Fun with digital scope

[bob91343]

I am lucky to have some nice gear.  I was trying to learn to use my Tektronix 2440 digital scope.  I thought it would be interesting to create an AM signal by multiplying an audio signal with an rf signal.

So I put 1 kHz into one channel and 5 MHz into the second vertical channel and selected MULT.  What I got on the screen was confusing, to say the least.  So I pressed the AUTO button and let the scope decide for itself how to display the result.

It was laughable.  Such nonsense I would never be able to create myself but the scope essentially went mad and showed three traces that made no sense to me.

Has anyone tried this?  Can it be made to work?  Or is multiplying not what I want to do?

[ataradov]

It would help of you show some captures or pictures.

But what I suspect is that is it hard to observe 1 kHz and 5 MHz on the same time scale, so if you set your time scale to be such that you can see 1 kHz envelope, then 5 MHz may be aliased and not display correctly.

[xmo]

In a digital oscilloscope, multiply is a mathematical operation where the trace data values are multiplied point by point and the result displayed.

It's quite useful when you want to see a power result where one channel input represents voltage and the other represents current.

Keep experimenting.  It would be interesting to set up a modulated waveform with a dual channel waveform synthesizer and see how the digital scope shows the modulated envelope.

[Grandchuck]

See attached:

Direct coax connection to the DS2202 from SDG 2122X, both outputs sine, 1 kHz @ 2Vpp and 5MHz @ 3 Vpp.  Math AxB

[Grandchuck]

Some fiddling for a nicer display of the double side band result and the two generator signals.

[xmo]

Bob.  Did you try trace addition?  That might be interesting too.

When you have had enough fun playing with your scope, mosey back over to ARF and tell Paul what's wrong with his RCA128.

[radiolistener]

I thought it would be interesting to create an AM signal by multiplying an audio signal with an rf signal.

So I put 1 kHz into one channel and 5 MHz into the second vertical channel and selected MULT.  What I got on the screen was confusing, to say the least.

This is not AM. This is DSB, you're forgot to add carrier to the result of multiplication.

AM modulation:
y(t) = cos(2πf_ct) + μ cos(2πf_mt) ∙ cos(2πf_ct)
      = cos(2πf_ct) + 0.5μ cos[2π(f_c − f_m)t] + 0.5μ cos[2π(f_c + f_m)t]

DSB modulation:
y(t) = cos(2πf_mt) ∙ cos(2πf_ct)
      = 0.5 cos[2π(f_c − f_m)t] + 0.5 cos[2π(f_c + f_m)t]

where
μ = modulation index [0..1]
f_c = carrier frequency
f_m = message frequency

In order to get AM with 1000 kHz carrier, 1 kHz message and modulation index 100%, you're needs to sum 3 signals:
1) 1000 kHz
2) half amplitude 999 kHz
3) half amplitude 1001 kHz

Another way is to multiply carrier with message and then add carrier.

Here is how AM 1000 kHz / 1 kHz signal looks on a digital oscilloscope (Siglent SDS1102X):

[radiolistener]

And here is DSB modulation of 1000 kHz carrier with 1 kHz message obtained with MATH multiply function on digital oscilloscope (the same SDS1102X) from two sources 1000 kHz and 1 kHz taken from PSG9080 signal generator:

As you can see, DSB signal has a little different shape than AM.

[bob91343]

Good show, guys!  Those are the waveforms I was seeking.  I still don't know how to obtain them.

When I use an amplitude modulated signal generator, I get the expected display on my analog scope.  Getting it on a digital scope is an entirely different matter, and I don't know how to do it.

[rf-loop]

Good show, guys!  Those are the waveforms I was seeking.  I still don't know how to obtain them.

When I use an amplitude modulated signal generator, I get the expected display on my analog scope.  Getting it on a digital scope is an entirely different matter, and I don't know how to do it.

Yoy told you have Tek 2440.
This is problem number 1.
Why?
Because its record length is 1024 samples aka 1k acquisition memory length.

These modern digital scopes have least thousand fold amount.

Take example.
Lets define imagined example. Scope have 1000 points memory, and display have 10 horizontal div and this memory length is equal with this display width. Now if your sample memory length is 1000 samples and your horizontal speed (aka timebase) is set so that this whole memory length take example 5ms  (5 cycle 1kHz modulating signal).
In this case your timebase is set for 500us/div.
Now I ask what is sampling speed. Yes Tek 2440 max sampling speed is 500MSa/s (without talking about how they did it with using CCD).

5ms and 1000 samples. Result is 200kSa/s. With this "Nyquist limit" is 100kHz.

Now if your modulated carrier is example 1MHz it is ten times higher than Nyquist limit.

With your scope you can try set carrier freq example to 50kHz and modulate it it using 1kHz.
This you can look with your scope so that it start somehow look as conventional AM shape.

Just this short memory was big problem in old digital scopes.

(I have old times owned and used just also this Tek 2440 model. But it was so long time ago I do not remember anymore all details... somehow I think it have 50% memory lenght on display and 25% overlap in both sides... but now this my memory may be messed with what ever other old times digitals...

Think about it...
You need keep sampling frequency, in theory, least 2 (in practice usual modern DPO with Sinc interpolation, 2.5x) times higher than frequency components in your signal under test.

If need look normal AM signals this 2440 is nearly or fully hopeless. Even when it is still nice well made scope for some  kind of use. Tens of years ago even with it and 2430/A we did many "miracles".


 

[bob91343]

Thank you rf-loop; you have explained it nicely.  Next opportunity I will try modulating 5 kHz with 1 kHz and see what happens.

[Ground_Loop]

I got this on my 2440. Multiply 1KHz with 1MHz. Needs to be viewed with ch 1 & 2 off and acquisition mode in envelope.

And AM modulation

[bdunham7]

I got this on my 2440. Multiply 1KHz with 1MHz. Needs to be viewed with ch 1 & 2 off and acquisition mode in envelope. (Attachment Link)

And AM modulation

(Attachment Link)

What happens when you try to look at the carrier, say at 500ns/div?

[Ground_Loop]

I get this in envelope mode


And in normal mode just the carrier

[bdunham7]

When I use an amplitude modulated signal generator, I get the expected display on my analog scope.  Getting it on a digital scope is an entirely different matter, and I don't know how to do it.

I think Groundloop has that figured out.  The special 'envelope' acquisition mode, which is a modified peak-detect, will work at the modulation frequency.  I'm not sure if or how you can display the typical AM modulation signal at the carrier frequency.

To generate an AM-modulated signal by multiplication, you have to add a DC bias equal to the amplitude of the carrier.  If you look at the post from radiolistener he refers to needing the 'add the carrier back in', this amounts to the same thing.  An AM signal at 100% modulation goes from 0% to 200% of the base carrier amplitude--it never goes negative.   Negative would flip the phase of the carrier 180 degrees.

[Ground_Loop]

With a 0.5 VDC positive offset on the modulating frequency I did get a good AM trace by multiplying 1 and 2
.

Thanks BD7 I learned something today.

[bob91343]

Wow this is great!  Now I have to try it.   But I thought I already did this.

More details please.  I put 1 kHz into Ch1 and 1 MHz into Ch2.  I shut off display of both channels.  Go into MULT.  Okay so far?

And where do I fall apart due to insufficient memory depth?

[Ground_Loop]

You need to use the envelope mode in the acquisition menu. See attached





You'll also need to add a DC offset of about a half volt to the 1KHz signal.
Trigger off the 1KHz signal.

[bob91343]

Do I need an actual offset to the signal, or just move the trace position?

I got an interesting display but it's not right yet.

[bdunham7]

Do I need an actual offset to the signal, or just move the trace position?

I got an interesting display but it's not right yet.

You need the actual offset, moving the trace does not affect the multiply operation and you can't have the modulation signal going negative if you want to simulate an AM signal.

[rf-loop]

I got this on my 2440. Multiply 1KHz with 1MHz. Needs to be viewed with ch 1 & 2 off and acquisition mode in envelope. (Attachment Link)

And AM modulation

(Attachment Link)

Naturally this can do. Lot of old digital scopes have peak detect / envelope mode implemented way or other, just because it is mandatory due to extremely acquisition memory what drops samplerate down with slow timebases. (And Tek2440 have some special nice things, in its time it was amazing tool for work. Also its internal working principle is (was in that time) brilliant)
 But carrier loosed depending its freq and mr Nyquist and Shannon. If stop and try look details - game over. Depending different old digital scope models how zoom/2nd timebase works if you need zoom in to carrier, no way due to undersampling - aliasing - again - game over. And "envelope" mode or "peak detect" mode do not help here anything. But, yes AM mod envelope figure can see. But if look inside there is no carrier.  Also this kind of solution with old dso's are many times in big troubles with trigger if modulating frequency change fast, depending available trigger features.

Today many modern DPO can easy go down to example 10ms/div and still whole HF band carrier freq range do not alias.
Also modern scopes trigger engines are far better than these old ones - in most cases. Example for trig rock solid to fast and large scale variable AM modulating frequency and modulating depth.


But yes, this all meet this thread topic, "Fun with digital scope" and there is possible to watch wide range of amazing phenomena and amazing patterns on the oscilloscope screen  -  when this is wanted.

[bdunham7]

But carrier loosed depending its freq and mr Nyquist and Shannon.
Today many modern DPO can easy go down to example 10ms/div and still whole HF band carrier freq range do not alias.
Also modern scopes trigger engines are far better than these old ones - in most cases. Example for trig rock solid to fast and large scale variable AM modulating frequency and modulating depth.

I don't see how Nyquist limits apply here.  In envelope mode, the peak detect circuits effectively eliminate the carrier, so there's no aliasing even when the sweep rate is slow. Ground_Loop clearly shows the 1kHz envelope without any ill effects.  And if the sample rate was an issue under different circumstances, the scope has the ETS (REPET) mode that should eliminate any aliasing well past the bandwidth limit of the scope.

Here is my ancient Tek 2221 (20MSa/s, 60MHz) displaying 1MHz modulated to 80% by 1kHz, and then at 20MHz (obviously "over Nyquist") by 1kHz.  The 20MHz ones were a bit touchy to set up as you need just the right acquisition mode and setup, and the displays look bad at first and take form over time.  The secret weapon is that on these hybrid scopes, you can set them up in analog and then go digital.

[rf-loop]

But carrier loosed depending its freq and mr Nyquist and Shannon.
Today many modern DPO can easy go down to example 10ms/div and still whole HF band carrier freq range do not alias.
Also modern scopes trigger engines are far better than these old ones - in most cases. Example for trig rock solid to fast and large scale variable AM modulating frequency and modulating depth.

I don't see how Nyquist limits apply here.  In envelope mode, the peak detect circuits effectively eliminate the carrier, so there's no aliasing even when the sweep rate is slow. Ground_Loop clearly shows the 1kHz envelope without any ill effects.  And if the sample rate was an issue under different circumstances, the scope has the ETS (REPET) mode that should eliminate any aliasing well past the bandwidth limit of the scope.

Here is my ancient Tek 2221 (20MSa/s, 60MHz) displaying 1MHz modulated to 80% by 1kHz, and then at 20MHz (obviously "over Nyquist") by 1kHz.  The 20MHz ones were a bit touchy to set up as you need just the right acquisition mode and setup, and the displays look bad at first and take form over time.  The secret weapon is that on these hybrid scopes, you can set them up in analog and then go digital.

But, perhaps my poor language or what ever...  there was now misunderstood.
Sampling speed is under Nyquist. But due to envelope mode carrier is loosed, of course and no aliasing visible on screen. But as I told you can not look carriage (of course),

but with more memory and enough sampling speed you can. With runtime zoom or stopping scope and zoom in. All is there.


But yep, fun images can do. 

[bob91343]

bdunham7 I don't quite get it.  Is the modulating signal the one that requires offset, or is it the carrier?  I am thinking the carrier, because the modulation can affect the carrier both increase and decrease.

Accomplishing this requires adding dc to the carrier signal without causing problems in the signal generator.  I guess a coupling capacitor and a battery or power supply.

[bdunham7]

bdunham7 I don't quite get it.  Is the modulating signal the one that requires offset, or is it the carrier?  I am thinking the carrier, because the modulation can affect the carrier both increase and decrease.

The modulating signal.  The carrier will swing from positive to negative and you want it to continue doing so.  However, if you multiply it by a negative number, you invert its polarity or flip its phase 180 degree, however you like to think of it.  So, you never want the modulation signal to be negative, thus the need for the DC bias.  I'm not sure the source for your modulating signal--on a cheapo modern DDS/AWG you can just set it directly.