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Typical EMC Related Formulas

**dBmW = dBµV - 107**
The constant
in the above equation is derived as follows. Power
is related to voltage according to Ohm's law.
The Log_{10}
function is used for relative (dB) scales, so applying
the logarithmic function to Ohm's law, simplifying, and
scaling by ten (for significant figures) yields:

Note, the resistance of 50 used above reflects that RF systems are matched to 50Ω. Since RF systems use decibels referenced from 1 mW, the corresponding voltage increase for every 1 mW power increase can be calculated with another form of Ohm's law:

Given a resistance of 50Ω and a power of 1 mW

The logarithmic form of Ohm's law shown above is provided to describe why the log of the corresponding voltage is multiplied by 20.

**dBmW/m**^{2} = dBµV/m - 115.8

The constant in this equation is derived following similar logic. First, consider the
poynting vector which relates the power density (W/m^{2})to the electric field
strength (V/m) by the following equation:

Where η is the free space characteristic impedance equal to 120p^{Ω}
Transforming this equation to decibels and using the appropriate conversion factor to
convert dBW/m^{2} to dBmW/m^{2} for power density and dBV/m to dBµV/m
for the electric field, the constant becomes 115.8

**dBµV/m = dBµV + AF**

Where AF is the antenna factor of the antenna being used, provided by the antenna manufacturer or a calibration that was performed within the last year.

**V/m = 10**^{{[(dBµV/m)-120]/20}}

Not much to this one, just plug away!

**dBµA/m = dBµV/m - 51.5**

To derive the constant for the above equation, simply convert the characteristic impedance of free space to decibels, as shown below:

**A/m = 10**^{{[(dBµA/m)-120]/20}}

As above, simply plug away.

**dBW/m**^{2} = 10Log_{10}[V/m - A/m]

A simple relation to calculate decibel-Watts per square meter.

**dBmW/m**^{2}= dBW/m^{2} + 30

The derivation for the constant in the above equation comes from the decibel equivalent of the factor of 1000 used to convert W to mW and vice versa, as shown below:

**dBpT = dBµA/m + 2.0**

In this equation, the constant 2.0 is derived as follows. The magnetic flux density, B in Teslas (T), is related to the magnetic field strength, H in A/m, by the permeability of the medium in Henrys per meter (H/m). For free space, the permeability is given as...

Converting from T to pT and from A/m to µA/m, and deriving the Log, the constant becomes:

View our other RF Conversion formula sheets:

Antenna Factor and Gain Calculations

dBm to Volts to Watts_Conversion

Magnetic field convertions

Field Intensity Calculation

Antenna Beamwidth Coverage Calculations

Frequency and Wavelength Calculator

VSWR Calculations

Typical EMC Related Formulas

P = V^{2}/ R

10Log_{10}[P] = 20Log_{10}[V] - 10Log_{10}[50^{Ω}]

Note, the resistance of 50 used above reflects that RF systems are matched to 50Ω. Since RF systems use decibels referenced from 1 mW, the corresponding voltage increase for every 1 mW power increase can be calculated with another form of Ohm's law:

V = (PR)^{0.5} = 0.223 V = 223000 µV

Given a resistance of 50Ω and a power of 1 mW

20Log_{10}[223000 µV] = 107 dB

The logarithmic form of Ohm's law shown above is provided to describe why the log of the corresponding voltage is multiplied by 20.

P=|E|^{2}/η

Where η is the free space characteristic impedance equal to 120p

Where AF is the antenna factor of the antenna being used, provided by the antenna manufacturer or a calibration that was performed within the last year.

Not much to this one, just plug away!

To derive the constant for the above equation, simply convert the characteristic impedance of free space to decibels, as shown below:

20Log_{10}[120p] = 51.5

As above, simply plug away.

A simple relation to calculate decibel-Watts per square meter.

The derivation for the constant in the above equation comes from the decibel equivalent of the factor of 1000 used to convert W to mW and vice versa, as shown below:

10Log_{10}[1000] = 30

In this equation, the constant 2.0 is derived as follows. The magnetic flux density, B in Teslas (T), is related to the magnetic field strength, H in A/m, by the permeability of the medium in Henrys per meter (H/m). For free space, the permeability is given as...

µ_{o} = 4p x 10^{-7} H/m

Converting from T to pT and from A/m to µA/m, and deriving the Log, the constant becomes:

240 - 120 + 20Log_{10}[4p x 10^{-7}] = 2.0

dBpT = dBuV + dBpT/uV + Cable Loss

dBuV/m = dBpT + 49.5 dB

dBuV/m = dBpT + 49.5 dB

View our other RF Conversion formula sheets:

Antenna Factor and Gain Calculations

dBm to Volts to Watts_Conversion

Magnetic field convertions

Field Intensity Calculation

Antenna Beamwidth Coverage Calculations

Frequency and Wavelength Calculator

VSWR Calculations

A.H. Systems, inc.

9710 Cozycroft Ave.

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