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How to Convert dBuA to EIRP

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tony_lth

tony_lth

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HI,
I estimated one equipment using 6.77MHz point freq.
The government requires that the magnetic field strngth is less than 42dBuA/m （QuasiPeak) at 10 meters away.
I need to calculate its EIRP with the following method, but I doubt it's right, could you help me? Thanks.
@10m
Magnetic Field Strength 42 dBuA/m
Magnetic Field Strength 125.8925412 uA/m
air impedance 377 ohms
voltage strength (V=I*R) 47461.48802 uV/m
voltage strength 0.047461488 V/m
voltage=E*L(10m) 0.47461488 V
Power=V^2/50 0.004505186 W
Power 6.537126961 dBm
 

No, your derivation is not correct.
You cannot multiply the voltage strength by the distance to obtain a voltage. Furthermore the "power" you have to calculate is not referred to the 50 ohm.

In case of a isotropic radiator (that is the power is equally distribuite over the surface of a sphere), from the EIRP we can calculate the Pointyng vector magnitude:

P = EIRP/(4*pi*d^2)

then we know that in far field P=Zo*H^2
where Zo = 377 ohm, H is the magnetic field in A/m

thus:

EIRP/(4*pi*d^2) = Zo*H^2 from which:

EIRP=(4*pi*d^2)*Zo*H^2

numerically:

EIRP = (4*pi*10^2)*377*(126e-6)^2 = 0.0075 W or 8.76 dBm

However this is an RMS value, the quasi-peak measurement requires a correction that depends from the waveform
 
Hi, albbg,
Many thanks.
Best,
Tony Liu
 

The other problem involved with the calculation is that 10 m is absolutely near field (lambda is about 40 m). Any calculation based on free space transmission or coupling of electric and magnetic field will give wrong results.

Simulating the exact shape of the transmitting coil and it's magnetic field will give you a much more accurate result. To estimate the power radiated to the far field, you can refer to radiation impedance formulas in antenna theory text books. Its percentage related to reactive and loss power is probably very small, and not actually addressed by EMI regulations.
 
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