## Parameter Selection

## I Litz wire features: Main influence of construction parameters

The performance of a litz wire is determined by its electrical, mechanical, thermal and chemical features. While the thermal, and chemical demands are determined by selection of suitable insulation materials, the electrical and mechanical properties depend mainly on the chosen parameters of the bunching construction.

The following table gives an overview of the mutual influences of the construction parameters on the most important electrical and mechanical features of a litz wire.

**General influencing aspects of construction litz wire parameters on litz wire features**

| construction parameters | ||||||||

conductor material | Ø | no. of single wires n | no. of bundles & bunching | SL per bunching step | SR per bunching step | thickness of enamelling | |||

| electrical | total cross section litz wire conductor A current resistance R | X | X | X | ||||

high frequency resistance R RF-losses | X | X | X | X | |||||

current density J = I/A | X | X | |||||||

A | X | X | X | X | X | ||||

breakdown voltage U_{BDV} | X | ||||||||

mechanical (A | outer diameter OD total cross section litz wire A | X | X | X | X | X | X | X | |

dimensional stability | X | X | X | X | X | ||||

flexibility | X | X | X | X | |||||

flex life performance | X | X | X | X | |||||

max. tensile strength | X | ||||||||

surface structure, roundness | X | X | X | X | X |

Table 1

On one hand you can see that each litz wire feature can be influenced by several construction parameters. On the other hand, it becomes obvious that each change of a construction parameter can impact various other litz wire features.

The following table shows an overview of litz criteria reduced to typical high frequency coils relevance:

**Main influencing parameters for HF-coils**

| construction parameters | ||||||

Ø | number single wires n | number bundles & bunching | SL per bunching step | SR per bunching step | |||

| electrical | total conductor cross section A_{Conductor,Litz;} direct current resistance R_{DC} | X | X | |||

resistance at high frequency R RF-losses | X | X | X | ||||

mechanical | outer diameter litz wire OD_{Litz;} total cross section litz wire A_{tot,Litz} | X | X | X | X | X | |

flexibility | X | X | X | X |

Table 2

Often there can be conflicting demands of each application that have to be thoughtfully worked out between Elektrisola and the customer. Elektrisola's expertise in litz design and construction coupled with the customers performance expectations for their application results in a final product exhibiting the best aspects of performance, processability, and cost effectiveness.

## II Selection of single wire nominal diameter

The correct choice of the single wire nominal diameter is one of the most important aspects in designing a litz wire, since this directly affects the RF performance of the litz wire (see R_{AC}/R_{DC}-Ratio). At the same time it influences also all mechanical features.

(see table 2.)

The relationship of the single wire diameter to the dominate operating frequency and the expected skin depth of the device is shown in the following table (see approximate values in table).

In general,

the higher the operating frequency, the smaller the nominal single wire diameter has to be. To consider interaction between several bundle diameters (ODBundle-) with skin depths δ in a simplified way, the maximum single wire diameter should be smaller or equal to nearly a third of δ:

**Ø _{ED} ≤ δ/3**

Example: f = 200 kHz, δ ≈ 0,172 mm, Ø_{ED} ≈ 0,063 mm;

Regarding the influence on the mechanical litz wire performance for equivalent total copper cross sections you can assume the following:

The smaller the nominal single wire diameter the

- more flexible and softer the litz wire
- smaller the minimal bending radius
- higher the flex life performance
- larger the total outer diameter of the litz wire
- smaller the litz wire filling factor
- higher the single wire costs

## III Selection of the bunching construction

When the number of single wires is determined for the application, the specific bunching construction can be chosen. Finer litz wire with a smaller number of single wires (typical < 60) are bunched in one step, thicker and more complex litz wires are bunched in multiple steps.

The bunching construction is specified by definition of length of lay (SL), pitch (bunching) direction (SR), and the number of bundles and bunching steps. Proper selection of bunching parameters is required to ensure optimal electrical, mechanical, and processing related litz wire characteristics.

**Number of bundles and bunching steps**

Parameters like total copper cross section, electrical resistance, or current density define the required number of single wires, which can be divided in several bundles and bunching steps. In consideration of these factors, Bundles of the first bunching step can be designed for optimal high frequency performance. In consideration of these factors, the number of single wires in one bundle is typically less than sixty.

There are 4 basic bunching constructions typically used in the final bunching step: They are 3, 4, 5 and concentric 7 bundle construction.

"5 bundle construction" | "7 bundle construction " |

3, 4 and 5 bundle constructions

These bunching constructions show a good bundling performance with statistically homogeneous distribution of the single wires across the litz wire cross section. These constructions are preferred for optimal high frequency performance. The 5 bundle construction is preferred due to its round profile, since roundness increases with the number of bundles.

7 bundle construction

These concentric constructions, also called “1+6 bundling“, they show both high flexibility and good dimensional stability and roundness. One bundle always runs centrally, so this construction is less suitable for applications with demand for best high frequency performance. In order to compensate for differences in bundle lengths for the final bunching step, the pitch direction of the central bundle is opposite to the direction of the concentric outer bundles. Therefore the pitch direction of the central bundle always represents the pitch direction of the final bunching step.

The previous basic constructions can be combined with each other independently from the number of bunching steps and complexity of electrical and mechanical demands. Special constructions are always possible.

**Selection of length of lay and pitch direction:**

The length of lay determines the mechanical compactness and the high frequency performance of a bundle. A measure for the tightness of a bunching step is the so called bunching factor (VF). It is the proportion of the length of lay (SL) to the outer diameter of the bundle and lies (if not otherwise specified) typically between 15-20 mm:

**Bunching factor VF = SL/OD _{Bundle}**

Example: VF = 5,0mm / 0,3mm = 16,7

Depending upon the pitch direction (SR), the bunching factor (V)F for prebunching steps is often chosen higher in many cases.

For the selection of length of lay (SL), and pitch direction (SR), the following basic statements can be assumed:

the smaller the length of lay,

- the more compact, stiffer, and more dimensionally stable the bunching construction

- the larger the outer diameter of the bundle

- if optimal high frequency performance is required, is suggested that all pitch directions be aligned
- counterrotating pitch directions of multiple bunching steps are preferred

for complex litz wire constructions, where high mechanical flexibility is demanded - for wound coils the length of lay should be in the range of the smallest winding diameter

**Different constructions of a litz wire 270 x 0.071 mm**

litz wire | construction | SR | SL [mm] | bunching factor VF | features |
---|---|---|---|---|---|

270 x 0.071 mm | (54 x 0.071 mm) x 3 | S,S | 20;26 | ≈ 15 | good HF-performance, rough textured three-sided litz wire profile |

((30 x 0.071 mm) x 3) x 3 | S,S,S | 20;26;26 | ≈ 20 | good HF-performance, compact bunching | |

((18 x 0.071 mm) x 3) x 5 | S,S,S | 20;26;26 | ≈ 20 | good HF-performance, compact bunching, even surface and litz wire profile | |

((18 x 0.071 mm) x 3) x 5 | S,S,Z | 20;20;26 | ≈ 15 | fine litz wire structure/-surface | |

(39 x 0.071 mm) x 7; concen. | S+Z,S | 20+20;24 | < 13 | very round, dimensionally stable litz wire profile, high flexibily |

Table 3

## IV Example: Litz wire for high frequency layer winding

In many cases high frequency coils are layer wound with a small number of windings. Usually those litz wires are silk or nylon served, since exact winding in layers is only possible with litz wires which keep their round shape on the coil bobbin with applied winding tension. In some cases unserved litz wires (basic litz wires) can be used. Here special attention is required to select solid and dimensionally stable constructions. Nevertheless, since small elliptical deformation is not avoidable, this has to be compensated by reducing the total outer diameter appropriately. For this reason, for a given maximum outer diameter, served litz wire can show a higher copper cross section than an unserved construction.

**Example**

An example shows the simplified preselection of a litz wire construction for a layer winding with 30 windings and an operating frequency of 200 kHz. Assumed is a winding window with an effective usable size of width x height = 25.8 mm x 8.0 mm.

Layer construction

Depending on winding technology, layer windings can be constructed in layers with equal or alternating number of windings.

For preselection, it is possible to roughly calculate the same number of single wires per layer. This results in 3 layers with 10 windings each for the winding window, and a calculated max. outer diameter for the processed litz wire of 25.8 mm/10 = 2.58 mm.

Single wire diameter

The higher the applied operating frequency the smaller the single wires will become. At the same time the costs for the single wire will increase with decreasing nominal diameter ØSW, as well as for the bunching process with increasing complexity of the bunching construction. Regarding the interaction between the thickness of the subbundles and the frequency dependent skin depth δ, the ratio ØSW ≤ δ/3 can be taken approximately as indicator for the choice of the nominal single wire diameter. In practice it represents a working compromise between frequency performance and costs. Depending on application and technical demands variations are allowable and common. In this case a nominal diameter of ØSW = 0.063 mm is sufficient for a first approach (see example above, section II).

Bunching construction

The total outer diameter of a litz wire depends on the dimensional stability of the individual wires bunched during the winding process. To take this into consideration as an empirical value the calculated max. outer diameter of the processed litz wire (Ø2.58 mm, see above) should be reduced by 10% (Ø2.32 mm) for the served and by 15-20% (Ø2.19 mm) for the unserved construction.The unserved litz wire should be bunched compactly, for example small lengths of lay and the same pitch direction per bunching step. Five or four bundle constructions are preferred.

The following table shows a comparison between suitable served and unserved litz wire constructions for operating frequencies of 50, 125, and 200 kHz.

**Litz wire design for a HF-coil using the example of a winding window: b x h = 25.8 mm x 8.0 mm**

practice-related approach | ||||

frequency [kHz] | 50 | 125 | 200 | |

total no. of windings N_{w,tot} | 30 | 30 | 30 | |

no. of layers N_{L} (winding layers) | 3 | 3 | 3 | |

no. of windings per layer N_{W,L} | 10 | 10 | 10 | |

| without servg. | 2.19 | 2.19 | 2.2 |

with servg. | 2.32 | 2.32 | 2.32 | |

| 0,100 | 0,080 | 0,063 | |

| without servg. | 48.2 | 46.5 | 46.1 |

with servg. | 47.0 | 45.4 | 44.9 | |

| without servg. | 25.9 | 25.6 | 24.9 |

with servg. | 29.1 | 28.0 | 27.2 | |

| without servg. | 225 x 0.100 mm 5x(45x0.100mm) | 350 x 0.080 mm 5x(5x(14x0.080mm) | 550 x 0.063 mm 5x(5x(22x0.063mm)) |

with servg. | 225 x 0.100 mm 5x(51x0.100mm) | 350 x 0.080 mm 5x(4x(19x0.080mm)) | 600 x 0.063 mm 5x(5x(24x0.063mm)) |

Table 4

You can see in this case, that for the desired layer winding

the copper filling factor of the served litz wire is a little bit smaller compared with the basic litz wire. The number of single wires and thus the total copper cross section of the unserved litz wire still increases.

the copper filling factor of the winding window lies typically in the range of 25-30%. It is higher for the served litz wire compared with the unserved basic litz wire due to its higher total copper cross section.

the 5 bundle construction enables a more symmetrical litz wire structure with subbundles of significantly less than 60 single wires.

If layer winding is not necessary and a randomly wound coil can be used, it’s possible to produce a very flexible and soft litz wire. In this case the coil windings cling to each other, intermediate spaces are filled optimally and thus the copper filling factor of the winding window can be increased once again. Alternatively the usage of profiled litz wires is possible as well. The copper cross section of the chosen litz wire construction should be in any case consistent with the required current capacity of the application.

## V Comparison: Preselection acc. to Charles R. Sullivan

A further method of simplified selection of litz wires for RF coils is proposed by Charles R. Sullivan from the Thayer School of Engineering in Dartmouth/USA in his study "Simplified Design Method for Litz Wire".

The parameters used are the skin depth, operating frequency, number of windings of the winding window, the width of the winding window; for this the calculated constant k is required. This method then proposes a number of suitable litz wire constructions, consisting of nominal single wire diameter, a maximum number of single wires for the first bunching step, and the number of bundles for any further bunching step.

**This is accomplished in the following steps:**

(1):

Determination of the skin depth δ calculated from the specific conductor resistance **ρ**, operating frequency f, and the permeability **µ _{o}**.

**δ = √(ρ/(π*f*µ _{o}))**

(2):

Definition of available width **b** of the winding window and the requested number of windings **N _{W,tot}** of a given coil construction. As an option constructions, with an air gap can be considered.

(3):

Calculation of tabular approximate values for the recommended total number of single wires **n _{e}** depending on several nominal single wire diameters

**Ø**. The effectively applied number of single wires for a specific nominal diameter can deviate from the calculated value up to ± 25%.

_{SW}**n _{e} = k*δ2*b/N_{W,tot}**

(4):

From here selection of single wire nominal diameter and -number of single wires is made. Following this selection, a determination is made which of the tabular single wire-diameters/-number combinations according given number of windings fits into the winding window. A winding window copper filling factor of 25-30% is assumed. Demands regarding litz wire resistance and current capacity have to be determined. Alternative constructions with bigger single wires are also possible.

(5):

The interaction between skin depth and bundle diameter is taken into account: Calculation of the maximum number of single wires **n1 _{,max}** of the first bunching step is dependent upon the frequency influenced skin depth

**δ**and the chosen nominal single wire diameter

**Ø**

_{SW}.**n _{1,max} = 4*δ2/ Ø_{SW}^{2 }**

(6):

The calculated total number of single wires, see (3), on several bunching steps respectively combinations of 3, 4, and 5 bundle constructions is now reviewed.

A recommendation of certain bunching lengths or directions of the constructions is not given in this context. It’s left to the litz wire manufacturers.

Table 5 compares the previously given practice related selection of Elektrisola typical constructions with those according Ch. R. Sullivan-method. It is related to a layer wound coil and a winding window of 25.8 mm x 8 mm and operating frequencies of 50, 125, and 200 kHz.

**Comparison of the design approaches by using the example of a winding window b x h 25.8 mm x 8.0 mm**

Elektrisola practice-related approach | approach acc. Ch. R. Sullivan | ||||||

frequency [kHz] | 50 | 125 | 200 | 50 | 125 | 200 | |

total no. of windings N_{W,tot} | 30 | 30 | 30 | 30 | 30 | 30 | |

no. of layers N_{L} (layer winding) | 3 | 3 | 3 | 3 | 3 | 3 | |

no. of winding per layer N_{W,L} | 10 | 10 | 10 | 10 | 10 | 10 | |

| 2.19 | 2.19 | 2.20 | 1.90 | 1.67 | 1.79 | |

| 0.100 | 0.080 | 0.063 | 0.100 | 0.063 | 0.050 | |

| 48.2 | 46.5 | 46.1 | 47 | 44.8 | 44.6 | |

| 25.9 | 25.6 | 24.9 | 19.4 | 17.2 | 16.4 | |

typ. litz wire construction | 225 x 0.100 mm 5x(45x0.100 mm) | 360 x 0.080 mm 5x(4x(18x0.080 mm)) | 550 x 0.063 mm 5x(5x(22x0.063 mm)) | 170 x 0.100 mm 5x(35x0.100 mm) | 375 x 0.063 mm 5x(5x(15x0.063 mm)) | 575 x 0.050 mm 5x(5x(23x0.050 mm)) |

Table 5

The table shows that the litz wires, selected with the practice related approach, correspond closely with those constructions selected with the Sullivan -method. They cover implicitly the recommended basic features:

- the total number of single wires of the practice related examples lie within the range suggested by Sullivan.
- the combined application of 3, 4, or 5 bundle constructions are an integrated part of Elektrisola typical litz wire designs (see table 5).
- the single wires of the basic bundles in the first bunching step are independent from the respective construction. Elektrisola litz wire can be free selected within 60 strands for a single bunching step (see table 5).
- cost reductions are possible with thicker single wires (
**Ø**) designed constructions (see table 5), which show mainly the Sullivan recommended ideal basic bundling of ≤ 64 to 36 single wires._{ED}≤ δ/3 - apart from cost reduction these constructions can additionally increase the filling factor of the litz wire and of the winding window (see table 5).
- Through careful selection of bunching length and direction, the product can be optimally specified for each unique application

Therefore Elektrisola's applied design concepts for high frequency litz wire typically include both practical and theoretical requirements.

**Abbreviations**

A | = | total conductor cross section of litz wire |

A_{ges,Litz} | = | total cross section of litz wire |

OD_{Litz} | = | outer diameter of litz wire |

OD_{Bundle} | = | outer diameter of bundle |

n_{sw} | = | number of single wires |

Ø_{sw} | = | nominal diameter of single wire |

VF | = | bunching factor |

SL | = | length of lay (bunching length) |

SR | = | pitch (bunching) direction |

R_{DC} | = | DC resistance |

R_{AC} | = | AC resistance |

f | = | frequency |

ρ | = | specific resistance of conductor |

µ_{O} | = | permeability of free space |

δ | = | skin depth |

J | = | current density |

U_{BDV} | = | breakdown voltage |

b | = | width of winding window |

h | = | height of winding window |

N_{W,tot} | = | total number of windings |

N_{L} | = | number of winding layers |

N_{W,L} | = | number windings per layer |

Fill_{Litz} | = | copper filling factor of litz wire |

Fill_{Win} | = | copper filling factor of winding window |

n_{e} | = | recommended total number of single wires |

n_{1,max} | = | number of single wires of basic bundle in 1st bunching step |

k | = | constant according Ch. R. Sullivan |