# [SI-LIST] Re: Units Conversion Question

*From*: Rob Hinz <rob@xxxxxxxxxx>*To*: cpad@xxxxxxxxx*Date*: Mon, 13 Aug 2001 13:38:49 -0700

Hi Chris, I am not sure I completely followed your derivation. The free space impedance relates the magnitude of the E-field and H-field in a TEM (plane) wave propagating in free space. So for an X-polarized plane wave propagating in the Z direction we get: Ex (V/m) / Hy (A/m) = sqrt(u/eps) = 377 (Ohms) So, just convert dBuV/m back to V/m and divide by 377 to get A/m For example, if you have X (dBuV/m): convert to V/m by 10^(X/20) uV/m = 10^(X/20)*10^(-6) V/m Now you have E-field strength, so convert to H-field by dividing E-field by free space impedance (10^(X/20)*10^-6)/377 A/m That should do it. As you can see from above, V/m is E-field, and A/m is H-field. So you actually ARE doing it with E's and H's. It would be improper to work with just V and I in this case. Now, if you want to go on and convert this to dBA/m, that may be done as follows: 20 Log ( ((10^(X/20)*10^-6)/377)/1 ) = 20 ( Log(10^(X/20)) + Log(10^(-6)) - Log(377) ) = 20 ( (X/20) + (-6) - (2.576) ) = X - 120 - 51.53 = X - 171.53 (dBA/m) I think this is correct as a mathematical proof, of sorts. I guess that means I agree with you. Apologies to your colleague. As you pointed out, his conversion would be correct if the initial units were dBV/m rather than dBuV/m as the 20Log(10^(-6)) = -120 term would not be present. Rob Hinz Senior Electromagnetics Specialist SiQual Corporation rob@xxxxxxxxxx phone (503)885-1231 x30 fax (503)885-0550 http://www.siqual.com At 11:39 AM 8/13/2001 -0700, Chris Padilla wrote: >Perhaps some of you can help me out here: > >In EMC/EMI, we often deal with units of dBuV/m (dB-microVolts per meter). > >What if I wish to convert the dBuV/m to A/m? > >For simplicity, use 120*pi Ohms or 377 Ohms as the impedance of free-space >(assume a plane wave, in the far-field, etc.) so Ohm's law in logarithms is: > >20*log I (dB-A/m) = 20*log V (dB-V/m) - 20* log R (dB-Ohms) (1) > >since our meter reads in dB-uV/m, we need to convert the voltage units: > >20*log V (dB-V/m) = [20*log V (dB-uV/m) - 120 dB] (2) > >next, we need to convert the impedance: > >20*log R (dB-Ohms) = [20*log R (dB-uOhm) - 120 dB] (3) > >Put (2,3) into (1) and: > >20*log I (dB-A/m) = [20*log V (dB-uV/m) - 120 dB] - [20*log R (dB-uOhm) - >120 dB] (4) > > >Now here is where my colleague and I differ: > >He simply cancels out the "120s" and gets as a final answer: > >20*log I (dB-A/m) = 20*log V (dB-uV/m) - 20*log R (dB-uOhm) or > >20*log I (dB-A/m) = meter reading (dB-uV/m) - 51.53 (dB-uOhm) (A) > >(recall that R = 377) > > >I don't think one can simply cancel the "120s" as that changes the >equation. The 120 in (2) must stay or the fact that it is (dB-uV/m) no >longer is true. Once the 120 is "cancelled" the units go back to >(dB-V/m)! Same thing with (3), the units are now (dB-Ohm). > >Therefore, I say that the final answer is: > >20*log I (dB-A/m) = meter reading (dB-uV/m) - 171.53 (dB-uOhm) > > >How can I mathematically validate either answer...I am just not seeing it >to make it elegant nor rigorous. Anyone clear me up here? I believe I am >right (I have done some simple circuits to prove it to myself). > >BTW, to be really rigorous, I should be doing this with E & H's but it >doesn't matter as that isn't the argument here I am trying to >understand--we cold drop the /m part on I and V to be more proper but that >doesn't change the problem. > > >Thanks----->Chris > > > >------------------------------------------------------------------ >To unsubscribe from si-list: >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field >For help: >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > >List archives are viewable at: > http://www.freelists.org/archives/si-list >or at our remote archives: > http://groups.yahoo.com/group/si-list/messages >Old (prior to June 6, 2001) list archives are viewable at: > http://www.qsl.net/wb6tpu > Rob Hinz Senior Electromagnetics Specialist SiQual Corporation rob@xxxxxxxxxx phone (503)885-1231 x30 fax (503)885-0550 http://www.siqual.com ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: http://www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu

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**[SI-LIST] Units Conversion Question***From:*Chris Padilla

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