Equivalent series resistance of antenna?

[magnusfelix]

Hi!

We entered a competition, and got the following question:

Modern hearing instruments use wireless communication between the two ears to optimize the performance of the sound processing. The wireless link is typically a magnetic link in the lower MHz range. With this kind of link, each hearing instrument has a loop antenna acting as an inductor and the wireless connection is simply formed by the very weak coupling coefficient between the two inductors. Assuming that the loop antenna has an inductance of 10 µH and a quality factor of 10 at 10 MHz – what is the equivalent series resistance of the antenna at 10 MHz?

Do you have some ideas?

Thanks in advance.

-Magnus

 

[Vailanor]

The equivalent series resistance of the antenna at 10 MHz can be calculated using the formula R = (2πfL) / Q, where f is the frequency, L is the inductance, and Q is the quality factor. So in this case, the equivalent series resistance would be equal to (2 * π * 10MHz * 10µH) / 10 = 0.6283Ω.