AN0005 Datasheet, PDF (1/2 Pages) RF Micro Devices – Converting Field Strength to Power

15
AN0005 Converting Field Strength to Power
AN0005
Converting Field Strength to Power
Background
Precompliance testing should be performed during the design process. This can be done with a GTEM cell or at a com-
pliance test laboratory. It is recommended that precompliance testing be performed so that there are no surprises during
final compliance testing. This will help keep the product development and release on schedule.
Working with a laboratory offers the benefit of years of compliance testing experience and familiarity with the regulatory
issues. Also, the laboratory can often provide feedback that will help the designer make the product compliant.
On the other hand, having a GTEM cell or an open air test site locally offers the designer the ability to rapidly determine
whether or not design changes impact the product's compliance. Set-up of an open air test site and the associated cali-
bration is not trivial. An alternative is to use a GTEM test cell.
After the design has been completed and passes compliance testing, final certifications will need to be obtained. Appli-
cation will need to be made with the respective regulatory bodies for the geographic region in which the product will be
operated.
Derivation of Conversion Factors
In the Code of Federal Regulations Title 47, Part 15 there are numerous tables containing limits for emission levels.
These limits are usually expressed as field strength in microvolts per meter at a given distance from the radiator. While
one could use a field strength meter to measure the emissions of a device, such a test setup is not available in all labora-
tories. However, most RF laboratories have spectrum analyzers. Thus, it would be desirable to establish a relationship
between field strength and power.
The following derivation is simplistic and makes the following assumptions:
• the emission is radiating isotropically
• the signal is being radiated into a sphere
• the power is being radiated evenly over the surface of that sphere
• the efficiency of the radiator is unity
Represent the power density as
P_Density
=
----^P---^T---^r---^a--ⁿ---^s---
4 ⋅ π ⋅ D²
15
Then the electric field, in microvolts per meter, can be represented as
E = 1 ⋅ 10⁶ -3---7---7----^â‹---^P----^T---^r--^a---ⁿ---^s
4 ⋅ π ⋅ D²
Now solve the equation to isolate transmitted power
P_Trans
=
4-----⋅_---π_-----⋅_---D_----²_-
377
⋅


-1----_â‹--^E-1---0---₆-_
2
For the preceding equations the unit of power (P) is Watts, the unit of field strength (E) is microvolt per meter, the unit of
distance (D) is meters.
Copyright 1997-2002 RF Micro Devices, Inc.
15-21