Correlation to far-field measurements

[thaanstad]

Can you please provide some background and intermediate calculation steps for the Correlation to far-field measurements equation that you derived using "ANTENNA GAIN-FACTOR EQUIVALENT FOR TEM CELLS". In your experience has this been a reasonable correlation to EMC testing in a RF chamber?

Thanks for all the info! I'm looking forward to building a TEM cell.

[PetteriAimonen]

I don't have much experience with correlating the results yet. I do know that one product that barely passed testing is also close to the limit line I ended up with for TEM cell measurements. But with the effects from orientation, resolution bandwidth, frequency dependence, effect of cables etc, it is not clear how close one could hope to get.

As for the formula

I started with the equations:

Divide second row (FAR) by first row (TEM) and you get:

$$\frac{P{FAR}}{P{TEM}} = \frac{g_r (\frac{1}{r})^2}{(\frac{4\pi Z_0}{η_0}) (\frac{1}{h})^2} = \frac{g_r h^2 η_0}{4\pi Z_0 r^2}$$

Then from Wikipedia take the ideal isotropic antenna factor (antenna gain G = 1 for isotropic antenna). Note that it is in terms of voltage, so to apply it to the power ratio we should square it.

$$\sqrt{g_r} = \sqrt{\frac{η_0}{Z_0 \times \frac{\lambda^2}{4\pi}}} = \sqrt{\frac{η_0 4\pi}{Z_0 \lambda^2}} $$

Combining these two equations gives:

$$\frac{P{FAR}}{P{TEM}} = \frac{h^2 η_0^2}{Z_0^2 r^2 \lambda^2}$$

Then take square root again to get from power ratio to voltage ratio. And 20 * log10() to convert from voltage ratio to dB.

I do hope I haven't made some silly mistake somewhere. At least the units check out :)

Various EMC standards have all kinds of test setups, e.g. semi-anechoid room or open air test site has a reflection from ground while fully anechoid room does not. And the antennas used are dipoles instead of isotropic. But all of these add up to a few dB at most, which is probably irrelevant for the kind of accuracy we can even hope for here.