EMC Related Formulae

1 Robert RichardsPage 103/30/03 EMC Related FormulaeLog Linear VoltagedB V to Volts()()20/12010 =VdBV Volts to dB V()120log20+=VVdB dBV to Volts()20/10dBVV=Volts to dBV()VdBVlog20=dBV to dB V120+=dBVVdB dB V to dBV120 =VdBdBV Log Linear PowerdBm to Watts()()10/3010 =dBmWWatts to dBm30)log(10+=WdBmdBW to Watts()10/10dBWW=Watts to dBW)log(10 WdBw=dBW to dBm30+=dBWdBmdBm to dBW30 =dBmdBWLog Linear CurrentdBuA to uA()20/10 AdBA =uA to dBuA)log(20 AAdB =dBA to A()20/10dBAA=A to dBA)log(20 AdBA=dBuA to dBA120 =AdBdBA dBA to dBuA120+=dBAAdB Log Linear ImpedancedB(ohms) to ohms()20/)(10ohmsdBZ=ohms to dB(ohms)()ZohmsdBlog20)(=Term ConversiondBm to dBuVdBmZvdB++=)log(1090 dBuV to dBm)log(1090 ZVdBdBm = dBuA to dBm90)log(10 +=ZAdBdBm dBm to dBuA90)log(10+ =ZdBmAdB dBuA to dBuV)log(20 ZAdBVdB+= dBuV to dBuA)log(20 ZVdBAdB = Volts to Amps & WattsZVA=ZVW2=Amps to Volts & WattsZAV*=ZAW*2=Watts to Volts & AmpsZWV*=ZWA=RF Related , Field Strength & Power DensitydBuV/m to V/m)20/)120)/(((10/ =mVdBmV V/m to dBuV/m()

2 120/log20/+=mVmVdB dBuv/m to =mVdBmdBm dBmW/m2 to +=mdBmmVdB dBuV/m to =mVdBmAdB dBuA/m to +=mAdBmVdB dBuA/m to dBpT2/+=mAdBdBpT dBpT to dBuA/m2/ =dBpTmAdB W/m2 to V/m377*)2/(/mWmV=V/m to W/m23772)/(2/mVmW=wound coil Flux Density),(20))((4mradiusampsturnsT =uT to =A/m to uT)/(* Robert RichardsPage 203/30/03 Antenna (Far Field)Gain, dBi to numeric)10/(10dBinumericGain=Gain, numeric to dBi)log(10numericGaindBi=Gain, dBi to Antenna )log(20 =dBiMHzAFAntenna Factor to gain in )log(20 =AFMHzdBiField Strength given Watts, Numeric Gain, Distance inmetersMetersGainwattsmVnumeric**30/=Fi eld Strength given Watts, dBi gain, Distance in metersMeterswattsmVdBi)10/(10**30/=Trans mit Power needed, given desired V/m, Antennanumeric gain, Distance in *30)*/(2=Transmit Power needed, given V/m, Antenna dBi gain,Distance in meters)10/(210*30)*/(dBimetersmVwatts=Am plitude ModulationPeak power, given CW power and modulation %.

3 (sine waveAM)2)) *%(1(ModWWCW peak+=Average power, given CW power level and modulation %(sine wave AM)2)) *%(2(*2 ModWWcwavg+=Average power, given peak power and modulation %22)) *%(1(*2)) *%(2(*ModModWWpeakavg++=Current ProbedB(ohm) to Zt (transfer impedance))20/)((10ohmdBtZ=Zt to dB(ohm))log(20)(tZohmdB=Conductance (Gt) in dB(s) to transfer impedance, (Zt) indB(ohms)tGtZ =Transfer Impedance in Zt (dB(ohms)), to Conductance in Gt(dB(s))tZtG =Power needed for BCI Probe (50 ), given voltage level into50 load (V) and Probe Insertion Loss LI.)10/))50/2log(10((10 VLIwatts+=Watts needed for 150 Ohm EM Clamp)10/))150/2log(10((10 VLIwatts+=Conducted current level using current measuring probegiven probe factor in dB(ohm) and probe terminal voltage indBuv)(ohmdBVdBAdB = Conducted current level, given probe factor in Zt (ohms) andterminal voltage in dBuv)log(20tZVdBAdB = dB calculationsCompute db delta (volts) =21log20 VVdBCompute dB delta (amps) =21log20 AAdBCompute dB delta (watts) =21log10 WWdBcompute new voltage w/ db delta + =20)log(20(10givenVdBnewVcompute new wattage w/ db delta + =10)

4 Log(10(10givenWdBnewWRobert RichardsPage 303/30/03 VSWR/reflection coefficient/return lossVSWR given Fwd/Rev PowerfwdrevfwdrevPPPPVSWR +=11 VSWR given reflection coefficient +=11 VSWRR eflection coefficient, , given Z1/Z2 ohms2121 ZZZZ+ = Reflection coefficient, , given fwd/rev powerfwdrevPP= Return Loss, given fwd/rev power =revfwdPPdBRLlog10)(Return Loss, given VSWR + =11log20)(VSWRVSWRdBRLR eturn Loss, given reflection coefficient)log(20)( =dBRLM ismatch loss, given fwd/rev power = revfwdfwdPPPdBMLlog10)(Mismatch loss, given reflection coefficient)1log(10)(2 =dBMLMiscLinear interpolation with log of freqLLULULXXXXFFLogFFLogValue+ =)(*)/()/(whereFL = lower frequencyFU = Upper frequencyXL = Value at lower frequencyXU = Value at upper frequencyFX = Frequency of desired valueTEM Cell Power NeededZHeightVWatts2) **(=whereV = field strength in V/mZ = TEM cell impedance in ohms))