Calculating dB Uncertainty for a LISN
12 Oct 2021
Calculating LISN Uncertainty in dB for an Uncertainty Budget
I am preparing the uncertainty budget for a Conducted emissions measurement. LISN Uncertainty is given in ohms... how can I convert it in dB?
Is this formula good enough? “You may convert percentage (linear) to dB (logarithmic) by using the following equations: dB = 10 log(1 + X) Example X = 1% Thus, dB = 10 log(1 + 0.01) dB = 0.0432” (copied from https://www.keysight.com/main/editorial.jspx?ckey=1785683&id=1785683&nid=-11143.0.00&lc=eng&cc=US)
No. The equation you quote is totally inappropriate for use in calculating the uncertainties in an EMC measurement, for two reasons:
It is about ‘Power dBs’, but you need ‘Voltage dBs’.
It is about converting percentages into dBs, which is not your situation.
The 1st reason:
For ratios of RMS Powers – we must use 10 log10 N (where N is the ratio to be converted to dB)
For ratios of RMS Voltages (or Currents) – we must use 20 log10 N (where N is the ratio to be converted to dB)
The reason for using ‘10 log10’ for powers but ‘20 log10’ for voltages or currents is that power is proportional to the squares of the voltages or currents, for example Watts = V2/R or I2R; and squaring a linear value is the same as doubling its dB value (i.e. from 10 to 20, in this case).
Your linked webpage is titled: “How do I convert a percentage(linear) to a dB(logarithmic) value as most of the accuracy values stated in power meter data sheet are in percentage?” and is about power and therefore uses the 10 log10 method.
BUT because the output of a LISN is a voltage: 20 log10 is the relevant calculation for LISNs.
The 2nd reason:
The example you provide concerns the specific issue of converting a percentage (which is one kind of ratio) into dB (which is a different kind of ratio). This is the reason for the (1+X) term in the equation they give – but we almost never come across percentages in the world of EMC, and never in connection with LISN uncertainties!
SO – the equation you quote is totally inappropriate for use in calculating the uncertainties in an EMC measurement, for two reasons!
What should you do instead?
The uncertainties in a LISNs calibration factors are either given in Ohms, or in dB with respect to 50 Ohms. If they are given in dB they should simply be added to the other dBs in our uncertainty budget calculations.
If they are given in Ohms instead, we need to convert them into dB with respect to 50 Ohms to use in our uncertainty budget calculations, like this: dB Ohms = 20 log10 [(50+X)/50]
– where X is the maximum uncertainty value stated as a number of Ohms greater than, or less than, 50 Ohms.
E.g. if X is given as, say: +2, -3 Ohms, we would calculate our +/- uncertainties in dB as 20 log10 [52/50] and 20 log10 [47/50], i.e. +0.3dB, - 0.54dB.
However, if X is given as, say: max 53 Ohms, min 46 Ohms, we don’t need to add 50 to X – we just use the given values instead, so in this example we would calculate our +/- uncertainties in dB as 20 log10 [53/50] and 20 log10 [46/50], i.e. +0.51dB, -0.72dB.
For more on dB conversions, see https://en.wikipedia.org/wiki/Decibel
For more on uncertainty budgeting, see https://incompliancemag.com/article/emc-and-measurement-uncertainty-lab-34-and-cispr-16-4-2/
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