Played with 4NEC2 a lot lately. Here are my results. Let the pictures do the talking, I have plenty of them
Simple Helical on infinite ground without impedance transformer, just to set a base line:
Same Helical on circular ground:
Same Helical on square ground:
Helical on infinite ground with parallel wire as impedance transformer:
Same Helical on circular ground:
Same Helical on square ground:
Helical on infinite ground with bent microstrip as impedance transformer:
Same Helical on circular ground:
Same Helical on square ground:
Animation of SWR for different microstrip positions, Helical on infinite ground.
Helical on infinite ground with wavetrap as impedance transformer: (something is wrong here)
Same Helical on circular ground: (something is wrong here)
Same Helical on square ground: (something is wrong here)
Notes:
- The parallel wire only has minimal effect. I couldn't get the wire closer to the ground without facing 4NEC2 limitations.
- 4NEC2 does not seem to handle the wavetrap accurately. The VSWR was all over the place. Sometimes it was even negative which by definition cannot be true. So unfortunately these results should be ignored.
- The bent microstrip does its job fairly well. Only the optimal impedance at a frequency that is about 10% lower than the design frequency.
Here comes the 4NEC2 model for all these Helicals:
Code:
CM Helical antenna
CM Martin7182
CM 18-jun-2015
CM ===
CM As reflector: either use 'ground plane' section
CM or use values of 'reflector square' or 'reflector circular',
CM combined with 'no ground plane' section.
CM ===
CM As impedance transformer: use 'parallel wire', 'wavetrap' or 'microstrip',
CM combined with their matching 'active element'.
CE
'==== general properties ===
SY F=2440 'Design frequency in MHz
SY N=5 'Number of turns
SY WRA=0.5 'Wire Radius active element
SY WRT=0.025 'Wire Radius transformer element
SY WRR=0.1 'Wire Radius reflector
SY SL=299792458 'Speed of light in vacuum in m/s
SY WL=SL/(F*1000) 'Wave length in mm
SY CIRC=1.1 'Circumfence factor
SY R=CIRC*WL/(2*pi) 'Radius helical turn in mm
SY H=1.0 'Height of the helical above reflector in mm
SY PA=13 'Pitch angle of turn in degrees
SY HDD=pi*R*tan(PA)/180 'Height delta per degree at radius distance
'==== feed ===
SY WRF=0.3 'Wire Radius feed
GW 2000 1 R 0 0 R 0 H WRF
'==== active element, no impedance transformer at all ===
SY A8=5 'Angle increment of a turn in degrees
SY XAD1=R*cos(A8) 'X active element delta
SY YAD1=R*sin(A8) 'Y active element delta
SY ZAD1=A8*HDD 'Z active element delta
SY N5=N*360/A8 ' Number of wires to copy
'GW 4000 1 R 0 0 XAD1 YAD1 ZAD1 WRA
'GM 1 N5 0 0 A8 0 0 ZAD1 4000
'GM 0 0 0 0 0 0 0 H 4000
'==== impedance transformer; parallel wire ===
SY A1=5 'Angle increment of a turn in degrees
SY A2=90 'Total angle, must be multiple of A1
SY XTD=R*cos(A1) 'X transformer delta
SY YTD=R*sin(A1) 'Y transformer delta
'GW 3000 1 R 0 H XTD YTD H WRA
'GM 1 A2/A1-1 0 0 A1 0 0 0 3000
'==== active element, combined with parallel wire ===
SY A3=5 'Angle increment of a turn in degrees
SY XAD2=R*cos(A3) 'X active element delta
SY YAD2=R*sin(A3) 'Y active element delta
SY ZAD2=A3*HDD 'Z active element delta
SY N6=(360-A2)/A3+(N-1)*360/A3 'Number of wires to copy
'GW 4000 1 R 0 0 XAD2 YAD2 ZAD2 WRA
'GM 1 N6 0 0 A3 0 0 ZAD2 4000
'GM 0 0 0 0 A2 0 0 H 4000
'==== impedance transformer; microstrip ===
SY LM=WL/8 'Length of flat microstrip
SY WM=LM/2 'Width
SY LMH=cos(PA)*LM 'Middle length in horizontal plane once mounted
SY NPWM=10 'Number of patches along width (max 20, need to
' comment/uncomment below GW rules)
SY X=int(NPWM/2) 'Outer radius position [0 .. NPWM]
SY NPLM=NPWM*LM/WM 'Number of patches along length
SY WX=WM*(2X-NPWM)/NPWM '[-WM .. WM] depending on X
SY Ri=R-WM+X*WM/NPWM 'Inner radius
SY Ro=Ri+WM 'Outer radius
SY Rm=(Ri+Ro)/2 'Middle radius
SY ADM=360*LMH/(NPLM*2*pi*Rm) 'Angle delta neighbouring patches in h plane
SY ADM0=360*LMH/(NPLM*2*pi*R) 'Angle delta0 neighbouring patches in h plane
SY SAM0=(90-NPLM*ADM0)/2 'Start angle0 of microstrip relative to feed
SY SAM=(SAM0*2R+45WX)/(2R+WX) 'Start angle of microstrip relative to feed
SY HDADM=HDD*ADM 'Height delta ADM
SY SHM=H+SAM*HDD 'Start height
SY R0=Ri+0WM/NPWM 'Radius #0
SY X0D=R0*cos(ADM) 'X delta #0
SY Y0D=R0*sin(ADM) 'Y delta #0
SY R1=Ri+1WM/NPWM 'Radius #1
SY X1D=R1*cos(ADM) 'X delta #1
SY Y1D=R1*sin(ADM) 'Y delta #1
SY R2=Ri+2WM/NPWM 'Radius #2
SY X2D=R2*cos(ADM) 'X delta #2
SY Y2D=R2*sin(ADM) 'Y delta #2
SY R3=Ri+3WM/NPWM 'Radius #3
SY X3D=R3*cos(ADM) 'X delta #3
SY Y3D=R3*sin(ADM) 'Y delta #3
SY R4=Ri+4WM/NPWM 'Radius #4
SY X4D=R4*cos(ADM) 'X delta #4
SY Y4D=R4*sin(ADM) 'Y delta #4
SY R5=Ri+5WM/NPWM 'Radius #5
SY X5D=R5*cos(ADM) 'X delta #5
SY Y5D=R5*sin(ADM) 'Y delta #5
SY R6=Ri+6WM/NPWM 'Radius #6
SY X6D=R6*cos(ADM) 'X delta #6
SY Y6D=R6*sin(ADM) 'Y delta #6
SY R7=Ri+7WM/NPWM 'Radius #7
SY X7D=R7*cos(ADM) 'X delta #7
SY Y7D=R7*sin(ADM) 'Y delta #7
SY R8=Ri+8WM/NPWM 'Radius #8
SY X8D=R8*cos(ADM) 'X delta #8
SY Y8D=R8*sin(ADM) 'Y delta #8
SY R9=Ri+9WM/NPWM 'Radius #9
SY X9D=R9*cos(ADM) 'X delta #9
SY Y9D=R9*sin(ADM) 'Y delta #9
SY R10=Ri+10WM/NPWM 'Radius #10
SY X10D=R10*cos(ADM) 'X delta #10
SY Y10D=R10*sin(ADM) 'Y delta #10
SY R11=Ri+11WM/NPWM 'Radius #11
SY X11D=R11*cos(ADM) 'X delta #11
SY Y11D=R11*sin(ADM) 'Y delta #11
SY R12=Ri+12WM/NPWM 'Radius #12
SY X12D=R12*cos(ADM) 'X delta #12
SY Y12D=R12*sin(ADM) 'Y delta #12
SY R13=Ri+13WM/NPWM 'Radius #13
SY X13D=R13*cos(ADM) 'X delta #13
SY Y13D=R13*sin(ADM) 'Y delta #13
SY R14=Ri+14WM/NPWM 'Radius #14
SY X14D=R14*cos(ADM) 'X delta #14
SY Y14D=R14*sin(ADM) 'Y delta #14
SY R15=Ri+15WM/NPWM 'Radius #15
SY X15D=R15*cos(ADM) 'X delta #15
SY Y15D=R15*sin(ADM) 'Y delta #15
SY R16=Ri+16WM/NPWM 'Radius #16
SY X16D=R16*cos(ADM) 'X delta #16
SY Y16D=R16*sin(ADM) 'Y delta #16
SY R17=Ri+17WM/NPWM 'Radius #17
SY X17D=R17*cos(ADM) 'X delta #17
SY Y17D=R17*sin(ADM) 'Y delta #17
SY R18=Ri+18WM/NPWM 'Radius #18
SY X18D=R18*cos(ADM) 'X delta #18
SY Y18D=R18*sin(ADM) 'Y delta #18
SY R19=Ri+19WM/NPWM 'Radius #19
SY X19D=R19*cos(ADM) 'X delta #19
SY Y19D=R19*sin(ADM) 'Y delta #19
SY R20=Ri+20WM/NPWM 'Radius #20
SY X20D=R20*cos(ADM) 'X delta #20
SY Y20D=R20*sin(ADM) 'Y delta #20
GW 5000 1 R0 0 0 X0D Y0D HDADM WRT
GW 5001 1 R1 0 0 X1D Y1D HDADM WRT
GW 5002 1 R2 0 0 X2D Y2D HDADM WRT
GW 5003 1 R3 0 0 X3D Y3D HDADM WRT
GW 5004 1 R4 0 0 X4D Y4D HDADM WRT
GW 5005 1 R5 0 0 X5D Y5D HDADM WRT
GW 5006 1 R6 0 0 X6D Y6D HDADM WRT
GW 5007 1 R7 0 0 X7D Y7D HDADM WRT
GW 5008 1 R8 0 0 X8D Y8D HDADM WRT
GW 5009 1 R9 0 0 X9D Y9D HDADM WRT
GW 5010 1 R10 0 0 X10D Y10D HDADM WRT
'GW 5011 1 R11 0 0 X11D Y11D HDADM WRT
'GW 5012 1 R12 0 0 X12D Y12D HDADM WRT
'GW 5013 1 R13 0 0 X13D Y13D HDADM WRT
'GW 5014 1 R14 0 0 X14D Y14D HDADM WRT
'GW 5015 1 R15 0 0 X15D Y15D HDADM WRT
'GW 5016 1 R16 0 0 X16D Y16D HDADM WRT
'GW 5017 1 R17 0 0 X17D Y17D HDADM WRT
'GW 5018 1 R18 0 0 X18D Y18D HDADM WRT
'GW 5019 1 R19 0 0 X19D Y19D HDADM WRT
'GW 5020 1 R20 0 0 X20D Y20D HDADM WRT
GW 5021 1 X0D Y0D HDADM X1D Y1D HDADM WRT
GW 5022 1 X1D Y1D HDADM X2D Y2D HDADM WRT
GW 5023 1 X2D Y2D HDADM X3D Y3D HDADM WRT
GW 5024 1 X3D Y3D HDADM X4D Y4D HDADM WRT
GW 5025 1 X4D Y4D HDADM X5D Y5D HDADM WRT
GW 5026 1 X5D Y5D HDADM X6D Y6D HDADM WRT
GW 5027 1 X6D Y6D HDADM X7D Y7D HDADM WRT
GW 5028 1 X7D Y7D HDADM X8D Y8D HDADM WRT
GW 5029 1 X8D Y8D HDADM X9D Y9D HDADM WRT
GW 5030 1 X9D Y9D HDADM X10D Y10D HDADM WRT
'GW 5031 1 X10D Y10D HDADM X11D Y11D HDADM WRT
'GW 5032 1 X11D Y11D HDADM X12D Y12D HDADM WRT
'GW 5033 1 X12D Y12D HDADM X13D Y13D HDADM WRT
'GW 5034 1 X13D Y13D HDADM X14D Y14D HDADM WRT
'GW 5035 1 X14D Y14D HDADM X15D Y15D HDADM WRT
'GW 5036 1 X15D Y15D HDADM X16D Y16D HDADM WRT
'GW 5037 1 X16D Y16D HDADM X17D Y17D HDADM WRT
'GW 5038 1 X17D Y17D HDADM X18D Y18D HDADM WRT
'GW 5039 1 X18D Y18D HDADM X19D Y19D HDADM WRT
'GW 5040 1 X19D Y19D HDADM X20D Y20D HDADM WRT
GM 1 NPLM-1 0 0 ADM 0 0 HDADM 5000
GW 6000 1 R0 0 0 R1 0 0 WRT
GW 6001 1 R1 0 0 R2 0 0 WRT
GW 6002 1 R2 0 0 R3 0 0 WRT
GW 6003 1 R3 0 0 R4 0 0 WRT
GW 6004 1 R4 0 0 R5 0 0 WRT
GW 6005 1 R5 0 0 R6 0 0 WRT
GW 6006 1 R6 0 0 R7 0 0 WRT
GW 6007 1 R7 0 0 R8 0 0 WRT
GW 6008 1 R8 0 0 R9 0 0 WRT
GW 6009 1 R9 0 0 R10 0 0 WRT
'GW 6010 1 R10 0 0 R11 0 0 WRT
'GW 6011 1 R11 0 0 R12 0 0 WRT
'GW 6012 1 R12 0 0 R13 0 0 WRT
'GW 6013 1 R13 0 0 R14 0 0 WRT
'GW 6014 1 R14 0 0 R15 0 0 WRT
'GW 6015 1 R15 0 0 R16 0 0 WRT
'GW 6016 1 R16 0 0 R17 0 0 WRT
'GW 6017 1 R17 0 0 R18 0 0 WRT
'GW 6018 1 R18 0 0 R19 0 0 WRT
'GW 6019 1 R19 0 0 R20 0 0 WRT
GM 0 0 0 0 SAM 0 0 SHM 5000
'==== impedance transformer; wavetrap ===
SY LW=WL/8 'Length of flat wavetrap
SY WW=LW/2 'Width
SY LWH=cos(PA)*LW 'Length in horizontal plane once mounted
SY NPWW=10 'Number of patches along width
SY NPLW=NPWW*LW/WW 'Number of patches along length
SY XWD=NPWW*WW/(2*NPWW*sqr(2)) 'X delta
SY YWD=NPWW*WW/(2*NPWW*sqr(2)) 'Y delta
SY HDE=sqr(R*R-(LWH/2)*(LWH/2)) 'H distance to edge of wavetrap from origin
SY SAW=atn((2/LWH)*HDE)-45 'Angle in horizontal plane; no acos in 4NEC2
SY XW=R*cos(SAW)-XWD 'X position
SY YW=R*sin(SAW)-YWD 'Y position
SY ZW=H+SAW*HDD 'Z position
'GW 7000 1 0 0 0 WW/NPWW 0 0 WRT
'GM 1 NPWW-1 0 0 0 WW/NPWW 0 0 7000
'GW 7100 1 0 0 0 0 LW/NPLW 0 WRT
'GM 1 NPWW 0 0 0 WW/NPWW 0 0 7100
'GM 1 NPLW-1 0 0 0 0 LW/NPLW 0 7000
'GW 7300 1 0 LW 0 WW/NPWW LW 0 WRT
'GM 1 NPWW-1 0 0 0 WW/NPWW 0 0 7300
'GM 0 0 PA 0 45 XW YW ZW 7000
'==== active element, combined with wavetrap / microstrip ===
'==== choose SAT=SAW for wavetrap, SAT=SAM for microstrip ===
'SY SAT=SAW 'Start angle transformer in horizontal plane
SY SAT=SAM 'Start angle transformer in horizontal plane
SY ALT=90-2*SAT 'Angle along circle through transformer
SY HT=ALT*HDD 'Height transformer
SY A4=10 'Angle increment of a turn in degrees
SY N2=3 'Number of wires leading/trailing to wavetrap
SY A5=SAT/N2 'Angle of leading/trailing wires
SY A6=0.7*A5 'Angle of last-1 leading/trailing wire
SY XL1=R*cos(A5) 'X leader 1
SY YL1=R*sin(A5) 'Y leader 1
SY ZL1=A5*HDD 'Z leader 1
SY XL2=R*cos((N2-1)*A5) 'X leader 2
SY YL2=R*sin((N2-1)*A5) 'Y leader 2
SY ZL2=(N2-1)*A5*HDD 'Z leader 2
SY XL3=R*cos((N2-1)*A5+A6) 'X leader 3
SY YL3=R*sin((N2-1)*A5+A6) 'Y leader 3
SY ZL3=((N2-1)*A5+A6)*HDD 'Z leader 3
SY XL4=R*cos((N2-1)*A5+A5) 'X leader 4
SY YL4=R*sin((N2-1)*A5+A5) 'Y leader 4
SY ZL4=((N2-1)*A5+A5)*HDD 'Z leader 4
SY ZT=HT+2*ZL4 'Z trailer (mirrored leader)
SY XA1=R*cos(90+A4) 'X end first wire segment starting at 90 deg
SY YA1=R*sin(90+A4) 'Y end first wire segment starting at 90 deg
SY ZA1=(90+A4)*HDD 'Z end first wire segment starting at 90 deg
SY N3=270/A4+(N-1)*360/A4 'Number of wires starting at 90 degrees
GW 4000 1 R 0 0 XL1 YL1 ZL1 WRA
GM 1 N2-2 0 0 A5 0 0 A5*HDD 4000
GW 4010 1 XL2 YL2 ZL2 XL3 YL3 ZL3 WRA/2
GW 4011 1 XL3 YL3 ZL3 XL4 YL4 ZL4 WRT*2
GM 1 1 0 180 270 0 0 ZT 4000
GW 4100 1 0 R 90*HDD XA1 YA1 ZA1 WRA
GM 1 N3 0 0 10 0 0 A4*HDD 4100
GM 0 0 0 0 0 0 0 H 4000
'==== reflector square ===
SY WG=WL 'Width, approximately
SY LG=WG 'Length, approximately
SY HLG=LG/2 'Half length
SY NPWL=40 'Number of patches per wave length
SY NPLG=int(NPWL*HLG/WL+0.5) 'Number of patches along length from center
SY GS=HLG/NPLG 'Grid size
SY HWG=WG/2 'Half width
SY NPWG=int(HWG/GS+0.5) 'Number of patches along width from center
SY XOFF=GS*(R/GS-int(R/GS+0.5)) 'X offset to match with feed
SY XLG=-NPWG*GS+XOFF 'Left edge
SY YBG=-NPLG*GS 'Bottom edge
SY YTG=NPLG*GS 'Top edge
'GW 1000 1 XLG YBG 0 XLG YBG+GS 0 WRR
'GM 1 2NPWG 0 0 0 GS 0 0 1000
'GW 1100 1 XLG YBG 0 XLG+GS YBG 0 WRR
'GM 1 2NPWG-1 0 0 0 GS 0 0 1100
'GM 1 2NPLG-1 0 0 0 0 GS 0 1000
'GW 1300 1 XLG YTG 0 XLG+GS YTG 0 WRR
'GM 1 2NPWG-1 0 0 0 GS 0 0 1300
'==== reflector circular ===
SY W=6*R 'Width
SY HW=W/2 'Half width
SY ADR=10 'Angle delta neigbouring segments
SY XR=HW*cos(ADR) 'X delta pie segment of length R
SY YR=HW*sin(ADR) 'Y delta pie segment of length R
SY N4=360/ADR-1 'Number of pie segments to copy
'GW 1000 21 0 0 0 HW 0 0 WRR
'GW 1001 1 HW 0 0 XR YR 0 WRR
'GW 1002 1 20HW/21 0 0 20XR/21 20YR/21 0 WRR
'GW 1003 1 19HW/21 0 0 19XR/21 19YR/21 0 WRR
'GW 1004 1 18HW/21 0 0 18XR/21 18YR/21 0 WRR
'GW 1005 1 17HW/21 0 0 17XR/21 17YR/21 0 WRR
'GW 1006 1 16HW/21 0 0 16XR/21 16YR/21 0 WRR
'GW 1007 1 15HW/21 0 0 15XR/21 15YR/21 0 WRR
'GW 1008 1 14HW/21 0 0 14XR/21 14YR/21 0 WRR
'GW 1009 1 13HW/21 0 0 13XR/21 13YR/21 0 WRR
'GW 1010 1 12HW/21 0 0 12XR/21 12YR/21 0 WRR
'GW 1011 1 11HW/21 0 0 11XR/21 11YR/21 0 WRR
'GW 1012 1 10HW/21 0 0 10XR/21 10YR/21 0 WRR
'GW 1013 1 9HW/21 0 0 9XR/21 9YR/21 0 WRR
'GW 1014 1 8HW/21 0 0 8XR/21 8YR/21 0 WRR
'GW 1015 1 7HW/21 0 0 7XR/21 7YR/21 0 WRR
'GW 1016 1 6HW/21 0 0 6XR/21 6YR/21 0 WRR
'GW 1017 1 5HW/21 0 0 5XR/21 5YR/21 0 WRR
'GW 1018 1 4HW/21 0 0 4XR/21 4YR/21 0 WRR
'GW 1019 1 3HW/21 0 0 3XR/21 3YR/21 0 WRR
'GW 1020 1 2HW/21 0 0 2XR/21 2YR/21 0 WRR
'GM 1 N4 0 0 ADR 0 0 0 1000
'=== scaling ===
GS 0 0 0.001 'All sizes are in mm
'==== no ground plane ====
'GE 0 'No ground
'GN -1 'Free space
'==== ground plane ====
GE 1 'Ground plane
GN 1 'Perfectly conducting ground
'====================================
EK
EX 0 2000 1 0 1 0 0
FR 0 1 0 0 F 0.000
EN
By default it uses design frequency 2.4GHz, 5 turns, infinite ground, bent microstrip as impedance transformer. But all parameters can be changed easily. If you need help, you know where to find me
Martin