[Phys-l] RV: Oscilloscope bandwith demonstration

["CARABAJAL PEREZ, MARCIAL ROBERTO" <mcarabajalp@ypf.com>]

Hello:



I found an article that can explain the origin of my supposed rule



http://www.analog.com/library/analogDialogue/archives/41-03/time_domain.html



Immediately before the paragraph   Bandwidth the following sentence appears:.





'To start, the signal bandwidth and rise time will limit the scope choices. A general guideline is that scope and probe bandwidth should be at least three to five times the bandwidth of the signal being measured.'



So, coming from an accredited manufacturer, the article is worth being taken into account, beyond their possible lack of rigor. I believe that this is consistent with the observations that you have done in the sense that they establish a framework to define the range of validity of this practical 'rule'.







Thanks very much.

Rob





On 11/1/2011 4:35 PM, Roberto Carabajal wrote:

> Hello:

>

> I am looking for the math demonstrations of the practice rule that the

> bandwidth of an oscilloscope should be at least five times greater

> than the higher component of the tested signal, in order to have an error<= +/- 2% .

> It is more a math problem that an electronics problem.

>

> I would really appreciate if you can suggest me any notes o textbook

> about this.

> My best regards.

> Rob

> _______

In my understanding, this is a rule of thumb for analog scopes, and is not really amenable to mathematical validation, which is why you saw the unaccustomed sight of John Denker

  spinning his wheels on such a demonstration.

Taking this rule of thumb as saying something about the design trades executed when

  designing analog scopes (a field akin to designing wooden cart-wheels, of late) let me at least speak to your question.

  A run of the mill analog voltmeter can be expected to be accurate to

+- 3% more or less,

and it is the case that the difficulty of maintaining accuracy with dynamic signals is greater.



The issue is the gain constancy of a deflection amplifier across its bandwidth. You may

  recall that operational amplifier chips are often specified in terms of gain bandwidth

  product - which is the engineer's way of reminding users that it is easier to hold gain

  constant across bandwidth at reduced gains, so the "excess gain" so to speak can be

  fed back for linearity's sake in the frequency domain.



The modern armamentarium of ICs allows one to provide sensibly constant gain with

  frequency to quite extended bands, and one might even notice a little gain increase

  towards the band edge.     The gain roll off at the band edge is never

precipitous:

  all to nothing - though that ideal can be approached with digital signal processing.



In addition, the analog scope designers expected to provide visible tracing of a level

  change which was used to trigger that trace - in other words, the deflection path

  was to be provided with some delay, compared to the triggering path.



So finally, I should mention that users expect to keep the highest frequency of

  interest within the scope deflection amp passband, before the roll off onset.



You have a rule of thumb in mind that the bandwidth should cope with perhaps five times the frequency represented by the signals repetition time, at least, which is a different kettle of fish. I can mention briefly that the parameter of prime interest these days is sampling rate - and that applies to digital scopes.



Brian W



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