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1. The Log of a product equals the sum of the Logs. Log_{a}(u * v) = Log_{a}(u) + Log_{a}(v) 2. The Log of a quotient equals the difference of the Logs. Log_{a}(u/v) = Log_{a}(u) - Log_{a}(v) 3. Log_{a}(u^{r}) = r * Log_{a}(u) ______________________________________________________________

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(R^{2}+ X^{2}) = 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 Log_{10}(W_{convert}/W_{ref}) ---- For power, W_{convert}is the power in watts to be converted to dB relative to W_{ref}. dB = 20 Log_{10}(AV_{convert}/AV_{ref}) -- For voltage or current, AV_{convert}is the Amps or Volts to be converted to dB relative to AV_{ref}. 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) ______________________________________________________________

Decibels relative to Power dB = 10 Log_{10}(P2/P1) ______________________________________________________________

Decibels relative to Voltage dB = 20 Log_{10}(V2/V1) ______________________________________________________________

Decibels relative to Current dB = 20 Log_{10}(A2/A1) ______________________________________________________________

Decibels relative to one milliWatt dBm = 10 Log_{10}(Power in watts/1mW) ______________________________________________________________

Decibels relative to one microvolt dBuV = 20 Log_{10}(Voltage in Volts/1uV) ______________________________________________________________

Decibels relative to one microamp dBuA = 20 Log_{10}(Current in Amps)/1uA) ______________________________________________________________

Conversion from dBW to dBm dBm = dBW + 30 ______________________________________________________________

dBuV = dBV + 120 ______________________________________________________________

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 Log_{10}(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 Log_{10}(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 ______________________________________________________________

dBW/M^{2}= 10 Log_{10}(V/M - A/M) Decibel-Watts per square meter. dBm/M^{2}= dBW/M^{2}+ 30 Where the constant 30 is the decibel equivalent of the factor 1000 used to convert between W and mW: 10 Log_{10}(1000) = 30 ______________________________________________________________

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

dBuA/M = dBuV/M - 51.5 Where 51.5 is the characteristic impedance of free space (120 * pi = 377ohms) converted into decibels: 20 Log_{10}(377ohm/1ohm) = 51.5 A/M = 10^{[({dBuA/M} - 120)/20]}Electric Field Current in amps per meter ______________________________________________________________