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Chapter 6: Technology

How Much Preamp Gain?

Dear Dr. SETI:
I have a wide band microwave receiver that I would like to set up for some non-traditional SETI work. This receiver is tunable over a frequency range of 1 to 18 Ghz. I am particularly interested in using its wide frequency capability as opposed to searching over a relatively narrow frequency span. I fully understand the limitations this imposes as to ultimate weak signal detectability.

My question is, in order to be able to receive signals at or slightly below the noise level, how much pre-amplification should I use?

The receiver has a noise figure of 20 dB. The narrowest IF bandwidth used will either be .5 Mhz, 2 Mhz, or 5 Mhz although I may at times use narrower bandwidths through additional IF filtering. (I understand the concept of noise bandwidth and the limitations in minimum received signal due to the large bandwidths.)

The receiver will be used with a 12 foot dish and a wide band horn for a feed. I plan to use a LNA at the antenna (actually, several that are switchable depending on frequency being scanned) with a noise figure of around 0.5 dB.

Feed line run will be around 100 feet or less and will be low loss coax.

My question is how much additional amplification over and above the LNA would be required in order to be able to receive signals at the noise level and with selectable IF bandwidths of 0.5, 2, and 5 Mhz ? Remember, the receiver noise figure is quite high at 20 dB.

Roy (via the ARGUS list)

The Doctor Responds:
Roy, I am envious of that broadband receiver. You have the start of a very fine SETI instrument.

When adding preamplifiers in front of a receiver, your goal is to have enough gain for the overall system noise figure to approach that of the preamplifier itself. The definitive work on noise figure for cascaded stages was done by H.T. Friis, and published in 1944. His equations are in the literature, but there is a rule of thumb you can use to simplify the computations. To a first order approximation, system noise figure will equal preamp noise figure only when the gain of the preamp exceeds the noise figure of everything that follows it, by at least 10 dB.

So, for your system with a wide-dispersion receiver having about 20 dB of noise figure, the appropriate gain for your preamplifier will be ten dB more than that noise, or 30 dB total.

Except that we have overlooked the noise contribution of your feedline. You say you will be using 100 feet or less of "low loss" coax, but even "low loss" is not zero loss (and 100 feet is still a pretty long feedline run). The loss of your coax will go up with frequency, so by the time you get up to 18 GHz, it will be considerable. And with an antenna mounted preamp driving coax driving a receiver, coax loss adds directly to your receiver's noise figure.

Let's optimistically assume that your coax loss is only 10 dB (at some particular frequency). Now the cascade of coax loss plus that 20 dB of receiver noise means that your preamp needs to overcome 30 dB of total noise. To do so, its gain has to be around 40 dB.

But wait a minute -- 40 dB of preamp gain can be a problem. That much gain crammed into a small box is likely to oscillate, or at least to exhibit only marginal stability.

Fortunately, there is another approach to applying the Friis Equation. Let's see if we can lower that 20 dB receiver noise figure, by putting a preamp not at the antenna, but directly in front of the receiver. With a 20 dB receiver noise figure, we're now back to needing only 30 dB of preamp gain to have the preamplifier's noise figure dominate. So, for example, if we use a 30 dB gain preamp with a 1 dB internal noise figure, directly in front of the receiver, the two together act just like a receiver with a 1 dB noise figure.

Now back to the coax. If we have 10 dB of coax loss in front of a 1 dB noise figure receiver, the cascade (looking into the coax) acts like an 11 dB overall noise figure. We can overcome all that noise by using a second preamp, directly at the antenna. It needs a gain of 10 dB more than that 11 dB we're trying to overcome, for a total of 21 dB. And now, whatever noise figure that 21 dB gain preamp has, it will establish the overall sensitivity of your system.

You may be wondering how a system with two preamps, having a total gain of 51 dB, can be stable. The cascade works only because of the coax loss, which acts as an attenuator between the two preamps. Oscillation is unlikely, and stability improved, by that 10 dB of coax attenuation. It causes the output of the antenna-mounted low noise amplifier, as well as the input to the second preamplifier in front of the receiver, to each be well terminated in the cable's characteristic impedance (typically 50 ohms). And well terminated amplifiers are happy amplifiers.

Now, Roy, go build up that wonderful broadband SETI station!

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