NVIS Antenna Addition

Using info from: L B. Cedbik Part I: Inductive Coupling http://on5au.be/content/link/link1.html
 

Mutual Inductance “M” Henrys is:

 

M = (La -Lo) / 4

Where

La is the sum of the two coils in addition, and

Lo is the sum of the two coils in opposition

 

I measured two 3/8 O.D. copper tubing loops, one 24 inches diameter and the other 15.25 inches diameter. See the accompanying photos.

 

The 24 inch measures 1.67μH on my DE5000 LCR Bridge meter at 100KHz. The 15.25 inch measures 1.025μH on the same meter. This is in close agreement with the calculated inductance of 1.616 μH and 0.916 μH using Yates & Sawiak “Small HF Loop Antenna Calculator ver. 1.22f https://www.aa5tb.com/aa5tb_loop_v1.22f.xlsx”

 

I then put the smaller loop inside the larger loop separated by about one inch at the closest point. I connected them in series with a 2 inch wire.

 

I arranged it so that I could flip the 15.25 loop over to change from series aiding to series opposing. I used my DE5000 meter to measure the combined inductance in each configuration. See Photos.

The results:

La = 3.337 μH

Lo = 1.992 μH

 

Using these measurements, I calculate

M = (3.337 – 1.992) / 4 = 0.33625 μH

 

Intuitively, It seems to me like the inductance of two inductors in series without any mutual coupling would just be the sum of the two inductance ie. 1.67 + 1.025 = 2.695, so the “mutual” effect must be the 3.337 – 2.695 difference or 0.642 μH which is almost twice what I calculate using Cedbik’s formula!

 

After re-reading Cedbik’s text, it may be that his calculation refers to the increase in inductance in each loop.

 

Also, I note that the inductance of a coil is proportional to the square of the number of turns. S it makes sense that the increase of the turns squared inductance over the sum of each turn's inductance when measured separately, must be due to the "Mutual" inductance effect of the turns combined magnetic fields!