S/N determination

[Mattias]

A very simple question that I don't know the answer of:

Do you use the full amplitude or half the amplitude of the noise when you do S/N measurements (the manual way with a ruler)

[zokitano]

I measure the full amplitude of the noise in a definite time interval. In that interval i draw a line connecting the upper amplitudes (maxima) and below, line-connecting the minima. Then I measure the shortest distance (perpendicular) between those two lines.

Best regards

[Mattias]

Thanks,

In my company people have always used half the amplitude of the noise when doing these S/N calculations. I cannot find any references in the guidelines of how to do.

The results will change by a factor of two, depending how you see it.

[Hollow]

If would like to have it referenced,
see PhEur Chapt. 2.2.46

They use the full amplitude of the noise (h) and the peak height H:

Then they calculate it as followed:

S/N=2H/h

[Mattias]

Perfect! Just what I needed.

So in fact, EP is also dividing the noise-amplitude with two (which ends up in the numerator)

Thanks!

[Rob Burgess]

Hi All,

Just to continue this debate (as it a hot topic within our dept. at the mo) - why would you measure S/N by height when most HPLC impurity assays are determined by area! Doesn't it therefore make more sense to calculate your S/N by area as well i.e. the same way as your quantification method.

[zokitano]

Hi All,

Just to continue this debate (as it a hot topic within our dept. at the mo) - why would you measure S/N by height when most HPLC impurity assays are determined by area! Doesn't it therefore make more sense to calculate your S/N by area as well i.e. the same way as your quantification method.

How would you measure the area of the noise?

[Rob Burgess]

Well S/N can also be expressed as: mean analytical response / standard deviation of that response. Therefore you don't actually have to measure the noise of the area.

It is interesting to note that the ICH define QL as the: lowest concentration of analyte that can be determined with suitable precision and accuracy. if this definition is taken it makes more sense to me to determine S/N>10 (i.e. Ql's) by area for chromatographic methods.

[zokitano]

Ok, when you use the response and standard deviation of the response (for an analyte) to measure S/N ratio you would need probably several injections before you could calculate it. That is convenient when one does method validation (and calculates the DL and QL).

But when one does only (in a routine analyses, as a part of the system suitability) one injection which is sufficient for S/N determination, then is more suitable to use the calculation method stated in the Pharmacopoeia for signal-to-noise ratio.

Regards

[HW Mueller]

This has been discussed several times before, a good reference given there somewhere is:

John W. Dolan, How is the detection limit determined?
LC.GC Europe January 2006, 12

[Dan]

HW Mueller, thanks for providing that reference. Here's the link:

http://www.lcgceurope.com/lcgceurope/ar ... al%20noise

This reference provides a good picture (image) for the determination of the S/N. I think that it is important to give both the equation and the pitcure. As I recall, EP 2.4.46 does provide both also.

Comparing this article and the EP equation provided by Hollow shows that the two references are different in the S/N determination. The difference being a factor of "2". I don't have the EP available at the moment for a better comparison.

There are a variety of methods to determine the S/N. You can use: peak-to-peak noise (Np-p), peak noise (Np), root mean square (RMS) noise (Nrms) or a form of standard deviation determination. In general a chromatography data system (CDS) will use RMS noise as that is what can be measured electronically, but the CDS may convert this to Np-p or Np for calculations.

So, you should know how your CDS is making the determination.

Also, you should document how the determination of S/N is made, either in an SOP or in your method validation report.

Regards,
Dan