ADC Input Frequency Bandwidth and Sampling Frequency

I want an ADC that samples at 3GS/s.

That means for a Nyquist converter - SAR ADC - I can sample signals at a maximum bandwidth of 1.5 GHz.

I want to sample signals from 0-40 GHz - which determines my input bandwidth.

If I sample a signal at a rate lower than my input bandwidth, am I under samplng ?

Then I want to measure the SNDR/SFDR. I assume though I am going to get 3GS/S. I go to the first nyquist band - 0 to 1.5 GHz. I sweep the sampling clock to see what the maximum sampling is without 3dB degradation is. I try 2.5 GS/S, 2.75 GS/S and 3GS/S. I see that the 3G/S sweep over frequency degrades my SNDR/SFDR by 3dB versus the 2.5GS/S sampling clock.

Therefore, my best SNDR/SFDR is for 2.5GS/S and not 3GS/S.

Next, I want to determine the large signal or input bandwidth of my ADC. I sweep the input frequency of the signal over frequency and with the signal input at odd multiples of the nyquist zone, or here 2.5 GHz, since I determined my best sampling clock is 2.5 GS/S. So I sweep my input frequency over odd multiples of frequency, 0-40GHz - 0, 2.5, 5, 7.5, 10, 12.5, etc until 40 GHz. I also do this for a 3GS/S clock just to compare.

I see that I get SNDR/SFDR degradation of 3dB at a higher input bandwidth for the 2.5GS/S clock versus the 3GS/S clock. So, I use the 2.5GS/S clock - I can get 40 GHz of input bandwidth out of it.

So, my question here is, since I am sampling at 2.5 GS/S and my input bandwidth is up to 40 GHz, according to nyquist, the maximum bandwidth I can sample is 1.25 GHz.

But my input bandwidth is up to 40GHz.

I can have an input signal at 100 MHz, or 37.5 GHz or any others from 0-40 GHz since these fall in my ADC input bandwidth.

So am I under sampling the 37.5 GHz signal but not the 100 MHz signal ?

What is going on here ?

Can someone explain the difference between input bandwidth and sampling frequency and nyquist zones ?

I am confused.

I want an ADC that samples at 3GS/s. That means for a Nyquist converter - SAR ADC - I can sample signals at a maximum bandwidth of 6 GHz.

If your sampling is 3 GS/s then, not to cause signal aliasing, the maximum bandwidth is 1.5 GHz (and somewhat less given that you can't have a brick-wall filter that can remove all frequencies above 1.5 GHz).

I want to sample signals from 0-40 GHz - which determines my input bandwidth. If I sample a signal at a rate lower than my input bandwidth, am I under sampling ?

Yes, you are but, this is something that can be done, providing that the bandwidth of the signal is less than 1.5 GHz.

Your input BW is determined by hardware in the signal chain before the actual ADC input. You have to be able to adequately sample and hold the signal during the ADC sampling period.

So, my question here is, since I am sampling at 2.5 GS/S and my input bandwidth is up to 40 GHz, according to Nyquist, the maximum bandwidth I can sample is 5 GHz.

No, your maximum bandwidth of signal you can reproduce in the digital domain is 1.25 GHz.

But my input bandwidth is up to 40GHz. I can have an input signal at 100 MHz, or 37.5 GHz or any others from 0-40 GHz since these fall in my ADC input bandwidth.

With an input BW of 40 GHz you can't hope to "capture" anything much higher than this unless of course the roll-off of the BW is not too great. I mean, if it's a single order roll-off then a signal (for instance) at 100 GHz will be attenuated roughly 2.5 times. 100 MHz is a stroll in the park.

So am I under sampling the 37.5 GHz signal but not the 100 MHz signal ?

37.5 GHz will be under sampled but, if that signal is wholly contained in a BW of 1.5 GHz then you can capture the information should it be present.

Can someone explain the difference between input bandwidth and sampling frequency and Nyquist zones ?

Image from here. In the picture above, the input BW will extend all the way from DC to the "6th alias" where the desired (but BW limited) RF signal is.

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It shows how that RF signal can be bumped down into the baseband by under-sampling. Image from Beyond the first Nyquist zone by Texas Instruments - it looks like a good read to me. This is also relevant if the BW of your signal is too high (same TI document): -

You will get base-band corruption (the magenta bit) due to the BW of the signal extending into the 2nd Nyquist zone.

You can sample at 3 GHz and you'll be able to capture into the digital realm any BW limited signal without corruption even though you may be under-sampling.

• Thanks, altered my numbers as they were wrong. So I understand now, the nyquist criterion has to do with the BW of the signal - wherever it is within the input bandwidth - and NOT the input bandwidth of the converter. So the converter has to be designed in a way that it can capture the signal in the first place and then the sampling has to do with capturing the entire bandwidth of the signal being captured. So designing the converter elements for maximum speed - if that is what you want - is very important. Commented Dec 21, 2021 at 22:01

I want an ADC that samples at 3GS/s.

That means for a Nyquist converter - SAR ADC - I can sample signals at a maximum bandwidth of 6 GHz.

Well, you probably meant maximum bandwidth of 1.5GHz: Nyquist limit = sample rate / 2. And the ADCs running at those frequencies are not successive approximation (SAR) types. They are flash pipeline converters, where the "flash" aspect may be implemented more cleverly than with a bunch of comparators, but the principle is the same.

But there are two misunderstandings here, and both are fairly common:

1. The Nyquist limit is a minimum requirement, not a sufficient requirement. If all you got is A/Ds that can sample at the Nyquist limit, you need two of them! Specifically, you need I/Q sampling. That means two A/D converters sampling at the Nyquist rate.

In your case, that means sampling a sine wave up to 1.5Ghz in frequency, at the sample rate of 3GS/s, using two ADCs. They should be taking samples spaced 90degrees (1/4 sample period) apart from each other, here that would be 1/(4*3E9)=83.(3)ps sample time offset between two A/Ds.

2. Nyquist sampling means the opposite of sampling at the Nyquist limit. Nyquist sampling means sampling a higher frequency but bandwidth-limited signal but using aliasing at the Nyquist sampling rate to down-convert the signal to the baseband.

What even is a "higher frequency" but "bandwidth limited" signal? Think of radio channels: you can have a speech radio channel at 1.000000GHz center frequency that is only a couple of kHz wide. Given an ADC with a suitably large useful bandwidth (past 1GHz) and a very narrowband preselector filter, you could sample this at 50kHz (for example).

But back to Nyquist sampling. An example: if you have a 1.5GHz signal with 200MHz bandwidth (1.4GHz-1.6GHz and nothing outside of those frequencies), you can sample it following two criteria:

1. Sample rate must be 400Ms/s minimum due to the Nyquist criterion.

2. The multiple of the sample rate must be the multiple of one end of the bandwidth, i.e. either 1.4Ghz or 1.6GHz.

It works out well in our case, since 400MS/s*4 = 1.6GHz. So, we take two ADCs set up as an I/Q pair, each sampling at 400MS=/s. Then, 1.6GHz gets aliased to 0Hz, and 1.4GHz gets aliased to 200MHz. The frequencies are reversed in the sampling process. This is OK for digital transmission protocols, typically, but if you want to display the spectrum or otherwise process the signals "as if" they were sampled with a "fast enough" ADC, then you need to flip the frequencies around, for example by running FFT, reversing the order of the spectrum components, then running FFT again to convert back to the time domain.

There certainly exist ADCs that have a bandwidth much wider than the Nyquist limit due to their sampling rate, although at the 4:1 signal to sampling ratio we got here, most ADCs won't be operating at their full power bandwidth, and there may be significant nonlinearities (distortion) - this really depends on what chip you're using.

Now, you may ask: what if you don't want two ADCs? You need to sample twice as fast as the Nyquist limit.

There is no free lunch: to sample arbitrary signals of bandwidth up to f, you must be taking at least 2f samples per second. Whether you do it two slower ADCs or one fast one is up to you (and to the specs of the parts you use). Sometimes, the faster ADC simply doesn't exist, so you are forced to do sampling at or slightly above the Nyquist limit but using two slower ones.

Now you may ask: but what if you only sample using one ADC at the Nyquist limit instead of two, or instead of sampling at twice that limit?

The "passband" from $$\f_S/4\$$ to $$\f_S/2\$$ is phase sensitive. At the Nyquist limit of $$\f_S/2\$$, you can only accurately sample signals at 0 and 180 degree phase relative to the sampling period. The signals at +/-90 degree phase appear as a zero DC value. Some people view this as "ah, we just lack amplitude accuracy" problem. No. It's not about "accuracy". It's about your ADC being in worst case completely insensitive to $$\f_S/2\$$ frequency, and misrepresenting the frequencies somewhat lower.

So the idea that you can "sample" frequency $$\f_S/2\$$ because "Nyquist theorem states so" misses the key aspect of what the theorem implies! Namely: the limit only has to do with aliasing or lack thereof. At Nyquist limit, you can only be accurately sampling a signal that's synchronous with the sample clock and with a known phase offset sufficiently far away from +/-90, +/-270, ... degrees. And below that limit, down to $$\f_S/4\$$, the signals you "sample" will be AM modulated, and there's no way around that. It will only be accurate every once in a blue moon, you will only get properly sampled amplitude every $$\1/(f_S-f_{\rm signal})/2\$$ seconds. So, if you sample 0.749_999GHz signal at 1.500_000GS/s, you'll see "correct" results every 0.5ms. And 0.5ms after you see the right signal, you'll be sampling a solid zero. Back and forth. The CW (continuous wave, fixed amplitude) 0.749_999GHz signal will appear as if it was AM modulated at 1kHz.

In other words, sampling at the Nyquist limit doesn't imply practical usefulness of such sampling for any purpose you have in mind. In most general terms, if your ADC is so speed-constrained that the Nyquist limit is close to frequencies of interest, the approach to the design of the signal chain changes dramatically, and it's more like a digital RF receiver than an oscilloscope.

"input bandwidth" deals with transistors and capacitances in the ADC itself and how fast they can possibly change state. It means that no matter what the sampling frequency (samples per second) might be, the chip itself can be thought of as having a low-pass filter 'built into it' that act on the input signal before it is sampled.

"sampling frequency" is just that, how many conversions can be completed per second. Be advised that some ADCs trade off sampling frequency (samples per second) for sampling resolution (bits per sample).

When it comes to ADCs, I've heard that Nyquist is very much a theoretical concern. Really you want to sample at least 5 times (more is better) the frequency of the highest bandwidth feature you want to preserve in your input signal. This has to do with effective number of bits (ENOB) among other things that I won't go into further here. Just want to make sure you don't proceed too naively on this front.