The Class Notes: Difference between revisions

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4 jan 2010


<math>Limit\ A\ \to \infty:</math>


The following are the notes as interpreted by [[Kirk Betz]] from ENGR 431 taught by Dr. Rob Frohne.
<math>X_0\ = \frac{1}{\beta}X_s\ \Rightarrow V_0 = \frac{R_1 + R_2}{R_1}V_{in}</math>
Electrical Magnetic Conversion is the study of magnetic circuits in all there forms.


<math> X_i\ = 0</math>


[[Image:Thebegining.JPG]]


Notes for reviewer
Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 4, 2010
Be sure all 'l' have been replaced with <math> \ell</math>


==EMEC Notes==
<math> V_{in}\ = V_0 (\frac {R_1}{R_1 + R_2})</math>.
''January 4, 2010''


'''Introduction to EMEC'''


Syllabus was handed out and an outline of the class structure what introduce. We where also briefed on what we would be talking about his quarter.
<math> V_0\ = \frac {1}{(\frac {R_1}{R_1 + R_2})}V_{in} </math>


==Magnetic Circuits ==
==Magnetic Circuits ==


jan 6 2010
''January 6 2010''

From circuits we know that V is a function of the E field.

<math> V\ = \int ed\ell </math>


The E field moves along a closed path of length <math> \ell </math>. By integrating E along the path <math> \ell </math> we find the Voltage V as shown in the above equation.


integrated the e field along the path


<math> \vec F\ = q \vec v \times \vec B </math>
<math> \vec F\ = q \vec v \times \vec B </math>


<math>d \vec F\ = I d \vec l \times \vec B </math>
<math>d \vec F\ = I d \vec\ell \times \vec B </math>


<math>\mathcal{F} = Hl_1 + Hl_2</math>
<math>\mathcal{F} = H\ell_1 + H\ell_2</math>


<math>V\ = R_1I + R_2I</math>
<math>V\ = R_1I + R_2I</math>
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[[Image:Magnetic_cir.JPG]]
[[Image:Magnetic_cir.JPG]]


Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010
Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010


==Magnetic Equations==
==Magnetic Equations==


<math>\int \vec Hd \vec l = \mathcal{F}</math>
<math>\int \vec Hd \vec\ell= \mathcal{F}</math>


<math>\oint \vec Hd \vec l = Ni = \sum_{n}Hl + Ni = 0 </math>
<math>\oint \vec Hd \vec\ell= Ni = \sum_{n}H\ell+ Ni = 0 </math>


<math>\oint \vec Bd \vec s = 0 </math>
<math>\oint \vec Bd \vec s = 0 </math>
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<math> \vec B = \mu \vec H\ Assumes\ Linearity </math>
<math> \vec B = \mu \vec H\ Assumes\ Linearity </math>


<math> \mathcal{R} \frac{l}{\mu A}</math>
<math> \mathcal{R} \frac{\ell}{\mu A}</math>


[[Image:BHField.JPG‎]]
[[Image:BHField.JPG‎]]
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What about chancing currents, etc.?
What about chancing currents, etc.?


[[Image:Magnetloop.JPG‎ ]]
Picture 5

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 8, 2010

<math> \oint \vec Hd \vec\ell= Ni </math>

Case i)

<math> \mu = 10^4 \mu_0\ in\ the\ core </math> Something about this part doesn't seem right.

<math>Find\ \vec B\ in\ the\ gap. </math>

Graph and picture 6

<math> H\ell\ = NI </math>, <math>\ I\ \varpropto H</math>

<math> NI\ = \mathcal{F} \backsim V</math>

<math> \mathcal{R} = \frac{\ell}{\mu A} \backsim R = \frac{\ell}{\sigma A} </math>

<math> \phi\ = BA \backsim I = JA</math>

<math> R_c= \frac{\ell_1}{\mu A} </math>

<math> R_g= \frac{g}{\mu_0 (\sqrt{A} + g)^2}</math>


<math> \phi\ = B(\sqrt{A} + g)^2 = \frac{NI}{R_g + R_c}</math>

<math> B_g \frac{NI}{(R_g + R_c)(\sqrt{A}+g)^2}</math>

==Magnetic Circuits Continued==

jan 11, 2010

some random graph here, can't really read it.

Case ii) Include non-linearity & find B in the Gap

<math> \oint \vec H d \vec \ell = NI = H \ell_1 + H_g = H(\ell_1 +g) </math>

<math> \phi\ = \int \vec B d \vec s = BA </math>

picture 7 goes here

<math> \phi\ = \frac {NI-H\ell_1}{R_g} = \frac{-1}{R_g}(H\ell_1) + \frac{NI}{R_g} </math> not sure about the -1 here

What energy is list in the hysteresis loop?

<math> P\ = vi</math>

<math> W\ = \int Pdt</math>

<math>\oint \vec E d \vec \ell = \frac {-d}{dt} \int \vec B d \vec s \quad Faraday's\ Law</math>

hmm check these

<math> \vec E = \frac {J}{\sigma} </math>

<math> \lambda\ = L i</math>

e is voltage

<math> e = \frac {d \lambda}{dt} = L \frac{di}{dt}</math>

<math> \lambda\ = N \phi </math>

<math> N \equiv number\ of\ turns</math>


<math> \oint \vec Hd \vec l = Ni </math>
<math> \phi \equiv Flux\ </math>

Latest revision as of 16:32, 27 January 2010


The following are the notes as interpreted by Kirk Betz from ENGR 431 taught by Dr. Rob Frohne. Electrical Magnetic Conversion is the study of magnetic circuits in all there forms.


Notes for reviewer Be sure all 'l' have been replaced with

EMEC Notes

January 4, 2010

Introduction to EMEC

Syllabus was handed out and an outline of the class structure what introduce. We where also briefed on what we would be talking about his quarter.

Magnetic Circuits

January 6 2010

From circuits we know that V is a function of the E field.


The E field moves along a closed path of length . By integrating E along the path we find the Voltage V as shown in the above equation.


integrated the e field along the path

Magnetic cir.JPG

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Magnetic Equations

BHField.JPG

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

BFieldsmall.JPG BFsmall.JPG

Pictures drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Magnetic Circuits Examples

What about chancing currents, etc.?

Magnetloop.JPG

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 8, 2010

Case i)

Something about this part doesn't seem right.

Graph and picture 6

,


Magnetic Circuits Continued

jan 11, 2010

some random graph here, can't really read it.

Case ii) Include non-linearity & find B in the Gap

picture 7 goes here

not sure about the -1 here

What energy is list in the hysteresis loop?

hmm check these

e is voltage