Solid vs. Stranded wire in coils

In the past I used loading coils to improve the efficiency of a short dipole on 80m.
The results, however, were disappointing. The main reason seemed to be the low Q factor of the coils.
These coils were made from 1 mm stranded wire.  In the literature stranded wire is considered just as good as solid wire with the same crossection. Some even believe that stranded wire is somewhat better because it has a larger surface area.

Skin effect and Proximity effect

It is well known that at high frequencies current is concentrated in a thin area on the outside of a conductor. This is called the skin effect. In a coil the combined magnetic field of neighbouring windings forces the current to flow on the inside of the coil. This is known as the proximity effect. A non-concentric distribution may be a problem in stranded wires. Since the individual wires in a strand spiral around the centre of the strand, the position of a wire will change along the length of the strand. In order to stay at the inner side of the coil the current must transfer from one wire to the other.  The contact resistance between individual wires may therefore play an important role in the total resistance of the coil, and hence its Q-factor.

coils

To investigate the difference between coils made with stranded and solid wire several samples were measured. Coil A is one of the original loading coils. It is made from 0.75 mm2 stranded wire. Coil B is purpose build with 1.5 mm2 solid wire. Coil C is made from 0.75 mm2 solid enamelled wire closely wound, and coil D is made from 0.75 mm2 stranded wire on a large diameter form. All Q measurements were made at about 3.4 MHz.

Coil
N
D
winding length
wire length
L
Q
Rac
Rdc
A
76
50 mm
175 mm
11.9 m
104 µH
138
15.7 Ω
0.29 Ω
B
82
50 mm
225 mm
12.9 m
99.6 µH
377
5.6 Ω
0.16 Ω
C
90
40 mm
104 mm
11.3 m
139 µH
261
11.3 Ω
0.24 Ω
D
39
113 mm
112 mm
13.8 m
184 µH
152
25.5 Ω
0.346 Ω

Although it is not straight forward to compare the results of the different coils, it is clear that the ones made with solid wire are better than the ones made from stranded wire. For instance, the difference between coil A and B is remarkable. The wire diameter of B is only 1.4 times higher than that of A. If the ac resistance is predominantly determined by the skin effect only, the ac resistance of A would only be about 1.4 times higher, somewhere around 8Ω. In reality it is almost 3 times higher. Even compared to the more compact coil C, having the same wire diameter, coil A performs worse.  Except for coil C the spacing between the wires created by twice the thickness of the insulation helps reducing the proximity effect. Nevertheless the proximity effect is strong enough to cause the extra loss in stranded wires.

Conclusion

In any application where Q-factor and efficiency is important : avoid stranded wire !