# Effect of oversampling on SFDR

Started by April 13, 2013
```Hi All

My question relates to the effect of oversampling on the SFDR obtained with
an ADC. I understand that the SNR of an ADC, considered over a certain
bandwidth of interest (BW), can be increased relative to the overall SNR by
sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
increase in SNR is 10log(Fs/2*BW). This has been clearly explained in the
responses to a previous post
(http://www.dsprelated.com/showmessage/72731/1.php).

Am I correct in assuming that oversampling will not alter the SFDR? If so,
is it reasonable to conclude that there is no point in oversampling to the
extent that SNR becomes much better than SFDR because, while this would
allow very small signals to be detected, these signals could not be
distinguished from spurs?

Thanks very much,
Sharon
```
```On 4/13/2013 1:32 PM, SRB wrote:

> My question relates to the effect of oversampling on the SFDR obtained with
> an ADC. I understand that the SNR of an ADC, considered over a certain
> bandwidth of interest (BW), can be increased relative to the overall SNR by
> sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
> increase in SNR is 10log(Fs/2*BW). This has been clearly explained in the
> responses to a previous post
> (http://www.dsprelated.com/showmessage/72731/1.php).

That's plain wrong, stupid and misleading. Forget it.

> Am I correct in assuming that oversampling will not alter the SFDR?

It depends.

> If so,
> is it reasonable to conclude that there is no point in oversampling to the
> extent that SNR becomes much better than SFDR because, while this would
> allow very small signals to be detected, these signals could not be
> distinguished from spurs?

It depends.

ADC does two different things in a row:

1. Applying a non-linear step ladder function to continuous time signal.
2. Sampling the result of non-linear function.

The (1) creates harmonics, the (2) wraps them into the band of interest.
Depending on what and how, oversampling may affect SFDR as well as SNR.

DSP and Mixed Signal Designs
www.abvolt.com

```
```On 4/13/13 4:08 PM, Vladimir Vassilevsky wrote:
> On 4/13/2013 1:32 PM, SRB wrote:
>
>> My question relates to the effect of oversampling on the SFDR obtained
>> with
>> an ADC. I understand that the SNR of an ADC, considered over a certain
>> bandwidth of interest (BW), can be increased relative to the overall
>> SNR by
>> sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
>> increase in SNR is 10log(Fs/2*BW). This has been clearly explained in the
>> responses to a previous post
>> (http://www.dsprelated.com/showmessage/72731/1.php).
>
> That's plain wrong, stupid and misleading. Forget it.
>

are you saying that oversampling to increase S/N is plain wrong, stupid

i am not saying that (without feedback and noise shaping), that it's
such a good idea, but i thought that it's widely accepted that for each
octave of oversampling, you get 3.01 dB of increase in S/N?  at least if
the input is dithered or has some noisiness that is naturally added.

to add one additional meaningful bit to the A/D converter, you need to
increase the sampling rate by a factor of 4.

>> Am I correct in assuming that oversampling will not alter the SFDR?
>
> It depends.
>
>> If so,
>> is it reasonable to conclude that there is no point in oversampling to
>> the
>> extent that SNR becomes much better than SFDR because, while this would
>> allow very small signals to be detected, these signals could not be
>> distinguished from spurs?
>
> It depends.
>
>
> ADC does two different things in a row:
>
> 1. Applying a non-linear step ladder function to continuous time signal.
> 2. Sampling the result of non-linear function.
>
> The (1) creates harmonics, the (2) wraps them into the band of interest.
> Depending on what and how, oversampling may affect SFDR as well as SNR.

there are probably some semantic issues here that i don't get.  maybe
conceptual issues as well.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```On Sat, 13 Apr 2013 17:15:58 -0400, robert bristow-johnson wrote:

> On 4/13/13 4:08 PM, Vladimir Vassilevsky wrote:
>> On 4/13/2013 1:32 PM, SRB wrote:
>>
>>> My question relates to the effect of oversampling on the SFDR obtained
>>> with
>>> an ADC. I understand that the SNR of an ADC, considered over a certain
>>> bandwidth of interest (BW), can be increased relative to the overall
>>> SNR by
>>> sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
>>> increase in SNR is 10log(Fs/2*BW). This has been clearly explained in
>>> the responses to a previous post
>>> (http://www.dsprelated.com/showmessage/72731/1.php).
>>
>> That's plain wrong, stupid and misleading. Forget it.
>>
>>
>
> are you saying that oversampling to increase S/N is plain wrong, stupid
>
> i am not saying that (without feedback and noise shaping), that it's
> such a good idea, but i thought that it's widely accepted that for each
> octave of oversampling, you get 3.01 dB of increase in S/N?  at least if
> the input is dithered or has some noisiness that is naturally added.

I have used this effect quite profitably, sampling 16-bit SAR ADCs at
rates pushing 50kHz, then averaging the snot out of the samples and
resampling at around 500Hz.

We needed upwards of 19 bits of precision at the same time that our
accuracy requirements were in the neighborhood of 15 bits -- sampling
like mad and averaging worked a charm.

In our case we didn't even need to add any dithering signal -- the ADCs
provided that free of charge, thanks to their noisy front end circuitry.

> to add one additional meaningful bit to the A/D converter, you need to
> increase the sampling rate by a factor of 4.
>
>>> Am I correct in assuming that oversampling will not alter the SFDR?
>>
>> It depends.
>>
>>> If so,
>>> is it reasonable to conclude that there is no point in oversampling to
>>> the
>>> extent that SNR becomes much better than SFDR because, while this
>>> would allow very small signals to be detected, these signals could not
>>> be distinguished from spurs?
>>
>> It depends.
>>
>>
>> ADC does two different things in a row:
>>
>> 1. Applying a non-linear step ladder function to continuous time
>> signal. 2. Sampling the result of non-linear function.
>>
>> The (1) creates harmonics, the (2) wraps them into the band of
>> interest. Depending on what and how, oversampling may affect SFDR as
>> well as SNR.
>
> there are probably some semantic issues here that i don't get.  maybe
> conceptual issues as well.

Vladimir forgot 0: adds noise.  And 1a: the step function is not
uniform.  And for most ADCs, the actual order of operations is:

1 -- sample
3 -- quantize (with not quite even steps)

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
```On Saturday, April 13, 2013 11:32:58 AM UTC-7, SRB wrote:
> Hi All
>
> My question relates to the effect of oversampling on the SFDR obtained with
> ... This has been clearly explained in the
> responses to a previous post
> (http://www.dsprelated.com/showmessage/72731/1.php).
...
> Am I correct in assuming that oversampling will not alter the SFDR? ...

First, it's great that someone actually searches to find answers. Unfortunately, searches can find garbage as well as gems. The problem with the "simplified explanation" in the reference is that it was and still is too simple to provide meaningful interpretation by the OP. There are a number of issues.

One issue relates to measurement bandwidth. ADC specs often refer to the ratio of a strong signal to the noise in the entire signal application bandwidth as SNR. For ideal white quantization noise, oversampling spreads the fixed noise power across a wider bandwidth. In the ADC spec terms the noise in this larger bandwidth is summed back up to the same total, SNR is the same. But, many instruments report noise power in a fixed bandwidth. Oversampling will then appear to reduce the quantization noise level. It depends on the units of measurement. Simplifying away the units isn't helpful, it's incompetent. An OP who searches can find the units of power vs units of power spectral density.

Next, quantization noise is not automatically white. An ideal quantizer will allow an arbitrarily small square wave to concentrate quantization noise in the harmonics of the square wave's fundamental. Avoiding that leads to the discussions of dither. An OP who searches can find these.

Next, noise in real systems isn't just quantization noise. When there is wideband background noise at levels noticeable compared to the quantization noise, increasing bandwidth by oversampling can increase the noise in the signal bandwidth. How does that effect the measurements? It depends upon the units: broadband vs fixed measurement band and the background noise power spectrum.

Next, spurs in real systems may come from the system itself or the outside. Changing a system to sample at a higher frequency can frequency scale Fs proportional spur frequencies out of the application bandwidth, it can also generate new spurs, and it won't change external interference. It depends on the source and coupling method of the spurs.

The problems are inadequate semantics and unstated and frequently invalid assumptions. Some may think that "It depends." isn't a good answer, but it can be resolved by continued communication. Hopefully inquiring minds will learn to try to improve their vague questions. I would prefer that (perhaps dubious) hope to sending those who have invested their time in asking questions off in happier ignorance (at least for most OPs). Maybe, sometimes, someone will take the time to provide answers that aren't inadequate to communicate to the OPs.

Dale B. Dalrymple
```
```Sharon

When you say that oversampling will not affect the SFDR, you are assuming that you would choose the same A/D for both the oversampled and non-oversampled cases, and that the only A/D impairment is non-ideal quantization levels. These assumptions may or may not hold in the real world.

Note that one advantage of oversampling is that low-order harmonic distortion terms do not alias back into the passband for high-frequency inputs.

Bob
```
```SRB <62352@dsprelated> wrote:

> My question relates to the effect of oversampling on the SFDR obtained with
> an ADC. I understand that the SNR of an ADC, considered over a certain
> bandwidth of interest (BW), can be increased relative to the overall SNR by
> sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
> increase in SNR is 10log(Fs/2*BW). This has been clearly explained in the
> responses to a previous post
> (http://www.dsprelated.com/showmessage/72731/1.php).

I didn't look at the page, but if you average N numbers with random
noise, the noise (uncertainty) is reduced by a factor of sqrt(N).

If you are careful with the math, you can consider the oversampling
as averaging, and so should reduce the S/N. But which noise is reduced?
If the samples can be considered independent measurements of the
underlying signal, then the random error in their measurement can
be averages out. Otherwise it won't.

-- glen
```
```On Sat, 13 Apr 2013 13:32:58 -0500, SRB wrote:

> Hi All
>
> My question relates to the effect of oversampling on the SFDR obtained
> with an ADC. I understand that the SNR of an ADC, considered over a
> certain bandwidth of interest (BW), can be increased relative to the
> overall SNR by sampling at a rate (Fs) such that Fs/2 >> BW, and that
> the resulting increase in SNR is 10log(Fs/2*BW). This has been clearly
> explained in the responses to a previous post
> (http://www.dsprelated.com/showmessage/72731/1.php).
>
> Am I correct in assuming that oversampling will not alter the SFDR? If
> so, is it reasonable to conclude that there is no point in oversampling
> to the extent that SNR becomes much better than SFDR because, while this
> would allow very small signals to be detected, these signals could not
> be distinguished from spurs?
>
> Thanks very much,
> Sharon

It's complicated.  If the spurs are "real", i.e., if they arise because
of nonlinearities in the ADC transfer curve, then no, oversampling won't
improve the SFDR.  There may be strategies that would use a combination
of dithering and oversampling that _would_ increase the SFDR, but I
wouldn't bet money on it.

simplistic -- you can often improve the noise floor by oversampling, but
this is only of use if you can tolerate the measurement inaccuracy
induced by those same ADC nonlinearities that cause the spurs.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
```>Hi All
>
>My question relates to the effect of oversampling on the SFDR obtained
with
>an ADC. I understand that the SNR of an ADC, considered over a certain
>bandwidth of interest (BW), can be increased relative to the overall SNR
by
>sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
>increase in SNR is 10log(Fs/2*BW). This has been clearly explained in the
>responses to a previous post
>(http://www.dsprelated.com/showmessage/72731/1.php).
>
>Am I correct in assuming that oversampling will not alter the SFDR? If
so,
>is it reasonable to conclude that there is no point in oversampling to
the
>extent that SNR becomes much better than SFDR because, while this would
>allow very small signals to be detected, these signals could not be
>distinguished from spurs?
>
>Thanks very much,
>Sharon
>

Thank you all for your responses to my post. I hadn't expected so many
replies (especially on a Sunday!), and I appreciate you responding in so
much detail. I need to go through all your comments and make sure I
understand them and then I'll post a more specific reply.

Sharon
```
```On Mon, 15 Apr 2013 06:22:36 -0500, SRB wrote:

>>Hi All
>>
>>My question relates to the effect of oversampling on the SFDR obtained
> with
>>an ADC. I understand that the SNR of an ADC, considered over a certain
>>bandwidth of interest (BW), can be increased relative to the overall SNR
> by
>>sampling at a rate (Fs) such that Fs/2 >> BW, and that the resulting
>>increase in SNR is 10log(Fs/2*BW). This has been clearly explained in
>>the responses to a previous post
>>(http://www.dsprelated.com/showmessage/72731/1.php).
>>
>>Am I correct in assuming that oversampling will not alter the SFDR? If
> so,
>>is it reasonable to conclude that there is no point in oversampling to
> the
>>extent that SNR becomes much better than SFDR because, while this would
>>allow very small signals to be detected, these signals could not be
>>distinguished from spurs?
>>
>>Thanks very much,
>>Sharon
>>
>>
> Thank you all for your responses to my post. I hadn't expected so many
> replies (especially on a Sunday!), and I appreciate you responding in so
> much detail. I need to go through all your comments and make sure I
> understand them and then I'll post a more specific reply.

Unfortunately, most of the answers to your question are going to boil
down to "it depends", and what it depends on is the specifics of the ADC
you're using and what you're trying to do.

If you have the time, a much better approach to take is to learn what
causes spurs in an ADC, and what noise processes there are, and how to
relate that to specific cases with specific ADCs and specific sampling
schemes.

Or hire someone to figure it out for your specific case.

General answers to your question (as you're finding out) are going to
contain a lot of "ifs" "maybes" and "as long as's".

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```