# Calculating dB Uncertainty for a LISN

12 Oct 2021

### Calculating LISN Uncertainty in dB for an Uncertainty Budget

Question:

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)

Response:

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!