[DESCRIPTION]
[Title of Invention]
ELECTRIC WIRE, COIL, APPARATUS FOR DESIGNING ELECTRIC WIRE, AND
ELECTRIC MOTOR
[Technical Field]
[0001]
The present invention relates to an electric wire, a coil,
an apparatus for designing the electric wire, and an electric
motor.
[Background Art]
[0002]
In winding wires and power cables of devices to which
high-frequency current is applied (transformers, motors,
reactors, induction heaters, magnetic head devices, and the
like), the magnetic field generated by the high-frequency
current causes an eddy current loss within a conductor, and the
AC resistance (high-frequency resistance) is therefore
increased (or the skin effect and the proximity effect are
increased). This causes heat generation and increases power
consumption. Countermeasures to prevent the increases in the
skin effect and proximity effect include, generally, reducing
the diameter of wires and employing litz wires including strands
individually coated and insulated (see Patent Literatures 1 to
5, for example).
[0003]
As one of electric wires used for winding wires and the
like, for example, copper-clad aluminum wire (hereinafter,
referred to as CCA wire) is known. The CCA wire includes
aluminum wire (hereinafter, referred to as Al wire) whose
surface is covered with a thin copper layer. However, in a
particular frequency range in which high-frequency wire is used,
it is difficult to make the AC resistance of the high-frequency
wire definitely lower than that of copper wire (hereinafter,
referred to as Cu wire) having a same diameter as that of the
high-frequency wire.
[Citation List]
[Patent Literature]
[0004]
PTL 1: Japanese Patent Laid-open Publication No.

2009-129550
PTL 2: Japanese Patent Laid-open Publication No.
S62-76216
PTL 3: Japanese Patent Laid-open Publication No.
2005-108654
PTL 4: International Publication No. 2006/046358
PTL 5: Japanese Patent Laid-open Publication No.
2002-150633
[Summary of Invention]
[0005]
In the light of the aforementioned problem, an object of
the present invention is to provide an electric wire, a coil,
a apparatus for designing an electric wire, and an electric
motor in which the AC resistance of the electric wire can be
reduced by making the eddy current loss equal to or less than
that of reference Cu wire.
[0006]
According to an aspect of the present invention, an
electric wire is provided, including: a conductive portion made
of a material having a volume resistivity higher than that of
copper, in which the volume resistivity of the conductive
portion is specified so that, in a frequency range in which the
electric wire is used, a ratio of AC resistance of the conductive
portion to AC resistance of reference copper wire is less than
1.
[0007]
In the aspect of the present invention, the reference
copper wire may have a same diameter as the conductive portion.
[0008]
In the aspect of the present invention, a DC resistance
value of the conductive portion per unit length may be specified
so that among a first frequency and a second frequency higher
than the first frequency, the second frequency is not less than
the upper limit of the frequency range in which the electric
wire is used, the first and second frequencies being frequencies
at which the AC resistance of the electric wire is equal to that
of the reference copper wire and between which the AC resistance
of the electric wire is lower than that of the reference copper
wire.
[0009]

In the aspect of the present invention, the DC resistance
value may be specified by a relationship of
0.7×10,0,925×lOgdc + 2.24) ≤ f2 ≤ 1.3×10(0.925xlogRdc + 2.24)
where Rdc is the DC resistance value and f2 is the second
frequency.
[0010]
In the aspect of the present invention, the conductive
portion may be made of any one of copper-clad aluminum and an
copper alloy selected from brass, phosphor bronze, silicon
bronze, copper-beryllium alloy, and copper-nickel-silicon
alloy.
[0011]
In the aspect of the present invention, the frequency
range in which the electric wire is used may include a
fundamental frequency to 20th order harmonic frequencies.
[0012]
In the aspect of the present invention, the frequency
range in which the electric wire is used may be 10 kHz to 1 MHz.
[0013]
According to another aspect of the present invention, a
coil is provided, including an electric wire as a strand, in
which the electric wire includes a conductive portion made of
a material having a higher volume resistivity than copper, and
the volume resistivity of the conductive portion is specified
so that, in a frequency range in which the electric wire is used,
a ratio of AC resistance of the conductive portion to AC
resistance of reference copper wire is less than 1.
[0014]
In the another aspect of the present invention, the
reference copper wire may have a same diameter as the conductive
portion.
[0015]
In the another aspect of the present invention, a DC
resistance value of the conductive portion per unit length maybe
specified so that among a first frequency and a second frequency
higher than the first frequency, the second frequency is not
less than the upper limit of the frequency range in which the
electric wire is used, the first and second frequencies being
frequencies at which the AC resistance of the electric wire is
equal to that of the reference copper wire and between which

the AC resistance of the electric wire is lower than that of
the reference copper wire.
[0016]
In the another aspect of the present invention, the DC
resistance value may be specified by a relationship of
0.7×10,0,925×lOgdc + 2.24) ≤ f2 ≤ 1.3×10(0.925xlogRdc + 2.24)
where Rdc is the DC resistance value and f2 is the second
frequency.
[0017]
In the another aspect of the present invention, the
conductive portion may be made of any one of copper-clad
aluminum and an copper alloy selected from brass, phosphor
bronze, silicon bronze, copper-beryllium alloy, and
copper-nickel-silicon alloy.
[0018]
In the another aspect of the present invention, the
frequency range in which the electric wire is used may include
a fundamental frequency to 20th order harmonic frequencies.
[0019]
In the another aspect of the present invention, the
frequency range in which the electric wire is used may be 10
kHz to 1 MHz.
[0020]
According to still another aspect of the present
invention, an apparatus of designing an electric wire made of
a material having a higher volume resistivity than that of
copper is provided, the apparatus including: a resistance
calculation unit calculating AC resistance of a conductive
portion as a candidate for the electric wire and AC resistance
of reference copper wire in a frequency range in which the
electric wire is used; a ratio calculation unit calculating a
ratio of AC resistance due to a proximity effect of the
conductive portion to AC resistance due to the proximity effect
of the reference copper wire; and a determination unit
determining that the candidate is applicable to the electric
wire if the ratio is less than 1.
[0021]
According to still another aspect of .the present
invention, an electric motor is provided, including: a
plurality of iron cores arranged on a circle; a plurality of

coils wound with an electric wire on the plurality of iron cores,
the electric wire including a central conductor made of aluminum
or aluminum alloy and a cover layer made of copper covering the
central conductor; and a rotor rotated by the plurality of coils
to which alternating-current is applied, in which the frequency
of alternating current applied to the coils is controlled by
an inverter method to fall between a first frequency and a second
frequency higher than the first frequency, the first and second
frequencies being frequencies at which the AC resistance of the
coil is lower than that of a coil wound with the reference copper
wire.
[Brief Description of Drawings]
[0022]
FIG. 1(a) is a cross-sectional view showing an example
of an electric wire according to a first embodiment of the
present invention, and FIG. 1(b) is another example of the
electric wire according to the first embodiment of the present
invention.
FIG. 2 is a schematic view for explaining the skin effect
according to the first embodiment of the present invention.
FIG. 3 is a schematic view for explaining the proximity
effect according to the first embodiment of the present
invention.
FIG. 4 is another schematic view for explaining the
proximity effect according to the first embodiment of the
present invention.
FIG. 5 is a cross-sectional view of a conductive wire of
a double-layer structure.
FIG. 6 is a schematic view showing an electromagnetic
field in the surface of the conductive wire through which
electric current flows.
FIG. 7 is a cross-sectional view of the conductive wire
of the double-layer structure when an external magnetic field
is applied thereto.
FIG. 8 is a schematic view showing an electromagnetic
field in the surface of the conductive wire when the external
magnetic field is applied thereto.
FIG. 9 is a graph illustrating the relationship between
frequency and AC resistance of the electric wire according to
the first embodiment of-- the present invention and a Cu wire

according to a comparative example.
FIG. 10 is a table showing production conditions of
magnetic field generating coils in which each strand is composed
of the brass wire according to the first embodiment of the
present invention or the Cu wire according to the comparative
example.
FIG. 11 is a graph illustrating the relationship between
the frequency and AC resistance of the magnetic field generating
coils in which each strand is composed of the brass wire
according to the first embodiment of the present invention or
the Cu wire according to the comparative example.
FIG. 12 is a table showing the relationship between the
frequency and AC resistance of the magnetic field generating
coils in which each strand is composed of the brass wire
according to the first embodiment of the present invention or
the Cu wire according to the comparative example.
FIG. 13 is a graph illustrating the relationship between
the frequency and AC resistance in the brass wire according to
the first embodiment of the present invention and the Cu wire.
FIG. 14 is a graph illustrating the relationship between
the frequency and AC resistance in the proximity effect
component and skin effect component according to the first
embodiment of the present invention.
FIG. 15 is a table showing calculation results of the ratio
of the AC resistance of various materials to that of the Cu wire
in the first embodiment of the present invention.
FIG. 16 is a schematic diagram illustrating an example
of an apparatus for designing the electric wire according to
the first embodiment of the present invention.
FIG. 17 is a flowchart for explaining examples of methods
of designing and manufacturing the electric wire according to
the first embodiment of the present invention.
FIG. 18 is a cross-sectional view showing an example of
an electric wire according to a second embodiment of the present
invention.
FIG. 19 is a graph illustrating the relationship between
the frequency and AC resistance in a CCA wire according to the
second embodiment of the present invention and a Cu wire.
FIG. 20 is a graph illustrating a primary winding current
waveform of a high-frequency transformer.

FIG. 21 is a graph for explaining the fundamental
frequency and harmonic components.
FIG. 22 is a table showing losses of CCA and copper winding
wires.
FIG. 23 is a schematic view showing an example of an
apparatus of designing the electric wire according to the second
embodiment of the present invention.
FIG. 24 is a flowchart for explaining an example of a
method of designing the electric wire according to the second
embodiment of the present invention.
FIG. 25 is a schematic view showing an example of an
electric motor according to a first example of the second
embodiment of the present invention.
FIG. 26 is a graph illustrating current response of a coil
which includes the Cu wire according to the comparative example
when the operating frequency thereof is 20 Hz.
FIG. 27 is a graph illustrating current response of the
coil which includes the Cu wire according to the comparative
example when the operating frequency thereof is 50 Hz.
FIG. 28 is a graph illustrating the responses of FIGs.
26 and 27 together.
FIG. 29 is a graph illustrating a frequency spectrum of
the current of FIG. 26.
FIG. 30 is a graph illustrating high-frequency resistance
due to the skin effect in the Cu wire according to the comparative
example, the Cu wire having a radius of 0.8 mm.
FIG. 31 is a graph illustrating the high-frequency loss
due to the proximity effect (Ho = 1 A/mm) in the Cu wire according
to the comparative example, the Cu wire having a radius of 0.8
mm.
FIG. 32 is a graph illustrating high-frequency resistance
static characteristics of a coil wound with the Cu wire
according to the comparative example.
FIG. 33 is a graph illustrating high-frequency resistance
dynamic characteristics of the coil wound with the Cu wire
according to the comparative example.
FIG. 34 is a graph illustrating the high-frequency
resistance static characteristics {No. 1) of coils wound with
the CCA wire and Al wire according to the first example of the
second embodiment of the present invention and a coil wound with

the Cu wire according to the comparative example.
FIG. 35 is a graph illustrating the high-frequency
resistance static characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the first example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 36 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 1) of the coils wound
with the CCA wire and Al wire according to the first example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 37 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the first example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 38 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different a value
in the first example of the second embodiment of the present
invention.
FIG. 39 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different value
of radius r in the first example of the second embodiment of
the present invention.
FIG. 40 is a schematic view showing an example of an
electric motor according to a second example of the second
embodiment of the present invention.
FIG. 41 is a graph illustrating high-frequency
resistances due to the skin effect in the CCA wire and Al wire
according to the second example of the second embodiment of the
present invention and the Cu wire according to the comparative
example, each wire having a radius of 1.0 mm.
FIG. 42 is a graph illustrating high-frequency lossesdue
to the proximity effect (H0 = 1 A/mm) in the CCA wire and Al
wire according to the second example of the second embodiment
of the present invention and the Cu wire according to the
comparative example, each wire having a radius of 1.0 mm.
FIG. 43 -.is a graph illustrating the high-frequency

resistance static characteristics (No. 1} of coils wound with
the CCA wire and Al wire according to the second example of the
second embodiment of the present invention and a coil wound with
the Cu wire according to the comparative example.
FIG. 44 is a graph illustrating the high-frequency
resistance static characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the second example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 45 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 1) of the coils wound
with the CCA wire and Al wire according to the second example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 46 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the second example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 47 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different a value
in the second example of the second embodiment of the present
invention.
FIG. 48 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different value
of radius r in the second example of the second embodiment of
the present invention.
FIG. 4 9 is a schematic view showing an example of an
electric motor according to a third example of the second
embodiment of the present invention.
FIG. 50 is a graph illustrating high-frequency
resistances due to the skin effect in the CCA wire and Al wire
according to the third example of the second embodiment of the
present invention and the Cu wire according to the comparative
example, each wire having a radius of 1.2 mm.
FIG. 51 is a graph illustrating high-frequency losses due
to the proximity effect (Ho = 1 A/mm) in the CCA wire and Al
wire according to the third example of the second embodiment

of the present invention and the Cu wire according to the
comparative example, each wire having a radius of 1.2 mm.
FIG. 52 is a graph illustrating the high-frequency
resistance static characteristics (No. 1) of coils wound with
the CCA wire and Al wire according to the third example of the
second embodiment of the present invention and a coil wound with
the Cu wire according to the comparative example.
FIG. 53 is a graph illustrating the high-frequency
resistance static characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the third example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 54 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 1) of the coils wound
with the CCA wire and Al wire according to the third example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 55 is a graph illustrating the high-frequency
resistance dynamic characteristics (No. 2) of the coils wound
with the CCA wire and Al wire according to the third example
of the second embodiment of the present invention and the coil
wound with the Cu wire according to the comparative example.
FIG. 56 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different a value
in the third example of the second embodiment of the present
invention.
FIG. 57 is a table showing the frequency range in which
the dynamic characteristic high-frequency resistance of the CCA
wire is lower than that of the Cu wire for each different value
of radius r in the third example of the second embodiment of
the present invention.
FIG. 58(a) is a cross-sectional view showing an example
of an electric wire according to a third embodiment of the
present invention, and FIG. 58(b) is a cross-sectional view
showing another example of the electric wire according to the
third embodiment of the present invention.
FIG. 59 is a graph illustrating the relationship between
the frequency and AC resistance of Cu wire and brass wire
according to the third embodiment of the present invention.

FIG. 60 is a table showing the reference DC resistance
and second frequency which are measured by varying the material
and diameter of the electric wire.
FIG. 61 is a graph illustrating the relationship between
the reference DC resistance and second frequency according to
the third embodiment of the present invention.
FIG. 62 is a table showing losses of brass and copper
winding wires.
FIG. 63 is a schematic diagram showing an example of an
apparatus for designing the electric wire according to the third
embodiment of the present invention.
FIG. 64 is a flowchart for explaining examples of methods
of designing and manufacturing the electric wire according to
the third embodiment of the present invention.
FIG. 65 is a cross-sectional view showing an example of
a high-frequency electric wire according to a fourth embodiment
of the present invention.
FIG. 66 is a graph illustrating a magnetic field strength
distribution of the Cu wire according to the comparative
example.
FIG. 67 is a graph illustrating a current density
distribution of the Cu wire according to the comparative example.
FIG. 68 is a table showing volume resistivity of the
materials of the high-frequency electric wire according to the
fourth embodiment of the present invention.
FIG. 69 is another graph illustrating a magnetic field
strength distribution of the Cu wire according to the
comparative example.
FIG. 70 is a graph illustrating a loss distribution of
the Cu wire according to the comparative example.
FIG. 71 is a graph illustrating a magnetic field strength
distribution of a silicon bronze wire according to the fourth
embodiment of the present invention.
FIG. 72 is a graph illustrating a loss distribution of
the silicon bronze wire according to the fourth embodiment of
the present invention.
FIG. 73 is a graph illustrating a magnetic field strength
distribution of a brass wire according to the fourth embodiment
of the present invention.
F€G. 74 is a graph illustrating a loss distribution o€

the brass wire according to the fourth embodiment of the present
invention.
FIG. 75 is a graph illustrating a magnetic field strength
distribution of a phosphor bronze wire according to the fourth
embodiment of the present invention.
FIG. 76 is a graph illustrating a loss distribution of
the phosphor bronze wire according to the fourth embodiment of
the present invention.
FIG. 77 is a graph illustrating the relationship between
the frequency and AC resistance (the proximity effect
component) of the brass wire, phosphor bronze wire, and silicon
bronze wire according to the fourth embodiment of the present
invention and the Cu wire according to the comparative example.
[Description of Embodiments]
[0023]
Next, with reference to the drawings, a description is
given of embodiments of the present invention. In the following
description of the drawings, same or similar parts are given
same or similar reference numerals . However, it should be noted
that the drawings are schematic and that the relationship
between thickness and planar dimensions, the proportion of
thicknesses of layers, and the like are different from real ones.
Accordingly, specific thicknesses and dimensions should be
determined with reference to the following description. It is
certain that some portions have different dimensional relations
and proportions between the drawings.
[0024]
The following embodiments show devices and methods to
embody the technical idea of the invention by way of example.
The technical ideas of the invention do not specify the
materials, shapes, structures, arrangements, and the like of
the constituent components to those described below. The
technical idea of the invention can be variously changed within
the scope of claims.
[0025]
(First Embodiment)

As shown in FIG. 1(a), an electric wire according to a
first embodiment of the present invention is an electric wire

used in a particular frequency range and includes a conductive
portion 11 made of a material having a higher volume resistivity
than that of copper. In the electric wire according to the first
embodiment of the present invention, the volume resistivity of
the conductive portion 11 is specified so that the ratio of the
AC resistance due to the proximity effect of the conductive
portion 11 to that of a reference Cu wire is less than 1 in the
particular frequency range.
[0026]
Herein, the particular frequency range refers to a
frequency range specified (set) as a frequency range in which
the electric wire (product) of interest is used. The upper and
lower limits and range of the particular frequency range are
properly set according to the specifications of each product
and are not particularly limited. The particular frequency
range may be about several kHz to 100 kHz or about 10 kHz to
1 MHz. In the case of IH cookers, the particular frequency range
may be about 20 kHz to 60 kHz. In the case of products directly
using the commercial power frequencies of Japan, the United
States, or Europe, the particular frequency range may be about
50. kHz to 60 kHz. Moreover, the "reference Cu wire" is
previously specified (set) and may have a same diameter as that
of the conductive portion 11 or may have a different diameter
from the same.
[0027]
The diameter of the conductive portion 11 is desirably
about 0.05 to 0.6 mm but is not particularly limited. The
material of the conductive portion 11 can be copper alloy
including brass, phosphor bronze, silicon bronze,
copper-beryllium alloy, and copper-nickel-silicon alloy. The
brass is an alloy (Ch-Zn) containing copper (Cu) and zinc (Zn)
and may contain small amounts of elements other than copper and
zinc. The silicon bronze is an alloy (Cu-Sn-Si) containing
copper, tin (Sn) , and silicon (Si) and may contain small amounts
of elements other than copper, tin, and silicon. The phosphor
bronze is an alloy (Cu-Sn-P) containing copper, tin, and
phosphor (P) and may contain small amounts of elements other
than copper, tin, and phosphor.
[0028]
These copper alloy wires are subjected to annealing, for

example, and may be plated with tin, copper, chrome (Cr) , or
the like. Moreover, the conductive portion 11 may have various
shapes including a cylinder and a rectangle.
[0029]
Moreover, as shown in FIG. 1(b), the electric wire
according to the first embodiment of the present invention may
be CCA wire including, as the conductive portion 11, a central
conductor 12 made of aluminum (Al) or aluminum alloy and a cover
layer 13 made of copper (Cu) covering the central conductor 12.
[0030]
The diameter of the entire CCA wire is desirably about
0. 05 mm to 0. 6 mm. The cross-sectional area of the cover layer
13 is not more than 15% of the cross-sectional area of the entire
electric wire composed of the central conductor 12 and cover
layer 13, desirably about 3% to about 15%, more preferably about
3% to about 10%, and still more preferably about 3% to about
5% . The lower the ratio of the cross-sectional area of the cover
layer 13 to that of the entire electric wire, the lower the AC
resistance. The central conductor 12 can be made of electrical
aluminum (EC aluminum) or aluminum alloy such as Al-Mg-Si alloy
(JIS6000s), for example. The aluminum alloy is more desirable
than the EC aluminum because the volume resistivity of the
aluminum alloy is higher than that of the EC aluminum.
[0031]
The winding wires of normal transformers, reactors, and
the like are composed of Cu wire coated and insulated with
polyurethane, polyester, polyesterimide, polyamide-imide, or
polyimide. As for coaxial cables, since high-frequency
current signals flow therethrough, coaxial cables are therefore
composed of CCA wire, for example, in the light of the skin effect
characteristics.
[0032]
As shown in FIG. 2, with regard to a conductor, eddy
currents are generated within the conductor by magnetic flux.
The generated eddy currents increase the AC resistance as the
skin effect. Moreover, as shown in FIGs. 3 and 4, eddy currents
are generated within the conductor by external magnetic flux,
and the generated eddy currents increase the AC resistance as
the proximity effect.
[0033]

The AC resistance Rac is expressed by the following
equation (1) where RdC is a DC resistance component, Rs is an
AC resistance due to the skin effect, and Rp is an AC resistance
(proximity effect component) due to the proximity effect.
[0034]

Herein, Ks is a skin effect coefficient.
[0035]
First, a description is given of an example of the method
of calculating the AC resistance Rs due to the skin effect in
the first embodiment of the present invention. As shown in FIG.
5, the consideration is given to a cylindrical conducting wire
having a double-layer structure and being distributed uniformly
in a direction z. It is assumed that the conductivities of the
inner and outer layers of the conducting wire are σ and σ2,
respectively, and that current flows through the conducting
wire in the direction z.
[0036]
In the following formulation, each magnetic field is
given by complex representation, and the time factor is
indicated by eωt. Herein, ω is an angular frequency.
[0037]
The flowing current generates a z-direction component Ez
of an electric field, which satisfies the following wave
equation (2) .
[Equation 1]

[0038]
Herein, μ0 indicates a magnetic permeability in vacuum. A
magnetic field Hθ has only a θ-direction component and is given
as follows.
[Equation 2]

[0039]

Herein, if
[Equation 3]

[0040]
then, the solution of the wave equation (2) can be as follows
[Equation 4]

[0041]
Jv(z) is a Bessel function of the first kind.

Hv is a Hankel function of the first kind.
[0042]
Under the boundary condition where Ez and He are continuou
at r=b.
[Equation 5]

[0043]
[Equation 6]

[0044]
Herein,


[0045]
From the equation (3), the following equation (12) is
obtained.
[Equation 7]

Total current I flowing through the conducting wire is obtained
according to the Ampere's rule as follows.
[Equation 8]

[0046]
Herein, represents line integral along the outer
circumference of the conducting wire. By substituting the
equations (8) and (9) into the equation (13), the following
equation (14) is obtained.
[Equation 9]

[0047]
On the other hand, the power flow into the conducting wire
shown in FIG. 6 is calculated from the Poynting vector as shown
in the following equation (15).
[Equation 10]

[0048]
Herein, represents surface integral over the

cylindrical surface of the conducting wire in FIG. 6. dS
represents a surface element vector in the normal direction.
P is the Poynting vector, and ar is a unit vector in a direction
r.
[0049]
By substituting the equations (7) and (12) into the
equation (15), the following equation (16) is obtained.
[Equation 11]

[0050]
Herein,

Accordingly, the following equation (17) is obtained.
[Equation 12]

[0051]
The AC resistance per unit length due to the skin effect is
therefore given as follows.
[Equation 13]

[0052]
Herein, represents a real part and indicates a DC
resistance Rdc when the frequency is 0.
[0053]
When the conducting wire has a single-layer structure,
from σ1 = σ2, the equations (10) and (11),
[Equation 14]

[0054]
The equation (18) becomes:
[Equation 15]


[0055]
[0056]
Next, a description is given of an example of the method
of calculating the proximity effect component Rp in the first
embodiment of the present invention. As shown in FIG. 7, it
is assumed that a high-frequency magnetic field He in the
direction x is applied to the outside of the conducting wire
as follows. Herein, ax is a unit vector in the direction x.
[Equation 16]

[0057]
Herein, if the magnetic potential satisfying H=VxA is
introduced,
[Equation 17]

[0058]
then, the following external potential
[Equation 18]

[0059]
gives a magnetic field expressed by the equation (22).
[0060]
The magnetic potential satisfies the following wave
equation (25).
[Equation 19]

[0061]
Herein, μo is a magnetic permeability in vacuum.
[0062]
The solution of the equation (25) can be provided as
follows.
[Equation 20]


[0063]
From the boundary condition where the tangent component
(Hθ) of the magnetic field and the normal component (μ0Hr) of
the magnetic flux density are continuous at each boundary,
[Equation 21]

[0064]
Herein,
[Equation 22]

[0065]
Herein,

and


[0066]
The magnetic field He is obtained as follows.
[Equation 23]

[0067]
Moreover, the electric field Ez is obtained as follows.
[Equation 24]

[0068]
The power flow penetrating from the surface of the
conducting wire to the inside thereof, which is shown in FIG
8, is calculated as the following equation (38).
[Equation 25]

[0069]
Herein, P represents the Poynting vector, and represents
surface integral over the surface of the conducting wire in FIG.
8.
[0070]
By substituting the equations (36) and (37) into the
equation (38) , the following equation (39) is obtained.
[Equation 26]

[0071]
[Equation 27]


[0072]
The loss PL of the conducting wire is calculated as
follows.
[Equation 28]

[0073]
When the conducting wire has a single-layer structure,
from o"i = 02, the equations (34) and (35),
[Equation 29]

[0074]
The equation (43) becomes the following equation (46).
[Equation 30]

[0075]
When the coil or the like is wound with one conducting
wire like a transformer, a reactor, or the like, the external
magnetic field is formed by current flowing through the
conducting wire. In that case, the strength of the
external magnetic field is in proportional to the magnitude
of the current as shown in the following equation (47).
[Equation 31]

[0076]
Herein, a is a proportional coefficient and depends on
how the conducting wire is wound. By substituting this into
the equation (43) , the resistance Rp per unit length due to the
proximity effect is given as follows.
[Equation 32]


[0077]
As shown in FIG. 9, the AC resistance due to the proximity
effect of the brass wire, phosphor bronze wire, silicon bronze
wire according to the first embodiment of the present invention
and the Cu wire according to the comparative example at an
external magnetic strength H of 1 (A/mm) are calculated using
the aforementioned equation (48) . FIG. 9 reveals that the AC
resistances of the brass wire, phosphor bronze wire, and silicon
bronze wire are lower than that of the Cu wire in the
predetermined frequency range.
[0078]
As shown in FIG. 10, magnetic filed generating coils for
an IH cooker were manufactured in such a manner that 55 strands
(diameter: 0.4 mm, length; 6.6 m) in a litz wire construction
are used to be wound in 17 turns. Each strand is composed of
the brass wire according to the first embodiment of the present
invention or Cu wire according to the comparative example. The
manufactured magnetic field generating coils are subjected to
characteristic confirmation tests. The test results are shown
in FIGs. 11 and 12. IH cookers generally use high frequency
current of about 20 kHz to 60 kHz. The test revealed that in
a frequency range including about 20 kHz to 60 kHz, the AC
resistance of the brass wire is lower than that of the Cu wire.
[0079]
As shown in FIG. 13, the AC resistances of the brass wire
and the Cu wire as the comparative example at an external
magnetic field strength H of 1 A/mm are calculated using the
aforementioned equations (1), (18), and (48), each wire having
a diameter of 0.4 mm. FIG. 13 shows that the AC resistance of
the brass wire is lower than that of the Cu wire having the same
diameter as that of the brass wire in a frequency range specified
between first and second frequencies f 1 and f2 . In other words,
in the frequency range lower than the first frequency fl, the
AC resistance of the brass wire is higher than that of the Cu
wire. At the first frequency fl, the AC resistance of the brass
wire equals to that of the Cu wire. In the frequency range
higher than the first frequency fl, the eddy current loss is
dominant, and the relative magnitudes of the AC resistances of
the brass wire and the Cu wire are therefore reversed. In the
frequency range between the first frequency fl and second

frequency f2, the AC resistance of the Cu wire is higher than
that of the brass wire. At the second frequency f2, the AC
resistance of the brass wire equals to that of the Cu wire again.
In the frequency range higher than the second frequency f2, the
proximity effect of the brass wire has a greater influence than
that of the Cu wire has, and the relative magnitudes of the AC
resistances of the brass wire and Cu wire are therefore
reversed.
[0080]
FIG. 14 shows calculation results of the sum of the skin
effect component Rs and DC resistance Rdc and the proximity
effect component Rp of the brass wire having a diameter of 0.4
mm at an external magnetic field strength H of 1 A/mm. The DC
resistance Rdc is a value when the frequency is 0 in the equation
(1) . As shown in FIGs. 9 and 11 to 13, the brass wire and the
like have AC resistances lower than that of the Cu wire in a
predetermined frequency range although the brass wire and the
like have high volume resistivities than that of cupper. The
reason why the above phenomenon occurs is because the AC
resistance highly depends on the proximity effect as shown in
FIG. 14 and there is a frequency range in which the higher the
voltage resistivity, the smaller the proximity effect. The
skin effect component Rs and proximity effect component Rp
depend on the frequency. However, when the frequency is less
than 1 MHz, the proximity effect component Rp is more dependent
on the frequency than the skin effect component Rs is, and the
dependency of the skin effect Rs is negligibly low.
[0081]
FIG. 15 shows the results of calculation of the ratio (Rp
ratio) of the AC resistance due to the proximity effect of
conductor materials to that of the reference Cu wire at an
external magnetic field strength H of 1 A/mm with a current
frequency of 100 kHz using the aforementioned equation (48).
In FIG. 15, the conductor materials used in the above
calculation are: aluminum wire in which the conductive portion
11 shown in FIG. 1(a) is made of pure aluminum; 5% CCA wire in
which the central conductor 12 shown in FIG. 1(b) is made of
aluminum and the cross-sectional area of the cover layer 13 is
5% of the cross-sectional area of the entire electric wire; 10%
CCA wire in which the central conductor 12 shown in FIG. l"-(b)

is made of aluminum and the cross-sectional area of the cover
layer 13 is 10% of the cross-sectional area of the entire
electric wire; 15% CCA wire in which the central conductor 12
shown in FIG. 1(b) is made of aluminum and the cross-sectional
area of the cover layer 13 is 15% of the cross-sectional area
of the entire electric wire; 5% CCA wire (alloy Al) in which
the central conductor 12 shown in FIG. 1(b) is made of aluminum
alloy and the cross-sectional area of the cover layer 13 is 5%
of the cross-sectional area of the entire electric wire; and
wires in which the conductive portion 11 shown in FIG. 1(a) is
made of brass, silicon bronze, and phosphor bronze. The volume
resistivity of the CCA wires is an equivalent volume resistivity
calculated by conversion using the ratio of the cross-sectional
areas of the two layers. FIG. 15 reveals that there is a
condition in which the Rp ratio is less than 1 even if the wire
has a larger diameter than the Cu wire in addition to the
condition where the diameter of the wire is equal to that of
the Cu wire.
[0082]
The first embodiment of the present invention therefore
focuses on this Rp ratio. Specifically, in the electric wire
according to the first embodiment of the present invention, the
volume resistivity of the conductive portion 11 is specified
so that the ratio (Rp ratio) of the AC resistance due to the
proximity effect of the conductive portion 11 shown in FIGs.
1(a) and 1(b) to that of the reference Cu wire is less than 1
in a particular frequency range in which the electric wire of
interest is used. The diameter of the reference Cu wire may
be equal to or different from that of the conductive portion
11 shown in FIGs. 1(a) and 1(b) and can be properly set.
[0083]
With the electric wire according to the first embodiment
of the present invention, when the electric wire is used in a
particular frequency range, the AC resistance of the electric
wire can be made equal to or lower than that of the reference
Cu wire.
[0084]

As shown in FIG. 16, an electric wire designing apparatus
according to the first embodiment of-- the present invention

includes a central processing unit (CPU) 110, a storage device
111, an input device 112, and an output device 113.
[0085]
The CPU 110 logically includes a resistance calculation
unit 101, a ratio calculation unit 102, and a determination unit
103 as modules (logical circuits) which are hardware sources.
[0086]
The resistance calculation unit 101 reads from the
storage device 111, wire type information including the
material, shape, and diameter of the conductive portion 11 of
candidates for electric wire which can be produced and the
particular frequency range in which the electric wire is used.
The resistance calculation unit 101 uses the aforementioned
equation (48) to calculate values of AC resistance due to the
proximity effect of the conductive portion 11 of the candidates
for the electric wire in the particular frequency range.
Moreover, the resistance calculation unit 101 reads from the
storage device 111, the particular frequency range in which the
electric wire of interest is used and the information concerning
the reference Cu wire and uses the aforementioned equation (48)
to calculate the value of AC resistance wire due to the proximity
effect of the reference Cu in the particular frequency range.
The values of AC resistance of the conductive portion 11 and
Cu wire may be calculated at plural frequencies in the
particular frequency range or may be at least one frequency in
the particular frequency range (for example, at the upper limit
of the particular frequency range). Moreover, the diameter of
the reference Cu wire may be equal to or different from that
of the conductive portion 11 of the candidates and can be
properly set.
[0087]
The ratio calculation unit 102 calculates, based on the
values of AC resistance due to the proximity effect of the
conductive portion 11 and Cu wire which are calculated by the
resistance calculation unit 101, the ratio (Rp ratio) of the
AC resistance values due to the proximity effect of the
conductive portion 11 as the candidate to that of the Cu wire
at a same frequency.
[0088]
The determination unit 103 determines based on the Rp

ratio calculated by the ratio calculation unit 102 whether the
candidate is applicable to the electric wire. For example, the
determination unit 103 determines whether the Rp ratio is less
than 1. If the Rp ratio is determined to be less than 1, the
determination unit 103 determines that the candidate is
applicable to the electric wire.
[0089]
The storage device 111 stores: information concerning the
equation (48) for calculating the AC resistance due to the
proximity effect; information of plural candidates for the
conductive portion 11; the particular frequency range used by
each device to which the electric wire is applied; the values
of AC resistance due to the proximity effect of the conductive
portion 11 and Cu wire which are calculated by the resistance
calculation unit 101; the Rp ratio calculated by the ratio
calculation unit 102; the determination results by the
determination unit 103; and the like.
[0090]
The storage device 111 can be a semiconductor memory, a
magnetic disk, an optical disk, or the like, for example. The
storage device 111 can be caused to function as a storage device
or the like storing programs executed by the CPU 110 (the
programs are described in detail). The storage device 111 can
be caused to function as a temporary data memory which
temporarily stores data used in the program execution process
of the CPU 110 or is used as a work area.
[0091]
The input device 112 can include a recognition device such
as a touch panel, a keyboard, a mouse, or an OCR, an image input
device such as a scanner or a camera, a voice input device such
as a microphone, or the like, for example. The output device
113 can include a display device such as a liquid crystal device
(LCD), an organic electroluminescence (EL) display, or a CRT
display, a printing device such as an ink-jet printer, a laser
printer, or the like.
[0092]

Using a flowchart of FIG. 17, a description is given of
an example of the method of manufacturing a high-frequency
electric wire including the designing method using fe-he electric

wire designing apparatus according to the first embodiment of
the present invention. Herein, the description is given of the
method of manufacturing a CCA wire, but it is certain that the
high-frequency electric wire is not limited to the same.
[0093]
i) In step S101, the resistance calculation unit 101 reads from
the storage device 111, information concerning the conductive
portion 11 as a candidate for the electric wire and a particular
frequency range in which the electric wire is used. The
resistance calculation unit 101 uses the aforementioned
equation (48) to calculate the value of AC resistance due to
the proximity effect of the conductive portion 11 in the
particular frequency range. Furthermore, the resistance
calculation unit 101 uses the aforementioned equation (48) to
calculate the value of AC resistance due to the proximity effect
of the reference Cu wire. The calculated values of AC
resistance of the conductive portion 11 and Cu wire are stored
in the storage device 111. The values of AC resistance of the
conductive portion 11 and Cu wire may be stored in the storage
device 111 in advance or may be inputted from the input device
112. The values of AC resistance of the conductive portion 11
and Cu wire may be actually measured instead of being calculated
using the theoretical formula.
[0094]
ii) In step S102, based on the values of the AC resistance due
to the proximity effect of the conductive portion 11 and Cu wire,
which are calculated by the resistance calculation unit 101,
the ratio calculation unit 102 calculates the ratio (Rp ratio)
of the value of the AC resistance due to the proximity effect
of the conductive portion 11 to that of the Cu wire.
[0095]
iii) In step S103, the determination unit 103 determines whether
the Rp ratio calculated by the ratio calculation unit 102 is
less than 1. If the Rp ratio is less than 1 as a result, it
is determined that the candidate is applicable to the electric
wire. The determination result is stored in the storage device
111.
[0096]
iv) In step S104, the electric wire is manufactured with the
material, shape, diameter, and the like of the candidate which

is determined by the determination unit 103 to be applicable.
In the case of CCA wire, for example, the central conductor 12
which has a diameter of about 9.5 to 12.0 mm and is made of
aluminum or aluminum alloy is prepared. The surface of the
central conductor 12 is covered with the cover layer 13 by
performing TIG welding, plasma welding, or the like with about
0.1 to 0.4 mm thick copper tape longitudinally attached to the
surface of the central conductor 12. Next, the central
conductor 12 covered with the cover layer 13 is subjected to
skin pass rolling to have a diameter of about 9.3 to 12.3 mm,
thus resulting in a base material composed of the central
conductor 12 covered with the cover layer 13. Next, the base
material is drawn through plural drawing dies (about 25 to 26
dies) . By causing the base material to pass through the plural
drawing dies, the final diameter of the electric wire is equal
to the determined diameter.
[0097]
According to the method of manufacturing a high-frequency
electric wire including the designing method using the electric
wire designing apparatus according to the first embodiment of
the present invention, the wire type can be determined based
on the Rp ratio calculated using the equation (48) for
calculating the AC resistance due to the proximity effect. It
is therefore possible to design the wire diameter of a
high-frequency electric wire which has a smaller eddy current
loss than that of the reference Cu wire and therefore has less
AC resistance corresponding to the particular frequency range
in which the high-frequency electric wire is used.
[0098]
The manufacturing method shown in FIG. 17 may be performed
by: in the step S102, calculating individual values of AC
resistance due to the proximity effect for plural candidates;
in the step S102, calculating the Rp ratio of each of the plural
candidates; and in the step S103, determining whether each of
the plural candidates is applicable. If some of the plural
candidates are applicable, in the step S104, the wire type of
one of the applicable candidates is properly selected.
[0099]

— The series of steps s~hown in FIG. 17, which includes: i)^~

the step of individually calculating the AC resistance due to
the proximity effect of the conductive portion 11, which is a
candidate for the electric wire, in the particular frequency
range and the AC resistance due to the proximity effect of the
reference Cu wire in the particular frequency range; ii) the
step of calculating the ratio of the AC resistance due to the
proximity effect of the conductive portion to that of the
reference Cu wire; iii) the step of determining based on the
calculated ratio whether the candidate is applicable to the
electric wire, can be executed by controlling the electric wire
designing apparatus shown in FIG. 16 through a program having
an algorithm equivalent to the method shown in FIG. 17.
[0100]
This program can be stored in the storage device 111 of
a computer system constituting the electric wire designing
apparatus of the present invention. This program can be stored
in a computer-readable recording medium. By loading this
recording medium into the storage device 111 or the like, the
series of steps of the first embodiment of the present invention
can be executed.
[0101]
Herein, the computer-readable recording medium refers to
a medium or the like in which programs can be recorded, for
example, such as a semiconductor memory, a magnetic disk, or
an optical disk. For example, the body of the electric wire
designing apparatus can be configured to incorporate or be
externally connected to a device to read the recording medium.
Furthermore, the programs in the recording medium can be stored
in the recording device 111 via an information processing
network such as a wireless communication network.
[0102]
(Second Embodiment)

An electric wire according to a second embodiment of the
present invention is an electric wire used in a particular
frequency range. As shown in FIG. 18, the electric wire is a
CCA wire including a central conductor 21 made of aluminum (Al)
or aluminum alloy and a cover layer 22 made of copper (Cu)
covering the central conductor 21. As for the electric wire
according to the second embodiment-of the present invention,

the particular frequency range falls within a frequency range
which is specified between the first and second frequencies at
which the AC resistance of the electric wire is equal to that
of a Cu wire having the same diameter as that of the electric
wire and in which the AC resistance of the electric wire is larger
than that of the Cu wire.
[0103]
The diameter of the entire electric wire is desirably
about 0 . 05 mm to 0 . 6 mm. The cross-sectional area of the cover
layer 22 is not more than 15% of that of the whole electric wire
including the central conductor 21 and cover layer 22, desirably
about 3% to about 15%, more preferably about 3% to about 10%,
and still more preferably about 3% to about 5%. The lower the
ratio of cross-sectional area between the cover layer 22 and
the entire electric wire, the lower the high-frequency
resistance.
[0104]
The central conductor 21 can be made of electrical
aluminum (EC aluminum) or aluminum alloy such as Al-Mg-Si alloy
(JIS6000s) , for example. The aluminum alloy is more desirable
than the EC aluminum because the aluminum alloy has a higher
volume resistivity than that of the EC aluminum.
[0105]
The AC resistances of the CCA wire according to the second
embodiment of the present invention and the Cu wire were
calculated through the simulation using the aforementioned
theoretical formula. This results in finding the
characteristics that the CCA wire has a smaller eddy-current
loss than the Cu wire of the same diameter has because of the
proximity effect and therefore has a lower AC resistance.
[0106]
FIG. 19 shows the relationship between the frequency and
AC resistance of CCA and Cu wires having diameters of 1.8 mm,
0.4 mm, and 0.2 mm. In the case of the Cu wire and CCA wire
having a diameter of 1.8 mm, in a frequency range lower than
a first frequency fll (not shown) of about 1 kHz, the AC
resistance of the CCA wire is higher than that of the Cu wire.
At the first frequency fll, the AC resistance of the CCA wire
equals to that of the Cu wire. In a frequency range higher than
the first frequency f-1, the eddy current loss is dominant, and

the relative magnitudes of the AC resistances of the CCA wire
and Cu wire are therefore reversed. In a frequency range Bl
between the first frequency fll and a second frequency f12 of
about 10 kHz, the AC resistance of the Cu wire is higher than
that of the CCA wire. At the second frequency fl2, the AC
resistance of the CCA wire equals to that of the Cu wire again.
In a frequency range higher than the second frequency fl2, the
proximity effect in the CCA wire has a larger influence than
that in the Cu wire, and the relative magnitudes of the AC
resistances of the CCA wire and Cu wire are therefore reversed.
[0107]
Also in the case of the Cu wire and CCA wire each having
a diameter of 0.4 mm, the AC resistance of the CCA wire equals
to that of the Cu wire at first and second frequencies f21 and
f22. In a frequency range B2 between the first and second
frequencies f21 and f22, the AC resistance of the Cu wire is
higher than that of the CCA wire.
[0108]
Also in the case of the Cu wire and CCA wire each having
a diameter of 0.2 mm, the AC resistance of the CCA wire equals
to that of the Cu wire at first and second frequencies f31 and
f32. In a frequency range B3 between the first and second
frequencies 31 and 32, the AC resistance of the Cu wire is higher
than that of the CCA wire.
[0109]
Moreover, as shown in FIG. 19, the characteristics are
found in which as the diameter of the CCA and Cu wires gets
smaller like 1.8 mm, 0.4mm, and 0.2 mm, the first and second
frequencies fll and fl2 are shifted to higher frequencies and
the frequency range (Bl, B2, andB3) specified between the first
frequency (fll, fl2, and fl3) and the second frequency (fl2,
f22, andf32) are therefore shifted to higher frequencies. Even
if the strength of the magnetic field increases, the second
frequency (f 12, f22, and f23) changes very little, but the first
frequency (fll, f21, and f31) moves to lower frequency.
[0110]
Moreover, in a winding wire of a high-frequency
transformer incorporated in a switching power supply, current
having a highly distorted waveform flows as shown in FIG. 20.
This is because the frequency of the alternating - current

contains many high-order harmonic components in addition to the
frequency of the fundamental {fundamental frequency).
Accordingly, the loss (copper loss) generated in the
high-frequency transformer is the sum of the direct-current
component and the fundamental and higher order harmonic
components- As shown in FIG. 22, for example, the loss of a
CCA winding wire (diameter: 0.2 mm) according to the second
embodiment of the present invention is 8.0 W, and the loss of
a Cu winding wire (diameter; 0.6 mm) according to the
comparative example is 14.5 W.
[0111]
Accordingly, it is preferable that the diameter, material,
cross-sectional area ratio, and the like of the CCA wire are
designed so that, as the frequency range of the alternating
current used in the CCA wire, the fundamental frequency and
higher order harmonics of the alternating current fall within
the frequency range (Bl, B2, or B3) specified by the first
frequency (fll, f21, or f31) and the second frequency (fl2, f22,
or f32) . It may be properly determined depending on the
intended purpose of the CCA wire which ones of the high-order
harmonic components are to be considered. For example, it is
possible to consider the frequency range from the fundamental
frequency . up to the tenth-order harmonic component or the
frequency range from the fundamental frequency up to the
twentieth-order harmonic component.
[0112]
When used in the particular frequency range, the CCA
strand according to the second embodiment of the present
invention can have an eddy-current loss equal to or smaller than
that of the Cu wire having the same diameter as that of the CCA
strand, and therefore the AC resistance of the CCA wire can be
reduced.
[0113]

As shown in FIG. 23, an electric wire designing apparatus
according to the second embodiment of the present invention
includes a central processing unit (CPU) 210, a storage device
211, an input device 212, and an output device 213.
[0114]
'The CPU 210 logically- ^includes an AC resistance

calculation unit 201, a frequency extraction unit 202, and a
diameter extraction unit 203 as modules (logical circuits) which
are hardware sources.
[0115]
The AC resistance calculation unit 201 reads information
necessary to calculate AC resistances of the target CCA wire
and the Cu wire from the storage device 211 and then, as shown
in FIG. 19, calculates the AC resistances of CCA wires having
plural diameters and Cu wires of the same diameters as those
of the CCA wires at different frequencies.
[0116]
The frequency extraction unit 202, based on the AC
resistances of the CCA wires having plural diameters and the
Cu wires having the same diameters as those of the CCA wires,
which are calculated by the AC resistance calculation unit 201,
as shown in FIG. 19, for each of the plural diameters of the
CCA and Cu wires, extracts the first frequency (fll, f21, or
f31 (fll is not shown) ) and second frequency (fl2, f22, or f32)
at which the AC resistance of the CCA wire is equal to that of
the Cu wire and between which the AC resistance of the CCA wire
is lower than that of the Cu wire.
[0117]
Herein, at the frequencies extracted as the first
frequency (fll, f21, or f31) and the second frequency (fl2, f22,
or f32) , the AC resistance of the CCA wire may not be strictly
equal to that of the Cu wire. For example, it is possible to
extract a frequency just before (lower frequency) or just after
(higher frequency) the relative magnitudes of the AC
resistances of the CCA wire and Cu wire are reversed.
Alternatively, it is possible to extract a frequency at which
approximate curves of the AC resistances of the CCA wire and
Cu wire, which are obtained from the calculation results thereof,
intersect each other.
[0118]
The diameter extraction unit 203 reads from the storage
device 211, a particular frequency range in which the CCA wire
is used. Based on the first frequency (fll, f21, or f31) and
the second frequency (fl2, f22, or f32) which are extracted by
the frequency extraction unit 202, the diameter extraction unit
203- extracts a diameter of the CCA wire ■ corresponding to-the - --

first and second frequencies so that the frequency range (Bl,
B2, or B3) specified between the extracted first frequency (fll,
f21, or f32) and second frequency (fl2, f22, or f32) falls in
the particular frequency range in which the CCA wire is used
(for example, a diameter of 0.4 mm is extracted corresponding
to the first frequency f21 and second frequency f22). The
particular frequency range in which the CCA wire is used may
include the fundamental frequency and tenth or less order
harmonic components shown in FIG. 21 or may include the
fundamental frequency and twentieth or less order harmonic
components.
[0119]
The storage device 211 shown in FIG. 23 stores information
necessary to calculate the AC resistances of CCA wires and Cu
wires having various diameters, a particular frequency range
in which each CCA wire is used, the AC resistances calculated
by the AC resistance calculation unit 201, the first frequencies
fll, f21, and f31 and the second frequencies fl2, f22, and f32
which are extracted by the frequency extraction unit 202, and
the diameter of the CCA wire which is extracted by the diameter
extraction unit 203. The storage device 211 can be a
semiconductor memory, a magnetic disk, an optical disk, or the
like, for example. The storage device 211 can be caused to
function as a storage device or the like storing programs
executed by the CPU 210 (the programs are described in detail) .
The storage device 211 can be caused to function as a temporary
data memory which temporarily stores data used in the program
execution process of the CPU 210 and is used as a work area.
[0120]
The input device 212 shown in FIG. 23 can include a
recognition device such as a touch panel, a keyboard, a mouse,
and an OCR, an image input device such as a scanner and a camera,
a voice input device such as a microphone, and the like, for
example. The output device 213 can include a display device
such as a liquid crystal device (LCD), an organic
electroluminescence (EL) display, and a CRT display, a printing
device such as an ink-jet printer and a laser printer, and the
like.
[0121]
--^---

Using a flowchart of FIG. 24, a description is given of
an example of the method of manufacturing a CCA strand including
the electric wire designing method using the electric wire
design apparatus according to the second embodiment of the
present invention.
[0122]
i) In step S201, the AC resistance calculation unit 201
calculates for different frequencies, the AC resistances of the
CCA wires of plural diameters and the Cu wire having the same
diameters as those of the CCA wires. This calculation results
are stored in the storage device 211. The material, the ratio
of cross-sectional area, and the like of the CCA wires to be
calculated can be properly set. The AC resistances of the CCA
and Cu wires may be actually measured instead of being
calculated.
[0123]
ii) In step S202, as shown in FIG. 19, the frequency extraction
unit 202, for each of the plural diameters, extracts the first
frequency (fll, f21, or f31 (fll is not shown) ) and the second
frequency (fl2, f22, or f32) at which the AC resistances of the
CCA wire and Cu wire of the same diameter are equal to each other
and between which the AC resistance of the CCA wire is smaller
than that of the Cu wire. The ranges of wire diameter and
frequency to be calculated can be properly set to ranges in which
the CCA wire can be used. The extracted first frequencies (fll,
f21, and f31) and second frequencies (fl2, f22, and f32) are
stored in the storage device 211.
[0124]
iii) In step S203, the diameter extraction unit 203 extracts
a diameter of the CCA wire corresponding to the first and second
frequencies so that the frequency range (Bl, B2, or B3)
specified between the extracted first frequency (fll, f21, or
f32) and second frequency (fl2, f22, or f32) fall within the
particular frequency range in which the CCA wire is used {for
example, a diameter of 1. 8 mm is extracted corresponding to the
first frequency fll and second frequency fl2) . The extracted
diameter is stored in the storage device 211.
[0125]
iv) In step S204, a CCA strand having the diameter stored in
the storage device- 211'-is manufactured. Specifically, the

central conductor 21 which is made of aluminum or aluminum alloy
and has a diameter of about 9.5 mm to 12.0 mm is prepared. The
surface of the central conductor 12 is covered with the cover
layer 13 by performing TIG welding, plasma welding, or the like
with about 0.1 mm to 0.4 mm thick copper tape longitudinally
attached to the surface of the central conductor 12. Next, the
central conductor 21 coated with the cover layer 22 is subj ected
to skin pass rolling so as to have a diameter of about 9.3 mm
to 12.3 mm, thus producing a base material composed of the
central conductor 21 covered with the cover layer 22. Next,
the base material is drawn through plural drawing dies (about
25 to 26 dies) . By causing the base material to pass through
the plural drawing dies, the electric wire finally has a
diameter equal to the diameter stored in the storage device 211.
[0126]
By the method of manufacturing a CCA strand including the
designing method using the electric wire designing apparatus
according to the second embodiment of the present invention,
it is possible to design the diameter of a CCA wire whose eddy
current loss can be made equal to or less than that of the Cu
wire having the same diameter and whose AC resistance can be
reduced corresponding to the particular frequency range in
which the CCA wire is used.
[0127]

The series of steps shown in FIG. 24, which includes: i)
the step of individually calculating the AC resistances of CCA
wires having plural diameters and the AC resistance of the Cu
wire having the same diameters as those of the CCA wire at
different frequencies; ii) the step of extracting, for each of
the plural diameters, the first frequency (fll, f21, or f31)
and the second frequency (fl2, f22, or f32) at which the AC
resistance of the CCA wire is equal to that of the Cu wire and
at which the AC resistance of the CCA wire is lower than that
of the Cu wire; iii) the step of extracting a diameter
corresponding to the first frequency (fll, f21, or f31) and the
second frequency (fl2, f22, or f32) so that the frequency range
Bl, B2, or B3 specified between the first frequency fll, f21,
or f31 and the second frequency (fl2, f22, or f32) falls within
the ^particular frequency range in which the CCA wire is used;

and the like, can be executed by controlling the electric wire
designing apparatus shown in FIG. 23 through a program having
an algorithm equivalent to the method shown in FIG. 24.
[0128]
This program can be stored in the storage device 211 of
a computer system constituting the electric wire designing
apparatus of the present invention. This program can be also
stored in a computer-readable recording medium. By loading
this recording medium into the storage device 211 or the like,
the series of steps of the second embodiment of the present
invention can be executed.
[0129]
Herein, the computer-readable recording medium refers to
a medium in which programs can be recorded, for example, such
as a semiconductor memory, a magnetic disk, or an optical disk.
For example, the main body of the electric wire designing
apparatus can be configured to incorporate or be externally
connected to a device to read the recording medium. Furthermore,
the programs in the recording medium can be stored in the storage
device 211 via an information processing network such as a
wireless communication network.
[0130]

Next, a description is given of an electric motor
according to the second embodiment of the present invention.
Electric motors using inverter devices and the like to control
the rotation speed and torque are highly efficient and are used
in a wide range of fields including drive of railway cars and
electric cars and inverter air conditioners in the field of
electrical appliances.
[0131]
A coil of an electric motor is configured by winding
conducting wire in a multiple manner. In the electric motor,
copper (Cu) has a lower resistivity than aluminum (Al) and can
be soldered. Conventional coils are generally composed of Cu
wires.
[0132]
However, this type of electric motor has a variable
rotation speed and is often used at a high rotation speed. The
driving current of the- elect-ric motor has a higher frequency

at a higher rotation speed. Moreover, the inverter device
properly controls on and off of direct-current voltage to
produce high frequency. The driving current therefore
includes the fundamental frequency component and higher
frequency components than the same.
[0133]
As the frequency increases, the resistance of the coil
increases because of the skin and proximity effects. The
resistance due to the skin effect of Al wire is always higher
than that of Cu wire, but the resistance due to proximity effect
of Al wire is not always higher than that of Cu wire. In the
case of a coil wound with Cu wire, the proximity effect increases
the high frequency resistance and therefore increases the loss
due to the same in some cases. Particularly in the cases where
the operating frequency of the electric motor is high, where
the electric motor is driven by using the inverter device, and
the like, the loss due to the proximity effect becomes
conspicuous.
[0134]
Herein, coils have various shapes. Coils having
different shapes have different ratios between the skin effect
and proximity effect of high frequency resistance of the
conducting wire. The skin effect depends on the
cross-sectional shape, the number, and the length of conducting
wires constituting a coil, but the proximity effect also depends
on how the coil is wound. The proximity effect becomes high
when the conducting wires are wound closely or are wound with
many turns. The high-frequency resistance per unit length of
conducting wires constituting a coil is expressed as the
following equation (49) .
[0135]

Herein, Rs (Q/m) is a high-frequency resistance due to the skin
effect per unit length; Pp (Q*m) is a high-frequency loss due
to the proximity effect per unit length; and a (1/m) is a shape
factor (structural factor) depending on the shape of the coil,
a is a constant little depending on the frequency. The more
closely the coil is wound, or the longer the wound conducting
wires are, the larger the a value is. a depends on necessary
output power of - the electric motor but varies. -,

[0136]
Rs and Pp are given by the following equations (50) and
(51) .
[Equation 33]

[0137]

As shown in FIG. 25, an electric motor (three-phase AC
synchronous motor) according to a first example of the second
embodiment of the present invention includes: plural iron cores
221 arranged on a circle; plural coils 223 wound on the plural
iron cores 221 with an electric wire 222 composed of Al or CCA
wire; and a rotor 224 which is rotated when current is applied
to the plural coils 223. The plural iron cores 221, the plural
coils 223, a coil holder 20, and the like constitute a stator.
[0138]
The electric motor according to the first example of the
second embodiment of the present invention has 12 coils. An
inner diameter a of the coil holder 20 is 150 mm; an outer
diameter b thereof is 200 mm; a length h of each iron core 221,
40 mm; a diameter e of an end thereof on the outer side, 30 mm;
and a diameter f of the other end thereof, 20 mm. The coil of
each pole is cylindrically wound with ten turns of the electric
wire 222 around the iron cores 21, the electric wire 222 having
a radius r of 0.8 mm. The entire length 1 is about 3.1 m. FIG.
25 shows only the U-phase coils 223. The V-phase and W-phase
coils (not shown) have structures similar to the coils 223.
[0139]
The rotator 224 is composed of a permanent magnet. The
rotator 224 is attracted and rotated by the peripheral rotating
magnetic field formed by alternating current applied to the
coils 223.
[0140]
In the electric motor according to the first example of
the second embodiment of the present invention^ the rotation

speed is controlled by adjusting the frequency of the driving
current in an inverter method using a variable voltage variable
frequency (VWF) type inverter device. The inverter device is
a three-phase output inverter including six switching elements,
for example, and uses the switching elements to produce
three-phase alternating current in a pseudo manner.
[0141]
Herein, the frequency of the alternating current applied
to the coils 223 is controlled by the inverter method so as to
fall between a first frequency and a second frequency higher
than the first frequency, the first and second frequencies being
frequencies between which the alternating current resistance
of the coils 223 is lower than that of a coil wound with Cu wire
having a same shape as the coils 223.
[0142]
Moreover, the driving current includes high frequency
components having amplitudes not less than 1/3 of that of the
fundamental frequency component and includes high frequency
components having powers not less than 1/9 of that of the
fundamental frequency component.
[0143]
FIGs. 26 and 27 show current waveforms of the electric
motor shown in FIG. 25 at operating frequencies of 20 Hz and
50 Hz. FIG. 28 shows a waveform obtained by extending the time
axis of FIG. 27 two and a half times and superimposing the same
on FIG. 26. FIG. 26 shows that the current has a fundamental
period of 0.05 s. However, for the inverter method is used to
clip variable voltage to produce high-frequency waves, many
drastic changes are included in the sinusoidal waveform. In
FIG. 27, the fundamental period is 0.02 s. FIG. 28 reveals that
the configuration of the sinusoidal waveform is substantially
constant without depending on the frequency of the current.
[0144]
FIG. 29 shows the frequency spectrum of FIG. 26. As shown
in FIG. 29, the current includes the fundamental frequency of
20 Hz and many other high frequency components. Because of the
existence of these high-frequency components, the
high-frequency resistance is increased, and therefore, the loss
due to the proximity effect therefore become pronounced.
[0145]

As a comparative example, FIG. 30 shows the
high-frequency resistance Rs per unit length due to the skin
effect of a coil wound with Cu wire having a radius r of 0.8
mm and a length 1 of 3.1 m. FIG. 31 shows the loss Pp per unit
length due to the proximity effect when the external magnetic
field HO is 1 A/mm.
[0146]
Moreover, the coil wound with the same Cu wire has a static
characteristic of the high-frequency resistance as shown in FIG.
32. Herein, the static characteristic refers to the
characteristic when sinusoidal current is applied to the
electric motor. In this case, the structural factor a in the
equation (49) is 3.9 mm-1.
[0147]
On the other hand, in the case of the driving current of
FIG. 26, the high-frequency resistance of the coil is calculated
from the spectrum of FIG. 29 as the following equation (52).
[Equation 34]

[0148]
fn is a frequency of an n-order high-frequency component.
[0149]
It is assumed that the driving current of FIG. 26 is
produced by an inverter device and the waveform constituting
the sinusoidal wave does not relatively change even if the
frequency changes. Calculation of the dynamic characteristic
of the high frequency resistance of the coil by the equation
(52) provides calculation results shown in FIG. 33. This
dynamic characteristic refers to the characteristic when the
periodic driving current as shown in FIG. 26 is applied to the
electric motor. The fundamental frequency at that time is
defined as a reciprocal of the period of the driving current.
FIG. 33 reveals that the dynamic characteristic significantly
increases compared with the static characteristic.
[0150]
On the other hand, FIGs. 34 and 35 show the static
characteristic in the electric motor according to the first
example of the second embodiment of the present invention whieh

is configured as follows: the electric wire 222 of the coils
223 is composed of CCA or Al wire. As shown in FIG. 18, the
CCA wire includes: the central conductor 21 made of aluminum
(Al) or aluminum alloy; and the cover layer 22 made of copper
(Cu) covering the central conductor 21 (b=0.78 mm, a=0.8 mm) .
Moreover, the cross-sectional area of the cover layer 22 is 5%
of that of the entire high-frequency wire {hereinafter, the CCA
wire is referred to as 5% CCA wire). Herein, the CCA and Al
wires have the same diameter. FIGs. 34 and 35 reveal that the
resistances of the CCA and Al wires are lower than that of Cu
wire in a range of the frequency f: 0.9 kHz ≤ f ≤ 27 kHz.
[0151]
FIGs. 36 and 37 show the dynamic characteristic of the
high-frequency resistance of coils wound with the same CCA and
Al wires. FIGs. 36 and 37 show that the resistances of the CCA
and Al wires are lower than that of the Cu wire in a range of
the frequency f: 65 Hz ≤ f ≤ 1173 Hz . In this case, by controlling
the frequency of the driving current in the range of 65 Hz ≤ f ≤ 1173 Hz with the first and second frequencies being set to
65 Hz and 1173 Hz, respectively, it is possible to obtain a
high-frequency resistance equal to or lower than that of the
Cu wire. The first and second frequencies at which each of the
CCA and Al wires has a high-frequency resistance equal to or
smaller than that of the Cu wire may be calculated using the
equations (49) to (52) based on the shape of the coils 223 or
may be actually measured.
[0152]
In the first example of the second embodiment of the
present invention, the electric wire 222 having a circular
cross-section is described. The cross-sectional shape of the
electric wire 222 may be flat or rectangular. An electric wire
made of CCA wire having a cross-sectional area of not less than
2. 0 mm2 can provide the same effect. Moreover, in the case where
the density of the winding and the length of the conducting wire
of the intended electric motor change, the same effect is
provided even if a changes in a range of 2.2 mm-1 ≤ a ≤ 5.5 mm-1.
[0153]
FIG. 38 shows frequency ranges corresponding to different
a values, in which the dynamic characteristic high-frequency
resistance of the CCA wire is lower than that of the Cu wire.

The larger the a value (for example, the more closely or more
turns the conducting wires are wound), the wider the frequency
range in which the CCA wire is advantageous.
[0154]
FIG. 39 shows frequency ranges in which the dynamic
characteristic high-frequency resistance of the CCA wire is
lower than that of Cu wire for each conducting wire having
different radii r at a same a = 3.9 mm-1. The CCA wire having
a larger diameter is more advantageous in the lower frequency.
[0155]
As described above, with the electric motor according to
the first example of the second embodiment of the present
invention, by using Al or CCA wire having a lower conductivity
than Cu wire and controlling the frequency of the driving
current between the first and second frequencies by the inverter
method, the high-frequency resistance of the Al or CCA wire can
be made equal to or lower than that of Cu wire. It is therefore
possible to reduce the loss of the electric motor.
[0156]
Furthermore, since aluminum (Al) is lighter than copper
(Cu) , use of the Al or CCA wire can reduce the weight of the
electric motor.
[0157]
Still furthermore, in the case of using CCA wire, the CCA
wire can be soldered as conventional, and the reduction in
high-frequency resistance and weight can be achieved without
degrading the workability. Moreover, if the skin depth of the
CCA wire is equal to the thickness of the copper layer, the loss
due to the skin effect becomes comparable with that of
conventional conducting wires.
[0158]

As shown in FIG. 40, an electric motor (three-phase AC
synchronous motor) according to a second example of the second
embodiment of the present invention includes: plural iron cores
221 arranged on a circle; plural coils 223 wound on the plural
iron cores 221 with electric wire 222 which is composed of Al
or CCA wire; and a rotor 224 which is rotated when current is
applied to the plural coils 223.
[0159]

The electric motor according to the second example of the
second embodiment of the present invention has 15 coils. An
inner diameter a of the coil holder 20 is 170 mm; an outer
diameter b thereof is 220 mm; a length h of each iron core 221
is 45 mm; a diameter e of an end thereof on the outer side, 33
mm; and a diameter f of the other end thereof, 25 mm. The coil
of each pole is cylindrically wound with ten turns of the
electric wire 222 around the iron cores 221. The electric wire
222 has a radius r of 1.0 mm and an entire length 1 of about
4.8 m. FIG. 40 shows only the U-phase coils 223. The V-phase
and W-phase coils {not shown) have similar structures to the
coils 223.
[0160]
The other configuration of the electric motor according
to the second example of the second embodiment of the present
invention is substantially the same as the electric motor
according to the first example of the second embodiment of the
present invention, and the overlapping description is omitted.
[0161]
As the coils 223 according to the second example of the
second embodiment of the present invention, 5% CCA wire and Al
wire having a radius r of 1.0 mm and a length of 4.8 m are used,
and as a comparative example, Cu wire is used. In the 5% CCA
wire, the outer diameter b of the coil holder 20 is 0.95 mm-,
and the inner diameter a of the coil holder 20 is 1 mm. FIG.
41 shows the high-frequency resistance Rs per unit length due
to the skin effect in the above case. FIG. 42 shows the loss
Pp per unit length due to the proximity effect when the external
magnetic field is H0 = 1 A/mm.
[0162]
Moreover, coils wound with the aforementioned conducting
wires provide the high-frequency resistance static
characteristics as shown in FIGs. 43 and 44. In that case, the
structural factor a in the equation (49) is 2.2 mm-1. In FIGs
43 and 44, the resistances of the CCA and Al wires are lower
than that of the Cu wire when the frequency f falls in a range
of 0.8 kHz ≤ f ≤ 17 kHz.
[0163]
FIGs. 45 and 46 show the high-frequency resistance
dynamic characteristics when it is assumed that the driving

current of FIG. 26 is produced by an inverter and the waveform
constituting the sinusoidal wave does not relatively change
even if the frequency changes. FIGs. 45 and 46 show that the
resistances of the CCA and Al wires are lower than that of the
Cu wire when the frequency f falls in a range of 59 kHz ≤ f ≤
742 kHz. In this case, by controlling the frequency of the
driving current in a range of 59 Hz ≤ f ≤ 742 Hz with the first
and second frequencies set to 59 Hz and 742 Hz, respectively,
it is possible to obtain a high-frequency resistance equal to
or lower than that of Cu wire.
[0164]
In the second example of the second embodiment of the
present invention, the electric wire 222 having a circular
cross-section is described. The cross-sectional shape of the
electric wire 222 may be flat or rectangular. An electric wire
made of CCA wire having a cross-sectional area of at least 3.1
mm2 can provide the same effect. Moreover, in the case where
the density of the winding and the length of the electric wire
222 of the intended electric motor change, the same effect is
provided even if a changes in a range of 1.0 mm-1 ≤ α ≤ 4.5 mm"1.
[0165]
FIG. 47 shows frequency ranges in which the dynamic
characteristic high-frequency resistance of the CCA wire is
lower than that of the Cu wire for each different a value. It
is therefore revealed that the larger the value a is (for example,
the more closely or more turns the conducting wire is wound) ,
the wider the frequency range in which the CCA wire is
advantageous to the Cu wire.
[0166]
FIG. 48 shows frequency ranges in which the dynamic
characteristic high-frequency resistance of the CCA wire is
lower than that of the Cu wire for the respective conducting
wires having different radii r at a same a = 2 . 2 mm-1. The thicker
the wire is, the CCA wire is advantageous at the lower frequency.
[0167]

As shown in FIG. 49, an electric motor (three-phase AC
synchronous motor) according to a third example of the second
embodiment of the present invention includes: plural iron cores
221; plural coils 223 wound with the electric wire 222 which

is composed of Al or CCA wire around the plural iron cores 221;
and a rotor 224 which is rotated when current is applied to the
plural coils 223.
[0168]
The electric motor according to the third example of the
second embodiment of the present invention has 18 coils. An
inner diameter a of the coil holder 20 is 180 mm; an outer
diameter b thereof is 230 mm; a length h of each iron core 221,
50 mm; a diameter e of an end thereof on the outer side, 36 mm;
and a diameter f of the other end thereof, 27 mm. The coil of
each pole is cylindrically wound with 11 turns of the electric
wire 222 around the iron cores 21, the electric wires 222 having
a radius r of 1.2 mm. The entire length 1 is about 7.0 m. FIG.
49 shows only the U-phase coils. The V-phase and W-phase coils
(not shown) have similar structures to the coils 223.
[0169]
The other configuration of the electric motor according
to the third example of the second embodiment of the present
invention is substantially the same as the electric motor
according to the first example of the second embodiment of the
present invention, and the overlapping description is omitted.
[0170]
As the coils 223 according to the third example of the
second embodiment of the present invention, 5% CCA wire and Al
wire each having a radius r of 1.2 mm and a length of 7.0 m are
used, and as a comparative example, Cu wire is used as a
comparative example. In the 5% CCA wire, the outer diameter
b of the coil holder 20 is 1.17 mm, and the inner diameter a
of the coil holder 20 is 1.2 mm. FIG. 50 shows the
high-frequency resistance Rs per unit length due to the skin
effect in the above case. FIG. 51 shows the loss Pp per unit
length due to the proximity effect when the external magnetic
field Ho = 1 A/mm.
[0171]
Moreover, coils wound with the aforementioned conducting
wires exert provide high-frequency resistance static
characteristics as shown in FIGs. 52 and 53. In that case, the
structural factor a in the equation (49) is 1.6 mm-1. In FIGs
52 and 53, the resistances of the CCA and Al wires are lower
than that of the Cu wire when the frequency f falls in a range

of 0.7 kHz ≤ f ≤ 12 kHz.
[0172]
FIGs. 54 and 55 show the high-frequency resistance
dynamic characteristics when it is assumed that the driving
current of FIG. 26 is produced by an inverter device and the
waveform constituting the sinusoidal wave does not relatively
change even if the frequency changes. FIGs. 54 and 55 show that
the resistances of the CCA and Al wires are lower than that of
the Cu wire when the frequency f falls in a range of 48 kHz ≤
f ≤ 511 kHz. In this case, by controlling the frequency of the
driving current in a range of 48 Hz ≤ f ≤ 511 Hz with the first
and second frequencies set to 48 Hz and 511 Hz, respectively,
it is possible to obtain a high-frequency resistance equal to
or lower than that of Cu wire.
[0173]
In the above description of the third example of the second
embodiment of the present invention, the electric wire 222 has
a circular cross-section. The cross-sectional shape of the
electric wire 222 may be flat or rectangular. An electric wire
made of CCA wire having a cross-sectional area of at least 4 . 5
mm2 can provide the same effect. Moreover, in the case where
the density of the winding and the length of the electric wire
222 of the intended electric motor change, the same effect is
provided even if a changes in a range of 0.9 mm-1 ≤ α ≤ 3.2 mm-1.
[0174]
FIG. 56 shows frequency ranges corresponding to different
a values in coils wound with conducting wires of a same shape,
in which the dynamic characteristic high-frequency resistance
of the CCA wire is lower than that of the Cu wire. The larger
the value a is {for example, the more closely or the more turns
the conducting wires are wound) , the wider the frequency range
in which the CCA wire is advantageous to the Cu wire.
[0175]
FIG. 57 shows frequency ranges in which the dynamic
characteristic high-frequency resistances of the CCA wire is
lower than that of Cu wire for each conducting wire of different
radii r at a same a = 1. 6 mm-1. FIG. 57 reveals that the thicker
the wire is, the CCA wire is advantageous at the lower frequency.
[0176]
In the second embodiment of the present invention, the

CCA wires and Cu wires having diameters of 1.8 mm, 0.4 mm, and
0.2 mm are described. However, the present invention is not
limited to the CCA and Cu wires having the above three different
diameters and may be applied to CCA and Cu wires having various
diameters.
[0177]
Moreover, as the electric wire according to the second
embodiment of the present invention, the CCA wire is described.
However, the electric wire according to the second embodiment
of the present invention can be Al wire.
[0178]
Furthermore, in the description of the electric motors
according to the first to third examples of the second
embodiment of the present invention, the examples are
three-phase AC synchronous motors. However, the electric wire
according to the present invention can be applied to electric
motor including various coils. The electric motor according
to the present invention can be applied to various types of
electric motors including coils wound with CCA or Al wire.
[0179]
{Third Embodiment)

As shown in FIG. 58(a), an electric wire according to a
third embodiment of the present invention includes a conductive
portion 31 made of a material having a volume resistivity higher
than that of copper. In the electric wire according to the third
embodiment of the present invention, direct current resistance
value per unit length, which is obtained by dividing the volume
resistivity of the conductive portion 31 by the cross-sectional
area thereof, is specified so that, among first and second
frequencies at which the AC resistance of the electric wire is
equal to that of Cu wire and between which the AC resistance
of the electric wire is lower than that of Cu wire, the second
frequency is not lower than the upper limit of the particular
frequency range.
[0180]
The diameter of the conductive portion 31 is desirably
about 0.05 mm to 0.6 mm but is not particularly limited. The
material of the conductive portion 31 can be copper alloy such
as brass, phosphor brenze, silicon bronze, copper-beryllium

alloy, and copper-nickel-silicon alloy. The brass is an alloy
(Ch-Zn) containing copper (Cu) and zinc (Zn) and may contain
small amounts of elements other than copper and zinc. The
silicon bronze is an alloy (Cu-Sn-Si) containing copper (Cu) ,
tin (Sn), and silicon (Si) and may contain small amounts of
elements other than copper, tin, and silicon. The phosphor
bronze is an alloy (Cu-Sn-P) containing copper, tin, and
phosphor (P) and may contain small amounts of elements other
than copper, tin, and phosphor.
[0181]
These copper alloy wires are subjected to annealing, for
example, and may be plated with tin, copper, chrome (Cr), or
the like. Moreover, the conductive portion 31 may have various
shapes such as a cylinder or a rectangle.
[0182]
Moreover, as shown in FIG. 58(b), the electric wire
according to the third embodiment of the present invention may
be CCA wire including, as the conductive portion 31, a central
conductor 32 composed of aluminum (Al) or aluminum alloy and
a cover layer 33 composed of copper (Cu) covering the central
conductor 32.
[0183]
The entire CCA wire desirably has a diameter of about 0. 05
mm to 0.6 mm. The cross-sectional area of the cover layer 33
is not more than 15% of the cross-sectional area of the entire
electric wire composed of the central conductor 32 and cover
layer 33, desirably about 3% to about 15%, more preferably about
3% to about 10%, and still more preferably about 3% to about
5%. The lower the ratio of the cross-sectional area of the cover
layer 33 to that of the entire electric wire, the lower the AC
resistance. The central conductor 32 can be made of electrical
aluminum (EC aluminum) or aluminum alloy such as Al-Mg-Si alloy
(JIS6000s), for example. The aluminum alloy is more desirable
than the EC aluminum because the volume resistivity of the
aluminum alloy is higher than that of the EC aluminum.
[0184]
The AC resistances of the electric wire according to the
third embodiment of the present invention and Cu wire as the
comparative example are calculated through simulation using the
aforementioned theoretical equation; This results in Sinding

characteristics that the electric wire according to the third
embodiment of the present invention has a smaller eddy-current
loss than Cu wire of the same diameter because of the proximity
effect and therefore has a lower AC resistance.
[0185]
FIG. 13 shows the relationship between the frequency and
AC resistance of brass wire and Cu wire as the comparative
example at an external magnetic strength H of 1 A/mm, the brass
wire and Cu wire having a diameter of 0.4 mm. In a frequency
range lower than the first frequency fl, the AC resistance of
the brass wire is higher than that of the Cu wire. At the first
frequency fl, the AC resistance of the brass wire is equal to
that of the Cu wire. In a frequency range higher than the first
frequency f 1, the eddy current loss is dominant, and the
relative magnitudes of the AC resistances of the brass wire and
Cu wire are therefore reversed. In a frequency range between
the first frequency fl and the second frequency f2, the AC
resistance of the Cu wire is higher than that of the brass wire.
At the second frequency f2, the AC resistance of the brass wire
equals to that of the Cu wire again. In a frequency range higher
than the second frequency f2, the proximity effect in the brass
wire has more influence than that in the Cu wire has, and the
relative magnitudes of the AC resistances of the brass wire and
Cu wire are therefore reversed.
[0186]
FIG. 14 shows a relationship in the brass wire having a
diameter of 0.4 mm between the frequency of current and the sum
of the skin effect component Rs and DC resistance component Rdc
and between the frequency and the proximity effect component
Rp at an external magnetic field strength H of 1 A/mm. The DC
resistance component Rdc is a value when the frequency is 0.
The skin effect component Rs and proximity effect component Rp
depend on frequency. As shown in FIG. 14, however, when the
frequency is less than 1 MHz, the proximity effect component
Rp is more dependent on the frequency than the skin effect
component Rs is, and the dependency of the skin effect component
Rs is negligibly low.
[0187]
FIG. 59 shows a relationship between the frequency and
AC resistance of brass wire and Cu wire when the external

magnetic field strength H is 1 or 5 A/mm. Herein, the brass
wire and Cu wire have a diameter of 0.4 mm. As shown in FIG.
59, the proximity effect component Rp is more strongly dependent
on the magnetic field strength than that of the skin effect
component Rs is. The AC resistances Rac of the Cu wire and brass
wire at the second frequency (f12, f22) , each of which is almost
occupied by the proximity effect component Rp, proportionally
increase as the magnetic field strength increases.
Accordingly, the second frequency (f12, f22) changes very
little. On the other hand, as the external magnetic field
strength increases, the proximity effect component Rp increases,
and the first frequency (fll, f21), which is greatly influenced
by the DC resistance component Rdc, shifts to lower frequency.
[0188]
Herein, the DC resistance per unit length, which is
obtained by dividing the volume resistivity of metal applied
to the conductor by the cross-sectional area thereof, is defined
as reference DC resistance. As shown in FIG. 60, the reference
DC resistance and second frequency are calculated by varying
the material and diameter of the conductor. FIG. 60 shows the
calculation results for the following materials of the
conductor: Al wire in which the central conductor 31 shown in
FIG. 58(a) is made of pure aluminum; 5% CCA wire in which the
central conductor 22 shown in FIG. 58(b) is made of aluminum
and the cross-sectional area of the cover layer 33 is 5% of the
cross-sectional area of the entire electric wire; 10% CCA wire
in which the central conductor 32 shown in FIG. 58(b) is made
of aluminum, and the cross-sectional area of the cover layer
33 is 10% of that of the entire electric wire; 15% CCA wire in
which the central conductor 32 shown in FIG. 58(b) is made of
aluminum and the cross-sectional area of the cover layer 33 is
15% of that of the entire electric wire; 5% CCA (alloy Al) wire
in which the central conductor 32 shown in FIG. 58 (b) is made
of aluminum alloy and the cross-sectional area of the cover
layer 33 is 5% of that of the entire electric wire; and wires
in which the conductive portion 31 shown in FIG. 58(a) is made
of brass, silicon bronze, and phosphor bronze. The volume
resistivity of CCA wires is an equivalent volume resistivity
calculated by conversion using the ratio of cross-sectional
areas-of-the two layers. The calculation results are subjected

to a regression analysis, thus providing a regression line as
represented by a solid line in FIG. 61. To be specific, FIG.
61 shows that the reference DC resistance and the second
frequency has a relationship of the following equation (49)
where the reference DC resistance is Rdc and the second frequency
is f2
[0189]
f2 = 10(0.925×log Rdc + 2.24) (53)
In the electric wire according to the third embodiment
of the present invention, the reference DC resistance value of
the conductive portion 31 is specified using the equation (53)
so that the second frequency is not less than the upper limit
of the particular frequency range in which the electric wire
is used. In other words, the volume resistivity,
cross-sectional area, material, shape, diameter, and the like
of the conductive portion 31 are specified so as to give the
specified reference DC resistance value.
[0190]
There is increasing use of devices driven by
high-frequency current of a frequency of about several kHz to
100 kHz. Accordingly, the second frequency is desirably set
to about 100 kHz or more, for example, and therefore the
reference DC resistance is desirably set to about 0.55 mQ/cm
or more.
[0191]
As shown in FIG. 10, magnetic field generating coils for
an IH cooker were manufactured in such a manner that 55 strands
(diameter: 0.4 mm, length: 6.6 m) in a litz wire construction
are used to be wound in 17 turns, each strand being composed
of the brass wire according to the third embodiment of the
present invention or the Cu wire according to the comparative
example. The manufactured coils were subjected to the
characteristic confirmation tests. The test results are shown
in FIGs. 11 and 12. IH cookers generally use high frequency
current of about 20 kHz to 60 kHz. The test revealed that in
a frequency range including about 20 kHz to 60 kHz, the AC
resistance of the brass wire is lower than that of the Cu wire.
[0192]
Moreover, in a winding wire of a high-frequency
transformer incorporated in a switching-power s-upply, as shown

in FIG. 20, current having a highly distorted waveform flows.
This is because the frequency of the alternating current
contains many high-order harmonic components in addition to the
frequency (fundamental frequency) of the fundamental.
Accordingly, the loss {copper loss) generated in the
high-frequency transformer is the sum of the direct-current
component and the fundamental frequency and high-order harmonic
components. As shown in FIG. 62, for example, the loss of a
brass winding wire according to the third embodiment of the
present invention, which has a diameter of 0.2 mm, is 5.3 W,
and the loss of a Cu winding wire according to the comparative
example, which has a diameter of 0.6 mm, is 14.5 W.
[0193]
Accordingly, it is preferable that the second frequency
is set to not lower than the high-order harmonic component of
used alternating current. It may be properly determined
depending on the intended purpose of the CCA wire which ones
of the high-order harmonic components are to be considered. For
example, it is possible to consider the frequency range from
the fundamental frequency up to the tenth-order harmonic
component or the frequency range from the fundamental frequency
up to the twentieth-order harmonic component.
[0194]
According to the high-frequency electric wire according
to the third embodiment of the present invention, the reference
DC resistance value of the conductive portion 31 of the electric
wire is specified using the equation (53) so that the second
frequency is not less than the upper limit of the particular
frequency range. As a result, when the electric wire is used
in a particular frequency range, the eddy current loss of the
electric wire can be made equal to or less than that of Cu wire
having the same diameter, and the AC resistance thereof can be
therefore reduced.
[0195]
FIG. 61 shows two dashed lines which are 0.7 and 1.3 times
the regression line represented by the solid line. In the third
embodiment of the present invention, the reference DC
resistance value may be specified in a range of the band width
between the two dashed lines shown in FIG. 61 in consideration
of variations of th"e regression line of about +/-30%. To be

specific, the reference DC resistance value Rdc of the
high-frequency electric wire according to the third embodiment
of the present invention may be specified as the following
relationship. Herein, the second frequency is indicated by f2-
0.7×10,0,925×lOgdc + 2.24) ≤ f2 ≤ 1.3×10(0.925xlogRdc + 2.24) (54)
This allows for a margin of the reference direct-current in an
effective range, thus enhancing the flexibility in designing
the volume resistivity, cross-sectional area, material, shape,
diameter, and the like of the conductive portion 31 which
determine the reference DC resistance value.
[0196]
In the above-described example, the reference DC
resistance value is specified in a range of +/-30% of the
regression line. However, from the perspective of ensuring
that the second frequency be equal to or more than the upper
limit of the particular frequency range, the reference DC
resistance value is specified preferably in a range of +/-20%
of the regression line and more preferably in a range of +/-10%
thereof.
[0197]
The reference DC resistance value Rdc may be specified
to as to satisfy the following equation.
f0 ≤ 10 (0.925×logRdc + 2.24) ...(55)
Herein, f0 is the upper limit of the particular frequency range.
The second frequency can be therefore set equal to or higher
than the upper limit of the particular frequency range.
Moreover, the reference DC resistance value can be specified
in a range satisfying the relationship of the equation (55).
This can therefore enhance the flexibility in designing the
volume resistivity, cross-sectional area, material, shape,
diameter, and the like of the conductive portion 31 which
determine the reference DC resistance value.
[0198]

As shown in FIG. 63, an electric wire designing apparatus
according to the third embodiment of the present invention
includes a central processing unit (CPU) 310, a storage device
311, an input device 312, and an output device 313.
[0199]
The CPU 310 logically includes a specific resistance

calculation unit 301, a frequency setting unit 302, a target
resistance calculation unit 303, and a wire type selection unit
304 as modules (logical circuits) which are hardware sources.
[0200]
The specific resistance calculation unit 301 reads
necessary information from the storage device 311 and
calculates a reference DC resistance value specific to each wire
type of electric wire which can be produced. The wire type
includes a combination of the material, shape, diameter, and
the like. The reference DC resistance value of each wire type
may be stored in the storage device 311 in advance or may be
inputted from the input device 312.
[0201]
The frequency setting unit 302 reads from the storage
device 311, the particular frequency range in which the designed
electric wire is used and sets, among the first frequency and
second frequency higher than the first frequency, the second
frequency which is equal to or higher than the upper limit of
the particular range, the first and second frequencies being
frequencies at which the AC resistance of the electric wire is
equal to that of Cu wire having the same diameter as that of
the electric wire and between which the AC resistance of the
electric wire is lower than that of the Cu wire. For example,
the second frequency is set equal to the upper limit of the
particular frequency range. At this time, the upper limit of
the particular frequency range which is set as the second
frequency may be a tenth-order harmonic frequency or higher or
may be a twentieth-order harmonic frequency or higher, for
example.
[0202]
The target resistance calculation unit 303 calculates a
target reference DC resistance value using the equations (53)
and (54) based on the second frequency set by the
frequencysetting unit 302. Moreover, the target resistance
calculation unit 303 may read from the storage device 311, the
particular frequency range in which the designed electric wire
is used and calculate the target reference DC resistance value
so as to satisfy the relationship of the equation (55).
[0203]
The wire type selection unit 304 selects the type of

electric wire according to the specific and target reference
DC resistance values which are calculated by the specific
resistance calculation unit 301 and target resistance
calculation unit 303, respectively. To be specific, the wire
type selection unit 304 selects one from the plural wire types
whose specific DC resistance value, which is calculated by the
specific resistance calculation unit 301, is not less than the
target reference DC resistance value calculated by the target
resistance calculation unit 303.
[0204]
The storage device 311 stores: information necessary to
calculate the reference DC resistance values of the plural wire
types; the particular frequency range used by each device to
which the electric wire is applied; information concerning the
equations (53) and (54); the reference direct current
resistance values calculated by the specific resistance
calculation unit 301; the second frequency set by the frequency
setting unit 302; the reference DC resistance value calculated
by the target resistance calculation unit 303; the wire type
determined by the wire type selection unit 304; and the like.
The storage device 311 can be a semiconductor memory, a magnetic
disk, an optical disk, or the like, for example. The storage
device 311 can be caused to function as a storage device or the
like storing programs executed by the CPU 310 (the programs are
described in detail) . The storage device 311 can be caused to
function as a temporary data memory or the like which
temporarily stores data used in the program execution process
of the CPU 310 or is used as a work area.
[0205]
The input device 312 can include a recognition device such
as a touch panel, a keyboard, a mouse, or an OCR, an image input
device such as a scanner or a camera, a voice input device such
as a microphone, or the like, for example. The output device
313 can be a display device such as a liquid crystal device (LCD),
an organic electroluminescence (EL) display, or a CRT display,
a printing device such as an ink-jet printer, a laser printer,
or the like.
[0206]

Using" a flowchart of FIG. 64, a description is given of

an example of the method of manufacturing a high-frequency
electric wire including the designing method using the electric
wire design apparatus according to the third embodiment of the
present invention. Herein, the description is given of the
method of manufacturing CCA wire, but it is certain that the
high-frequency electric wire is not limited to the same.
[0207]
i) In step S301, the specific resistance calculation unit 301
reads necessary information from the storage device 311 and
calculates the reference DC resistance value for each wire type
of high-frequency electric wire, which includes a combination
of the material, shape, diameter, and the like. The calculated
reference DC resistance values are stored in the storage device
311. The reference DC resistance value of each wire type may
be stored in the storage device 311 in advance or may be inputted
from the input device 312. Alternatively, the reference DC
resistance values specific to the respective wire types may be
actually measured instead of being calculated using the
theoretical equations.
[0208]
ii) In step S302, the frequency setting unit 302 reads from the
storage device 311, the particular frequency range in which the
designed electric wire is used and sets, among the first
frequency and second frequency higher than the first frequency,
the second frequency equal to or higher than the upper limit
of the particular frequency range, the first and second
frequencies being frequencies at which the AC resistance of the
electric wire is equal to that of Cu wire having the same diameter
as that of the electric wire and between which the AC resistance
of the electric wire is lower than that of the Cu wire. The
set second frequency is stored in the storage device 311.
[0209]
iii) In step S303, the target resistance calculation unit 303
calculates the target reference DC resistance value using the
equation (53) or (54) based on the second frequency set by the
frequency setting unit 302. the calculated reference DC
resistance value is stored in the storage device 311. Moreover,
the target resistance calculation unit 303 may read from the
storage device 311, the particular frequency range in which the
designed electric wire is used and calculate the target

reference DC resistance value so as to satisfy the relationship
of the equation (55).
[0210]
iv) In step S304, the wire type selection unit 304 determines,
among the plural wire types, a wire type whose specific DC
resistance value, that is calculated by the specific resistance
calculation unit 301, is not less than the reference DC
resistance value calculated by the target resistance
calculation unit 303. The determined wire type is stored in
the storage device 311.
[0211]
v) In step S305, electric wire of the wire type determined by
the wire type selection unit 304 is manufactured, the wire type
being determined by a combination of the material, shape,
diameter, and the like. In the case of CCA wire, for example,
the central conductor 32 which has a diameter of 9.5 mm to 12.0
mm and is made of aluminum or aluminum alloy is prepared. The
surface of the central conductor 31 is covered with the cover
layer 32 by performing TIG welding, plasma welding, or the like
with about 0.1 mm to 0.4 mm thick copper tape longitudinally
attached to the surface of the central conductor 32. Next, the
central conductor 31 covered with the cover layer 32 is
subjected to skin pass rolling to have a diameter of about 9.3
mm to 12 . 3 mm, thus producing a base material composed of the
central conductor 21 covered with the cover layer 22. Next,
the base material is drawn through plural drawing dies (through
about 25 to 26 dies). By causing the base material to pass
through the plural drawing dies, the electric wire finally has
a diameter equal to the determined diameter.
[0212]
By the method of manufacturing a high-frequency electric
wire including the designing method using the electric wire
designing apparatus according to the third embodiment of the
present invention, the wire type can be determined from the
reference resistance value calculated using the equation (53)
or (54) . As a result, the second frequency is set higher than
the upper limit of the particular frequency range in which the
high-frequency electric wire is used. Accordingly, in the
particular frequency range, the eddy current loss of the
high-frequency electric wire can be made equal to or less than

that of Cu wire having the same diameter, so that the diameter
of the high-frequency electric wire can be designed to reduce
the AC resistance.
[0213]

The series of steps shown in FIG. 64, which includes: i)
step of calculating a DC resistance value per unit length for
each wire type of the high-frequency electric wire which
includes a combination of the material, shape, diameter, and
the like; ii) step of, among the first frequency and the second
frequency higher than the first frequency, setting the second
frequency to a value equal to or higher than the upper limit
of the particular frequency range, the first and second
frequencies being frequencies at which the alternating-current
of the electric wire is equal to that of the Cu wire having a
same diameter as the electric wire and between which the
alternating-current of the electric wire is lower than that of
the Cu wire; iii) step of calculating the reference DC
resistance value from the second frequency; iv) step of
determining the type of electric wire according to the reference
DC resistance value; and the like, can be executed by
, controlling the electric wire designing apparatus shown in FIG.
63 through a program having an algorithm equivalent to the
method shown in FIG. 64.
[0214]
This program can be stored in the storage device 311 of
a computer system constituting the electric wire designing
apparatus of the present invention. This program can be also
stored in a computer-readable recording medium. By loading
this recording medium into the storage device 311 or the like,
the series of steps of the third embodiment of the present
invention can be executed.
[0215]
Herein, the computer-readable recording medium refers to
a medium in which programs can be recorded, for example, such
as a semiconductor memory, a magnetic disk, or an optical disk.
For example, the body of the electric wire designing apparatus
can be configured to incorporate or be externally connected to
a device to read the recording medium. Furthermore, the
pro grams in the recording medium can be stored in the recording

device 111 via an information processing network such as a
wireless communication network.
[0216]
The relational equation between the reference DC
resistance RdC and the second frequency f2 is described in the
equation (53) or (54) by way of example. In the description,
the reference DC resistance is calculated using this example.
However, to be strict, the relationship between the reference
DC resistance RdC and the second frequency f2 is not limited to
the equation (53) or (54) . The reference DC resistance may be
calculated using another theoretical equation.
[0217]
(Fourth Embodiment)

A high-frequency electric wire according to a fourth
embodiment of the present invention is an electric wire used
in a frequency range of about 10 kHz to about 1 MHz and, as shown
in FIG. 65, includes a conductive portion 41 made of copper alloy
having a higher volume resistivity than that of copper.
[0218]
The diameter of the conductive portion 31 is desirably
about 0.05 mm to 0.6 mm but is not particularly limited. The
copper alloy layer 1 is made of brass, phosphor bronze, silicon
bronze, or the like, for example. The brass is an alloy (Cu-Zn)
containing copper (Cu) and zinc (Zn) and may contain small
amounts of elements other than copper and zinc. The silicon
bronze is an alloy (Cu-Sn-Si) containing copper (Cu) , tin (Sn) ,
and silicon (Si) and may contain small amounts of elements other
than copper, tin, and silicon. The phosphor bronze is an alloy
(Cu-Sn-P) containing copper, tin, and phosphor (P) and may
contain small amounts of elements other than copper, tin, and
phosphor.
[0219]
Normal winding wires of transformers, reactors, and the
like are composed of Cu wire coated and insulated with
polyurethane, polyester, polyester, polyesterimide,
polyamide-imide, polyimide, or the like. In a coaxial cable,
high-frequency current signals flow. Accordingly, coaxial
cables are composed of CCA wire, which includes Al wire covered
with a thin copper layer outside, for example, in the light of

the skin effect characteristics.
[0220]
In recent years, there are increasing applications of
devices through which high-frequency current of several kHz to
several hundreds kHz passes, including high-frequency
transformers, high-speed motors, reactors, induction heaters,
and magnetic head devices. In the high-frequency electric wire
used in such devices, generally, thinner winding wires or litz
wires are generally used for the purposes of reducing the
alternating-current loss. However, there is a limit in
thinning wires because the work of removing the insulation
coating at the soldering process for connection becomes
difficult and the number of strands is increased. On the other
hand, with the high-frequency electric wire according to the
fourth embodiment of the present invention, electric wires
which are thinned to prevent an increase in AC resistance can
be further provided with the effect of preventing an increase
in AC resistance without using litz wire construction.
[0221]
As for high-frequency electric wire and high-frequency
coils including the same as the strands, the external magnetic
field tends to avoid the high-frequency electric wire. However,
in a comparatively low frequency range less than several
hundreds kHz, the external magnetic field cannot avoid the
high-frequency electric wire and uniformly enters the inside
of the high-frequency electric wire to induce eddy currents due
to the proximity effect. At this time, the higher the
conductivity of the material of the high-frequency electric
wire {or the smaller the volume resistivity), the larger the
eddy current is, and the higher the AC resistance.
[0222]
Furthermore, in a comparatively high frequency range not
lower than about several tens MHz, as shown in FIG. 4, the
external magnetic field hardly enter the inside of the
high-frequency electric wire as shown in FIG. 4. At this time,
the higher conductivity the material of the high-frequency
electric wire has (or, the smaller volume resistivity) , the more
the magnetic field is concentrated in the surface layer of the
high-frequency electric wire, so that current in the surface
layer is strengthened. Accordingly, it is learned that the

higher the frequency, the more the eddy current loss is because
of the proximity effect and the higher the AC resistance.
[0223]
FIGs. 66 and 67 respectively show the magnetic field
strength distribution and the current density distribution of
Cu wire with a radius of 0.2 mm along the axis y (in the
cross-section direction) when high-frequency currents of 10 kHz,
100 kHz, and 1 MHz are applied to the Cu wire in an external
magnetic field of 1 A/mm. FIG. 66 shows that the higher the
frequency, the higher the magnetic field strength in the surface
layer of the Cu wire. FIG. 67 shows that the higher the
frequency, the higher the current density in the surface layer
of the Cu wire and the larger the eddy currents.
[0224]
Accordingly, in the fourth embodiment of the present
invention, copper alloy having a larger volume resistivity than
that of copper is applied to a high-frequency electric wire.
As shown in FIG. 68, each of brass, phosphor bronze, and silicon
bronze has a volume resistivity higher than copper at 20°C.
Although pure aluminum has a volume resistivity higher than that
of copper, Al wire is covered with oxide film, which is difficult
to remove. On the other hand, copper alloy such as brass,
phosphor bronze, and silicon bronze does not have such a problem
and are advantageous.
[0225]
As described above, in the high-frequency electric wire
according to the fourth embodiment of the present invention,
the conductive portion 41 is made of copper alloy having a volume
resistivity higher than that of copper, such as brass, phosphor
bronze, and silicon bronze. Accordingly, in the case of using
the high-frequency electric wire, the eddy current loss thereof
is smaller than that in the case of using Cu wire in the
predetermined frequency range, and the AC resistance can be
therefore reduced.
[0226]

As a first example, a description is given of measurement
results of the magnetic field strength distribution and loss
distribution of the high-frequency electric wire according to
the fourth embodiment of the present invention.. . FIGs.. -69 and

70 respectively show the magnetic field strength distribution
and loss distribution of Cu wire having a radius of 0.2 mm along
the y axis when current of 100 kHz is applied to the Cu wire
at an external magnetic strength of 1 A/mm. FIGs. 71 and 72
respectively show the magnetic field strength distribution and
loss distribution of silicon bronze wire (the radius: 0.2 mm)
as the high-frequency electric wire according to the fourth
embodiment of the present invention, along the y axis when
current of 100 kHz is applied to the silicon bronze wire at an
external magnetic strength of 1 A/mm. Comparison of FIGs. 71
and 69 reveals that the magnetic field strength of silicon
bronze in the surface layer is smaller than that of Cu wire.
Moreover, comparison of FIGs. 72 and 70 reveals that the eddy
current loss of the silicon bronze wire is smaller than that
of the Cu wire.
[0227]
FIGs. 73 and 74 respectively show the magnetic field
strength distribution and loss distribution of brass wire (the
radius: 0.2 mm) as the high-frequency electric wire according
to the fourth embodiment of the present invention, along the
y axis when current of 100 kHz is applied to the brass wire at
an external magnetic strength of 1 A/mm. Comparison of FIGs.
73 and 69 reveals that the magnetic field strength in the surface
layer of the brass wire is smaller than that of Cu wire.
Moreover, comparison of FIGs. 74 and 70 reveals that the eddy
current loss of the brass wire is smaller than that of the Cu
wire.
[0228]
FIGs. 75 and 76 respectively show the magnetic field
strength distribution and loss distribution of phosphor bronze
wire (the radius of 0.2 mm) as the high-frequency electric wire
according to the fourth embodiment of the present invention
along the y axis when current of 100 kHz is applied to the
phosphor bronze wire at an external magnetic strength of 1 A/mm.
Comparison of FIGs. 75 and 69 reveals that the magnetic field
strength in the surface layer of the phosphor bronze wire is
smaller than that of Cu wire. Moreover, comparison of FIGs.
76 and 70 reveals that the eddy current loss of the phosphor
bronze wire is smaller than that of the Cu wire.
[022 9]

As a second example, FIG. 77 shows AC resistances
(proximity effect component) of the brass wire, phosphor bronze
wire, and silicon bronze wire according to the fourth embodiment
of the present invention and the Cu wire according to the
comparative example, the AC resistance being calculated at an
external magnetic strength H of 1 {A/mm) . FIG. 77 shows that
the AC resistance of each of the brass wire, phosphor bronze
wire, and silicon bronze wire is smaller than that of the Cu
wire in a predetermined frequency range.
[0230]

As a third example, using each of the brass wire, phosphor
bronze wire, and silicon bronze wire according to the fourth
embodiment of the present invention and the Cu wire according
to the comparative example, 14 strands having a diameter of 0.4
mm are wound 80 turns into a reactor. FIG 9 shows the
measurement results represented by the AC resistance per unit
length of the reactor. In FIG. 9, the AC resistance of each
of the brass wire, phosphor bronze wire, and silicon bronze wire
is smaller than that of the Cu wire. Moreover, compared with
a case of the strands shown in FIG. 77, it is revealed that in
the case of the reactor, the high-frequency electric wire
according to the fourth embodiment has a larger effect on
preventing the AC resistance.
[0231]

As shown in FIG. 10, magnetic field generating coils for
an IH cooker were manufactured in such a manner that 55 strands
(diameter: 0.4 mm, length: 6.6 m) in a litz wire construction
are used to be wound in 17 turns, each strand being composed
of the brass wire according to the first embodiment of the
present invention or the Cu wire according to the comparative
example. The manufactured coils were subjected to the
characteristic confirmation tests. The test results are shown
in FIGs. 11 and 12. General IH cookers use high frequency
current of about 20 kHz to 60 kHz. In a frequency range
including about 20 kHz to 60 kHz, the AC resistance of the brass
wire is lower than that of the Cu wire.
[0232]

Next, a description is given of an example of the method
of manufacturing the high-frequency electric wire according to
the fourth embodiment of the present invention. The
manufacturing method below is shown by way of example and is
not particularly limited. The high-frequency electric wire
according to the fourth embodiment of the present invention can
be manufactured by various manufacturing methods.
[0233]
i) A copper alloy material having a volume resistivity higher
than that of copper, including brass, phosphor bronze, and
silicon bronze, is prepared. The material has a diameter of
about 9.5 mm to 12.0 mm.
[0234]
ii) Next, the copper alloy member is drawn through plural
drawing dies (about 20 dies) . By causing the copper alloy
member to pass through the plural drawing dies, the electric
wire finally has a diameter of about 0.05 mm to about 0.6 mm.
The high-frequency electric wire including the conductive
portion 41 made of copper alloy shown in FIG. 65 is thus
completed.
[0235]
(Other Embodiment)
As described above, the present invention is described
based on the embodiments. However, it should not be understood
that the present invention is limited by the description and
drawings constituting a part of this disclosure. From this
disclosure, various substitutions, examples, and operational
techniques will be apparent to those skilled in the art.
[0236]
The electric wires (high-frequency electric wires)
according to the first to fourth embodiments of the present
invention are strands (solid wires) in the above description.
Some electric wires are bundled into an integrated cable or
stranded as a litz wire. In the cases of the integrated cable
and litz wire, it is possible to reduce the AC resistance more
effectively.
[0237]
Moreover, the theoretical equations of the AC resistance
Rs due to the skin effect and the AC resistance Rp due to the

proximity effect are described in the equations (1) to (52) by
way of example. However, the methods of calculating the AC
resistance Rac, the AC resistance Rs due to the skin effect, and
the AC resistance Rp due to the proximity effect are not
particularly limited to those equations. Moreover, it is
certain that the AC resistances Rs due to the skin effect and
the alternating-current resistance Rp due to the proximity
effect are actually measured instead of being calculated using
the theoretical formula.
[0238]
Moreover, the high-frequency electric wires according to
the first to fourth embodiment of the present invention may be
enamel wires whose surfaces are covered with an insulating cover
layer such as polyurethane.
[0239]
As described above, it is obvious that the present
invention includes various embodiments not shown in the
drawings. Accordingly, the technical scope of the present
invention is determined by only the features of the invention
according to proper claims.
[Industrial Applicability]
[0240]
The electric wire of the present invention is applicable
to the electronic device industry including manufacturing of
various types of devices such as high-frequency transformers,
motors, reactors, choke coils, induction heaters, magnetic
heads, high-frequency power supply cables, DC power units,
switching power supplies, AC adaptors, displacement
sensor/flow detectors of the eddy current method or the like,
IH cooking heaters, non-contact power supplies, and
high-frequency current generators.

[CLAIMS]
[Claim 1]
An electric wire, comprising:
a conductive portion made of a material having a volume
resistivity higher than that of copper, wherein
the volume resistivity of the conductive portion is
specified so that, in a frequency range in which the electric
wire is used, a ratio of AC resistance of the conductive portion
to AC resistance of reference copper wire is less than 1.
[Claim 2]
The electric wire according to claim 1, wherein the
reference copper wire has a same diameter as the conductive
portion.
[Claim 3]
The electric wire according to claim 1 or 2, wherein a
DC resistance value of the conductive portion per unit length
is specified so that among a first frequency and a second
frequency higher than the first frequency, the second frequency
is not less than the upper limit of the frequency range in which
the electric wire is used, the first and second frequencies
being frequencies at which the AC resistance of the electric
wire is equal to that of the reference copper wire and between
which the AC resistance of the electric wire is lower than that
of the reference copper wire.
[Claim 4]
The electric wire according to claim 3, wherein the DC
resistance value is specified by a relationship of
0.7×10,0,925×lOgdc + 2.24) ≤ f2 ≤ 1.3×10(0.925xlogRdc + 2.24)
where Rdc is the DC resistance value and f2 is the second
frequency.
[Claim 5]
The electric wire according to any one of claims 1 to 4,
wherein the conductive portion is made of any one of copper-clad
aluminum and a copper alloy selected from brass, phosphor bronze,
silicon bronze, copper-beryllium alloy, and
copper-nickel-silicon alloy.

[Claim 6]
The electric wire according to any one of claims 1 to 5,
wherein the frequency range in which the electric wire is used
includes a fundamental frequency to 20th order harmonic
frequencies.
[Claim 7]
The electric wire according to any one of claims 1 to 6,
wherein the frequency range in which the electric wire is used
is 10 kHz to 1 MHz.
[Claim 8]
A coil, comprising an electric wire as a strand, wherein
the electric wire includes a conductive portion made of
a material having a higher volume resistivity than copper, and
the volume resistivity of the conductive portion is
specified so that, in a frequency range in which the electric
wire is used, a ratio of AC resistance of the conductive portion
to AC resistance of reference copper wire is less than 1.
[Claim 9]
The coil according to claim 8, wherein the reference
copper wire has a same diameter as the conductive portion.
[Claim 10]
The coil according to claim 8 or 9, wherein a DC resistance
value of the conductive portion per unit length is specified
so that among a first frequency and a second frequency higher
than the first frequency, the second frequency is not less than
the upper limit of the frequency range in which the electric
wire is used, the first and second frequencies being frequencies
at which the AC resistance of the electric wire is equal to that
of the referential copper wire and between which the AC
resistance of the electric wire is lower than that of the
reference copper wire.
[Claim 11]
The coil according to claim 10, wherein the DC resistance
value is specified by a relationship..of

0.7×10,0,925×lOgdc + 2.24) ≤ f2 ≤ 1.3×10(0.925xlogRdc + 2.24)
where Rdc is the DC resistance value and f2 is the second
frequency.
[Claim 12]
The coil according to any one of claims 8 to 11, wherein
the conductive portion is made of any one of copper-clad
aluminum and a copper alloy selected from brass, phosphor bronze,
silicon bronze, copper-beryllium alloy, and
copper-nickel-silicon alloy.
[Claim 13]
The coil according to any one of claims 8 to 12, wherein
the frequency range in which the electric wire is used includes
a fundamental frequency to 20th order harmonic frequencies.
[Claim 14]
The coil according to any one of claims 8 to 13, wherein
the frequency range in which the electric wire is used is 10
kHz to 1 MHz.
[Claim 15]
An apparatus of designing an electric wire made of a
material having a higher volume resistivity than that of copper,
the apparatus comprising:
a resistance calculation unit calculating AC resistance
of a conductive portion as a candidate for the electric wire
and AC resistance of reference copper wire in a frequency range
in which the electric wire is used;
a ratio calculation unit calculating a ratio of AC
resistance due to a proximity effect of the conductive portion
to AC resistance due to the proximity effect of the reference
copper wire; and
a determination unit determining that the candidate is
applicable to the electric wire if the ratio is less than 1.
[Claim 16]
An electric motor, comprising:
a plurality of iron cores arranged on a circle;
a plurality of coils wound with an electric wire on the

plurality of iron cores, the electric wire including a central
conductor made of aluminum or aluminum alloy and a cover layer
made of copper covering the central conductor; and
a rotor rotated by the plurality of coils to which
alternating-current is applied, wherein
the frequency of alternating current applied to the coils
is controlled by an inverter method to fall between a first
frequency and a second frequency higher than the first frequency,
the first and second frequencies being frequencies at which the
AC resistance of the coil is lower than that of a coil wound
with the reference copper wire.