sun. That means that about a hundredth (10 squared) of the energy reaching your detector came from the Sun. The other 99% of the signal falling on your dish comes from space, a much colder thermal source. In an ideal world, the blackbody temperature of that other 99% of your dish's signal would be 3 Kelvin (the cosmic background radiation temperature). In fact, wherever you are pointing your dish, there are likely to be lots of background stars, galaxies, and interstellar gasses in the beam, so that sky temperature may be as much as a few tens of Kelvin. Still, compared to a 5780 Kelvin local star, that energy is negligible. So, the actual power to your detector is probably 100 times weaker than what we computed, or around 400 femtoWatts -- very far below the threshold of your detector.

That being the case, how can total power radiometers ever work as radio telescopes? The trick is to put a lot of gain ahead of your power detector. Maybe you have a good low-noise amplifier (LNA) for your Argus station. Let's say it has a gain of +30 dB (a power ratio of 1,000). If you put it on your LNA, and put your power sensor on its output connector, and assuming it has the same ideal 500 MHz bandwidth as your assumed antenna feed, then (in theory) the noise available to your power meter comes up by the same factor of 1,000. If we neglect the internal noise of your preamplifier, the recovered sun noise is now slightly above the threshold of your detector -- this might even work!

We could add even more preamplifier gain, and eventually be able to see a healthy microwave signal from the Sun on a laboratory power meter. This does in fact work, but there are some limitations. First off, the more microwave gain we add, the better the chance our preamplifiers will oscillate -- that would mess up our measurements, wouldn't it? Even if we tame the gain circuits, remember that microwave amplifiers generate internal noise of their own. This is measured in units of noise figure, noise factor, or noise temperature. Whatever unit of measure you choose, you can see that preamp noise will decrease the ability of your system to detect Sun noise. A good LNA has perhaps 30 to 50 K of internal noise, which has to be factored in to the sensitivity calculation.

One way to improve noise temperature and sensitivity of a radiometer, without risking oscillation, is to spread your gain across multiple frequencies. This can be done with a downconverter, just the way a superheterodyne receiver works. Say you have 30 dB or so of microwave gain, and that you downconvert to VHF, where you have a whole bunch more gain. If you balance gain, noise, and filtering properly, you can end up with a very clean IF signal, whose power can be measured with your microwave power meter. This is how most total power radiometers actually work.

There is a trap, however. My DEMI RX-1420 downconverter has lots of gain, low internal noise, and a clean 144 MHz output signal for an applied 1420 MHz signal. But its IF bandwidth is narrow, maybe about 10 MHz. That's only 2% of the 500 MHz antenna bandwidth we assumed when computing kTB, so we've just decreased our captured noise by 17 dB. So, the downconverter needs some additional gain, just to compensate for its narrower bandwidth. As you see, radiometry involves multiple tradeoffs. Still, if done right, we have an attractive method for measuring Sun noise, as well as the noise temperature of various other astrophysical phenomena.

One practical total power radiometer that a lot of SETI League members are using is the Little Bitty Telescope or LBT (see for a complete description). This demonstration radio telescope is based upon a standard, inexpensive Direct Broadcast Satellite (DBS) dish with its usual low-noise block downconverter and feedhorn assembly (LNBF). This is essentially the system I described above, except that the dish is small, operates at Ku-band, and the broadband feedhorn and downconverter shift the signal to L-band, at about 500 MHz of bandwidth. The detector in this case is not an expensive laboratory instrument, but rather a $100 calibration meter used by satellite TV installers to peak customers' dishes on the TV satellite. It turns out that, in these receivers, the Sun is just about as strong as a satellite. The Moon, though a much colder thermal blackbody, is also detectable with the IBT. If you want to learn about total power radiometry, this is about the least expensive approach to getting reasonable results.

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