RF Calculations & RF Unit Conversions

Note: The decimal point "." is used as decimal separator for both input and output:

Calculate wavelength from frequency:

__Formula: __

λ = c/f

λ: Wavelength in meters

c: Speed of light (299792458 m/s)

f: Frequency in Hz

Input frequency in Hz:

Calculate frequency from wavelength:

__Formula: __

λ = c/f

λ: Wavelength in meters

c: Speed of light (299792458 m/s)

f: Frequency in Hz

Input wavelength in m:

Conversion between different units of Power Flux Density:

Power Flux Density in W/m^{2}:

Power Flux Density in mW/m^{2}:

Power Flux Density in uW/m^{2}:

Power Flux Density in W/cm^{2}:

Power Flux Density in mW/cm^{2}:

Power Flux Density in uW/cm^{2}:

Calculate 3-axis Field Intensity from 1-axis Mesurement:

__Formula: __

Field Intensity = √ (x^{2} + y^{2} + z^{2})

E: 3-axis Field intensity, measured in V/m

X, Y, Z: Single axis field intensity, measured in V/m.

__ Note: __

Some instruments only measure single axis field intensity. This calculation is used to calculate the 3-axis field intensity from 3 single axis measurements.

Single axis Field Intensity (x-axis) in V/m:

Single axis Field Intensity (y-axis) in V/m:

Single axis Field Intensity (z-axis) in V/m:

Calculate Field Intensity from Power Flux Density:

__Formula: __

P_{d} = E^{2}/Z_{0} = Z_{0}*H^{2}

P_{d}: Power Flux Density, measured in W/m^{2}

E: Field Intensity for the electric field, measured in V/m.

H: Magnetic field, measured in A/m.

Z_{0}: Impedance of free air = 120π = 377Ω

__ Note: __

I far-field conditions Field intensity and Power Flux Density is related by free air impedance. This calculation is therefore only valid for far-field conditions.

Power Flux Density in W/m^{2}:

Calculate Power Flux Density from Electric Field Intensity:

__Formula: __

P_{d} = E^{2}/Z_{0} = Z_{0}*H^{2}

P_{d}: Power Flux Density, measured in W/m^{2}

E: Field Intensity for the electric field, measured in V/m.

H: Magnetic field, measured in A/m.

Z_{0}: Impedance of free air = 120π = 377Ω

__ Note: __

I far-field conditions Field intensity and Power Flux Density is related by free air impedance. This calculation is therefore only valid for far-field conditions.

Electric Field Intensity in v/m:

Calculate Power Flux Density from an Isotropic Antenna:

__Formula:__

P_{d} = P_{t} / (4 * π * d^{2})

P_{d}: Power Flux Density, measured in W/m^{2}

P_{t}: Transmitter Output Power, measured in W

d: Distance, measured in meters

Transmitter Output Power in Watts:

Distance in meters from transmitter:

Calculate Power Flux Density from an Directional Antenna:

__Formula:__

P_{d} = (P_{t} * G_{t}) / (4 * π * R^{2})

P_{d}: Power Flux Density, measured in W/m^{2}

P_{t}: Transmitter Output Power, measured in W

G_{t}: Transmitter antenna gain (linear)

d: Distance, measured in meters

Transmitter Output Power in Watts:

Distance in meters from transmitter:

Gain (linear, non-dimensional) for transmitter antenna:

Conversion from Gain in dB to linear gain:

__Formula:__

G_{linear} = 10^{(GdB / 10) }

G_{linear}: Gain measured in linear terms (dimensionless)

G_{dB} : Gain measured in dB

__ Note: __

Gain can be measured either as a purely matematical construct - in which case it is referred to as dB.

It can also be measured in decibels referenced to an isotropic antenna - in which case it is referred to as dBi

Since the gain of an isotropic antenna is 1, these units are interchangeable. 1 dB gain is equal to 1 dBi gain, but the term dBi denotes the reference to the isotropic antenna.

An alternative definition compares the antenna to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd.
Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is: gain in dBd = gain in dBi - 2.15 dB

Gain in dB:

Conversion from power in dBm to power in Watt:

__Formula: __

P_{(W)}Power = 1W * 10^{(P(dBm)/10)} / 1000

P_{(W)} : Electrical Power, measured in W

P_{(dBm)} : Electrical Power, measured in dBm

__ Note: __

dBm denotes a measurement in decibels referenced to a milliWatt

Power in dBm:

Conversion from power in dBW to power in Watt:

__Formula: __

P_{(W)}Power = 1W * 10^{(P(dBW)/10)}

P_{(W)} : Electrical Power, measured in W

P_{(dBW)} : Electrical Power, measured in dBW

__ Note: __

dBW denotes a measurement in decibels referenced to a Watt

Power in dBW:

Conversion from power in Watt to power in dBm:

__Formula: __

P_{(dBm)} = 10 * log10(1000 * P_{(W)})

P_{(W)} : Electrical Power, measured in W

P_{(dBm)} : Electrical Power, measured in dBm

__ Note: __

dBm denotes a measurement in decibels referenced to a milliWatt

Input power in Watt:

Conversion from power in Watt to power in dBW:

__Formula: __

P_{(dBW)} = 10 * log10(1 * P_{(W)})

P_{(W)} : Electrical Power, measured in W

P_{(dBm)} : Electrical Power, measured in dBW

__ Note: __

dBW denotes a measurement in decibels referenced to a Watt

Input power in Watt:

Calculate EIRP from Transmitter Power and Gain:

__Formula:__

EIRP = P_{t} * G_{t}

P_{t}: Transmitter Power, measured i W

G_{t}: Transmitter Gain, measured as a linear ratio

Transmitter Power in Watt:

Linear Gain:

Calculate EIRP from Electric Field and Distance:

__Formula:__

EIRP = (E * d)^{2} / 30

E: Electrical Field, measured in V/m

d: Distance, measured in meters

Electric Field in V/m:

Distance in m:

Calculate ERP from EIRP:

__Formula:__

ERP = EIRP / 1.64

EIRP:

Friis Transmission Formula (calculation of received power) solved for wavelength:

__Formula:__

P_{r} = (P_{t} * G_{t} * G_{r} * λ^{2} ) / (4*pi*d)^{2}

P_{r} : Received Power, measured in W

P_{t} : Transmittet Power, measured in W

G_{t} : Transmitter Antenna Gain, linear

G_{r} : Receiver Antenna Gain, linear

λ : Wavelength, measured in meters

d : Distance, measured in meters

Transmitter Power (W):

Transmitter gain (linear):

Receiver gain (linear):

Wavelength (m):

Distance (m):

Calculate Safety Distance from a transmitter:

__Formula:__

P_{d} = (P_{t} * G_{t}) / (4 * π * d^{2})

P_{d}: Power Flux Density, measured in W/m^{2}

P_{t}: Transmitter Power, measured in W

G_{t}: Transmitter Antenna Gain, linear

d: Distance, measured in meters

__Note:__

Safety distances are calculated using:

SBM2008 "No Concern"-Limit: 0.0000001 W/m^{2}

BioInitiative 2012 "Precautionary Level": 0.000003 W/m^{2}

Transmitter Output Power in Watts:

Gain (linear, non-dimensional) for transmitter antenna: