A simulated 40m multi-turn small transmitting loop

The following is a multi-turn loop model that achieves 50% efficiency at 7 MHz when simulated in 4nec2. It is a 7-turn square loop, with side length 0.64m, and a total length of 1m. The loop is made of copper conductor 12mm in diameter. A long 20m roll of soft 12mm copper tubing should be rollable by hand into this structure with no joints and minimal loss. Resonating capacitance for 7 MHz is 6 pF.

To open the model in 4nec2, copy and paste the text between the dashed lines and save it to a file, then open the file in 4nec2.

----------

CM 3D multi-turn loop
CM qrp.gaijin@yahoo.com (2014/04)
CE
SY C=5.85e-12
SY r=6e-3
SY s=5
GW 17 3 -2.22e-16 1 3.6 -2.22e-16 1 3.75 r
GW 18 5 0 1 3.75 0 0 3.75 r
GW 19 3 0 0 3.75 0 0 3.6 r
GW 20 s 0 0 3.6 0.45 0.03571429 3.15 r
GW 21 s 0.45 0.03571429 3.15 5.5511e-17 0.07142857 2.7 r
GW 22 s 5.5107e-17 0.07142857 2.7 -0.45 0.10714286 3.15 r
GW 23 s -0.45 0.10714286 3.15 -1.11e-16 0.14285714 3.6 r
GW 24 s -1.102e-16 0.14285714 3.6 0.45 0.17857143 3.15 r
GW 25 s 0.45 0.17857143 3.15 5.5511e-17 0.21428571 2.7 r
GW 26 s 5.5107e-17 0.21428571 2.7 -0.45 0.25 3.15 r
GW 27 s -0.45 0.25 3.15 -1.11e-16 0.28571429 3.6 r
GW 28 s -1.102e-16 0.28571429 3.6 0.45 0.32142857 3.15 r
GW 29 s 0.45 0.32142857 3.15 5.5511e-17 0.35714286 2.7 r
GW 30 s 5.5107e-17 0.35714286 2.7 -0.45 0.39285714 3.15 r
GW 31 s -0.45 0.39285714 3.15 -1.11e-16 0.42857143 3.6 r
GW 32 s -1.102e-16 0.42857143 3.6 0.45 0.46428571 3.15 r
GW 33 s 0.45 0.46428571 3.15 5.5511e-17 0.5 2.7 r
GW 34 s 5.5107e-17 0.5 2.7 -0.45 0.53571429 3.15 r
GW 35 s -0.45 0.53571429 3.15 -1.11e-16 0.57142857 3.6 r
GW 36 s -1.102e-16 0.57142857 3.6 0.45 0.60714286 3.15 r
GW 37 s 0.45 0.60714286 3.15 5.5511e-17 0.64285714 2.7 r
GW 38 s 5.5107e-17 0.64285714 2.7 -0.45 0.67857143 3.15 r
GW 39 s -0.45 0.67857143 3.15 -1.11e-16 0.71428571 3.6 r
GW 40 s -1.102e-16 0.71428571 3.6 0.45 0.75 3.15 r
GW 41 s 0.45 0.75 3.15 5.5511e-17 0.78571429 2.7 r
GW 42 s 5.5107e-17 0.78571429 2.7 -0.45 0.82142857 3.15 r
GW 43 s -0.45 0.82142857 3.15 -1.11e-16 0.85714286 3.6 r
GW 44 s -1.102e-16 0.85714286 3.6 0.45 0.89285714 3.15 r
GW 45 s 0.45 0.89285714 3.15 5.5511e-17 0.92857143 2.7 r
GW 46 s 5.5107e-17 0.92857143 2.7 -0.45 0.96428571 3.15 r
GW 47 s -0.45 0.96428571 3.15 -1.11e-16 1 3.6 r
GE -1
LD 5 17 0 0 58000000
LD 5 18 0 0 58000000
LD 5 19 0 0 58000000
LD 0 18 3 3 0 0 C
LD 5 20 0 0 58000000
LD 5 21 0 0 58000000
LD 5 22 0 0 58000000
LD 5 23 0 0 58000000
LD 5 24 0 0 58000000
LD 5 25 0 0 58000000
LD 5 26 0 0 58000000
LD 5 27 0 0 58000000
LD 5 28 0 0 58000000
LD 5 29 0 0 58000000
LD 5 30 0 0 58000000
LD 5 31 0 0 58000000
LD 5 32 0 0 58000000
LD 5 33 0 0 58000000
LD 5 34 0 0 58000000
LD 5 35 0 0 58000000
LD 5 36 0 0 58000000
LD 5 37 0 0 58000000
LD 5 38 0 0 58000000
LD 5 39 0 0 58000000
LD 5 40 0 0 58000000
LD 5 41 0 0 58000000
LD 5 42 0 0 58000000
LD 5 43 0 0 58000000
LD 5 44 0 0 58000000
LD 5 45 0 0 58000000
LD 5 46 0 0 58000000
LD 5 47 0 0 58000000
GN 2 0 0 0 3 0.0004
EK
EX 0 18 3 0 0 0 0
FR 0 0 0 0 7 0
EN

----------

The simulation results are as shown in the following image.

Addendum 2015-01-03

From the above current diagram (where blue represents lower current flow and red represents higher current flow) it is clear that there is little current flowing in the horizontal section of the antenna connecting the two loop ends. This horizontal section of the antenna contains the loop resonating capacitance of 6 pF. Therefore, there is very little current flowing through the resonating capacitor. This is because the multi-turn loop structure is almost self-resonant by itself with no capacitor.

It follows that by adjusting the turn spacing or diameter, the structure can be made self-resonant with no need for an additional resonating capacitor.

Then, the proper term for this kind of a long, multi-turn, self-resonant radiator is a "normal mode helix". Here is an article describing practical construction and matching of a normal-mode helix for VHF use: w6nbc.com/articles/2011-06QST2mhelices.pdf .

Though I yet haven't built one, I see nothing that would prevent a similar antenna from being built for HF use.