Originally posted Feb 28, 2015
Intuition is powerful but if you don’t frame questions well it can mislead you
Contrary to the popular stereotype, good engineers are creative and intuitive. Indeed, these characteristics are essential tools for successful engineering.
I have great respect for the power of intuitive approaches to problems, and I see at least two big benefits. First, intuition can gather diffuse or apparently unrelated facts that enable exceptionally powerful analysis. Second, it often provides an effective shortcut for answers to complex questions, saving time and adding efficiency.
Of course, intuition is not infallible, and I’m always intrigued by its failure. It makes sense to pay attention to these situations because they provide lessons about using intuitive thinking without being misled by it. Two of my favorite examples are the Monty Hall Problem and why mirrors appear to reverse left and right but not up and down.
I’d argue that a common factor in most intuition failures is not so much the reasoning process itself but the initial framing of the question. If you start with a misapprehension of some part of the problem or question, even a perfect chain of reasoning will fail you.
As a useful RF example, let’s look at an intuition failure in “sub-kTB” signal measurements. Among RF engineers, kTB is shorthand for -174 dBm/Hz*, which is the power delivered by a 50Ω thermal source into a 50Ω load at room temperature. It should therefore be the best possible noise level—or, more accurately, noise density or PSD—you could obtain in a signal analyzer that has a perfect 0 dB noise figure.
Not surprisingly, many engineers also see this as the lowest possible signal level one could measure, a kind of noise floor or barrier that one could not see beyond or measure beneath. As a matter of fact, even this level should not be achievable because signal analyzers contribute some noise of their own.
This intuitive expectation of an impenetrable noise floor is logical but flawed, as demonstrated by the measurement example below that uses Keysight’s Noise Floor Extension (NFE) feature in a signal analyzer. Here, a multi-tone signal with very low amplitude is measured near the signal analyzer’s noise floor.
The noise marker shows that the effective noise floor of the measurement (blue) is actually below kTB after NFE removes most of the analyzer’s noise. The inset figure shows how a signal produces a detectable bump in the analyzer’s pre-NFE noise floor (yellow), even though it’s about 5 dB below that noise floor.
I’ve previously described NFE, and for this discussion I’ll summarize by saying that it allows some analyzers to accurately estimate their own noise contribution and then automatically subtract most of it from the measurement. The result is a substantial improvement in effective noise floor and the ability to separate very small signals from noise.
While it is indeed correct that kTB is a noise floor that cannot be improved, or even matched in an analyzer, the error in intuition is in associating this in a 1:1 fashion with an ultimate measurement limit. As discussed previously, signal and noise power levels—even very small ones—can be reliably added or subtracted to refine raw measurement results.
kTB and related noise in analyzers are phenomena whose values, when averaged, are predictable when the measurement conditions and configuration are known. Consequently, subtracting analyzer noise power can be seen as adding information to the measurement process, in turn allowing more information to be taken from the measurement result.
OK, so measuring below kTB is perhaps more of a parlor trick than a practical need. However, an intuitive understanding of its possibility illuminates some important aspects of making better RF measurements of those tiny signals that so frequently challenge us.
* You may instead see the figure -177 dBm/Hz for kTB. This refers to a slightly different noise level measurement than that of a spectrum or signal analyzer, as explained at the link.