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# Theory & Principle

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#### Fleming's right & left hand law

induction heating principle by using CCA litz wire

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HF(High Frequency) heating used for the metal heating is called to HF induction heating by e.m.f.(electromagnetic induction). The conductor which located in a coil flowing alternating current of high frequency occurs heat by resistance of the eddy current loss and hysteresis loss.

Alternate magnetic flux is generated by alternating current passed around the coil as the above picture. Therefore, the induced current is generated in the conductor placed in a magnetic field.

We call it the eddy current which electrical power blocking magnetic force changing generated in the conductor and the joule heat occurs by the resistivity of main heating body and the eddy current, and it is called the eddy current loss and it is a pyrogen of induction heating.

Therefore, it is limited to the electric conductor, which may be induction heating, whereas, in case of non-conductors, we have to use an application technique. The hysteresis loss and the eddy current loss due to magnetization make better efficiency as well as easier heating than non-ferrous metals among the electric conductors of non-magnetic material.

The eddy current flows along the surface of the conductor which means most of the current density flows where shorter the distance from the surface, not central. We call this skin effect. The skin effect is related to the frequency so that higher frequency also increases the skin effect.

If the critical frequency changes the frequency of the same heated object, the calorific value increases in proportion to the square of the frequency when the frequency is low, on the other hand, it increase in proportion to the square of the square root when the frequency is more than certain value. It is known as the critical frequency of induction heating at which the boundary of the both features and the radius of the heated material is the frequency as 2.25 times of the penetration depth. We generally use the higher frequency than the critical frequency for increasing the efficiency.

1. Characteristics of the induction heating
– The direct heating possible
– The local heating possible
– The high energy density
– The easy control
– No flame emission

2. Advantages of the induction heating apparatus
– The heating efficiency is very high by direct heating.
– The easy workability
– It generates a metallurgical improvements.

3. Benefits of using the Litz Cable as power supply for the induction heating
– Saving the electricity of 70% to 80%
– It can be reduced more than 90% of heat generated in the cable prior to the induction heating apparatus.
– Single installation, Long using.
– It can greatly reduce the diameter of the cable.
– The working speed is higher and reducing the time so that lot of goods are manufactured and make your profits more increasing.

### Induction heating

The induction range used for induction heating principle is sold a lot nowadays. The inductor is used to heat the desired object. The principle is as following. First, it the primary copper coil is winding around the secondary metal to be heated, the magnetic field is changed and then the induction current flows in the secondary. When this induction current flows through the metal, the metal itself becomes hot due to its own resistance. The famous “Maxwell equation” is a heating method.

### Maxwell’s Equation

It is an equation forms the basis of electromagnetism, which describes all aspects of electromagnetic phenomena in short. Based on this equation, Maxwell established the electromagnetic field theory.
Maxwell’s equation is called as following; the Gauss law, the Gauss law regarding magnetism, Faraday’s law, and Amper’s law which Maxwell revised. Maxwell showed that electromagnetic phenomena can be fully described on the basis of the above four equations. That is, any equation related to the electromagnetic field can be accurately derived from this equation. The following figure shows the Maxwell equation.

Gauss’s law

1. Gauss’s law describes electric fields by charge and can be used to derive Coulomb’s law.

The Gauss’s law for magnetism

2. The Gauss’s law for magnetism is that magnetic lines are continuous and there is no magnetic monopole. The absence of magnetic polarity means that even if the magnet is cut very small, it is divided into N and S poles.

3. Faraday’s law is that a time-varying magnetic field can create an electric field.

Ampere’s law Maxwell modified

4. Ampere’s law Maxwell modified is based on Ampere’s law that a time-varying electric field can generate a magnetic field and Maxwell added another one. This additional term is called displacement current and depends on the time change rate in the electric flux.

M. Faraday’s proximity theory of electromagnetic fields was mathematically theorized by J. C. Maxwell and the appropriately approximated by the various laws of electronic representation have the form contained in this equation. However, the fact that this equation has physically important significance not only describes all aspects of the electronic representation in a unified way, but also includes a term in it that does not correspond to the various laws of the so-called displacement current.

In other words, in Maxwell’s study of physical meaning, the electrical displacement of the medium expressed by this term exists as a process (electromagnetic wave) propagating space through the magnetic interaction. He established the electromagnetic theory of light from the fact that the calculated value of the propagation velocity coincided with the speed of light.

For your reference, please see below formula when you use L-R-C on litz wire circuit.

formula A.

– L : inductance
– R : resistance
– C : capacitance
– e : voltage

When alternating current flows on the circuit of Litz Wire, there are some factors which are not to flow its electric current-flow-interference. The factors are the L(inductance value) and C(capacitance) and R(resistance) of the entire circuit, the total value of Z(impedance) shows R(resistance), L(inductance), C(capacitance). That is Z = V / I [Ω] as the sum of the voltage V [V] represents the current I [A] is obtained. Now obtained when the absolute value of the impedance Z, resistance R, inductance L, capacitance C, are connected in series.

formula B.

– Z : Impedance
– ω = 2πf (π : 3.14, f : frequency)

formula C.

– E : voltage
– I : ampere

To calculate Inductance value, litz wire is multi-strands-twisted together of insulated copper wire, and skin effect is mainly effective on primary at transformer in reducing losses. Because skin effect loss is proportional to the square of the frequency. This means that material costs(litz wire) are reduced and weight product volume can be reduced. Inductance value calculation (of impedance value) is the same as copper wire.

L = inductance(μH)
l = length(mm)
d = wire diameter(mm)

Tip! If you need to increase L(inductance), you have to increase C(Capacitance, Ampere) and initial permeability by using a blackout curtain(=ferrite core) as well as number of strands and turns increasing. For your reference, if you want to enhance Q factor, please come by Q factor page and get information you find.

AC Resistance

The AC resistance of the conductor is always greater than the DC resistance. The main reasons for this are’skin effect’ and’proximity effect’. Both are detailed below.

Skin and proximity effects taking into account the following formula:

• R = the dc resistance of the conductor
• γs = a skin effect factor
• γp = a proximity effect factor

Skin Effect

As the frequency of the current increases, the flow of electricity tends to be more concentrated around the outside of the conductor. Hollow conductors are often used for this reason at very high frequencies. Changes in resistance due to skin effects are less pronounced at power frequency (typically 50 or 60 Hz).

Skin effect factor ‘γs‘ is provided as follows:

• f = frequency, Hz
• ks = skin effect coefficient from the table below
• R = the dc resistance of the conductor

Proximity Effect

Proximity effects are related to the magnetic fields of conductors close together. The distribution of the magnetic field is not uniform, but depends on the physical arrangement of the conductors. In the state where the flux cutting conductor is not uniform, the current distribution across the conduit becomes uneven and the resistance changes.

The formula for proximity effect coefficients depends on whether we are talking about 2 or 3 cores.

– two core cables or two single-core cables

– for three core cables or three single core cables

where (for both cases):

• dc = diameter of the conductor(mm)
• s = distance between conductor axis(mm)
• kp = proximity effect coefficient from the table below

You should enhance HF transformer or inductor through our Litz Wire for performance improvement of Skin effect, Proximity effect and Skin depth as followings.

Occurrence Principle of Skin Effect in an Alternating Current

ref. 1

When alternating current flows through the electric wire, the distribution of current density in the electric wire is not uniform, and the current density increases as the center portion is small and closer to the peripheral portion.

This is because the current flowing through the center portion of the wire interlinkages with the electron flux produced by the electric current, so the greater the center of gravity in the cross section of the wire, the greater the number of magnetic flux linkages and the greater the inductance. As a result, the reactance is greater in the center of the wire, which makes it difficult for the electric current to flow, and tends to flow more electric current toward the electric wire surface. This is called the skin effect.
The skin effect increases as the frequency higher, the cross-sectional area of ​​the wire higher, the conductivity higher and the relative permeability higher.

Frequency-dependent Skin Effect (based on Copper Conductor)

Skin effect
1) When exchange flows in a conductor, the current density distribution in the conductor are not same. The inductance is larger because of the lots of magnetic flux interlinkaged with current of the central conductor in part as above ref.1. This phenomenon is called the skin effect.
2) The skin effect increases as the frequency or the cross-sectional area of the conductor and the conductivity increases.
3) Exchange flows in a conductor, the current density tends to grow closer to the surface than at the center.
4) Surface currents flowing : e-1=36.8%
5) The point should be considered when designing and producing litz-wire
– Skin effect is the tendency for high-frequency currents to flow on the surface of a conductor. Proximity effect is the tendency for current to flow in other undesirable patterns loops or concentrated distributions due to the presence of magnetic fields generated by nearby conductors. In transformers and inductors, proximity effect losses typically dominate over skin-effect losses. In litz-wire windings, proximity effect may be further divided into internal proximity effect (the effect of other currents within the bundle) and external proximity effect (the effect of current in other bundles).
6) Current penetration depth(mm) in steel : ex. 60Hz(150mm), 1000Hz(5mm), 400KHz(0.75mm)
7) The more the cross sectional area of conductor is getting bigger, the more the resistance ratio of the skin-effect is increased and the more the frequency is higher, it is increased. Therefore, the cross-sectional area of the wire does not mean to be used more effectively.
8) The technologies using skin effect are as followings : a) the hollow cable (wire in the middle of the empty wire), b) OF cable (the wire oil tube entered for cooling the heat), c) The case is that the cable of transmission line is to use corridor or multi-conductor, d) If the thickness of the thick cable with twisted pair is the case here.

Proximity effect
1) Conductor current phenomenon gravitated to one side by the current of the proximity conductor
2) Opposite direction to the current : Facing
3) Current in the same direction : Across the faset
4) Copperplate design overlapped high-frequency induction heating output line is required for reduction of the proximity effect and leakage magnetic field.
5) In case of a lot of close-conductor placed, according to each conductor’s size, orientation and frequency, you may know the phenomenon which current density distribution is changed by flowing in the cross-sectional area of each conductor.
6) DC does not occur in the proximity effect so you must consider wires’ arrangement regarding alternating current. The effective resistance is used as a basis to judge.
7) The red area as below ref. 2 is the direction of the current and the red portion represents the current density. Current flows in the wire itself, but where the repulsion caused, on the outside of two wires, more current flows and in case of absorption, more current flows inside.

ref. 2

Skin depth
1) Selecting suitable frequency to heat metal effectively
2) If the thickness of the material is greater than or equal to three times the skin depth and the heating coils in the lamination of the cross-sectional area ratio is greater, efficient heating should be possible.
3) In case of Fe, 100℃, μr=200 : 500Hz(5mm), 1kHz(3.5mm), 3kHz(2mm), 6kHz(0.216mm), 20kHz(0.112mm), 30kHz(0.096mm), 100kHz(0.053mm)
4) Figure shows the skin effect in metals depending on the relationship between the frequency and extent to the depth of current penetration levels do shows. The higher the frequency of the signal to the surface of the conductor to concentrate the current phenomenon is called skin effect, then the depth of current flow is called the epidermis in depth. It is appropriate for the high-frequency conductivity can find out the thickness of the metal.

ref. 1) Fleming’s right-hand law
Make thumb, index and middle finger of right hand stand on lines at right angles to each other. If index finger’s direction is Magnetic Field(B) and a right thumb’s direction is Conductor Moving Direction(F), the Induced Current Direction(I) flowing in the conductor wire is a middle finger as the above picture.

ref. 2) Fleming’s left-hand law
Make thumb, index and middle finger of left hand stand on lines at right angles to each other. If Magnetic Field(B) is index finger and Current Direction(I) is middle finger, the current’s direction received from Magnetic Field(B) is thumb, Power(F).

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