## A22 Conversion Of Radiofrequency Rf Field Strength To Power

Many radio engineers are accustomed to working in the power domain (e.g., dBm, dBW). For example, we may wish to know the receive signal level (RSL) at the input to the first active stage of a HF receiver. In the power domain, the characteristic impedance is not a consideration, by definition.

HF engineers traditionally work with field strength usually expressed in microvolts per meter ( ^V/m). When we convert fiV / m to dBm, characteristic impedance becomes important. We remember the familiar formula

where E is expressed in volts and I in amperes, and we can consider R to be the characteristic impedance.

* Section A2.2 is based on Technical Issues #89-1 (Dave Adamy), Association of Old Crows, Alexandria, VA, 1989.

Carrying this one step further,

(impedance of free space)

The impedance of free space is 120^ or 377 O. The effective antenna area is ga2

where A = effective antenna area (m2)

G = antenna gain (numeric, not dB) A = wavelength (m)

E 2A2

We rewrite equation (A2.12) expressed in frequency rather than wavelength:

where c = velocity of propagation in free space, or 3 X 108 m/s. Convert to more useful units: express P in milliwatts, E in microvolts per meter, and f in megahertz. Then

Here E is expressed in microvolts per meter. We now derive

where E is the field strength in microvolts per meter and f is expressed in megahertz. To convert back to field strength

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