CM Quadrifilar helicoidal antenna for the NOAA satellites, an nec2 helix and arc example with comments
CM Created by Roger Walker, GW6HRU
CM
CM Arcs and helix are difficult to enter in nec2. They draw at 0,0,0 and are moved using the Coordinate Transformation (GM) command
CM
CM Wire Arc Specification (GA):
CM GA {ID} {NS} {AR} {A1} {A2} {RAD}
CM {ID} Tag number assigned to all segments of the wire arc.
CM {NS} Number of segments into which the arc will be divided.
CM {AR} Arc radius (center is 0,0,0 and is about the y axis).
CM {A1} Angle of first end of the arc
CM {A2} Angle of the second end of the arc.
CM {R} Wire radius.
CM Note: The angles are in degrees, around Y-axis, starting from x=0 in a left-hand direction (anti-clockwise)
CM
CM Helix/Spiral Specification (GH):
CM GH {ID} {NS} {SP} {HL} {X1} {Y1} {X2} {Y2} {R}
CM {ID} Tag number assigned to all segments of the helix or spiral.
CM {NS} Number of segments into which the helix or spiral will be divided.
CM {SP} Spacing between turns.
CM {HL} Total height of the helix.
CM {X1} Radius in x at z = 0.
CM {Y1} Radius in y at z = 0.
CM {X2} Radius in x at z = HL.
CM {Y2} Radius in y at z = HL.
CM {R} Radius of wire.
CM Note: The number of turns is HL/S, and can be <1 (so HL=0.5 SP=1.0 gives a 180 degree helix)
CM
CM Coordinate Transformation (GM):
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
CM {II} ID Increment - What value to add to the created ID(s)
CM {RP} Repeat count, 0=Move
CM {RX} Angle in degrees to rotate about the X-axis. +ve = right handed
CM {RY} Angle in degrees to rotate about the Y-axis. +ve = right handed
CM {RZ} Angle in degrees to rotate about the Z-axis. +ve = right handed
CM {SX} Linear shift in X
CM {SY} Linear shift in Y
CM {SZ} Linear shift in Z
CM {ID} ID of segments to move/repeat, 0 (or missing) means all IDs
CM
CM For the QHA we use this sequence
CM Draw the lower arc for the larger diameter / Move it to it's final place
CM Draw the larger diameter 1/2 helix / Move it to it's final place
CM Draw the upper arc for the larger diameter / Move it to it's final place
CM Draw the lower arc for the smaller diameter / Move it to it's final place (rot 90deg)
CM Draw the smaller diameter 1/2 helix / Move it to it's final place (with rot 90deg)
CM Draw the upper arc for the smaller diameter / Move it to it's final place (rot 90deg)
CM Do a copy, with a single repeat, with 180 degree rotation, and +5 ID increment
CM Draw the feed point, and the other 3 horizontal bars
CE
CM Inputs
SY H=2 'Height from ground to centre of antenna
SY T=0.5 'Half turn
SY N=1.0 'One wavelength
SY F=0.44 'Height/Width factor
SY R=0.0035 'Conductor radius
SY B=0.015 'End bend radius
SY I=1.025 'Inner/Outer scaling factor
SY S=1.0 'Scale for SWR (allows for wire diameter and proximity to ground)
CM Calculated
SY CL=S*299.792458/137.5 'Adjusted one wavelength length
SY CA=B*(2-(PI/2)) 'How much smaller is a 90deg arc, vs the 2 sides of the square
CM Actual length of 1 turn of a helix is sqrt((PI()*D)^2+P^2) Where D is diameter, and P is pitch
CM We have a ratio and outer length, this can be rearranged to give:
CM diameter = 0.5*(circumference / (1 + sqrt(1/(ratio^2) + (turns*PI())^2)))
SY CLC=(CL*N*I)+4*CA 'Effective larger loop circumference
SY CLD=0.5*(CLC / (1 + sqr(1/(F^2) + (T*PI)^2))) 'Larger loop diameter
SY CLH=(CLD/F) 'Get height from ratio
SY CLR=CLD/2 'Get radius
SY CSC=(CL*N/I)+4*CA 'Effective smaller loop circumference
SY CSD=0.5*(CSC / (1 + sqr(1/(F^2) + (T*PI)^2))) 'Larger loop diameter
SY CSH=(CSD/F) 'Get height from ratio
SY CSR=CSD/2 'Get radius
CM Draw one spiral of the larger helix, with the end arcs
CM GA {ID} {NS} {AR} {A1} {A2} {RAD}
GA 11 3 B 270 360 R 'Arc from 0,-R,0 to R,0,0
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 90 0 CLR-B H-(CLH/2) 11 'Move ID=11 with 90 rot
CM GH {ID} {NS} {SP} {HL} {X1} {Y1} {X2} {Y2} {R}
GH 12 40 CLH/T CLH CLR CLR CLR CLR R 'Draw large helix
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 90 0 0 H-(CLH/2) 12 'Move ID 12, rot 90, then move to H
CM GA {ID} {NS} {AR} {A1} {A2} {RAD}
GA 13 3 B 0 90 R 'Arc from R,0,0 to 0,R,0
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 270 0 -(CLR-B) H+(CLH/2) 13 'Move ID=13 with 270 rot
CM Draw one spiral of the smaller helix, with the end arcs
CM GA {ID} {NS} {AR} {A1} {A2} {RAD}
GA 21 3 B 270 360 R 'Arc from 0,-R,0 to R,0,0
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 0 CSR-B 0 H-(CSH/2) 21 'Move ID=21 with 0 rot
CM GH {ID} {NS} {SP} {HL} {X1} {Y1} {X2} {Y2} {R}
GH 22 40 CSH/T CSH CSR CSR CSR CSR R 'Draw small helix
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 0 0 0 H-(CSH/2) 22 'Move ID 22, rot 0, then move to H
CM GA {ID} {NS} {AR} {A1} {A2} {RAD}
GA 23 3 B 0 90 R 'Arc from R,0,0 to 0,R,0
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 0 0 0 0 180 -(CSR-B) 0 H+(CSH/2) 23 'Move ID=23 with 180 rot
CM Now create a copy of everything so far, with an ID increment of 5, so 11,12,13 21,22,23 copied to 16,17,18 26,27,28
CM GM {II} {RP} {RX} {RY} {RZ} {SX} {SY} {SZ} {ID}
GM 5 1 0 0 180 0 0 0 0 'Copy with 180 rot, inc 5
CM Now draw the top/bottom wires, including the feed point
GW 10 15 0 -(CLR-B) H-(CLH/2+B) 0 (CLR-B) H-(CLH/2+B) R ' Larger bottom (feed point)
GW 15 15 0 -(CLR-B) H+(CLH/2+B) 0 (CLR-B) H+(CLH/2+B) R ' Larger top
GW 20 15 -(CSR-B) 0 H-(CSH/2+B) CSR-B 0 H-(CSH/2+B) R ' Smaller bottom
GW 25 15 -(CSR-B) 0 H+(CSH/2+B) CSR-B 0 H+(CSH/2+B) R ' Smaller top
GE 1
LD 5 0 0 0 58000000
GN 3 0 0 0 4 0.003
EK
EX 0 10 8 0 3 0 0 'Feed in the middle of the larger bottom wire
FR 0 0 0 0 137.5 0
EN