Products > Test Equipment
Trying to display bandwith via Math on Siglent SDS2k+/2kHD/800X HD
gf:
For a single impulse (differentiated edge) inside the FFT window, definitively use a rectangular window function.
If multiple periods of the pulse train are within the FFT window, you still need to use a non-rectangular windowing function. And you need to make sure that you have at least (say) 10 periods of the pulse train inside the FFT window to keep the amplitude error of the resulting comb teeth within the scalloping loss of the window function. A rectangular window is not suitable in this case. See attachment.
EDIT: With a huge number of FFT points, the leakage of the rectangular window no longer has such a strong effect as demonstrated, but the scalloping loss remains, and it is still worse than with a flattop window.
Martin72:
I found an application note by Lecroy that is enlightening for me, at least on the first three pages.
I'm slowly understanding more and more, it takes a while, but still. ;)
gf:
--- Quote from: Performa01 on March 19, 2024, 06:40:36 pm ---
SA44_Pulsetrain_1MHz_W1ns_RT500ps
--- End quote ---
@Performa01, I was thinking about that again.
The spectrum of rectangular impulses is not flat, but is expected to have a sinc-shaped roll-off. And the tapering of the edges introduces additional roll-off. So they are not well suited for an application that requires a flat stimulus spectrum (unless they are so narrow that the roll-off can be neglected -- but then they can no longer be generated by the AWG).
What do you think about using a train of sinc-like pulses instead of rectangular pulses? They are bandwidth limited (so they can be reproduced by an AWG based on Shannon-Nyquist reconstruction from samples), and they still have a flat spectrum up to a certain frequency (with a sharp roll-off beyond this corner).
Plots of two example pulses are attached, designed for a 950-1000MHz transition band and for a 1000-1250MHz transition band. According to the specs, I assume that the SDG7000A should be able to reproduce these waveforms well. [By the way, does the SDG7000A promise 0.3dB amplitude flatness up to 1GHz?]
Performa01:
--- Quote from: gf on March 24, 2024, 10:56:24 am ---What do you think about using a train of sinc-like pulses instead of rectangular pulses? They are bandwidth limited (so they can be reproduced by an AWG based on Shannon-Nyquist reconstruction from samples), and they still have a flat spectrum up to a certain frequency (with a sharp roll-off beyond this corner).
--- End quote ---
It certainly is a good idea and I have done a few experiments with this, as described below.
--- Quote from: gf on March 24, 2024, 10:56:24 am ---Plots of two example pulses are attached, designed for a 950-1000MHz transition band and for a 1000-1250MHz transition band. According to the specs, I assume that the SDG7000A should be able to reproduce these waveforms well. [By the way, does the SDG7000A promise 0.3dB amplitude flatness up to 1GHz?]
--- End quote ---
Thanks a lot for your effort again! The SDG7102A “promises” +/- 0.3 dB flatness up to 1 GHz, you can find an actual frequency response measurement (SDG7102A_1000MHz_-10dBm) attached.
This is for sine waves though; we cannot expect the spectrum of a pulse to be that accurate.
I had a quick go at it and found a pre-defined Sinc pulse amongst the built-in arbitrary waveforms. This is 32768 points though and the pulse width is some microseconds. Of course, I can downsample it, yet the shortest possible length is 64 points. At 2.5 GSa/s, the resulting frequency was much too high at ~39 MHz, yet I still did a first check with the SA:
SDG7102A_AWG_Sinc_64pts
This is the corresponding peak table:
1,39.071413 MHz,-15.08 dBm,0.000000 Hz,0.00 dB
2,78.128540 MHz,-15.39 dBm,39.057127 MHz,-0.32 dB
3,117.185668 MHz,-15.49 dBm,78.114255 MHz,-0.42 dB
4,156.271366 MHz,-15.38 dBm,117.199953 MHz,-0.30 dB
5,195.299922 MHz,-15.42 dBm,156.228509 MHz,-0.35 dB
6,234.357050 MHz,-15.49 dBm,195.285637 MHz,-0.42 dB
7,273.442748 MHz,-14.99 dBm,234.371335 MHz,0.09 dB
8,312.499876 MHz,-15.38 dBm,273.428463 MHz,-0.31 dB
9,351.557003 MHz,-14.72 dBm,312.485590 MHz,0.36 dB
10,390.642702 MHz,-14.80 dBm,351.571289 MHz,0.28 dB
11,429.699829 MHz,-14.60 dBm,390.628416 MHz,0.47 dB
12,468.728385 MHz,-14.61 dBm,429.656972 MHz,0.47 dB
13,507.814084 MHz,-14.80 dBm,468.742671 MHz,0.28 dB
14,546.871211 MHz,-15.11 dBm,507.799798 MHz,-0.04 dB
15,585.928338 MHz,-15.06 dBm,546.856925 MHz,0.02 dB
16,625.014037 MHz,-16.12 dBm,585.942624 MHz,-1.05 dB
17,664.071164 MHz,-15.14 dBm,624.999751 MHz,-0.07 dB
18,703.128292 MHz,-16.35 dBm,664.056879 MHz,-1.28 dB
19,742.185419 MHz,-15.12 dBm,703.114006 MHz,-0.04 dB
20,781.271118 MHz,-22.15 dBm,742.199705 MHz,-7.08 dB
It can be seen that the harmonics should be accurate to 0.5 dB up to at least 586 MHz. Generally, the pretty accurate odd harmonics up to 742 MHz are quite striking, just like the fact that even the 64 points sinc-pulse at 2.5 GSa/s can still produce such strong harmonics up to 742 MHz.
Of course, there is no point in trying to display bandwidth with a high frequency like 39 MHz. Even though it would have been tempting to generate my own version of a Sinc pulse, maybe getting the real pulse a little faster with still enough “padding” samples to achieve a reasonably low repetition frequency when played back, I’ve rather utilized the sequence-function of the AWG, by just adding 2436 samples of a zero signal to the 64 points Sinc.
With this, the time domain signal looks like this:
SDS6204_Pro_H12_Sinc_Pulse
The pulse width is 772 ps and the rise time should be around 360 ps (assuming ~230 ps rise time of the SDS6204).
With the padding, the pulse is now played back at a rate of 1 MHz at 2.5 GSa/s.
The result on the SDS800X HD is not too bad – certainly much better than all the previous attempts to measure its bandwidth using a pulse train.
SDS824X HD_FFT_Sinc_1MHz
This looks about right, including the cable reflections because of less than perfect impedance matching.
Martin72:
--- Quote ---The SDG7102A “promises” +/- 0.3 dB flatness up to 1 GHz
--- End quote ---
According to your picture, this is once again a typical siglent understatement.
Nice generator btw.... 8)
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