is it true, oscilloscope must reach at least 4x observed freq?

[Someone]

Please give us some examples where 2.5x is inadequate. 

Please provide the band limited signal source that has zero energy above the measurement frequency and I'm sure it would be difficult.

I'll take that as a no.

Its not some simple every situation works at 2.5x or everything is fine

No, but in the real world there are some very simple cases that fail below 2.5x. 2.5x is a good starting point.

FWIW: I was observing the AM modulation effect below 2.5x using a hardware reconstruction filter.

Again, this can keep going around. You stick with 2.5x as the magic figure yet with none of the other simultaneous conditions/requirements specified or quantified. Complete nonsense. If you want to talk about 2.5x sample rate vs frequency being some accurate or significant number, then you need to work through the rest of the maths that justifies that. "hardware reconstruction filter" says nothing of its form/length/characteristics and is something that is usually undocumented in an oscilloscope.

Observing something which looks "ok" to you, is not quantifying anything. When you are the one being so insistent on 2.5 as some magic quantification. 2.5x is a massive gross simplification that looks ok in most cases for a single frequency sine wave.

[Fungus]

When you are the one being so insistent on 2.5 as some magic quantification.

Me? I'm not the only one. Rigol/Siglent/etc. have been building it into their oscilloscopes for many years and people are happy with the results.

What number would you suggest as a workable compromise for building real devices?

[Someone]

When you are the one being so insistent on 2.5 as some magic quantification.

Me? I'm not the only one. Rigol/Siglent/etc. have been building it into their oscilloscopes for many years and people are happy with the results.

What number would you suggest as a workable compromise for building real devices?

As I keep saying, there is no single figure. It depends on what the desired outcome/performance requirement actually is. These things can be quantified and discussed, but instead the shortcut/"rule of thumb" is shouted as some absolute (by you and others) who actually have no understanding of its basis. The short and oversimplified answer is easy to communicate, and is dominating the discussion. While the complex and actual answer is buried by the noise.

[BillyO]

Point made.  Too bad.

[EEVblog]

some people say, if I wanna observe 100MHz, I must use an oscilloscope that reaches at least 400MHz.

Technically not true, but a good rule of thumb. It depends on the front end bandwidth filter shape and the interpolation used. IIRC there is a Tek paper somewhere that goes through the math for x2.4 is the minimum or something for a gausian shape front end.

[The Electrician]

The Agilent DSO5054 does not have sin x/x interpolation.

It has. It says in the datasheet but not in the manual. It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip. BTW: I used to own an MSO7000A which is basically the same hardware platform as your DSO5054 so I have some hands-on experience with these models.

Post a link to said datasheet, please.

Here's what I get with a sine wave at the probe tip.  The scope didn't live up to the data sheet's promise: "It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip."

[Fungus]

Technically not true, but a good rule of thumb. It depends on the front end bandwidth filter shape and the interpolation used. IIRC there is a Tek paper somewhere that goes through the math for x2.4 is the minimum or something for a gausian shape front end.

I searched the Tek web site and found a couple of places where it says "2.5x":

eg. https://www.tek.com/en/documents/application-note/real-time-versus-equivalent-time-sampling

(see appendix for math)

This one says:

Code: [Select]

Oscilloscope Sample Rate > 2.5x highest frequency component of signal (For sin(x)/x interpolation)

Oscilloscope Sample Rate > 10x highest frequency component of signal (For linear interpolation)

So that explains the "x10" rule that the old fogies occasionally mutter around here when they see Rigols/Siglents - they were using 'scopes with linear interpolation(!) 

[gf]

... "It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip."

What was the timebase and sample rate for the screenshot?

Maybe the automatic interpolation is only available at a couple of fastest timebase settings, where the sample rate is already at maximum, so that the resolution in samples/div cannot be increased any more by increasing the sample rate.

(That's at least what my cheap Chinese scope does.)

[wasedadoc]

2.5x is a massive gross simplification that looks ok in most cases for a single frequency sine wave.

If the specific combination of sampling rate and reconstruction filter gives an acceptable result on that single frequency sine wave it will also give an acceptable result on any lower frequency single sine wave.  Then by the superposition principle it will also give an acceptable result on any combination of such sine waves.  That is any waveform which does not contain frequencies above that sampling rate divided by 2.5.

The 2x is the theoretical limit for perfect reconstruction of the original. As the sampling rate is decreased down towards 2x the reconstruction filter requirements for perfect reconstruction become more and more demanding. In practice a sampling rate of 2.5x is a good compromise between practically realisable filter complexity and accuracy of reconstruction.

The Nyquist limit (half sampling frequency) applies when the input signal can contain any frequencies up to that limit.  There are situations when the input signal spectrum is not continuous. For example has "gaps" such as monochrome TV signals where the energy is largely confined around integer multiples of the TV line frequency.  (Those gaps were used by the NTSC composite colour system by arranging that most of the energy of the modulated colour subcarrier is confined around n+0.5 multiples of the TV line frequency.)  In the case of non-continuous spectrum signals it is quite possible to employ sub-Nyquist sampling with the alias components folding back into the vacant areas.  And it is possible to unfold them later and reconstruct the original signal. 

[nctnico]

The Agilent DSO5054 does not have sin x/x interpolation.

It has. It says in the datasheet but not in the manual. It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip. BTW: I used to own an MSO7000A which is basically the same hardware platform as your DSO5054 so I have some hands-on experience with these models.

Post a link to said datasheet, please.

I'm pretty sure you can find that yourself. And yes, sin x/x is supported on the DSO5054 so either you found the 'sweet' spot where it doesn't work or your settings are incompatible. I don't recall my MSO7104A ever showing a signal like yours (I checked some of my old screenshots to be sure).

[Someone]

2.5x is a massive gross simplification that looks ok in most cases for a single frequency sine wave.

If the specific combination of sampling rate and reconstruction filter gives an acceptable result on that single frequency sine wave it will also give an acceptable result on any lower frequency single sine wave.  Then by the superposition principle it will also give an acceptable result on any combination of such sine waves.  That is any waveform which does not contain frequencies above that sampling rate divided by 2.5.

Cool, now go and read what the OP actually wrote. Nothing about single frequency sine waves and ideal sampling/reconstruction. Again I keep saying it, 2.5 is some vague compromise with unspecified criteria. What is actually important? amplitude accuracy? relative phase? waveform shape?

I interpret the OP's question as much more toward the balance of fundamental frequency of a clock/signal and the bandwidth limit of the scope, since both are expressed in MHz and nowhere is sampling mentioned.

So all this chest beating by people who want to talk about Nyquist (without actually pointing to how it applies to oscilloscopes and their antialiasing + reconstruction) is off topic, and in many points wrong. Band limited signals are pure imagination, they dont exist. Perfect antialiasing filters dont exist, any real sampled signal has errors that should be quantified if you want to start putting some limit on their effect.

[adam4521]

Yes, sin x/x on Agilent/Keysight only on short time bases/maximum sample rate. If there is any decimation going on (eg you are zoomed in on a longer capture) it will join the dots with straight lines.

[Fungus]

So all this chest beating by people who want to talk about Nyquist (without actually pointing to how it applies to oscilloscopes and their antialiasing + reconstruction) is off topic, and in many points wrong. Band limited signals are pure imagination, they dont exist. Perfect antialiasing filters dont exist, any real sampled signal has errors that should be quantified if you want to start putting some limit on their effect.

Practical experience has found a good balance: Sample at 2.5x the analog bandwidth of the oscilloscope's input circuitry and use sin(x)/x reconstruction to display it on screen.

It's good enough for Australians.

PS: Most DSOs can get double/quadruple the basic sample rate by limiting the number of enabled channels.

[EEVblog]

Oscilloscope Sample Rate > 10x highest frequency component of signal (For linear interpolation)

So that explains the "x10" rule that the old fogies occasionally mutter around here when they see Rigols/Siglents - they were using 'scopes with linear interpolation(!) 

I don't think so. The "old fogie x10 rule" started with the Tek TDS210, it was the first "real time" digital scope that looked and acted like an analog scope, and it had 1GS/s for 100MHz bandwidth and also SinX/x. So x10 kinda became the defacto standard that gave everyone the "warm fuzzy" that digital scopes were now fast enough to look and feel like a "real scope" when you turned on the sample dots and could see how many samples it was taking.

[EEVblog]

Cool, now go and read what the OP actually wrote. Nothing about single frequency sine waves and ideal sampling/reconstruction. Again I keep saying it, 2.5 is some vague compromise with unspecified criteria. What is actually important? amplitude accuracy? relative phase? waveform shape?

Remember that the input wave shape gets changed by the input bandwidth response of the scope front end. Different scopes and models have different input antialiasing filters and responses.
This is why the shape of the input filters matters in these dicsussions. Gaussian response is usually assumed unless otherwise specificed.

Tek mention a x5 rule here:
https://www.tek.com/en/documents/primer/evaluating-oscilloscopes

[EEVblog]

The Tek x2.5 reference with the math explained for Sinx/x:
https://www.tek.com/en/documents/application-note/real-time-versus-equivalent-time-sampling

[nctnico]

Cool, now go and read what the OP actually wrote. Nothing about single frequency sine waves and ideal sampling/reconstruction. Again I keep saying it, 2.5 is some vague compromise with unspecified criteria. What is actually important? amplitude accuracy? relative phase? waveform shape?

Remember that the input wave shape gets changed by the input bandwidth response of the scope front end. Different scopes and models have different input antialiasing filters and responses.
This is why the shape of the input filters matters in these dicsussions. Gaussian response is usually assumed unless otherwise specificed.

Gaussian response is long gone. The typical anti-aliasing filters are much steeper. If you want a Gaussian response, then you'll need to set the bandwidth limiter. IMHO this is one of the reasons higher end scopes have multiple bandwidth settings so the user can choose to have maximum bandwidth or a slow (first order) roll-off.

[tggzzz]

Cool, now go and read what the OP actually wrote. Nothing about single frequency sine waves and ideal sampling/reconstruction. Again I keep saying it, 2.5 is some vague compromise with unspecified criteria. What is actually important? amplitude accuracy? relative phase? waveform shape?

Remember that the input wave shape gets changed by the input bandwidth response of the scope front end. Different scopes and models have different input antialiasing filters and responses.
This is why the shape of the input filters matters in these dicsussions. Gaussian response is usually assumed unless otherwise specificed.

Gaussian response is long gone. The typical anti-aliasing filters are much steeper. If you want a Gaussian response, then you'll need to set the bandwidth limiter. IMHO this is one of the reasons higher end scopes have multiple bandwidth settings so the user can choose to have maximum bandwidth or a slow (first order) roll-off.

Personally I like having the option to turn off interpolation and simply see dots representing samples.

[The Electrician]

The Agilent DSO5054 does not have sin x/x interpolation.

It has. It says in the datasheet but not in the manual. It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip. BTW: I used to own an MSO7000A which is basically the same hardware platform as your DSO5054 so I have some hands-on experience with these models.

Post a link to said datasheet, please.

I'm pretty sure you can find that yourself. And yes, sin x/x is supported on the DSO5054 so either you found the 'sweet' spot where it doesn't work or your settings are incompatible. I don't recall my MSO7104A ever showing a signal like yours (I checked some of my old screenshots to be sure).

The only data sheet I can find is: https://www.keysight.com/us/en/assets/7018-08449/data-sheets/5989-6110.pdf

It doesn't say "It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip."  Why is there no mention of an exception where this doesn't work; and I certainly wouldn't call a failure to perform as claimed a "sweet spot".

The data sheet I found says on page 13: "Sinx/x interpolation (single shot BW = sample rate/4 or bandwidth of oscilloscope, whichever is less) with vectors on and in real-time mode".  It doesn't say a word about linear interpolation, which I've demonstrated that the actual oscilloscope can do.  If the scope can do both, why don't they mention both?  Perhaps the mention of "Sinx/x interpolation" was something they intended to do when the data sheet was written, but they chose not to include in the actual hardware when it came time meet a deadline and get something to market.

If you don't post a link to a data sheet that says "It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip.", your credibility is zero.  You're claiming something you haven't backed up.

Then there is the user manual: https://www.keysight.com/us/en/assets/9018-01896/user-manuals/9018-01896.pdf

Which says on page 187: "When enabled, Vectors draws a line between consecutive waveform data points."  No mention anywhere of sin x/x.

And there is the performance of an actual DSO5054 which I show in Reply #80

[Fungus]

Personally I like having the option to turn off interpolation and simply see dots representing samples.

Some people even turn the screen persistence way up then enable dot mode and pretend they can see the real signal building up on screen. 

[gf]

Some people even turn the screen persistence way up then enable dot mode and pretend they can see the real signal building up on screen. 

If the fundamental frequency is not an exact integral fraction of the sample rate and if the trigger point is interpolated between the adjacent samples, then it is not impossible.

[tggzzz]

Personally I like having the option to turn off interpolation and simply see dots representing samples.

Some people even turn the screen persistence way up then enable dot mode and pretend they can see the real signal building up on screen. 

Why "pretend"? In some cases that is what happens.

Linear (r higher order) interpolation is a fiction designed to help those that never mentally completed "join the dots"  puzzles as a kid

[Someone]

Cool, now go and read what the OP actually wrote. Nothing about single frequency sine waves and ideal sampling/reconstruction. Again I keep saying it, 2.5 is some vague compromise with unspecified criteria. What is actually important? amplitude accuracy? relative phase? waveform shape?

Remember that the input wave shape gets changed by the input bandwidth response of the scope front end. Different scopes and models have different input antialiasing filters and responses.
This is why the shape of the input filters matters in these dicsussions. Gaussian response is usually assumed unless otherwise specificed.

Gaussian response is long gone. The typical anti-aliasing filters are much steeper. If you want a Gaussian response, then you'll need to set the bandwidth limiter. IMHO this is one of the reasons higher end scopes have multiple bandwidth settings so the user can choose to have maximum bandwidth or a slow (first order) roll-off.

Gaussian analog anti-aliasing filters aren't disappearing (as they are cost effective), the work is being shifted to digital. Tek front end ASIC comparison below.

A modern scope has multiple different sampling rates with all sorts of filtering going on along the chain, its far removed from the simple models people keep trying to attach to it.

[David Hess]

If you want to see anything other than the fundamental sine wave component of the 100 MHz signal, then the oscilloscope bandwidth needs to be much higher to cover the harmonics.  Otherwise a 100 MHz oscilloscope viewing a 100 MHz signal will only display the 100 MHz fundamental sine wave component, and possibly with a 3dB amplitude error.

FTFY.

It need be noted label BW can be substantially different from actual -3dB BW as is the case with the 100 MHz rated SDS2104X Plus which the 1st we received I tested with 3 yes 3 signal sources to convince myself the ~185 MHz result was actually real !

Some oscilloscopes are weird.  Even old high bandwidth instruments often break the Gaussian response -3dB rule, and the 0.35 rule does not apply to them either.  For other instruments, the specified bandwidth was more of a guideline than a rule, and the instrument was *at least* that fast.  Modern examples of weirdness include the Rigol 1000Z series where full power bandwidth varies with the V/div setting.

Supporting that result is they are also supplied with 200 MHz probes.

Tektronix specified their oscilloscopes for -3dB bandwidth *at the probe tip*, so a 200 MHz Tektronix oscilloscope with a 200 MHz Tektronix probe yielded 200 MHz.  At least for them, the probe bandwidth specification represents the highest frequency which the probe will reproduce faithfully and not the -3dB bandwidth.

As pointed out by tggzzz, a bandwidth limited signal can be reconstructed with a sampling rate greater than twice the bandwidth no matter where in the frequency spectrum it is, within the bandwidth of the sampler.

In theory? Yes.

In practical terms? Not so much. The reconstruction filter would become very unwieldy as you approach Nyquist.

In a subsampling bandpass application, the input signal bandwidth is tightly constrained by a high selectivity bandpass filter, so the difficulty of reconstruction is considerably relaxed.  Ideally aliasing products will be close to or below the noise floor.

ie. I've sat a potentiometer and manually dialed a frequency where I no longer observe the AM modulation effect mentioned earlier. The frequency I ended up with was right there in the 2.5x ballpark. Maybe it could have been 2.4x but it's definitely not as low as 2.2x.

2.5x may be a "non-specific/vague figure" but it works in practice.

I find 2.5x times to be optimistic when sin(x)/x reconstruction is required.  The effect you mention can be modeled as the result of non-linear mixing between a pure sine wave and the sampling clock, with aliasing of some of the mixing products.  The reconstruction then has multiple solutions and each pass shows one of those solutions.  When a fast edge is applied, the same thing happens even when the reconstruction filter correctly filters the higher frequency aliasing products because the mixing products are still there close to the aliasing frequency.  I find the result annoying in the extreme.

The solution is to use a faster sample rate.  Sometimes there is no substitute for high bandwidth and fast sampling rate.

This scope is old enough that it doesn't have sin x/x interpolation.  As switchabl mentioned the older Agilent scopes typically use linear interpolation, and it isn't at all useless.  If your choices are dot mode and linear interpolation, linear interpolation is just fine.  When your signal is oversampled, you can't tell the difference anyway.  This scope has rated max sample rate of 4 Gsa/s, and analog bandwidth of 500 MHz, so it's 4 times oversampled at rated bandwidth, and much more than that for lower bandwidth signals.

For Tektronix you have to go back to 1990 and the 2232 series of DSOs for the last of their DSOs which did not support sin(x)/x reconstruction, and those are what I consider to be the first "modern" DSOs, at least from Tektronix.  Their 2430 series first made in 1986 had sin (x)/x reconstruction and I think all of their instruments after that, other than the 2232 series, did.

Honestly I have never missed sin(x)/x reconstruction on the 2230 and 2232.  Usually equivalent time sampling removes the need, and cases where single shot acquisitions need to be made with full bandwidth signals are rare.

[radiolistener]

some people say, if I wanna observe 100MHz, I must use an oscilloscope that reaches at least 400MHz.

Is it true?

No, for 100 MHz signals, the oscilloscope bandwidth should be about 1 GHz (10 times).

This is because you're needs to see at least 10 harmonics of square wave in order to see waveform distortions. Otherwise you will see just a sine and cannot see signal distortions and glitches.

You can still use 400-600 MHz bandwidth oscilloscope, but it's ability to see 100 MHz waveform details will be very limited. For example, you can see if signal exists, and can see if it's clean sine. But cannot see if it has glitches or distortions.

Note, that oscilloscope bandwidth is applied for a clean sine wave. If you're dealing with other kind of waveform it consists of high order harmonics and oscilloscope should be able to see it, otherwise your scope input will works like low pass filter and all what you can see is just a 100 MHz sine despite the fact that signal waveform is actually square wave, triangle or other type.