m6032550g3ysin1

Sheet1

udonpittayanukoon school udonthani 
physics40205
teacher(Kru);mr.sathaporn promdeeraj
Email;satha_por_n(add)hotmail.com
12/1/08 20:17
เลขที่
ชื่อ
60307
น.ส.เจษฎางค์  ปักษา
60317
น.ส.นลินรัตน์  อินทะวงษ์
60329
น.ส.วรรณวิสาข์  แก้วสังข์
60334
น.ส.วิไลลักษณ์  เศรษฐการุณย์
60336
น.ส.ศิรินาถ  เพียงเทพพงศธร
no.
theory
1
2
3
4
5
r4x=sum(ri*cos(phase_i))
6
r4y=sum(ri*sin(phase_i))
7
r4=sqrt(r4x^2+r4y^2)
8
tan(phase4)=r4y/r4x
9
phase4(deg)=atan(r4yr4x)*180*pi()
y=r*sin(theta+phase)
wave1
wave2
wave3
wave4
wave4_modulation_code
input r(amplitude)=
1
1
1
2.00
 =SQRT($E$27^2+$E$28^2)
input phi(phase)=
0
60
120
40.89
 =ATAN($E$28/$E$25)*180/PI()
Rx=R*COS(phase)
1.000
0.500
-0.500
1.000
 =SUM(B27:D27)
Ry=R*SIN(phase)
0.000
0.866
0.866
1.732
 =SUM(B28:D28)
Theta(deg.)
y=r*sin(theta+phase)
y2
y3
0
0.000
0.866
0.866
1.732
15
0.259
0.966
0.707
1.932
30
0.500
1.000
0.500
2.000
45
0.707
0.966
0.259
1.932
60
0.866
0.866
0.000
1.732
75
0.966
0.707
-0.259
1.414
90
1.000
0.500
-0.500
1.000
105
0.966
0.259
-0.707
0.518
120
0.866
0.000
-0.866
0.000
135
0.707
-0.259
-0.966
-0.518
150
0.500
-0.500
-1.000
-1.000
165
0.259
-0.707
-0.966
-1.414
180
0.000
-0.866
-0.866
-1.732
195
-0.259
-0.966
-0.707
-1.932
210
-0.500
-1.000
-0.500
-2.000
225
-0.707
-0.966
-0.259
-1.932
240
-0.866
-0.866
0.000
-1.732
255
-0.966
-0.707
0.259
-1.414
270
-1.000
-0.500
0.500
-1.000
285
-0.966
-0.259
0.707
-0.518
300
-0.866
0.000
0.866
0.000
315
-0.707
0.259
0.966
0.518
330
-0.500
0.500
1.000
1.000
345
-0.259
0.707
0.966
1.414
360
0.000
0.866
0.866
1.732
2.000
MAX(E14:E38)
 =MAX(E30:E54)
NOTE
IF A*SIN(theata)+B*COS(theata) =C*SIN(theata+phase)
IF A*SIN(theata)+B*COS(theata) =C*SIN(theata+phase)
then C=SQRT(A^2+B^2) and phase = ATAN(B/A)
SIN(A+B) = SINACOSB+COSASINB
NOTE
IF A*SIN(theata)+B*COS(theata) =C*SIN(theta+phase) 
then
A=C*COS(phase)
B=C*SIN(phase)
tan(phase)=B/A
A^2+B^2 = C^2*[1]
A^2+B^2 = C^2
such  that C=SQRT(A^2+B^2)
Q.E.D.1
and  phase =atan(B/A)
Q.E.D.2
exercise
Y=R*SIN(theata+phase)
r1
phase1
r2
phase2
r3
phase3
r4
phase4
1
1.SIN(theata)+COS(theata)=?
2
2.SIN(theata)+SIN(theata+37o)=?
3
3.SIN(theata)+SIN(theata-60o)=?
4
4.SIN(theata)-COS(theata+120o)=?
5
5.SIN(theata)-SIN(theata-360o)=?
6
6.SIN(thase)+COS(120o)=?
Amplitude Modulation
IF R1*sin(theta+phase1)+R2*sin(theta+phase2)=R3*sin(theta+phase3) 
then R3=sqrt(R3x^2+R3y^2)
and tan(phase3)=R3y/R3x
LHS= R1*sin(theta+phase1)+R2*sin(theta+phase2)
LHS= R1*[sin(theta)cos(phase1)+cos(theta)sin(phase1)]+R2*sin(theta)cos(phase2)+cos(theta)sin(phase2)]
LHS= [R1*cos(phase1)+R2*cos(phase2)]*sin(theta)+[R1*sin(phase1)+R2*sin(phase2)]*cos(theta)
LHS= R3x*sin(theta)+R3y*cos(theta)
LET ;R3x= [r1*cos(phase1)+r2*cos(phase2)]=Sum(Ri*cos(phase(i))
LET ;R3y= [r1*sin(phase1)+r2*sin(phase2)]=Sum(Ri*sin(phase(i))
RHS=R3*sin(theta+phase3) 
RHS=(R3*cos(phase3)*sin(theta) +(R3*sin(phase3)*cos(theta)
LET;R3x=(R3*cos(phase3)
LET;R3y=(R3*sin(phase3)
then R3=sqrt(R3x^2+R3y^2)
Q.E.D.1
and ; tan(phase3)=R3y/R3x
and ;phase3=Arctan(R3y/R3x)
Q.E.D.2

Sheet2

Sheet3