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I hope you have time for a dumb question Paul. My system has been acting strangely for a while, so took the Head End electronics down, pulled out the LNA (Radio Astronomy Supplies, 28 dB gain), and set it up on my bench. When I have the LNA input terminated in a good 50 ohm terminator, I get 36 dBm out of the LNA as measured on my HP Power Meter and 8484 sensor. I don't see anything on my spectrum analyzer, but it only goes to 1.5 GHz so it my be oscillating at a higher frequency. The power supply is solid and quiet. Question  What should I see on a terminated LNA that is working right? Jim, California The Doctor Responds: First off, Jim, there are no dumb questions. Dumb means mute, and since you're asking the question, you're obviously not that. So, asking a question to which you don't know the answer is not dumb, but rather, wise. The output of any properly terminated amplifier is simply broadband noise. The power level of that noise equals the input noise power, amplified by the amplifier's gain. The input noise power is in turn the thermal noise generated by the terminating resistor, added to the internal noise of the amplifier (that is, its Noise Figure or Noise Factor). So, let's calculate: As a first order approximation, let's consider the amplifier's noise figure to be near zero. That is, its internally generated noise is negligible  it is a Low Noise amplifier, after all. So, all we have to do now is calculate the noise generated by your dummy load resistor. (Note that, in this context, dumb is appropriate...) Let's consider that load resistor to be a thermal black body. Boltzmann's Law says its noise power (in watts) equals kTB. In this equation, k is Boltzmann's Constant (1.38 x 10^23 Joules/Kelvin). T is the physical temperature of the black body, in Kelvins (for lab temperature, you can assume 300K). And B is the bandwidth in which the noise power is being measured, in Hz (that is, cycles per second).
Invoking unit analysis, we can prove that the Boltzmann equation is dimensionally consistent: kTB = (Joules/Kelvin) x (Kelvins) x (Cycles/Sec) Now, since you're measuring noise with an HP 8484 power sensor, whose passband is 10 MHz to 18 GHz, you might assume the bandwidth B to use in this calculation to be about 18 GHz. But, remember that the power sensor is going to be placed at the output of an amplifier with a much more modest bandwidth. Thus, the only part of the load resistor's noise power that counts is that part within the LNA's passband. Let's say your LNA passes frequencies from 1.3 to 1.7 GHz. That's a 400 MHz bandwidth, which is what we'll use for B in Boltzmann's Equation.
OK, let's calculate. Noise power Pn (coming out of the load resistor, in the amplifier's passband) is kTB Pn = kTBConverting to logarithmic measure, that's a power level of 88 dBm. This is the noise power that gets amplified by your LNA. Your LNA has 28 dB of gain, so the 88 dBm of noise, after being amplified, comes out of the amplifier at a level of 60 dBm. OK, now the noise you're seeing on the power meter is 36 dBm, which is a whopping 24 dB stronger than the noise you should be seeing. That's a power level about 250 times higher than it should be. From this, I conclude that, yes, your amplifier is probably oscillating. How's that for a long answer to a simple question? My main point is, the noise power coming out of a properly operating amplifier is entirely calculable (and, now, you know how to calculate it). Editor's Note: Dr. SETI thanks Kevin Murphy, ZL1UJG, for pointing out a glaring mathematical error in an earlier version of this column.

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