Ham Radio  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
dBµv = 20 log [Signal (µV)/1µV]
Decibels relative to one microvolt across same resistance
Decibel Conversion: Microamps
dBµA = 20 log [Signal (µA)/1µA]
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 dBµv
dBµv = dBv + 120
Conversion from dBv to dBµv.
Voltage to Power Conversion: dBµv to dBm
dBm = dBµv  107
Where the constant 107 is as follows: * RF systems are matched to 50Ω
P = V^{2}
/ R
10Log_{10}[P] = 20Log_{10}[V]  10Log_{10}[50Ω]
V = (PR)^{0.5} = 0.223 V = 223000
µV
For a resistance of 50Ω and a power of 1 mW:
20Log_{10}[223000µV] = 107 dB
Power Density
dBw/M^{2} = 10Log_{10}[V/M  A/M]
DecibelWatts 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:
10Log_{10}[1000] = 30
Electric Field to Power Density
dBm/M^{2} = dBµV/M  115.8
Where the constant 115.8 is as follows: P=E^{2}/Z_{o}
Where Z_{o} is the free space characteristic
impedance (Ω), equal to 120π.
Change this equation to decibels, converting dBW/M^{2}
to dBmW/M^{2} for power
density and dBV/M to dBµV/M for the electric field. This yields 115.8
Electric Field Voltage
V/M = 10^{{[(dBµV/M) 120]/20}}
Electric Field Voltage in volts per meter
Electric Field Current
dBµA/M = dBµv/M  51.5
Where the constant 51.5 is a conversion of the characteristic impedance of free space (120π) into decibels:
20Log_{10}[120π] = 51.5
A/M = 10^{{[(dBµA/M) 120]/20}}
Electric Field Current in amps per meter
Antenna Factor
AF_{dB} = E_{dB}  Vr_{dB}
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: µ_{o}
= 4π x 10^{7}
H/M
Convert from T to pT and from A/M to µA/M, and take the Log:
240  120 + 20Log_{10}[4π x 10
^{7}] = 2.0
Units
dB = decibels (Log10)
m = milli = 10E3
µ = micro = 10E6
p = pico = 10E12
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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