This is based on a Wireless World article by N Darwood in November 1982.
It listed a way of generating 3, 5, and 7 phase sinewaves.
It suggested itteraing the equations:
A=A+n*(B-C) B=B+n*(C-A) C=C+n*(A-B)
Using the starting conditions
A=0 B=0.866 C=-B
This does produce a three phase signal. Why?
So what really are the bracketed terms?
In the starting conditions, A=0, B = sin 2pi/3, C = sin 4 pi /3
The step size is choosen as SquareRoot? 3 * n
Here is a plot using the awk script below.
Some AWK that generates curves:
#################################################### # # T3phase.awk - A simple demo of three phase sinewave # ####################################################
BEGIN {
FS = "," lastX = 0 lastY = 0
re = 4 im = 0 lastRe = re lastIm = im n = 1 / 4
# Start the DXF file F_header()
A=0
B=0.866
C=-B
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
line( x,-14,x+1,-14,0) line( x,4-14,x,-4-14,0) text( x, 0-14, 0, " "+x)
}
#n = 1 / 8
A=0
B=0.866
B=4
C=-B
lastA = A lastB = B lastC = C
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
A=A+n*(B-C) B=B+n*(C-A) C=C+n*(A-B)
line( x,lastA-14,x+1,A-14,1) line( x,lastB-14,x+1,B-14,2) line( x,lastC-14,x+1,C-14,5)
lastA = A lastB = B lastC = C
} }
END {
# draw Axis
# line( 0,0,100,0,0) # black # line( 0,1,100,1,1) # red # line( 0,2,100,2,2) # yellow # line( 0,3,100,3,3) # green # line( 0,4,100,4,4) # cyan # line( 0,5,100,5,5) # blue # line( 0,6,100,6,6) # magenta # line( 0,7,100,7,7) # Black # line( 0,8,100,8,8) # black # line( 0,9,100,9,9) # black # And finally tidy up the DXF file F_end()
}
I did a select all of the DXF opened by DeltaCAD? and pasted this into Serif Draw 7.0, and did a view in browser, which I saved.
#################################################### # # T3phase.awk - A simple demo of three phase sinewave # # bmawk -f t3ph.awk -f dxf_fns.awk t.txt > t3ph.dxf # # ####################################################
BEGIN {
FS = "," lastX = 0 lastY = 0
re = 4 im = 0 lastRe = re lastIm = im n = 1 / 8
# Start the DXF file F_header()
A=0
B=0.866
C=-B
YD = 14
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
line( x,-YD,x+1,-YD,0) line( x,4-YD,x,-4-YD,0) text( x, 0-YD, 0, " "+x)
}
A=0
B=0.866
B=4
C=-B
C=-1
lastA = A lastB = B lastC = C
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
A=A+n*(B-C) B=B+n*(C-A) C=C+n*(A-B)
line( x,lastA-YD,x+1,A-YD,1) line( x,lastB-YD,x+1,B-YD,2) line( x,lastC-YD,x+1,C-YD,5)
lastA = A lastB = B lastC = C
}
# 7 phase
A=0
B=4
C=0
C=0
YD=30
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
line( x,-YD,x+1,-YD,0) line( x,4-YD,x,-4-YD,0) text( x, 0-YD, 0, " "+x)
}
A=0
B=4
B=4
C=-B
A=0*10.0 B=0.78*10.0 C=0.97*10.0 D=0.43*10.0
# E=-0.43*10.0 # F=-0.97*10.0 # G=-0.78*10.0
E=-D F=-C G=-B
lastA = A lastB = B lastC = C lastD = D lastE = E lastF = F lastG = G
for ( x = 0 ; x < (3.14*2*1/n-1) ; x ++ ) {
A=A+n*(B-C+D-E+F-G) B=B+n*(C-D+E-F+G-A) C=C+n*(D-E+F-G+A-B) D=D+n*(E-F+G-A+B-C) E=E+n*(F-G+A-B+C-D) F=F+n*(G-A+B-C+D-E) G=G+n*(A-B+C-D+E-F)
line( x,lastA-YD,x+1,A-YD,1) line( x,lastB-YD,x+1,B-YD,2) line( x,lastC-YD,x+1,C-YD,3) line( x,lastD-YD,x+1,D-YD,4) line( x,lastE-YD,x+1,E-YD,5) line( x,lastF-YD,x+1,F-YD,6) line( x,lastG-YD,x+1,G-YD,7)
lastA = A lastB = B lastC = C lastD = D lastE = E lastF = F lastG = G } }
END {
# draw Axis
# line( 0,0,100,0,0) # black
# line( 0,1,100,1,1) # red
# line( 0,2,100,2,2) # yellow
# line( 0,3,100,3,3) # green
# line( 0,4,100,4,4) # cyan
# line( 0,5,100,5,5) # blue
# line( 0,6,100,6,6) # magenta
# line( 0,7,100,7,7) # Black
# line( 0,8,100,8,8) # black
# line( 0,9,100,9,9) # black
# And finally tidy up the DXF file
F_end()
}