Re: [Phys-l] Oscilloscope bandwith demonstration

[brian whatcott <betwys1@sbcglobal.net>]

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