EMC Reference Stuff

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Laws of Logarithms

1. The Log of a product equals the sum of the Logs.
   Loga(u * v) = Loga(u) + Loga(v)

2. The Log of a quotient equals the difference of the Logs.
   Loga(u/v) = Loga(u) - Loga(v)

3. Loga(ur) = r * Loga(u)
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Conversion Units

    E = Electromotive Force (measured in volts)
    V = Volts = Electromotive Force also referred to as E
    A = Amps  = Current also referred to as I
    I = Current (measured in amps)

    R = Resistance (measured in ohms)
    X = Reactive Resistance (measured in ohms) (resistance due to coils/inductors/inductance/capacitors)
    Z = The hypotenuse of the right angle triangle made up of R and X
    Z = sqrt(R2 + X2) = hypotenuse Z

    P = Power (measured in watts)
    W = Watts

    M = Meter (Metric Unit of Measure)

    m = milli = 10E-3  = 0.001
    u = micro = 10E-6  = 0.000001
    n = nano  = 10E-9  = 0.000000001
    p = pico  = 10E-12 = 0.000000000001

   dB = 10 Log10(Wconvert/Wref) ---- For power, Wconvert is the power in watts to be converted to dB relative to Wref.
   dB = 20 Log10(AVconvert/AVref) -- For voltage or current, AVconvert is the Amps or Volts to be converted to dB relative to AVref.

  dBW = decibels relative to one watt (1 Watt)
  dBm = decibels relative to one milliwatt (0.001 Watt)

  dBV = decibels relative to one volt (1 Volt)
 dBuV = decibels relative to one microvolt (0.000001 Volt)

  dBA = decibels relative to one Amp (1 Amp)
 dBuA = decibels relative to one microamp (0.000001 Amp)
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Decibel Conversion for Power

Decibels relative to Power
dB = 10 Log10(P2/P1)
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Decibel Conversion for Voltage

Decibels relative to Voltage
dB = 20 Log10(V2/V1)
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Decibel Conversion for Current

Decibels relative to Current
dB = 20 Log10(A2/A1)
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Decibel Conversion for milliWatts (mW)

Decibels relative to one milliWatt
dBm = 10 Log10(Power in watts/1mW)
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Decibel Conversion for microvolts (uV)

Decibels relative to one microvolt
dBuV = 20 Log10(Voltage in Volts/1uV)
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Decibel Conversion for microamps (uA)

Decibels relative to one microamp
dBuA = 20 Log10(Current in Amps)/1uA)
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Power Conversion dBW to dBm

Conversion from dBW to dBm
dBm = dBW + 30
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Voltage Conversion dBV to dBuV

dBuV = dBV + 120
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Voltage to Power Conversion dBuV to dBm and dBm to dBuV

dBm  = dBuV - 107dB
dBuV = dBm  + 107dB

107 derived for a 50 ohm system as follows:

    The voltage across a resistance of 50 ohms necessary to produce 1mW is:
    V = sqrt(P * R)
    V = sqrt(1mW * 50ohms) = 0.2236V
    One milliwatt dissipated across a resistance of 50 ohms requires 0.2236V across the resistance.
 
    Converting 0.2236 to dBuV yields 107dBuV as follows:
    20 Log10(0.2236V/1uV) = 20 x log(0.2236/0.000001) = 107dBuV

    Converting 1mW to dBm yields 0dBm as follow:
    1 mW = 0.001 watts = 0dbm per the equation:
    10 Log10(0.001/0.001) = 0dBm


    Therefore, it follows that 0dBm = 107dBuV in a 50 ohm system.

    Using 107db as the scale factor yields:

     107dBuV - 0dBm = 107db difference
           and
     dBm = dBuV - 107dB
           and
    dBuV = dBm  + 107dB
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Power Density

dBW/M2 = 10 Log10(V/M - A/M)
Decibel-Watts per square meter.

dBm/M2 = dBW/M2 + 30
Where the constant 30 is the decibel equivalent of the factor 1000 used to convert between W and mW:
10 Log10(1000) = 30
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Electric Field Voltage

Electric Field Voltage in Volts per meter 
V/M = 10[({dBuV/M} - 120)/20]
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Electric Field Current

dBuA/M = dBuV/M - 51.5
Where 51.5 is the characteristic impedance of free space (120 * pi = 377ohms) converted into decibels: 20 Log10(377ohm/1ohm) = 51.5 

A/M = 10[({dBuA/M} - 120)/20]
Electric Field Current in amps per meter
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