eEngineer - RF Units Conversion
Decibel Conversion: Power

dB = 10 log [P2/P1]

Decibels relative to Power

Decibel Conversion: Voltage

dB = 20 log [V1/V2]

Decibels relative to Voltage across same resistance

Decibel Conversion: Current

dB = 20 log [I1/I2]

Decibels relative to Current through same resistance

Decibel Conversion: Milliwatts

dBm = 10 log [Signal (mW)/1mW]

Decibels relative to one milliwatt

Decibel Conversion: Microvolts

dBv = 20 log [Signal (V)/1V]

Decibels relative to one microvolt across same resistance

Decibel Conversion: Microamps

dBA = 20 log [Signal (A)/1A]

Decibels relative to one microamp through same resistance

Power Conversion: dBw to dBm

dBm = dBw + 30

Conversion from dBw to dBm.

Voltage Conversion: dBv to dBv

dBv = dBv + 120

Conversion from dBv to dBv.

Voltage to Power Conversion: dBv to dBm

dBm = dBv - 107

Where the constant 107 is as follows:
* RF systems are matched to 50
Ω
P = V2 / R
10Log10[P] = 20Log10[V] - 10Log10[50Ω]
V = (PR)0.5 = 0.223 V = 223000 V
For a resistance of 50Ω and a power of 1 mW:
20Log10[223000V] = 107 dB
Power Density

dBw/M2 = 10Log10[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:
10Log10[1000] = 30

Electric Field to Power Density

dBm/M2 = dBV/M - 115.8

Where the constant 115.8 is as follows:
P=|E|
2/Zo
Where Zo is the free space characteristic impedance (Ω), equal to 120π.
Change this equation to decibels, converting dBW/M
2 to dBmW/M2 for power density and dBV/M to dB
V/M for the electric field.
This yields 115.8

Electric Field Voltage

V/M = 10{[(dBV/M) -120]/20}

Electric Field Voltage in volts per meter
Electric Field Current

dBA/M = dBv/M - 51.5
Where the constant 51.5 is a conversion of the characteristic impedance of free space (120π) into decibels:
20Log10[120π] = 51.5

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

AFdB = EdB - VrdB
where:
AF = Antenna Factor in dB/M
E  = Field strength at the antenna in dBµv/M
Vr  = Output voltage from receiving antenna in dBµv

AF (for 50 Ω) = 20 log f (MHz) - G(dBi) - 29.78 dB.
where f is the measured frequency (MHz), G is the antenna gain (dBi) over isotropic.


(E) dBµv/M = (Vo) dBµv + (AF) dB/M

AF is the antenna factor of the measuring antenna (as per calibration or per antenna manufacturer).
E is the unknown or measured electric field strength.
Vo is the adjusted (calibrated for cable & connector losses) spectrum analyzer output.


Magnetic Flux Density

dBpT = dBµA/M + 2.0

Where the constant 2.0 is as follows:
The magnetic flux density B is in Teslas (T)
The permeability of the medium is in Henrys per meter (H/M)
The permeability in free space is:
µo = 4π x 10-7 H/M
Convert from T to pT and from A/M to µA/M, and take the Log:
240 - 120 + 20Log10[4π x 10 -7] = 2.0
Units

dB = decibels (Log10)
m = milli = 10E-3
µ = micro = 10E-6
p = pico = 10E-12
dBi = decibels relative to an isotropic antenna
dBw = decibels relative to one watt
dBm = decibels relative to one milliwatt
dBv = decibels relative to one volt
dBµv = decibels relative to one microvolt
dBµA = decibels relative to one microamp
dBpT = decibels relative to one picoTesla
π = pi = 3.14159265
V = Volts
A = Amps
I = Current
R = Ohms (50)
W = Watts
P = Power
H = Henrys
T = Teslas
AF = Antenna Factor
M = Meters


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