Lumped Coil Yagi HF antenna

Below are the tabled results of a lumped component coil ( inductor ) Yagi beam antenna for low band HF operation.

The principle of operation is substitute the wire or rod antenna element inductance value with the same coil wound inductor, this coil equating to the same inductance as the inductive value of the Yagi beam antenna elements, from the reflector through to the di-pole and 5 director elements. Three Yagi antenna designs are shown below, an 80m , 40m and 20m Yagi beam antenna.

Below the tabled results is the BBC Basic computer code that is used to calculate the antenna design parameters, the BBC Basic code shown in a text window, for a copy and paste into ones favourite Basic language IDE platform. Be warned, the code below uses defined function coding, so I suggest downloading the free version of the BBC Basic for windows IDE, as this will not time out as to date and will be sufficient to run the below coding.

The understanding behind my Yagi antenna design, is that each part of the antenna produces an phase shift of the over radio signal as it propagates along the antenna as whole. You may perhaps notice from the tabled results, that the reflector dimensions are greater that would perhaps be the case. I found from deduction, that the overall large reflector provides a 180 degree flip over of the dipole signal flowing into the reflectors direction, and this dipole signal rebound due to the 180 degree phase shift by the reflector, then sending back the dipole emission towards the reflector, into the direction of the antenna's compass bearing.

Then on from this, each director provides a gradual phase shift the forward send dipole signal, each phase shift bending the dipole signal into a forward concentrated direction. The combination of the phase shift signal elements, at the receiving antenna will then vector add to provide the intended Yagi beam shaping experience found when using such an antenna design.

Now normally the Yagi antenna elements are positioned to a rule of thumb ruling, the distance between the dipole and the reflector usually around 10% of the wavelength of the frequency in use, and so on down the antenna beam length. However, as each elements produces a phase shift to the intended signal on each separate part of the Yagi antenna design, the separation between each antenna segment may not need to follow the usual understood parameters. As long as the dipole signal is being received and induced into the antenna elements, the element separation need not follow the usual convention. The antenna elements need to say just be 30cm or one foot apart, just far enough apart not to allow signal sparking between each element, according to the transmitter power used, say 100 watts or the legal limit in your country. By separating between say each 30cm gap, the overall lumped component Yagi antenna design would be in the region of some "2.1metres" in overall physical length. This is irrespective of the HF band in use for the design construction of the coiled beam Yagi antenna.

Now the inductance values shown or illustrated in the tabled results, relate to just one side of the Yagi beam antenna design. One just needs to replicate the same coil spec's to add to the opposite side assembly, remembering to electrical connect together both halves of the antenna, from the reflector and each director element, creating a complete electrical circuit for each one of the directors and the reflector. The dipole however, each half section is connected to the coax in the usual way, even if intersected by the use of a unbalance to balance balum. In all, the complete antenna would then be constructed.

Now the coils shown as to the number of turns, to a 50mm diameter and 30mm coil length, say 6·86 turns, is 6 turns and (0·86 * 360 degrees of arc) trim to the turns measurement. Alternatively, the "XL reactance" listed on the tabled results relates to the inductive value of the coil on the band of operation of use, hence its design spec. By scanning over the three tabled results, one may have determined that the "XL reactance" values are common to each of the three antenna design listings. The impedance arc of angle to a 50ohms load is also equally the same for each of the three designs. However, in factual fact, these figures are common to all designs, provided it is used for the intended band in use.

One may have noticed that the dipole half section, i.e. one side of the dipole, usually 1/4 wavelength, has an inductive reactance of 100ohms. Once the each 100ohm section is connected to the coax, each half section will be in parallel with each other, thus present a 50ohm impedance match to the coax cable. It is the size if the inductive reactance relative to the dipole impedance that determines the degree of required phase shift between each part of the Yagi beam antenna design to throw forward the directional control of the overall beam antenna design. When each part of the antenna half is connected to its opposite side element, the impedance of each part would become relevant, and thus produce its impedance design, as with the dipole assembly, but for the dipole via the coax, but for the rest of the antenna elements, each is connected electrical it its opposite part to create that part of the antenna's electrical circuit, per element section.

It is suggested that the each 2cm or 6nH mounting wire is soldered together, and then held down by a clamping piece of wood, so not to add to its inductance by virtue of a wood metallised screw. As for the dipole, soldered to the coax or via a "un-balance to balanced balum", the balanced output connected to the dipole.

The section of the tabulated results regarding "load uH, pF" relates to the load component match to the direct connection to a 100ohm coax as a vertical antenna. The large capacitance found on the dipole section, means that phase shift of the connecting vector to match the cable is low to not required.

The program code line 220 "reactance_resonant_impedance = 100" relates to the antenna design element calculated relative to the dipole half section inductive reactance impedance.

The common design process or perhaps measuring the inductive reactance of each element part of the Yagi beam antenna design would simplify the construction assembly of the antenna as a whole.

Happy building.

Up-date for new design info.

Now many radio ham may be using beam Yagi antenna that have a cross type dipole in use. Now as a full wave wire has a 550ohm inductive reactance, a dipole with its two sides of 100ohm inductive reactance, would equate the total of 200ohms from the dipole and when aligning this to the full wave wire, the dipole seems to have an efficiency of 2/5th's, ( 200 ohms / 550 ohms ) * 100% = 40% efficient. Now the doubling of the dipole to a cross section or a folded dipole would increase the overall inductive reactance.

However as the complete folded dipole circular inductance reactance adds up to 800ohms, diagram below each element 200ohms, even with the cross dipole, the efficiency would perhaps be ( 800ohms / 550ohms ) * 100% = 145%, or 5·6dB. Now bearing in mind a dipole is 40% efficient, any beam signal directional concentration gain, would be 7·5dB down. With a proposed antenna listed as 21dB directional concentration signal gain with a standard dipole radiator element, would be in effect 13·5dB over the transmitter power,. If the radiating dipole was then replaced by 50ohm cross dipole, my sums say with a signal gain of 1·5dB up over the transmitter power, then a standard format Yagi beam antenna, would perhaps then to equate to ( 13·5dB + 1·5dB ), perhaps the proposed listed 21dB antenna would be perhaps then a hopefully good 15dB overall ( 31·6 times directional gain or signal concentration ), over the transmitter power or what ever turns up at the antenna connection.

Now for the cross dipole to still present a 50ohm reactance would require each section of the cross dipole, that is each half section of either two coils or two rod wires, need to be designed with an 200ohms inductive reactance each. Thus so, each half section of the 200ohm line rod or inductive coil would be soldered together at one end only, this end connected to the coax cable. The resulting design would be a construction assembly of two 200ohms coils or wire rods inductive reactance, one assembly connected to the coax core the other assembly is connected to the coax braid, or both assemblies attached to either one or other side wire connection of the balanced output of a "unbalanced to balanced" balum. The shown diagram below is a connection to a 50ohm coax cable. The folded dipole is one complete series linked 200ohm coils, then each end of the overall circuit connected as shown below.

The remainder of the lumped component coil Yagi beam would remain the same as listed below, for the reflector and each director. The reason why the top and lower section of the folded dipole would create a 100ohm each side impedance reactance, is due to the virtual ground centre of the top section of the folded dipole, giving the top section each side of 200ohms.

You may have been wondering why a 100ohm per side dipole is a 50ohms @ 63·435 degrees. Well the bases for this is the matched load impedance angle. The equation used is "Inv Tan" or to say Tan^-1( load / output ). The load of 50ohms and the transmitter output of 50ohms, equates then to the load impedance angle of 45 degrees, the prove as " 45 degrees = Tan^-1( 50 / 50 ) ". Thus therefore a matched load has an impedance angle of 45 degrees @ 50ohms. If a 75ohm dipole was made a terminated by a 50ohm coax, this would be as follows " 56 degrees = Tan^-1( 75 / 50 ) ". It is on this bases the impedance angle is calculated within the BBC Basic code.

Text Box

10

20

30 REM the principle of focusing the twin beam of a dipole is to phase shift the radiated dipole into one direction

40 REM This is achieved by using the bame antenna elements as phase shifting components. The variation in size

50 REM of the beam antenna elements are either inductive or capacitive at the frequency of operation.

60 REM The reactive components would either phase shift by leading or lagging the intended radiated antenna signal

70 REM throughout the beam antenna design. The overall effect would be to phase shift the overall dipole radiated

80 REM signal by the use of the beam antenna elements, focusing the radiated dipole signal into one direction.

90 REM The focused beam signal is the effective signal gain of the antenna signal.

100 REM

110 REM

120

130

140

150 REM length_inches = (174.06/f)*12 "reference = 174.06", equates to 100ohms reactance for 50ohms dipole match

160 REM reference phase shift angles = 180,45,22.5,11.25,5.625,2.18125,1.40625

170 REM reactance_resonant_impedance = 100 "equates to the design reactance impedance match resonance, if 300ohm feeder, use the value of 600"

180 REM f = the frequency of operation of the designed requirement

190 REM air spaced coil inductance sizes in "mm"

200 diameter = 50

210 length = 30

220 reactance_resonant_impedance = 100

230 reference = 174.06

240 scale_factor = reference * ( reactance_resonant_impedance / 100)

250 f = 7.15

260 PRINT

270 PRINT TAB(7);" air space coil diameter = ";diameter;"mm"

280 PRINT TAB(7);" air space coil length = ";length;"mm"

290 PRINT TAB(7);" 50 ohm coax match to dipole ( marked as 45 degree line )"

300 PRINT

310 PRINT

320 PRINT TAB(7);" yagi elements list ( induced phase shift for directional gain )"

330 PRINT

340 PRINT TAB(7);" reflector ( 180 degrees <full return fold about reflection>)"

350 PRINT TAB(7);" dipole ( 45 degrees )"

360 PRINT TAB(7);" 1st director ( 22.5 degrees )"

370 PRINT TAB(7);" 2nd director ( 11.25 degrees )"

380 PRINT TAB(7);" 3rd director ( 5.625 degrees )"

390 PRINT TAB(7);" 4th director ( 2.8125 degrees )"

400 PRINT TAB(7);" 5th director ( 1.40625 degrees)"

410 PRINT

420 PRINT TAB(7);" listed also air spaced lumped antenna coil elements <including 2cm ( 6nH ) mounting wire>"

PRINT

430 PRINT TAB(7);" antenna gain = 21dB power due to signal directional concentration"

440 PRINT

450 PRINT

460 PRINT

470 PRINT TAB(7);"Tx/Rx ";TAB(17);"side length(m) ";TAB(33);" Lump Value";TAB(48);"XL reactance";TAB(65);"load: uH , pF";TAB(83);"Zo ohms + Phase angle";TAB(110);"Beam +/-";TAB(130);"air space coil turns"

480 PRINT

490

500

510

520

530 REM Yagi calculations

540 phase_angle =180

550 PROC_element_reflector

560 PROC_coil

570 PROC_reactance

580

590 phase_angle = 45

600 PROC_element_dipole

610 PROC_coil

620 PROC_reactance

630

640 phase_angle= 22.5

650 PROC_element_director

660 PROC_coil

670 PROC_reactance

680

690 phase_angle = 11.25

700 PROC_element_director

710 PROC_coil

720 PROC_reactance

730

740 phase_angle = 5.625

750 PROC_element_director

760 PROC_coil

770 PROC_reactance

780

790 phase_angle = 2.8125

800 PROC_element_director

810 PROC_coil

820 PROC_reactance

830

840 phase_angle = 1.40625

850 PROC_element_director

860 PROC_coil

870 PROC_reactance

880

890

900 ORIGIN 100,200

910 *CHDIR C:\Users\alastair\Pictures

920 *SCREENSAVE 10metre_beam_antenna.bmp 1,1,2000,1200

930 END

940

950 DEF PROC_element_reflector

960

970 res_freq = f-((phase_angle/360)*f)

980 length_inches = ((scale_factor)/res_freq)*12

990 length_metres = (length_inches * 2.54)/100

1000 length_answer = length_metres

1010 l = length_metres*(300E-9)

1020 ENDPROC

1030

1040 DEF PROC_element_dipole

1050

1060 res_freq = f-((phase_angle/360)*f)

1070 length_inches = ((scale_factor)/res_freq)*12

1080 length_metres = (length_inches * 2.54)/100

1090 length_answer = length_metres

1100 l = length_metres*(300E-9)

1110

1120

1130 DEF PROC_element_director

1140

1150 res_freq = f+(((45-phase_angle)/360)*f)

1160 length_inches = ((scale_factor)/res_freq)*12

1170 length_metres = (length_inches * 2.54)/100

1180 length_answer = length_metres

1190 l = length_metres*(300E-9)

1200 ENDPROC

1210

1220 DEF PROC_coil

1230 REM calculation of single layer air cored inductor diameter

1240

1250

1260 ANSWER = 0

1270 ANSWERS =0

1280 UP = 0

1290 upper =0

1300 REM d = diameter of coil in mm

1310 dia = diameter

1320 REM z = length of coil in mm

1330 len = length

1340 REM inductance with 2cm ( 6nH ) on holding wire to antenna supporting boom

1350 inductance = l - 6E-9

1360 ind = inductance * 1E6

1370 up =10*SQR(5*ind*(0.9*dia+2*len))

1380

1390 ANSWER = up/dia

1400

1410 ENDPROC

1420

1430

1440

1450 DEF PROC_reactance

1460 XL= (2*PI*(f*1E6)*l)

1470 REM RL is low to 50ohms, thus the wire is capacitive and needs inductive loading

1480 IF XL <= reactance_resonant_impedance THEN PROC_low

1490

1500 REM RL is high to 50ohms, thus thwe wire is inductive and needs capacitive loading

1510 IF XL > reactance_resonant_impedance THEN PROC_high

1520 ENDPROC

1530

1540

1550

1560

1570 REM RL is low to 50ohms, thus the wire is short and capacitive thus needs inductive loading

1580 DEF PROC_low

1590 Xc_low = SQR(reactance_resonant_impedance^2 - XL^2)

1600 REM Xc_low used as XL, as opposite reactance required

1610 XLoad = Xc_low/((2*PI*(f*1E6)))

1620 lump_comp = XL/((2*PI*(f*1E6)))

1630 imped_ance = SQR((XL^2) + (Xc_low^2))

1640 IF lump_comp >= 1E-6 THEN PRINT TAB(7);f;"MHz";TAB(19);length_answer;"m";TAB(33);length_answer*300;"nH";TAB(47);XL;"ohms"TAB(65);XLoad*1E9;"nH";TAB(82);"50ohms @ angle ";DEG(ATN(XL/50));TAB(110);phase_angle;" degrees";TAB(135);INT( 100* ANSWER)/100

1650 IF lump_comp < 1E-6 THEN PRINT TAB(7);f;"MHz";TAB(19);length_answer;"m";TAB(33);length_answer*300;"nH"TAB(47);XL;"ohms"TAB(65);XLoad*1E9;"nH";TAB(82);"50ohms @ angle ";DEG(ATN(XL/50));TAB(110);phase_angle;" degrees";TAB(135);INT( 100* ANSWER)/100

1660 ENDPROC

1670

1680 REM RL is high to 50ohms, thus the wire is long and inductive thus needs capacitive loading

1690 DEF PROC_high

1700 XL_high = SQR(XL^2 - reactance_resonant_impedance^2)

1710 REM XL used as Xc, as opposite reactance required

1720 Xcload = 1/((2*PI*(f*1E6)*XL_high))

1730 imped_ance = SQR((XL^2) - (XL_high^2))

1740 lump_comp = XL/((2*PI*(f*1E6)))

1750 IF lump_comp >= 1E-6 THEN PRINT TAB(7);f;"MHz";TAB(19);length_answer;"m";TAB(33);length_answer*300;"nH";TAB(47);XL;"ohms"TAB(65);Xcload*1E12;"pF";TAB(82);"50ohms @ angle ";DEG(ATN(XL/50));TAB(110);phase_angle;" degrees";TAB(135);INT( 100* ANSWER)/100

1760 IF lump_comp < 1E-6 THEN PRINT TAB(7);f;"MHz";TAB(19);length_answer;"m";TAB(33);length_answer*300;"nH";TAB(47);XL;"ohms"TAB(65);Xcload*1E12;"pF";TAB(82);"50ohms @ angle ";DEG(ATN(XL/50));TAB(110);phase_angle;" degrees";TAB(135);INT( 100* ANSWER)/100

1770 ENDPROC