Switch-Synchronous Sampling in SMPS's

Isn't there a belief that better (less noisy) sensor signals can be
acquired in a SMPS when the ADC samples at the switching frequency and
the ADC sample times are synchronized to sample between the switching
times, so that less noise is captured by the ADC?

I'm having a hard time seeing how this works. A time-domain argument is
used, but the noise from switching spikes is still there in the
frequency domain independent of sampling phase, and convolution in
frequency of the infinite impulse train and this wideband noise indicate
switching noise will be aliased back into the Nyquist band.

What am I missing?
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

I don't know the problem, but the time domain argument makes sense to me. 

For example, in this paper power spectra of a time domain product are
calculated
http://downloads.hindawi.com/journals/asp/2004/256395.pdf
but this requires assumptions on the signal ("Gaussian-ness": first page,
second column) that are clearly violated in your example.

Without the assumption, I'd have to revert to using the Fourier transform
of the signals, multiply, and only then take the power spectrum. I'd expect
that somewhere along the way, pairs of product terms cancel, or something
similar happens.

This shows the flaw of the usual frequency domain thinking for signals that
aren't random enough: signal powers can only add up, but complex signal
amplitudes may cancel. 

"Randy Yates" <yates@digitalsignallabs.com> wrote in message 
news:87k3wq222j.fsf@randy.site...
> Isn't there a belief that better (less noisy) sensor signals can be
> acquired in a SMPS when the ADC samples at the switching frequency and
> the ADC sample times are synchronized to sample between the switching
> times, so that less noise is captured by the ADC?
>
> I'm having a hard time seeing how this works. A time-domain argument is
> used, but the noise from switching spikes is still there in the
> frequency domain independent of sampling phase, and convolution in
> frequency of the infinite impulse train and this wideband noise indicate
> switching noise will be aliased back into the Nyquist band.
>
> What am I missing?

Odd and even. Sin and Cos. Othogonal. Got it?

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

On Wed, 22 Aug 2012 14:50:44 -0400, Randy Yates
<yates@digitalsignallabs.com> wrote:

>Isn't there a belief that better (less noisy) sensor signals can be
>acquired in a SMPS when the ADC samples at the switching frequency and
>the ADC sample times are synchronized to sample between the switching
>times, so that less noise is captured by the ADC?
>
>I'm having a hard time seeing how this works. A time-domain argument is
>used, but the noise from switching spikes is still there in the
>frequency domain independent of sampling phase, and convolution in
>frequency of the infinite impulse train and this wideband noise indicate
>switching noise will be aliased back into the Nyquist band.
>
>What am I missing?
>-- 
>Randy Yates
>Digital Signal Labs
>http://www.digitalsignallabs.com

Time-Division Multiplexed signals can enjoy orthogonality strictly by
their separation in time, even if they occupy the same frequency.
The spectral "noise" generated by one won't affect the other if they
are truly isolated in time.

Likewise your sampler will not be susceptible to any noise from the
switcher if they are truly separated in time.   If the duration of the
sensor sampling function occurs at a time isolated from the duration
of any transients related to the power switching, then they'll be
orthogonal in time.  Regardless of the spectrum occupied by the switch
transients it won't affect the sensor sampling if they're genuinely
orthogonal  (i.e., isolated, independent)  in time.


Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

>> Odd and even. Sin and Cos. Othogonal. Got it?

Bingo.

"Vladimir Vassilevsky" <nospam@nowhere.com> writes:

> "Randy Yates" <yates@digitalsignallabs.com> wrote in message 
> news:87k3wq222j.fsf@randy.site...
>> Isn't there a belief that better (less noisy) sensor signals can be
>> acquired in a SMPS when the ADC samples at the switching frequency and
>> the ADC sample times are synchronized to sample between the switching
>> times, so that less noise is captured by the ADC?
>>
>> I'm having a hard time seeing how this works. A time-domain argument is
>> used, but the noise from switching spikes is still there in the
>> frequency domain independent of sampling phase, and convolution in
>> frequency of the infinite impulse train and this wideband noise indicate
>> switching noise will be aliased back into the Nyquist band.
>>
>> What am I missing?
>
> Odd and even. Sin and Cos. Othogonal. Got it?

Switching noise is not sinusoidal. You could argue that at least you get
rid of the first harmonic, I suppose, but there may still be significant
energy at higher harmonics, and those harmonics may not be orthogonal.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

eric.jacobsen@ieee.org (Eric Jacobsen) writes:

> On Wed, 22 Aug 2012 14:50:44 -0400, Randy Yates
> <yates@digitalsignallabs.com> wrote:
>
>>Isn't there a belief that better (less noisy) sensor signals can be
>>acquired in a SMPS when the ADC samples at the switching frequency and
>>the ADC sample times are synchronized to sample between the switching
>>times, so that less noise is captured by the ADC?
>>
>>I'm having a hard time seeing how this works. A time-domain argument is
>>used, but the noise from switching spikes is still there in the
>>frequency domain independent of sampling phase, and convolution in
>>frequency of the infinite impulse train and this wideband noise indicate
>>switching noise will be aliased back into the Nyquist band.
>>
>>What am I missing?
>>-- 
>>Randy Yates
>>Digital Signal Labs
>>http://www.digitalsignallabs.com
>
> Time-Division Multiplexed signals can enjoy orthogonality strictly by
> their separation in time, even if they occupy the same frequency.
> The spectral "noise" generated by one won't affect the other if they
> are truly isolated in time.
>
> Likewise your sampler will not be susceptible to any noise from the
> switcher if they are truly separated in time.   If the duration of the
> sensor sampling function occurs at a time isolated from the duration
> of any transients related to the power switching, then they'll be
> orthogonal in time.  Regardless of the spectrum occupied by the switch
> transients it won't affect the sensor sampling if they're genuinely
> orthogonal  (i.e., isolated, independent)  in time.

Hi Eric,

Although I'm not sure I like the use of the word "orthogonal" applied
here, I'll go with it.

You're not really saying anything new - I already knew this notion of
isolating the sampling from the switching transients is the argument for
the technique. And if I hadn't analyzed the technique using the
frequency domain, I would probably buy it. It "sounds" feasible.

But something seems wrong. First we have the fact that a frequency
domain analysis doesn't support the same conclusion. Also, consider the
following thought experiment. Consider a sine wave at frequency Fs / 4,
with sampling at the 0, 90, 180, 270 points. Let the sine wave have a
noise spike at 45 degrees. Then using the same sort of thinking, one
could say that we can sample this signal and obtain a perfect sine wave.
But that would violate Nyquist, which says that we could reconstruct the
signal with the samples!
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On Wed, 22 Aug 2012 14:50:44 -0400, Randy Yates wrote:

> Isn't there a belief that better (less noisy) sensor signals can be
> acquired in a SMPS when the ADC samples at the switching frequency and
> the ADC sample times are synchronized to sample between the switching
> times, so that less noise is captured by the ADC?
> 
> I'm having a hard time seeing how this works. A time-domain argument is
> used, but the noise from switching spikes is still there in the
> frequency domain independent of sampling phase, and convolution in
> frequency of the infinite impulse train and this wideband noise indicate
> switching noise will be aliased back into the Nyquist band.
> 
> What am I missing?

The fact that frequency-domain analysis is there for when the math is too 
hard in the time domain.  It's not there for when an easy answer can be 
had using time domain analysis.

If the math is easy -- or unnecessary -- with time domain analysis, use 
that instead.

If you absolutely, positively must think about this in the frequency 
domain, then take the Fourier transform of a narrow pulse, convolve it 
with itself (to test the case where the sampling lies on top of the 
noise), then convolve it with itself multiplied by e^(j*tau*s), where tau 
is longer than the pulse width.  You'll find that things cancel out to 
zero.

Then ask yourself why you went to all that trouble when the time domain 
analysis was so patently easy.

-- 
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 Wed, 22 Aug 2012 17:05:25 -0400, Randy Yates wrote:

> eric.jacobsen@ieee.org (Eric Jacobsen) writes:
> 
>> On Wed, 22 Aug 2012 14:50:44 -0400, Randy Yates
>> <yates@digitalsignallabs.com> wrote:
>>
>>>Isn't there a belief that better (less noisy) sensor signals can be
>>>acquired in a SMPS when the ADC samples at the switching frequency and
>>>the ADC sample times are synchronized to sample between the switching
>>>times, so that less noise is captured by the ADC?
>>>
>>>I'm having a hard time seeing how this works. A time-domain argument is
>>>used, but the noise from switching spikes is still there in the
>>>frequency domain independent of sampling phase, and convolution in
>>>frequency of the infinite impulse train and this wideband noise
>>>indicate switching noise will be aliased back into the Nyquist band.
>>>
>>>What am I missing?
>>>--
>>>Randy Yates
>>>Digital Signal Labs
>>>http://www.digitalsignallabs.com
>>
>> Time-Division Multiplexed signals can enjoy orthogonality strictly by
>> their separation in time, even if they occupy the same frequency. The
>> spectral "noise" generated by one won't affect the other if they are
>> truly isolated in time.
>>
>> Likewise your sampler will not be susceptible to any noise from the
>> switcher if they are truly separated in time.   If the duration of the
>> sensor sampling function occurs at a time isolated from the duration of
>> any transients related to the power switching, then they'll be
>> orthogonal in time.  Regardless of the spectrum occupied by the switch
>> transients it won't affect the sensor sampling if they're genuinely
>> orthogonal  (i.e., isolated, independent)  in time.
> 
> Hi Eric,
> 
> Although I'm not sure I like the use of the word "orthogonal" applied
> here, I'll go with it.
> 
> You're not really saying anything new - I already knew this notion of
> isolating the sampling from the switching transients is the argument for
> the technique. And if I hadn't analyzed the technique using the
> frequency domain, I would probably buy it. It "sounds" feasible.
> 
> But something seems wrong. First we have the fact that a frequency
> domain analysis doesn't support the same conclusion.

I don't think you're doing your frequency domain analysis correctly.  See 
my comment on phase shifting and convolution in my reply.

> Also, consider the
> following thought experiment. Consider a sine wave at frequency Fs / 4,
> with sampling at the 0, 90, 180, 270 points. Let the sine wave have a
> noise spike at 45 degrees. Then using the same sort of thinking, one
> could say that we can sample this signal and obtain a perfect sine wave.
> But that would violate Nyquist, which says that we could reconstruct the
> signal with the samples!

The spike has lots of high-frequency components, you are sampling well 
under those frequencies, and you are failing to reconstruct the spike.  
How are you going counter to Nyquist's theorem here?

-- 
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

Tim Wescott <tim@seemywebsite.com> wrote:

(snip)
> The fact that frequency-domain analysis is there for when the math is too 
> hard in the time domain.  It's not there for when an easy answer can be 
> had using time domain analysis.

> If the math is easy -- or unnecessary -- with time domain analysis, use 
> that instead.

And also the other way around. Don't do time-domain when the
frequency-domain analysis is easy.

But sometimes you have a case where neither is easy.

-- glen