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Design Guide To Creating Your Next Inductor

Using C-Cut Cores


 
Welcome to the December edition of DRF's Newsletter. In this month Saad Thabit presents a guide for designing custom inductor using  C Cut-Core

Do you have a new inductor design in mind but don't know what to use?

Look no further. Amorphous metal and nanocrystalline are the best available options for your designs requiring the highest efficiency,  and here's why:

  • High permeability leads to increased inductance and reduces winding turns, resulting in reduced I2R losses.
  • High saturation induction will reduce size of the inductor.
  • High frequency used in range from 50Hz up to 100KHz.
  • High operating temperatures of up to 120℃.
  • Low coercivity increases the efficiency and reduces hysteresis loss.  
  • Low core loss reduces energy consumed and minimizes the temperature rise.

For filter inductor designs, the values of the inductance, inductor current, operating frequency, ripple current and power losses will be determined by the application.

How to calculate the inductor voltage:

V_ind = 2*π*f*L*I_Peak

Where:

f=Inductor operating fundamental frequency
L= Inductance value
I_Peak=Inductor peak current

 

How to calculate the cross-sectional area product Ap:

Ap=[V_ind*I_peak*10^4] / [Kf*Ku*B_peak*f*J]

Where: Ap units is in cm4

Where:

Kf =4.44 for sine waveforms
Ku is the core window utilization fill factor
BPeak is the flux density in Tesla
f is the operating frequency in Hz
J is the current density in Amp/ cm2

 

Typical values of the fill factor Ku:
0.5 for round wire inductor
0.65 for foil winding inductor
 
Figure 1

The Ap product of a C-type cut core is the product of the available window area (Wa) of the core in square centimeters (cm2) multiplied by the effective cross sectional area (Ac ) in square centimeters (cm2).

 

which may be stated as:

A p = W a x  Ac         [cm4]

Figure 1 above shows the outline form of a C-core type inductor, typical of those shown in the catalogs of suppliers.
From this, it can be seen that [Wa] is the BC product and [Ac] is the AD product.

The AC inductor must support the applied voltage Vind. The number of turns is calculated from Faraday’s Law shown below:

N=[V_ind*10^4] / [L*Kf*B_peak*f*Ac]        [Turns]

       

Now we can calculate the air gap with the equation below:

Lg=[0.4*π*N^2*Ac*10^-8]/ L

Where:

L is the inductance in Henry

AC is measured in cm2

Lg is the gap in cm.

Keep in mind that the fringing flux will decrease the total reluctance of the magnetic path,  therefore increasing the inductance by a factor F. All of which can be found in the formula below.

F=[1+(Lg/sqrtAc) *(Ln(2*C/Lg))]

Useful hint: To design for specific inductance value, you can either reduce the number of turns by factor F or increase the gap by factor F.

 

Now that our major inductor parameters have been identified, we need to determine the inductor wire size.

Calculate inductor bare wire area Awire
 

Awire=   I_peak/J       [cm2]

Select the wire from the wire manufacturer table, for reference you can use the table supplied in this link.   
Now we determined the wire size. If we also know the mean turn length as well as the number of turns, then we can determine the total length of the wire. From there we can calculate the DC winding resistance.

R_dc= MLT*N*resistance per unit length    [Ohm]

Where:
Resistance per unit length as read from the wire tables for the selected wire size.

 

The losses in an ac inductor are made up of three components:
1. Copper loss, Pcu
2. Iron loss, Pfe
3. Gap loss, Pg
  • Copper Losses, Pcu

Pcu = (IL)^2 *R_dc   [Watts]
 



  •  Iron losses, Pfe

For amorphous metal use the following equation:

Watt/Kilogram=6.5 * f(KHz)^1.51*Bac(T)^1.74


For Nano-crystalline use the following equation:

Watt/Kilogram=1.8 * f(KHz)^1.53*Bac(T)^1.52
 

Where Bac is the flux density and can be calculated using the formula below:

Bac =[ L*di] / [2*N*A]       [Tesla] 

Variables:
 L inductance in Henry
 Ac core cross section area in m²



 
  • Gap loss, Pg
Pg=Ki* a*Lg*f*Bac^2   [watt]
 
Where 
a is the core strip width in cm (see Figure 1 above)
f is frequency in Hertz
Lg is the gap width in cm
Ki is the Gap loss Coefficient

 
There are two effects, skin and proximity effects, which can cause the winding losses to be significantly greater than (IL)^2* R_dc. Both Skin and proximate effects arise from eddy currents which are induced by varying magnetic fields in the winding.   
To calculate total indicator losses use the following equation:
P_total = Pcu+Pfe+Pg         [Watts]

From here you can calculate the inductor temperature rise after  calculating the inductor surface area.
As the resistivity of the copper winding increases with temperature, the winding loss increases with temperature as well. In the magnetic materials, the core loss increases with the increasing temperature above approximately 100 degree C. The value of the saturation flux density becomes smaller with increases in the temperature.
Winding and core loss causes the temperature increase, therefore the loss must be kept below some maximum value. In practice the maximum temperature is usually limited to 100-125 degree C by several considerations which include the reliability of the insulation on the copper winding and inductor insulation system.
For Additional assistance in inductor designs, contact DRF Engineering Services with your custom inductor design request.
 

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