Calculating Radiated Power and Field Strength for Conducted Power Measurements
The Federal Communications Commission (FCC) Regulations for Radio Frequency Devices defines power andradiated limits in terms of electric field strength measured in volts/meter (typically at a distance of 3 meters) from the source. Unless the engineer has access to a RF anechoic chamber, GigaHertztransverse electromagnetic (GTEM) cell, or open area test site (OATS), most measurements will be made as conducted power measurements into the 50 Ω load presented by the test equipment. Thisapplication note will explain the relationship between conducted power levels and radiated power field strengths.
3 Antennas and Power Density
3.1 Isotropic Antennas
Since we are concerned with theradiated field generated from the antenna, we will consider the point source radiator or isotropic antenna. The performance of most practical antennas is often referenced in terms of this basic radiator. Theisotropic antenna radiates energy equally in all directions; hence the radiation pattern in any plane is circular, as illustrated below in Figure 1.
Figure 1: Isotropic RadiatorIn the case of the isotropic radiator at point O which is fed with a power P watts. The power flows outwards from the origin and must flow through the spherical surface, S, of radius, r. We can definethe power density, Pd, at the point Q as:
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Calculating Radiated Power and Field Strength forConducted Power Measurements
Poynting’s theorem defines the relationship between the power density to the E-field and H-field vectors as defined below:
3G = ( × +
The magnitude of thepower density is thus:
( , where π is the impedance of free space or approximately 377Ω. π ( ( 3 From the above, we can see that = π , and thus, = + π πU _ 3G _= (+ =
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