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Is 100Mhz enough? (calculations + charts included)

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pepelevamp:
TLDR: Is the 100MHz fast enough for my project? Will I get sloppiness?

Hello friends.
You may know me from such threads as https://www.eevblog.com/forum/testgear/noob-scope-like-the-tds-2024b where I'm deciding on a scope. Well, I'm stuck between two scopes.

One scope is 200MHz 2ch, the other scope is 100MHz 4ch. I want the 4 channels, but I am concerned if 100MHz is enough for my project.

I'll give you the details of what I'm trying to view in the scope and the actual scope so you can see if it'll work.
 
I wish to sample a 20,000Hz sine wave made up of 256 segments. An 8-bit DAC, unsmoothed.
I need to see each of the 256 digital segments as clearly as I can. Eg, the more squarey the better.

20,000Hz * 256 = 5,120,000Hz.

Since I'm wanting to view square waves, I am aware that its a game of 'how many upper harmonics of my fundamental can the scope see? enough to make it squarey?'.
I am aware that 100,000,000Hz is in the neighborhood of 19x my 5.1MHz fundamental.

But I know that scopes roll off near their upper bandwidth limit and I am concerned I may be in for a shit sandwich.


Attached is a chart showing a square wave (perfect,red) at the granularity I want for my project. I basically need to see square waves that sharp in the scope. My teensy will be generating them. That part is fine.

I couldn't low-pass using desmos, but I thought I would construct the square wave out of harmonics available up to 25MHz, with the idea that near 50MHz the scope will be rolling off.
The blue line is sorta what I'd accept as passable. I just need to see it in steps, discretely. I dont want a sine. I know in real-life it wouldn't look like that - it'd be a blobby wave, but its just how I'm trying to estimate precision.

The scopes I am eyeballing are:
Siglent SDS1202X-E 200 Mhz, 2 Channels
Siglent SDS1104X-U 100 Mhz,  4 Channels.


Please excuse the crudity of the chart - I didn't have time to make it to scale or paint it.



SDS1202X-E
https://siglentna.com/product/sds1202x-e/
Key Features

* 200 MHz Bandwidth
* 1 GSa/s Real-Time Sampling Rate
* 14 MPts Waveform Memory
* 500 uV/div Sensitivity
* Maximum waveoform capture rate: 100,000 frames / second (Standard mode), 400,000 frames / sec (Sequence mode)
* Serial bus decode & trigger: standard
* Digital trigger provides low jitter
* Intensity-Graded display / Color-Temperature display mode
* Video triggering / HDTV
* Cursors * Measurement functions
* USB and LAN interfaces
* 7″ (diagonal) display
* Sequence trigger mode
* History function
* Secure erase feature


-----------



SDS1104X-U
https://siglentna.com/product/sds1104x-u/
 100 MHz bandwidth
 Real-time sampling rate up to 1 GSa/s
 Record length up to 14 Mpts
 Serial bus triggering and decoder supports protocols I2C, SPI, UART, CAN, LIN
 Advanced measurements on full memory (14 Mpts)
 Large 7-inch TFT-LCD display with 800 * 480 resolution




gf:

--- Quote from: pepelevamp on January 21, 2022, 12:23:49 pm ---I wish to sample a 20,000Hz sine wave made up of 256 segments. An 8-bit DAC, unsmoothed.
I need to see each of the 256 digital segments as clearly as I can. Eg, the more squarey the better.

--- End quote ---

If you want to see each step, then I would worry more about the vertical resolution, than about 100 MHz bandwidth.
What is the reason why you think that you need to see each individual step? What kind of problem are you trying to investigate?

bdunham7:
The 8-bit DAC will give you 256 vertical levels, but what is the sample rate of the DAC?  Also what is the analog bandwidth of the output circuitry of the DAC?  You may have trouble seeing the 'squarey' signal as you might imagine it should be, but it won't be because of the bandwidth limitation of any of those scopes.

gf:

--- Quote from: bdunham7 on January 21, 2022, 01:40:41 pm ---The 8-bit DAC will give you 256 vertical levels, but what is the sample rate of the DAC?  Also what is the analog bandwidth of the output circuitry of the DAC?  You may have trouble seeing the 'squarey' signal as you might imagine it should be, but it won't be because of the bandwidth limitation of any of those scopes.

--- End quote ---

In the OP, the sample rate was said to be  5.12 MSa/s, and the DAC output was said to be "unsmoothed". So 100MHz is likey well sufficient. But I wonder how to resolve 256 step w/o missing codes, when the scope has only an 8-bit ADC? This could only work if the levels of the DAC and scope ADC were exactly aligned.

dmulligan:
If you can stretch your budget a little more there is the SDS1104X-E which can be hacked to 200MHz.

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