The calculator converts from electric field strength in dBμV/m (deciBel microvolt-per-meter) at 3 meters to power in dBm at the output of the transmitter.
Formula
PdBm = EdBμV/m – 95.2
Example Calculation
In this example we compute the maximum transmitter power in dBm from the level of the radiated field measured at a distance of 3 meters away.
This transmit power is also known as the Effective Isotropic Radiated Power (EIRP).
The Effective Radiated Power (ERP) is given by
ERP = EIRP – 2.15
For frequencies above 960 MHz, the FCC stipulates a maximum radiation limit of 500 uV/m at 3 meter distance from the transmitter. Use this calculator to convert uV to dBuV.
500 uV/m equates to 54 dBuV/m.
A field strength value of 54 dBuV/m equates to a power level of -41.2 dBm at the transmitter.
This information can be used in the design of the transmitter to ensure that it is compliant and therefore does not ever exceed the level of -41.2 dBm.
Background
What is dBm?
dBm stands for deciBel referenced to one milliwatt. The unit is commonly used by RF engineers in the context of absolute power levels associated with various components such as filters, amplifiers, splitters and more.
PdBm = 10*log10(PmW)
where
- PmW is the power expressed in milliwatt.
- PdBm is the power expressed in dBm
What is dBuV/m?
dBμV/m or dBuV/m (where u is substituted for the symbol μ), is a unit for the measurement of electric field strength. It is used in relation to the measurement of radiated field emissions from an electronic product.
Formula and Derivation
Consider an isotropic source that radiates equally in all directions.
The power density Pd = P/(4*π*r2)
The power density decreases with increasing distance from the source r. The FCC stipulates radiated emissions at a distance of 3 meters away from the source and hence we will use r=3 in the equation above.
Pd is also given by the equation
Pd = E2/Zo
Where E is the field strength and Zo is the characteristic impedance of free space, equal to 377 Ω.
Therefore,
P/(4*π*r2)= E2/Zo
which simplifies to
P = 0.3*E2
Converting Power from Watt to dBm and field from uV/m to dBuV/m gives
PdBm = EdBμV/m – 95.2
Output Power of Wholehouse FM Transmitter
We can use this calculator to find the output transmit power of the Whole House FM transmitter.
The FCC report shows a maximum field-strength level of 43.5 dBuV/m in the FM band. This translates to an EIRP (Effective Isotropic Radiated Power) of -51.7 dBm at the output of the FM transmitter.
This information is used by a Radio Frequency engineer to design the product.
The EIRP is calculated as
EIRP = PTx – LC + GAnt
where
- PTx = Transmit Power (dBm)
- GAnt = Antenna gain (dBi)
- LC = Cable Loss (dB)
Assuming a certain antenna gain (either an embedded antenna or a user-provided one), the max transmit power can be calculated. Note that the limit varies with frequency.
Similar analyses have to be performed using the conducted emissions. The FCC stipulates limits on those as well. One of the differences is that conducted emissions are specified from 150 kHz to 30 MHz. Radiated emissions are specified from 30 MHz and up.
References
[1] How to convert dBμV/m test results into Effective Isotropic
Radiated Power (EIRP)