Technical Information
Litz Wire
By definition, the Litz constructions covered in this section are made with individually insulated strands. Common magnet wire film insulations such as: polyvinylformal, polyurethane, polyurethane/nylon; solderable polyester, solderable polyester/nylon, polyester/polyamide-imide, and polyimide are normally used. The outer insulation and the insulation on the component conducts, in some styles, may be servings or braids of nylon, cotton, nomex, fiberglass or ceramic. Polyester, heat sealed polyester, polyimide, and PTFE tape wraps along with extrustions of most thermoplastics are also available as outer insulation if the applications dictate special requirements for voltage breakdown or environmental protection.
Litz Design
Typically, the design engineer requiring the use of Litz knows the operating frequency and RMS current required for the application. Since the primary benefit of a Litz conductor is the reduction of AC losses, the first consideration in any Litz design is the operating frequency. The operating frequency not only influences the actual Litz construction, but is also used to determine the individual wire gauge.
Ratios of alternating-current resistance to direct-current resistance for an isolated solid round wire (H) in terms of a value (X) are shown below.
Table 1
X |
0 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
H |
1.0000 |
1.0003 |
1.0007 |
1.0012 |
1.0021 |
1.0034 |
1.005 |
The value of X for copper wire is determined by the following formula.
Formula 1
X = 0.271 D_{M} √F_{MHz}
Where:
D_{M } = Wire diameter in mils
F_{MHz }= frequency in megahertz
From table 1 and other empirical data the following table of recommended wire gauges Vs. frequency for most Litz constructions has been prepared.
Table 2
Frequency |
Recm'd Wire Guage |
Nom. Dia. Over Copper |
D Res. Ω/M (Max) |
Single Strand R_{AC}/R_{DC} "H" |
60 Hz to 1k Hz |
28 AWG |
0.0126 |
66.37 |
1.0000 |
1k Hz to 10k Hz |
30 AWG |
0.0100 |
105.82 |
1.0000 |
10k Hz to 20k Hz |
33 AWG |
0.0071 |
211.70 |
1.0000 |
20k Hz to 50k Hz |
36 AWG |
0.0050 |
431.90 |
1.0000 |
50k Hz to 100k Hz |
38 AWG |
0.0040 |
681.90 |
1.0000 |
100k Hz to 200k Hz |
40 AWG |
0.0031 |
1152.30 |
1.0000 |
200k Hz to 350k Hz |
42 AWG |
0.0025 |
1801.0 |
1.0000 |
350k Hz to 850k Hz |
44 AWG |
0.0020 |
2873.0 |
1.0003 |
850k Hz to 1.4M Hz |
46 AWG |
0.0016 |
4544.0 |
1.0003 |
1.4M Hz to 2.8M Hz |
48 AWG |
0.0012 |
7285.0 |
1.0003 |
After the individual wire gauge has been determined and assuming that the Litz construction has been designed such that each strand tends to occupy all possible positions in the cable to approximately the same extent, the ratio of AC to DC resistance of isolated Litz conductor can be determined from the following formula.
Formula 2
Resistance to Alternating Current |
= H + K (N D_{i }/ D_{o})^{2} G |
Resistance to Direct Current |
Where:
H = Resistance ratio of individual strands when isolated (taken from Table 1 or Table 2)
G = Eddy-current basis factor = (D_{i}√F / 10.44)^{4}
F = Operating frequency in Hz
N = Number of strands in the cable
D_{i} = Diameter of the individual strands over the copper in inches
D_{o} = Diameter of the finished cable over the strands in inches
K = Constant depending on N, given in the following table
N |
3 |
9 |
27 |
∞ |
K |
1.55 |
1.84 |
1.92 |
2 |
The DC resistance of a Litz conductor is related to the following parameters:
The following formula derived from these parameter for the DC resistance of any Litz construction is:
Formula 3
R_{DC} = |
R_{S }(1.015) ^{N}_{B }(1.025) ^{N}_{C} |
N_{S} |
Where:
R_{DC} = Resistance in ohms/1000 ft.
R_{S }= Maximum DC resistance of the individual strands
(taken from Table 2)
N_{B} = Number of bunching operations
N_{S }= Number of individual strands
Following is an example of the calculations required to evaluate a Type 2 Litz construction consisting of 450 strands of 40AWG single-film polyurethane-coated wire operating at 100 kHz. This construction, designed with two bunching operations and one cable operation, would be written 5X3/30/40 (NEEWC uses "X" to indicate a cabling operation and "/" to indicate a bunching operation).
R_{DC} = |
1152.3 x (1.015) ^{2}_{ }(1.025) ^{1} |
or 2.70 ohms / 1000 ft. |
450 |
R_{AC} |
= 1.0000 + 2 ( |
450 x .0031 |
) ^{2} 7.8 x 10^{-5} or 1.0344 |
R_{DC} |
.094 |
The value of Litz can easily be seen if the above example is compared with a solid round wire with equivalent cross sectional area, 65.8 mils in diameter. Using the same operating parameters, the D.C. resistance is 2.395 ohms /1000 ft. However, the A.C./D.C. resistance ratio increase to approximately 21.4 making the A.C. resistance 51.3 ohms /1000 ft.
The following tables list examples of Litz constructions which can be manufactured by NEEWC. These are categorized by operating frequency and by equivalent AWG size. Round, braided, and rectangular Litz conductors are shown separately to provide the greatest possible selection for any design application.
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