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 DM FMHz

Where:

DM = Wire diameter in mils

FMHz = 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 RAC/RDC "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 Di / Do)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 = (DiF / 10.44)4

F = Operating frequency in Hz

N = Number of strands in the cable

Di = Diameter of the individual strands over the copper in inches

Do = 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:

  1. AWG of the individual strands.
  2. Number of strands in the cable.
  3. Factors relating to the increased length of the individual strands per unit length of cable (take-up). For normal Litz constructions a 1.5% increase in DC resistance for every cabling operation are approximately correct.

The following formula derived from these parameter for the DC resistance of any Litz construction is:

Formula 3

RDC =

RS (1.015) NB (1.025) NC

NS

Where:

RDC = Resistance in ohms/1000 ft.

RS = Maximum DC resistance of the individual strands

(taken from Table 2)

NB = Number of bunching operations

NS = 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).

  1. Calculate the D.C. resistance of the Litz construction using formula 3.
  2. RDC =

    1152.3 x (1.015) 2 (1.025) 1

    or 2.70 ohms / 1000 ft.

    450

  3. Calculate the A.C. to D.C. resistance ratio using formula 2.
  4. RAC

    = 1.0000 + 2 (

    450 x .0031

    ) 2 7.8 x 10-5 or 1.0344

    RDC

    .094

  5. The A.C. resistance is, therefore, 1.0344 X 2.70 or 2.79 ohms /1000 ft.

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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