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Problem 1: Airgap Fields and Inductance For each of the cases below, sketch the

ID: 2248390 • Letter: P

Question

Problem 1: Airgap Fields and Inductance For each of the cases below, sketch the two specified winding functions (identifying key features) and evaluate the requested quantities. Unless otherwise indicated, assume that both windings are configured so that their fundamental components are maximum along the =0 mechanical radian axis and that each winding consists of N turns connected in series. To express inductance values assume, airgap length, g, airgap radius, r, and core length, 1. Ignore leakage components other than harmonic leakage. Where ratios are requested give the results as "winding /winding 2" a) Winding 1: 2-pole, concentrated coil, Winding 2: 2-pole, uniformly distributed coil T/2 3t/4 2n Mech. Rad Ratio of self-inductances: Ratio of fundamental component self- inductances: Ratio of currents to give the same peak airgap flux density, B Mutual inductance, assuming that the angle between the axes of the two windings is rad:

Explanation / Answer

enter the following program in matlab to get the tone mary had a little lamb

fsamp=44100;

% 44100 samples per sec

% 261.63 Hz => Nper = 44100/261.63

song = zeros(1,fsamp/4);

A = [1.0000 -2.4584 1.8539 -0.2387 -0.0466 -0.1614 -0.1004 0.1980 -0.0420];

fc=261.63;

fd=293.66;

ff=349.23;

fg=392.00;

Nfc=ceil(fc);

Nfd=ceil(fd);

Nff=ceil(ff);

Nfg=ceil(fg);

Npc = ceil(44100/fc);% period of note c

Npd = ceil(44100/fd);% period of note d

Npf = ceil(44100/ff);% period of note f

Npg = ceil(44100/fg);% period of note g

b=0.1;

Nper=Npc;

M = Nfc/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1 yout1];

Nper=Npd;

M = Nfd/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1];

Nper=Npc;

M = Nfc/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1];

Nper=Npg;

M = Nfg/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1];

Nper=Npg;

M = Nfg/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1];

Nper=Npf;

M = Nff/2;

xin = zeros(1,M*Nper);

for ii=1:M

xin(1+(Nper-1)*ii) = 1;

end

yout=filter(b,A,xin);

Ny=size(yout,2);

u=[0:Ny-1];

wt=sin(pi*u/Ny);

wt=wt.*wt;

yout1=yout.*wt;

song=[song yout1];

plot(song)

Fs=44100;

bits=16;

soundsc(song,fsamp);

audiowrite('hb.wav', song, Fs, 'BitsPerSample', bits);

amp=10;

audioplayer(amp*song,fsamp)

the tone is as follows