### Inductor Design
There are a few things I need to know as I attempt to wind this inductor:
1. What type of cores I have and their specs
2. What type of wire I have, and its spec
3. How to determine a parameter for additional inductance/wrap and wire resistance/wrap.
#### 1. Core Specs
Here are some generic Ferrite Toroidal Cores I got on Amazon and their specs:
![[Pasted image 20250116061427.png]]
```
Color: Black
Material: Nickel Zinc Ferrite
Squareness Ratio: 10
Bs: 400T
Br: 150mT
Tc: 120°C
Hc: 13A/m
ρ: 4.9g/cm3
μi: 650-1000
Outer Diameter: 17.5mm/0.69 inch, 18mm/0.71 inch, 20mm/0.79 inch, 22.5mm/0.89 inch, 25mm/0.98 inch
Inner Diameter: 9.5mm/0.37 inch, 10mm/0.39 inch, 10mm/0.39 inch, 13.8mm/0.54 inch, 15mm/0.59 inch
Thickness: 12.7mm/0.5 inch, 10mm/0.39 inch, 10mm/0.39 inch, 10mm/0.39 inch, 12mm/0.47 inch
Packing List: 20 x Toroids (4 Pieces For Each Size)
```
##### Ferrite Core Parameters Breakdown
| Parameter | Value | Meaning |
| -------------------------------- | ------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Color** | Black | Refers to the external appearance of the ferrite core. Black is typical but does not inherently define its performance characteristics. |
| **Material** | Nickel Zinc Ferrite | Composed of NiZn ferrite, characterized by high resistivity, low permeability, and suitability for high-frequency applications. |
| **Squareness Ratio** | 10 | The squareness ratio is the ratio of remanent flux density (Br) to saturation flux density (Bs), defined as Squareness Ratio=BrBs\text{Squareness Ratio} = \frac{B_r}{B_s}. |
| **Bs (Saturation Flux Density)** | 400 T | The maximum magnetic flux density the material can achieve when fully magnetized. Indicates the core's ability to handle strong magnetic fields. |
| **Br (Remanent Flux Density)** | 150 mT | Residual magnetization when the external magnetizing field is removed. Important for hysteresis behavior and energy storage capabilities. |
| **Tc (Curie Temperature)** | 120°C | The temperature at which the material loses its ferrimagnetic properties. Operation should stay below this temperature. |
| **Hc (Coercive Field Strength)** | 13 A/m | The magnetic field intensity required to reduce the magnetization of the core to zero after saturation. Indicates low coercivity and easy magnetization. |
| **ρ (Density)** | 4.9 g/cm³ | The mass per unit volume of the material. Impacts mechanical robustness and thermal dissipation capabilities. |
| **μi (Initial Permeability)** | 650-1000 | Relative permeability of the material in a weak magnetic field. Indicates good magnetic coupling and efficient flux transfer. |
*Note - Squareness as Br/Bs does not calculate to 10. Someone has bad info here.*
#### 2. Wire Specs
This is the #1 magnet wire retailer on Amazon:
![[Pasted image 20250116063017.png]]
| **Parameter** | **Value** | **Meaning** |
| ---------------------------- | ----------------------- | --------------------------------------------------------------------------------------------------------------------------------------------- |
| **Material** | Copper | The conductor material, offering excellent electrical conductivity and mechanical flexibility for coil winding. |
| **Insulation Type** | Solderable Polyurethane | The insulation layer provides electrical isolation and allows direct soldering without requiring prior removal of the coating. |
| **Insulation Standard** | NEMA MW-80-C | Meets the National Electrical Manufacturers Association (NEMA) standard for magnet wire insulation quality and specifications. |
| **Temperature Rating** | 155°C (311°F) | Specifies the maximum continuous operating temperature the insulation can handle without degrading. Suitable for thermal overload conditions. |
| **Short-Circuit Protection** | Yes | The insulation prevents adjacent coil turns from short-circuiting, ensuring reliable operation in inductors and transformers. |
| **Drawn Copper Standard** | 28 AWG | The raw copper is processed to meet precise diameter and cross-sectional tolerances for consistent electrical and mechanical properties. |
This table summarizes the known specifications of the wire and its relevance to transformer and inductor applications. Additional details like wire gauge, dielectric strength, and resistance would enhance design considerations further.
#### 3. Calculating Inductance per Turn
##### Inductance Per Turn
To find the inductance per additional turn of wire around a toroid core, we start with the following relationship:
$
L = \frac{{\mu_0 \cdot \mu_r \cdot N^2 \cdot A}}{{l}}
$
- L is the inductance (H)
- μ0 = 4π×10−7 H/m is the permeability of free space
- μr is the relative permeability of the core material (650 to 1000 for this ferrite)
- N is the number of turns
- A is the cross-sectional area of the core (m²)
- l is the mean magnetic path length (m)
And in this case, inductance per turn can be understood as: $ \frac{\Delta L}{\Delta N} $For a single additional turn, ΔN=1=N=1. *(?)*
Now the marginal inductance per turn:
$ΔL≈\frac{2⋅μ0⋅μr⋅A}{l} $
##### Core Specifications and Final Values
Equation for `Cross-Sectional Area`:
$A = Thickness\frac{(OD-ID)}{2} $
and `Mean Magnetic Path Length`:
$l = \pi\frac{(OD+ID)}{2} $
And finally our table for the different Core Sizes:
| Core No. | Outer Diameter (mm) | Inner Diameter (mm) | Thickness (mm) | Mean Magnetic Path Length (m) | Cross-Sectional Area (m2) | Inductance per Turn (uH) | Turns for 100 uH |
| -------- | ------------------- | ------------------- | -------------- | ----------------------------- | ------------------------- | ------------------------ | ---------------- |
| 1 | 17.5 | 9.5 | 12.7 | 0.04 | 0.0000508 | 2.48 | 41 |
| 2 | 18 | 10 | 10 | 0.04 | 0.0000400 | 1.89 | 54 |
| 3 | 20 | 10 | 10 | 0.05 | 0.0000500 | 2.20 | 46 |
| 4 | 22.5 | 13.8 | 10 | 0.06 | 0.0000435 | 1.58 | 64 |
| 5 | 25 | 15 | 12 | 0.06 | 0.0000600 | **1.98** | 51 |