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**

**P _{dBm} = E_{dBμV/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.

**P _{dBm} = 10*log_{10}(P_{mW})**

where

**P**is the power expressed in milliwatt._{mW}**P**is the power expressed in dBm_{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 **P _{d} = P/(4*π*r^{2})**

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.

P_{d} is also given by the equation

**P _{d} = E^{2}/Z_{o}**

Where **E** is the field strength and **Z _{o}** is the characteristic impedance of free space, equal to 377 Ω.

Therefore,

**P/(4*π*r ^{2}**)=

**E**

^{2}/Z_{o}which simplifies to

**P = 0.3*E ^{2}**

Converting Power from Watt to dBm and field from uV/m to dBuV/m gives

**P _{dBm} = E_{dBμV/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** = **P _{Tx} – L_{C} + G_{Ant}**

where

**P**= Transmit Power (dBm)_{Tx}**G**= Antenna gain (dBi)_{Ant}**L**= Cable Loss (dB)_{C}

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)