Calibration Curves, Part II: What are the Limits? - - Chromatography Online
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Calibration Curves, Part II: What are the Limits?
Apr 1, 2009
By: John W. Dolan
LCGC North America

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John W. Dolan


This is the second installment in a series of "LC Troubleshooting" articles on calibration curves for liquid chromatography (LC) separations. Last month's column (1) looked briefly at single-point, two-point, and multipoint calibration curves. Then the multipoint calibration curve was used to illustrate the importance of deciding whether or not to force the curve through the origin (x = 0, y = 0). This month we will look at the signal-to-noise ratio and its relationship to uncertainty in a measurement. We will use this information as a tool to set the lower limits for a method. Next month, we will look at some additional ways to evaluate calibration curves.

Signal-to-Noise and %-Error



Before we look at method limits, we need to examine the signal-to-noise ratio (S/N) and how it relates to %-error — this is the basis of the lower limits for a method. S/N is determined as shown in Figure 1. If measured manually, print an expanded chromatogram or work with an expanded version on the computer monitor, then draw horizontal lines at the bottom and top edges of the baseline that bracket most of the noise; the distance between these is the noise (0.18 units in Figure 1; the measurement units are unimportant, because they cancel). The signal is the distance from the middle of the baseline noise to the top of the peak (1.14 units in Figure 1). S/N is simply the ratio of these two values (1.14/0.18 = 6.3). The data system might be able to measure the noise automatically by averaging the noise over a selected time, using a root-mean-square (RMS) algorithm. The signal is the peak height (be sure to use the same units of measurement for both signal and noise). Noise, of course, is superimposed on the signal at the top of the peak, so picking the magnitude of the signal is somewhat uncertain, which adds error to the measurement. As the peak gets larger, the errors contributed by measurements at the baseline and the peak top become a smaller proportion of the total, so their contribution to the uncertainty of the reported peak area (or height) becomes smaller. The error contributed by S/N can be estimated by

Thus, from the data of Figure 1, the %RSD (percent relative standard deviation) is (50/6.3) ≈ 7.9%. We can use equation 1 to make a plot of %RSD versus S/N, as in Figure 2, where the error in the measurement (%RSD) is negligible at large ratios of S/N, and grows larger with diminishing S/N. One way to define trace analysis is that it encompasses analyte concentrations at which the overall method error is affected by S/N. When S/N exceeds 50–100, its RSD will be <1%, which is negligible in most methods, so methods with S/N < 100 might be considered trace analysis. The lower limits of the method are in this region of trace analysis, so S/N can be an important factor in the overall method error.

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Comments from our Readers
Philippe De Raeve / Donstiennes, BELGIUM
 Posted 2009-07-30 10:08:03.0
Can you tell me where equation (1) is coming from ? Please note that the drawing of S in figure 1 do not correspond to the definition in the text: "distance from the middle of the baseline noise..."
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