EE568-Selected Topics in Electrical Machines

class: center, middle

# EE-568 Selected Topics in Electrical Machines

## Ozan Keysan

[keysan.me](http://keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

---
### Electric motors can be small

--
### Each one of you carry at least one of these:
--
<img src="http://upload.wikimedia.org/wikipedia/commons/e/ee/Vibramotor.jpg" alt="Drawing" style="width: 350px;"/>

---
# Electric Machines

### But they can also be big:

Siemens Ship Propulsion Motors (Induction Motor)
---

## Very Big

Enercon 7.5 MW, Direct-Drive Wind Turbine Generator (Synchronous Motor)

---
## Very Very Big: [700 MW Synchronous Generator](https://www.itaipu.gov.br/en/energy/generating-units)
--

### Itaipu Dam, Brasil: 16 m diameter, 91 rpm, Rotor Mass: 2650 t
---
## In Industry,
--
 what percentage of energy used by electric motors?
--

- # 65%
--

## What is the percentage of energy used by electric motors overall?
--

- # 45%

## What is the percentage of energy produced by electric machines?
--

- # 97%
---
# Richard Feynman: Electricity
--

---
## So let's see how these machines work?
--
<img src="https://www.bbvaopenmind.com/wp-content/uploads/2016/06/bbva-openmind-maxwell-1-ppal.jpg" alt="Drawing" style="width: 750px;"/>
---
## So let's see how these machines work?

---
# Maxwell Equations

### $$ \nabla\cdot{\bf E} = \dfrac{\rho}{\epsilon_0} $$
### $$ \nabla\cdot{\bf B} = 0 $$
### $$ \nabla\times{\bf E} = - {{\partial{\bf B}}\over{\partial t}} $$
### $$ \nabla\times{\bf H} = {\bf J} + {\epsilon_0{\partial{\bf E}}\over{\partial t}} $$

#### [More info](http://www.maxwells-equations.com/), [Who's afraid of Maxwell equations?](http://majr.com/docs/Whos_Afraid_of_Maxwells_Equations_By_Elya_Joffe.pdf)
---

# Maxwell Equations:

### $$\textrm{Gauss' Law}\quad \nabla \cdot \vec{E}  =  \frac{\rho}{\varepsilon_0} $$
--

### $$\textrm{Faraday's Law} \quad \nabla \times \vec{E}  = - \frac{\partial \vec{B}}{\partial t}$$
--

## Need a reminder for vector calculus?

## [Curl](http://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/), [Divergence](http://betterexplained.com/articles/divergence/), [Cross Product](http://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/)
---
# Divergence: \$\nabla \cdot\$

--
## 1,2,3: Positive divergence, 4: Negative

---
# Curl: \$\nabla \times \$

--
## 1,2,3,4,5: High Curl, 6-7: No Curl

---
### $$\textrm{Faraday's Law} \quad \nabla \times \vec{E}  = - \frac{\partial \vec{B}}{\partial t}$$

---
# Gauss' Law:

# $$ \nabla \cdot \vec{E}  =  \frac{\rho}{\varepsilon_0} $$
--

## Integral form:

# $$\oint_S {E dA} = {Q \over \varepsilon_0}$$

---
# Gauss' Law (for Magnetic Field):

## $$\nabla \cdot \vec{B}  =  0 $$
--

## $$\oint_S {B dA} = 0$$
--

### Practical Meaning: 
### - There are no magnetic flux sources. 
### - No magnets with single pole!

---
# Faraday's Law

### !! The most important equation for motor design
--

### $$\nabla \times \vec{E}  = - \frac{\partial \vec{B}}{\partial t}$$
--

### $$\oint_C \vec{E} dl  = - \frac{\partial \Phi}{\partial t} = -\frac{d}{dt}\iint B dA$$

### (-) Sign: Lenz Laz
--

### [Induction Melting](https://www.youtube.com/watch?v=8i2OVqWo9s0), [Levitation](https://www.youtube.com/watch?v=txmKr69jGBk)

---
# Ampere's Law:
--

### $$\nabla \times \vec{H}  =  \vec{J} + \varepsilon_0\frac{\partial \vec{E}}{\partial t}$$

### Neglecting the [displacement current](https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law) part (i.e. quasi-static state)
### and in integral form.

### $$\oint_C {\vec{H}.d\vec{\ell}} = \iint \vec{J}dA = \sum I_n $$
---

# Ampere's Law:

### Problem of neglecting displacement current:
 
<img src="./images/ee564/displacement_current.png" alt="Drawing" style="width: 350px;"/>

---
# Ampere's Law:

### $$\oint_C {\vec{H}.d\vec{\ell}} = \iint \vec{J}dA = \sum I_n $$

### Magnetic field intensity(H) is independent of the material properties!

![](http://farside.ph.utexas.edu/teaching/302l/lectures/img740.png)

---
## Material Properties:
--

## \$\sigma\$
--
: Conductivity
--

## \$\rho\$
--
: Resistivity
--

# \$\mathbf{J}=\sigma \mathbf{E}\$

--
## Resistivity and Conductivity of Copper?
--

## \$\sigma = 5.96\,10^{7}\$
--
S/m, or 1/Ωm

--
## \$\rho = 1.68\,10^{-8}\$ Ωm

---
## Material Properties:
--

## \$\varepsilon\$
--
: Electric Permittivity
--

# \$\mathbf{D}=\varepsilon \mathbf{E}\$
--

## \$\varepsilon_0\$: Permittivity of free space
--

## \$\varepsilon_0= 8.85\,10^{-12}\$
--
 F/m, or
--
 As/Vm

### Materials with high permittivity (dielectric constant) used in capacitors, (mica, ceramis, metal oxides etc)

---

## Material Properties:
--

## \$\mu\$
--
: Magnetic Permeability
--

# \$\mathbf{B}=\mu \mathbf{H}\$
--

## \$\mu_0\$: Permeability of free space
--

## \$\mu_0= 4\pi\,10^{-7}\$
--
 H/m, or
--
 Vs/Am

### Materials with high permeability (ferromagnets) used in inductors

---
# Material Properties
--

## Other Important Parameters for Motor Design
--

# Thermal:

- ## Thermal Conductivity, Heat Capacity...

# Mechanical:

- ## Density, Strength, Young's Modulus...

---
# Material Properties:
--

## Isotropic:
--
Parameter is constant for all directions

## e.g.: \$\mu_x=\mu_y=\mu_z\$
--

## Otherwise it is anisotropic

## Can be constant (linear material)
--

## Can be non-linear (for example magnetic saturation)

## Can be depedent to temperature (e.g. conductivity)...
---

## Electric Materials
--

## Conductors:
--
 Copper, Aluminium, Iron...
--

## Insulators: Plastic, Air...

## How conductive copper is compared to air?
--

### Copper is \$10^{22}\$ times more conductive than air.
--

### Copper is \$10^{7}\$ times more conductive than sea water.

---
# Electric Materials

## What is the best conductor?

--
- ## **Copper:** \$1.68 \; 10^{-8} \; \Omega.m \$

--
- ## **Aluminium:** \$2.82\; 10^{-8} \; \Omega.m \$
--

- ## **Silver:** \$1.59 \; 10^{-8} \; \Omega.m \$

--
- ## **Gold:** \$2.44 \; 10^{-8} \; \Omega.m \$
---
## Why some connectors are gold plated?

![](http://www.safestchina.com/products_image/hdmi-cable-1-3v-1080p-gold-plated-41946.jpg)

### Gold Plated High Speed HDMI cable [1400 TL](https://www.hepsiburada.com/qed-qe-6024-performance-active-hdmi-kablo-15-mt-p-HBV00000OM1LM): SCAM!

---
# What about the price?
--

# Copper vs. Aluminium
--
<img src="./aluminium_price.png" alt="Drawing" style="width: 600px;"/>

---
# What about the price?

# Copper vs. Aluminium

<img src="./copper_price.png" alt="Drawing" style="width: 600px;"/>
---

# Electric vs. Magnetic Materials
--

## Conductors --> 
--
Ferromagnets
--
 (e.g. Iron, Cobalt)

## Large permeability ( `$\mu_r >> 1$`)
<img src="https://c1.staticflickr.com/3/2716/4468925382_6c3ceecbfe.jpg" alt="Drawing" style="width: 450px;"/>

---
# Non-magnetic Materials
--

## Paramagnetic 
### ( `$\mu_r \gtrsim 1$`) (very slightly attracted)
### E.g.:Aluminium
--

## Diamagnetic 
### ( `$\mu_r \lesssim 1$`) (very slightly repulsed)

### E.g.: Copper, Water, [Frogs](https://www.youtube.com/watch?v=KlJsVqc0ywM)

---
# Electric Circuits

## Analogy to Hydraulic System

### - Voltage --> Pressure
### - Electric Current --> Water Current
### - Hydraulic Resistance --> Resistance

---

# Magnetic Circuits

## Magnetic circuits are analogous to electric circuits:

<img src="magnetic_electric_circuit.png" alt="Drawing" style="width: 800px;"/>
---
# Magnetic Circuits

## Materials:

| Electric Circuits | Magnetic Circuits |
| -- | -- | -- |
| **Conductors:** Copper, Aluminum | **Ferromagnets**: Iron, Electrical Steel |
| **Insulators:** Air, Plastic | **Non-magnetics:** |
||Copper, Water (Diamagnetic)|
|| Air, Aluminum (Paramagnetic) |

---
# Magnetic vs Electric Circuit
--

## Copper is \$10^{22}\$ times more conductive than air.
--

## What about permeability of Iron vs Air?
--

## Iron is JUST 3000 times more "permeable" than air

## Therefore, air is a circuit element in magnetic circuits!

---
# Magnetic Circuits

## Flux (Wb)
--

## Flux Density (Wb/m\$^2\$ or T)
--

## Magneto-motive Force (MMF), (A.turns)

---
# Ohm's Law (for Magnetic Circuit)

### Electric Circuits:

### $$V=IR$$
--

### Magnetic Circuits

### $$\mathcal{F} = \Phi \mathcal{R}$$
--

### Reluctance

### $$\mathcal{R} = \frac{l}{\mu A}$$
---
#  A note on symbols.

## $$\mathcal{F} = \Phi \mathcal{R}$$

## In some [textbooks](https://books.google.com.tr/books?id=7XkxDQAAQBAJ&pg=PA60&lpg=PA60&dq=current+linkage+MMF&source=bl&ots=sEturQtDGU&sig=bm5WgK8_CeKLG82Hq526OWLDn7E&hl=tr&sa=X&ved=0ahUKEwj4lezSoLDZAhVKCcAKHR8RBKsQ6AEIJzAA#v=onepage&q=current%20linkage%20MMF&f=false):
--

- ## Magneto-motive force = NI = [Current Linkage](http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-46)
--

## $$ NI = MMF =\mathcal{F} = \Theta$$

### For latest offical, symbols refer to [IEC Standars](http://www.electropedia.org/iev/iev.nsf/index?openform&part=121)

### [Conventional Magnetic Symbols](https://www.d.umn.edu/~snorr/ece4501s4/MAGCKTS.PDF)

---
# Current Density vs. Magnetic Flux Density

## Current Density = Conductivity x Electric Field

## $$\vec{J}=\sigma \vec{E}$$

--
## Flux Density = Permeability x Magnetic Field

## $$\vec{B} = \mu \vec{H}$$

---

# Magnetic Circuits

### Magnetic circuits are analogous to electric circuits:

---

# Linearity vs. Non-linearity
--

## $$\vec{B} = \mu \vec{H} $$
--

# Linear B-H Characteristics

- ## Air

---
# B-H Curve of Air (Linear)
--

<img src="http://www.coolmagnetman.com/images/magfund071.gif" alt="Drawing" style="width: 400px;"/>
--

- ## Slope gives permeability (\$\mu = \frac{B}{H}\$)
--

- ## Constant Slope = Linear Material

---

## Non-Linear B-H Characteristics

- ### Iron, Cast-Steel ...

## B is limited by saturation

---
# Magnetic Saturation

## Residual Magnetism
<img src="http://www.edmsauce.com/wp-content/uploads/2014/05/Sonys-New-Cassette-Tape-Holds-64750000-Songs.jpg" alt="Drawing" style="width: 320px;"/>
--
<img src="http://keysan.me/presentations/images/ee361/ego_karti.jpg" alt="Drawing" style="width: 350px;"/>
---
# Hysteresis Loss

--
## Hysteresis Loss \$\propto\$ Frequency
---
# Hysteresis Loss

## Variable Hmax
<img src="./images/ee361/B-H_loop.png" alt="Drawing" style="width: 700px;"/>

---
# Lenz's Law

## Why there is a negative sign?
## \$e = -\frac{d \Phi}{dt}\$

### An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.

---
# Eddy Current Losses
### Created by Induced Voltage in a Conductor

#### [Magnet in a Copper Tube](http://www.youtube.com/watch?v=keMpUaoA3Tg)
--

### Power Dissipated: \$P= \frac{ V \pi^2 B_{peak}^2 d^2 f^2}{k \rho}\$

---
# AC Resistance vs DC Resistance
## Which one is higher?

--
- ## AC Resistance > DC Resistance
- ## Why?

---
# Skin Depth
# Distribution of Current in a Wire
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Skin_depth.svg/450px-Skin_depth.svg.png)
---
# Skin Depth

### Due to circulating eddy currents
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Skineffect_reason.svg/293px-Skineffect_reason.svg.png)

---
# Skin Depth

## Current Distribution: \$ J = J_S e ^{-d/\sigma}\$

## Skin depth: \$\sigma = \sqrt{\frac{2 \rho}{\omega \mu_r \mu_0}}\$

---
# Skin Depth for Copper:
- ## 50 Hz --> 9.3 mm

--
- ## 1 kHz --> 2.1 mm

--
- ## 10 kHz --> 0.66 mm

--
- ## 100 kHz --> 0.21 mm

--
- ## 1 MHz --> 66 um

---
## How to increase conductor area without increasing thickness?

## Bundled Conductors

### Also helps to reduce [Corona discharge](http://www.electricaleasy.com/2016/07/corona-discharge.html)
---
## How to increase conductor area without increasing thickness?

## Foil Conductors
<img src="https://hollandshielding.com/content/3201/3201-Mu-copper-tape.png" alt="Drawing" style="width: 600px;"/>

---
## Hollow Conductors
<img src="http://sub.allaboutcircuits.com/images/52013.jpg" alt="Drawing" style="width: 400px;"/>
---
# AC Resistance

## AC Resistance [Calculator](http://www.clemson.edu/ces/cvel/emc/calculators/Resistance_Calculator/round.html)

--
## Rule of Thumb: For 50 Hz power systems
## $$Rac \simeq 1.1 Rdc$$
---
## Power Dissipated due to Eddy Currents

# \$P= \frac{ V \pi^2 B_{peak}^2 d^2 f^2}{k \rho}\$

## Notice the \$f^2\$ element

---

# Hysteresis Loss \$\propto\$ Frequency

# Eddy Loss \$\propto\$ Frequency\$^2\$

---
# Applications

### Eddy Current Brake
### Induction Heater

[Levitating Coil](http://www.youtube.com/watch?v=VydPQuLyEns), [Induction Heater](http://www.youtube.com/watch?v=aOsbIP3y2Wg)

---

## Assumptions we used to make in EE361, but not in this course

--
## - All flux contained in magnetic circuit (no leakage)
--

## - Uniform flux distribution in the core
--

## - Flux travels straight in airgaps (no fringing)
--

## - In some cases infinite permeability is assumed

---

# Faraday's Law of Induction
--

### \$\nabla \times \vec{E}  = - \dfrac{\partial \vec{B}}{\partial t}\$

### which equals to:

--
### $$\oint_C \vec{E} dl  = - \dfrac{d\Phi}{dt} = -\dfrac{d}{dt}\iint \vec{B} dA$$

---
# Faraday's Law of Induction

### Induced Voltage in a Coil

## $$ e= \oint \vec{E} dl = -\dfrac{d \Phi}{dt}$$

## $$ e = -\dfrac{d \Phi}{dt} = -\dfrac{d}{dt}\int \vec{B} dA$$
---
# Ways to generate voltage in a coil
--

- ## Time variation of flux (e.g. AC excitation)
--

- ## Due to conductor movement in a stationary field
--

- ## Rotation (e.g. motors)
--

- ## Deformation of coil (Area changes)

---
# Faraday's Law of Induction

## Total voltage in a coil with N turns
## \$V_{coil} = N\dfrac{d \Phi}{dt} = \dfrac{d \lambda}{dt}\$
---

# Flux Linkage

### \$\lambda\$ : Flux Linkage (Warning, in the textbook shown by [\$\Psi\$)](http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-24)
### \$\Phi\$ : Flux per turn

### \$\lambda = N_{turns} \Phi \$ (turn. Weber)

---

# Relation between Magnetic and Electric Circuits

--
<img src="http://2.bp.blogspot.com/-Lm15GER7L20/VieZ0DjOoRI/AAAAAAAAAXA/RQHcpv7aBfk/s1600/inductor%2Bsymbol.jpg" alt="Drawing" style="width: 300px;"/>
--

# \$ L = \dfrac{d \lambda}{d I}\$

---
# Relation between Magnetic and Electric Circuits

## What happens if you double the number of turns?
--

## Inductance increases with \$N^2\$
---
# Inductance

## Inductance is the flux linkage created per ampere

## \$ L =  N \dfrac{d \Phi}{dI}= \dfrac{d \lambda}{d I}\$

## \$ L =  \dfrac{N^2}{R}\$

---
# Mutual Inductance:

## Magnetic Interaction between two coils.

## Exists if current in one coil induces voltage in another coil.

[Example](https://www.miniphysics.com/uy1-mutual-inductance.html)

---
# Mutual Inductance:

## \$ V_{2} = M \frac{dI_1}{dt} \$
<img src="https://ozank.gitbooks.io/ee361/content/images/mutual_flux.png" alt="Drawing" style="width: 380px;"/>

---
# Magnetic Stored Energy

## What is the energy stored in an inductor?
--

## \$W = \dfrac{1}{2} L i^2 \$

## But why? And what if L is variable?

---

# Magnetic Energy
## \$dw = \mathcal{F}(t) d \Phi(t) \$

--
## \$W = \int_{\Phi_1}^{\Phi_2} \mathcal{F} d \Phi \$

--
## Magnetic Energy Density
## \$W = \int_{B_1}^{B_2} H d B \$

---
# Total Energy Stored (Linear Systems)

## Initial B=0

## \$W = \dfrac{1}{2}R \Phi^2 =\dfrac{1}{2}\dfrac{\mathcal{F}^2}{R}\$
or
## \$W = \dfrac{1}{2}\dfrac{Volume}{\mu} B^2 \$

---
# Magnetic Materials
---

# Electrical Steel Laminations

- ## Used for Low Frequency (50-500 Hz)
--

- ## Easy to [manufacture](https://www.youtube.com/watch?v=qmg_W_pcYhY) & [Cheap](https://www.alibaba.com/product-detail/electrical-silicon-steel-laminates_1891355946.html)
---
## Electrical Steel Lamination Types
--

## - Silicon Steel (Electrical Steel)
![](https://image.made-in-china.com/202f0j00wQuRsTVrqGqh/Silicon-Steel-Sheets-Electrical-Silicon-Steel-Motor-Rotor-Stator.webp)
--

- ### Added silicon increases the resistance  (reduces eddy losses)

---
## Electrical Steel Lamination Types

### - Cold Rolled Lamination Steel

<img src="http://retrorenovation.com/wp-content/uploads/2012/02/stainless-steel-countertop.jpg" alt="Drawing" style="width: 400px;"/>
--

- ### Lowest Cost
--

- ### Higher Core Losses

---
##  Nickel Alloys

<img src="https://www.vacuumschmelze.com/Assets-Web/image-thumb__875__fullImage/RET_WMM32462%20gespiegelt.png" alt="Drawing" style="width: 400px;"/>
--

- ### Higher cost than silicon steel
--

- ### High permeability, low core losses
---

## - Cobalt Alloys

<img src="https://staging.vacpim.com/Assets-Web/image-thumb__711__16-to-9/RET_WMM32487-V2.webp" alt="Drawing" style="width: 400px;"/>
--

- ### Highest cost
--

- ### High saturation (up to 2.2 T)
--

- ### Suitable for mass critic applications (aerospace, military)
---

# Magnetic Alloy Comparison

## [More information](https://sinotech.com/products/motor-components/laminations/)

---
# Ferromagnets

## Motor Core Lamination Manufacturing

- [Lamination Stamping-1](https://www.youtube.com/watch?v=RgWh2G-2XuU)
- [Lamination Stamping-2](https://www.youtube.com/watch?v=dZ9FySos1t0)
- [Lamination Stamping-3](https://www.youtube.com/watch?v=7kKjxHOdC1A)
- [Continuous Stamping](https://www.youtube.com/watch?v=dcjlH8eq0hM)

---
# Ferromagnets

## Reading List-Catalogue
- [Proto Laminations](http://www.protolam.com/page3.html)
- [JFE Steel](http://www.jfe-steel.co.jp/en/products/electrical/catalog/f1e-001.pdf)
- [Cogent Catalogue](http://perso.uclouvain.be/ernest.matagne/ELEC2311/T2006/NOFP.pdf) (page 5-6)
- [Grain Oriented Steel Catalogue](https://www.atimetals.com/Documents/goes_technical_data2_v1.pdf)
- [Enpay Transformer Core](http://www.travek.elektrozavod.ru/sites/default/files/images/production/enpay/Amorphous%20Core%20Catalogue.pdf)
- [Sura Catalogue](http://www.sura.se/Sura/hp_main.nsf/startupFrameset?ReadForm)
- [Cogent Elecrical Steel](https://cogent-power.com/products/non-oriented-electrical-steel/technical-specifications)
- [VacuumSchemlze](http://www.vacuumschmelze.com/en/products/materials-parts/soft-magnetic.html)
- [Motor Laminations](http://laminationspecialties.com/products.htm)

---
# (Soft) Ferrite Cores

<img src="https://www.electronicsb2b.com/wp-content/uploads/2018/07/Ferrite-core-483x420.jpg" alt="Drawing" style="width: 500px;"/>
--

- ### Sintered Iron Oxide + Manganese/Zinc
---

# (Soft) Ferrite Cores

- ### Sintered Iron Oxide + Manganese/Zinc
--

- ### Low Saturation Point (0.4-0.5 T)
--

- ### Brittle
--

- ### High Permeability (\$\mu_r\$: 1500-3000)

---
# (Soft) Ferrite Cores

## Used as [Chokes](https://www.youtube.com/watch?v=LuMlM8zWQFk) and Filters
--

<img src="https://hottconsultants.files.wordpress.com/2014/03/ch05fg322.jpg" alt="Drawing" style="width: 500px;"/>
--

---
#Quick Question
--

## Is it easier to store energy with high or low permeable material for the same flux density?
--

## \$W = \dfrac{1}{2}\dfrac{Volume}{\mu} B^2 \$

## Sometimes, air-gaps are added deliberately to increase energy storing capacity of a core.

---
## E-core without gap
--

---
## E-core with gap
--

---
##Gapped Toroids

---
# A Better Solution?
--

## Distributed Gap Cores

---
# Distributed Gap Cores
--

- ## Low Permeability (\$\mu_r\$: 20-200)
--

- ## Has different types:
--

- ## KOOL Mu Powder
- ## MPP
- ## Iron Powder

---
## KOOL Mu Powder Core

---
## KOOL Mu Powder Core

### Lower Core Loss wrt Steel

---
# Distributed Gap Cores

---
# Distributed Gap vs. Gapped Ferrite
--

### [Comparison](https://www.mag-inc.com/Products/Powder-Cores/Learn-More-about-Powder-Cores/Gapped-Ferrite-Comparison)

---
## Distributed Gap vs. Gapped Ferrite
--

- ### Fringing flux increases copper losses in gapped cores
--

- ### Ferrite has sharp saturation, whereas powder cores has [soft saturation](https://www.mag-inc.com/getattachment/Products/Powder-Cores/Kool-Mu-Cores/Large-Kool-Mu-Core-Shapes/Kool-Mu-and-Gapped-Ferrite-Comparison/KoolMuvsFerriteDCBIAS.png)
--

- ### Powder cores are usually smaller
--

- ### Powder cores magnetic properties does not change much with temperature
--

- ### But powder cores have higher inductance tolerances.

---
# Soft Saturation vs Hard Saturation

<img src="https://www.mag-inc.com/getattachment/Design/Design-Guides/Inductor-Cores-Material-and-Shape-Choices/High-Flux-Soft-saturation.jpg" alt="Drawing" style="width: 800px;"/>
---
# Design Exercise
--

- ## Let's choose a [powder core toroid](https://www.mag-inc.com/Products/Powder-Cores/Kool-Mu-Cores)

- ## [Toroid Core Example](https://www.mag-inc.com/Media/Magnetics/Datasheets/0077354A7.pdf)

### Useful Links

- ### [Design Guides](https://www.mag-inc.com/Design/Design-Guides)

- ### [Powder Core Loss Calculation](https://www.mag-inc.com/Design/Design-Guides/Powder-Core-Loss-Calculation)

- ### [Powder Core Calculations](https://www.mag-inc.com/Design/Design-Guides/Powder-Core-Calculations)

---
## Amorphous and Nanocrystalline Laminations

- ## Very High Permeability (\$\mu_r\$: up to 10.000)
- ## High Efficiency transformers (for medium frequency)
- ## Expensive

---
# Comparison of Materials

---
# Comparison of Materials

---
# More Reading Materials

- ### [Soft Magnetic Core Application Notes](http://www.allegromicro.com/~/media/Files/Technical-Documents/Arnold/Soft-Magnetics-Applications-Guide.ashx?la=en)

- ### [TI Magnetic Core Characteristics](http://www.ti.com/lit/ml/slup124/slup124.pdf)

- ### [Practical and Potential Applications of Soft Magnetic Powder Cores](http://global-sei.com/technology/tr/bn82/pdf/82-02.pdf)

- ### [Choice of the Magnetic Core](http://www.sirio-ic.com/index.php/en/i-magneticore-en.html)

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## You can download this presentation from: [keysan.me/ee568](http://keysan.me/ee568)