Another benefit of rules of thumb is that they provide a means to check the calculations done through other more complex means which may have errors. It is easy to slip a decimal point on a calculator or to miskey numbers. Having a rule of thumb estimate prevents serious errors (like failing to convert English to metric units for the 1999 doomed Mars Climate Orbiter). It would also have prevented the clerk at Taco Bell from charging me $325.00 for a single taco because that was what the register reported. Fortunately, he was amendable to reason and agreed he must have fat fingered the quantity as 100.
If the answer doesn't fit the rule of thumb, it is worth investigating why. Perhaps the circuit does support an alternative frequency or voltage - but be sure that you're doing it intentionally.
Before you guys go off on ripping me a new one, I might gently suggest that you read the "homework assignment" first.
These questions are taken from a series of rules of thumb columns I write for EDN. There are two important points about rules of thumb you might want to keep in mind.
1. rules of thumb should never be used for sign-off on a design. They are meant as a tool to quickly get you to an answer. The answer is not meant to be accurate. it is mean to be quick and give you a rough approximation. Read rule of thumb #0.
2. Every approximation, whether rule of thumb, or more accurate analytical approximation, has assumption behind it. I tell my grad students, and anyone else who will listen, never use an approximation without understanding the assumptions behind it, or when the approximation breaks down.
I tried to add in each rule of thumb posted, a little bit of the background of the origin of the rule of thumb and in what context it is useful.
In these examples, if you are trying to distinguish between a bandwidth of 1.67 GHz and 1.8 GHz, you are mis-using the term bandwidth. If this distinction is important in your application, don't use the single, approximate, figure of merit of bandwidth, use the entire spectrum of the signal.
This is the essence of the principle behind the value of a rule of thumb.
I think, and I "preach" this in my classes, that rules of thumb are one of a number of valuable tools to have in your tool box, along with approximations and numerical simulation tools. Use the appropriate tool depending on the accuracy with which you need the answer and how much effort you are willing to put in.
To a measurement guy like me, who's done both scopes and spectrum analyzers, I have to say that "data wins". A teacher who won't accept that they are wrong and another answer is correct doesn't deserve to be a teacher.
I would also argue that using 5x the clock rate for bandwidth is arbitrary. At Tektronix, we used 10x. If you used 3 dB as a bandwidth indicator, 3x would be sufficient (if I did my rough-approximation math right).
Since I'm on a roll here (I hope:)), I'll also comment that using the factor 0.35 is also somewhat arbitrary, although quite a bit less so. That value can be derived from integrating the rise time of a single-pole filter from 10% to 90%; I actually went through this exercise about 30 years ago to prove to myself where that number comes from. Not all pulses are determined by a single dominant pole, however, and not all rise times are defined from 10% to 90% (ECL used 20% to 80%). Real circuits will vary from this value, although usually not very far. I've seen measured values for digital scopes (from 15-20 years ago) where the conversion was more like 0.4 (although that value is from long-ago memory, so take it with a large grain of salt).
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