interpreting 50MHz. signal on 25MHz. digital scope

[HAL]

No sooner do i purchase a 25MHz. scope, thinking 25MHz. will be adequate for my needs, i have a project that generates a 50MHz. clock.  When i test the 50MHz. signal, the 25MHz. scope recognizes the signal as 50MHz., but what should be a square wave is instead an attenuated triangle wave, that increases in size and takes on the shape of a square wave as i lower the frequency.  It looks just like you'd expect from a square wave that has gone through a slew rate limited op-amp.

Since i have always been lucky enough to use a 100MHz. scope until now, i'm not sure if this distortion is and artifact of the limitations of my 25MHz. scope, or if my clock circuit is causing the distortion because it is slew rate limited at 50MHz.

My question is - is this the typical response of a 25MHz. digital scope to a 50Mhz. square wave signal, or should i suspect the incoming clock circuit?  For now, i am presuming this is the scope being limited by its anti-aliasing filter, but i would appreciate confirmation before i rule out a problem with the clock circuit.

The scope is a "Circuit Test" brand - very much like a Rigol - couldn't find a Rigol in my area.

Thanks for your help.
   

[ejeffrey]

A first order lowpass filter looks like an integrator in the attenuation band.  The integral of a square wave is a triangle wave.  So I would say that your results can be explained by the small-signal behavior of the oscilloscope, although it is hard to make any definitive statements.  The important components of your square wave are at 150 MHz and 250 MHz in terms of identifying the waveform shape.  You are asking a lot of a 25 MHz scope to try and make any sense at all out of such high frequency signals.

[bruce273]

It wouldn't suprise me, the input to the scope would have an anti-aliasing low pass filter to prevent frequencies outwith the scopes bandwidth from confusing the input DAC. The filter  would smooth out a square wave to appear more triangle.

[HAL]

Thanks ejeffrey, bruce273.  I'm sure you're right.  Your point about the edges being up at 150-250MHz. is a good one.  I'm just glad the scope is able to do as well as it does at 50MHz.   

I'm going to go ahead and assume the clock circuit is working properly for now.

[ejeffrey]

It is actually quite a good sign for the scope.  It probably means the high frequency roll off is a well behaved single-pole filter over a reasonably wide bandwidth.  Incidentally, this is one reason why no matter how much you believe nyquist, you really want your scope to have 10*f_3dB sample rate rather than 3-5.  For good time domain behavior you want gradual filters that still leak power several octaves above the 3dB point, and you don't want aliasing of these components.

[alm]

Most mid end scopes and up use a 'brick wall' filter as opposed to a Gaussian roll-off, because it gives better transient response and flatness over the rated bandwidth. This allows them to use a lower sampling rate (eg. 3-5x the rated bandwidth). Agilent has an appnote about this.

Brick wall filters are more complex, however. Calculating the total system response is also harder. If all components are Gaussian, you can just use the square root of the sum of squared rise times, since the response of the system is also Gaussian. With a brick wall response, the solution is 'ask the manufacturer', since there's no universal solution and they don't publish the filter response.

[ejeffrey]

That only really works because they also use DSPs to compensate for the filter response. It also requires your rolloff to be well characterized.  So yes, this really only applies to ~ 1-2 GHz and lower scopes.  Beyond that, the cost of higher sample rates rises faster than the cost of the extra DSP and calibration necessary to get away with lower oversampling.

Coincidentally, I just got an email advertising the Tek DPO70000 scopes.  33 GHz and 100 GS/s, but only 5.5 bits effective resolution

[alm]

I wouldn't count on an ENOB more than 5.5 for low BW scopes either, especially near their rated bandwidth. They may claim that the ADC is 8 bits, but I would expect the ENOB to be more like 4 or 5 at say 50MHz or 100Mhz.

[Neilm]

  Incidentally, this is one reason why no matter how much you believe nyquist, you really want your scope to have 10*f_3dB sample rate rather than 3-5. 

Nyquist says you need more than 2*f samples to detect the presence of a signal frequency - not to measure it or determine any data from it.

Neil

[Zero999]

What sort of oscilloscope is it? You may be able to hack it to 50MHz or more.

You'll need a 500MHz 'scope or even more to accurately judge the rise/fall times of the signal. If all you want is the frequency and voltage there are simpler and cheaper ways to do this than an expensive 'scope, i.e. a frequency counter and a peak detector.

[Mechatrommer]

Incidentally, this is one reason why no matter how much you believe nyquist, you really want your scope to have 10*f_3dB sample rate rather than 3-5.

Nyquist says you need more than 2*f samples to detect the presence of a signal frequency - not to measure it or determine any data from it.
Neil

not just to detect the presence, but to completely/perfectly reconstruct it.

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

but as usual people argue. this is because nyquist theorem based on:
1) perfect sampling dt1=dt2=dt3...
2) no freq component higher than the said freq (in other word noiseless).
which never happen in reality, thats why 10*BW DSO sampling. and signal attenuation is another story. imho.

[ejeffrey]

Nyquist says you need more than 2*f samples to detect the presence of a signal frequency - not to measure it or determine any data from it.

To expand on what mechatrommer says:  The nyquist theorem states that you can perfectly reconstruct a band-limited signal from the sampled date.  The original nyquist theorem is based on analog sampling: the voltage measurements are assumed to be of infinite precision, and if so there is no error whatsoever in the reconstruction.  Even when you include quantization error it is no problem to dither such that the quantization noise is just white noise uncorrelated with your signal.

The problem with blindly applying nyquists theorem is that signals of interest are rarely band limited.  In fact, technically no band limited signal can convey information.  If you turn on a lamp, there is no way to represent that function as a band limited signal.  A band limited signal is automatically what is known as 'analytic' which means that in principle you can completely reconstruct the signal at all times from sufficiently detailed knowledge about the signal in the neighborhood of a single point (i.e., the value of the signal and all of its derivatives).  This is completely impractical in real life, but the difference is: a switch turning on can't be predicted even in principle from measurements done before the switch turns on.  All information carrying signals are non-analytic and not band-limited.

In practice, this is not really a problem -- our measurements don't extend for infinite time in either direction, and high frequency components fall off below the noise floor quickly for most interesting signals.  However, it means the sharper you make your filters -- the more they approach a 'brick wall' filter, the weirder your transient response becomes and the more effort you have to put in on the DSP side to display a proper looking waveform.

[Zero999]

Nyquist says you need more than 2*f samples to detect the presence of a signal frequency - not to measure it or determine any data from it.

To expand on what mechatrommer says:  The nyquist theorem states that you can perfectly reconstruct a band-limited signal from the sampled date.  The original nyquist theorem is based on analog sampling: the voltage measurements are assumed to be of infinite precision, and if so there is no error whatsoever in the reconstruction.  Even when you include quantization error it is no problem to dither such that the quantization noise is just white noise uncorrelated with your signal.

Detecting the phase difference between two signals is also a limiting. For example, a perfect two channel oscilloscope with a sample rate of 1GHz on both channels, can't discern the phase difference of two 500MHz signals to an accuracy any better than 180^o in real time.

EDIT:
A better solution of course would be to just use a phase comparator.