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This project started with the "jerry rigging" of 2 current projects. Having 2 projects, each half finished, rapidly combined during an opening, with good results!
    I have had an interest in six meters for some time. Remembering times during solar peaks and at unusual times tv stations from other states would suddenly come in.
  So While antennas were small but "six" exotic and expensive until relatively recently, it remained out of reach.
  Enter Icom 706****G/no antenna.  So, after reading arrl handbook,antenna book, and Bill Orr's Antenna Handbook~again~ I decided on building a Quad and a Dipole.
The quad antenna has a superior gain over most easily built antenna's.  According to the truth table a single element loop has erp "gains"  over the imaginary isotropic, ground plane, and dipole respectfully of:
                           GAIN                   GAIN               GAIN 
   ISOTROPIC       -0-                      -.3                    -2.1
   GND PLN           + .3db                 -0-db                -1.7
   DIPOLE              2.1db              + 1.7db                  -0-
    5/8 wL                3.3                    3                     + 1.6
   QUAD                 4.1                    3.8                      2.1
   2 el Yagi             7.1                    6.8                      5.1
   2 el Quad            9.1                    8.8                     7.1
   3 el Yagi            10.1                    9.8                     8.1
   2 el Quagi           9.5                     9.2                     7.5
   4 el Yagi             12.1                 11.7                    10
   3 el Quad           12.1                 11.7                     10
   4 el Quad           14.1                 13.7                     12
  Additional requirements are cheap inexpensive materials, lightweight, and portable.   Sounds like an expensive backpacking rig.  Fortunately, I have a well stocked junk box of pvc/aluminum pipes and tubes with various assorted hardware.  A trip to the Boeing surplus store years earlier scored me 2000' of #12 enamled wire. 
   Next task was to calculate the size.
        1005/fmhz of the loop to determine:
            A. spar arm length.
            B. boom length
            C, need wire @#12enamled OR vinyl jacket. (junk box reigns)
Why reiterate the truth Table?  For the truth of course. Why build an antenna based on hype?  Laid out in front like this, I can see the "PHYSICS" of truth and decide my antenna accordingly!  I want a high gain antenna with minimal size.  On HF Decibels of gain rate an honorable mention. Decibels are not critical there.  Build a "reasonable antenna" and you can expect reasonable results.  In VHF and  decibels are "CRITICAL"!   Polarization is too!   Since most VHF DX operators choose horizontal polarization, I went that way too.   In the future, I plan on building and experimenting with circular polarization.
    The two antennas I decided to build were a 2 elementa quad and a 3 element yagi. When 6 opened, I hurriedly combined the two half finished antennas into a quagi with positive results!
This is some of the "junque" I had available.  Scrounging for Junk PVC pipe, a cornucopia of uhf antenna pieces have accumulated in the shack.
Assortment of:  2 1/2 in schdule 40 white PVC, 1" lengths of 5', assortment of PVC Schd 40 of various sizes in lengths less than 1 foot, assortment of couplings, joints,fittings of various sizes. 

At 6 meters UHF, Absolute accuracy is not a mandate!  At 80 meters an error can be very large and still not affect an antennas overall performance.  Six meters is one of those "transition bands".  So, Accuracy allows some inches.for error!
  Basic formula for hf Quads applie to the uhf frequencies also.   So working with the basic formula for a quadratic 1005/Fmhz=Lg in feet .  Okay, figuring for an operating center of 50.2 the formula is  1005/50.2=20.01992'  or 240.23". That figure is easy.
A wavelength based in space traveling at light speed, but I am using vinyl and enameled coated copper #12 wire.  So, I have to make the adjustments for velocity factor to get a correct physical length.  So I can usually figure about .66 for coax and .98 for uncoated copper#22.  I often use 8x and that has a VF of .72.  So Now 240.23"x Vf= Lg.   The wavelength in a physical conductor is always shorter than in "free space". Remember the isotropic?  Both are imaginary! so VF=1 divided by  the square root of the dielectrict constant.  Whew. That work is already done, So it is a matter of looking up the VF of different lines in the handbooks. 
  So, The coated Vinyl  has about  a .94 VF.....resulting in 240.23x.98= 225.8162 inches or 18.81 feet. or 4.7 feet / 56.454" per side.  If accuracey isn't critical, why did I carry out the math so far?  Well, I want an accurate answer.  I can make any deviations based on the correct figures!  So, What if I made it 56 1/2 inches per side?  No big deal.  This would be the figure for the physical length of the Driven Element at 50.Mhz.  The reflector 5% larger and the director 5% smaller. saves me refiguring each element.  5%=.05 so  225.8162x1.05= 237.1005". 
  The reflector is smaller than the original driven element figure.   Velocity factor is important!
  The director is 225.8162 X .95 = 214.52539".
A total of 677.44209" of wire needed for 3 elements.  56.453507'.
I am bypassing all of the nuances of element interaction and just sweating the big stuff.  So what is and how much will it help me to figure out the interaction of elements?  Most of this work has been done so I only need to "scale" element spacing.  Two options are available.  A tight focused beam with reduced rejections, or higher Fto B ratios and sacrifice some gain?   I thought I would just put it together and hoped it worked!  
So here is What happened to the Quad
Using a 5 1/2'  foot section of 2 1/2"  Schedule 40 white  Pvc (it was free),7/8" holes were drilled near one end enableing a support arm to be pushed thru.  One inch forward, another whole was drilled at 90deg to the first and a second cross arm was pushed thru the "boom" creating an "X".
  well, I was creating a plumbers nitemare.  Not having support pieces long enough, I settled on a Diamond instead of a square.  Kepplers laws say that I won't lose area.  This is good! Antenna easier to build and still effective. I cut a "reflector" element wire, pushing wire thru holes drilled in the support arms.  The ends of the loop are joined physically and electrically.  realizing I had only enough boom length for a two element quad,(at this time) I measured  the approximate spacing,(arrl antenna book) and drive four more holes to support cross members.
  I had built to this point, a reflector element on a 5 1/2 foot boom and drilled holes in the opposing end for the driven element.   
THE DIPOLE is an easy one.  1/2 wl can be fed and hung in trees or whever there is room and a support.  Higher is better at uhf, but a half wavelength at 6 meters is about 10 '.   So, I have heard six propagation on antennas cut for other bands so a quickly constructed dipole posed no obstacle.   I measured a driven element with the standard 462/Fmhz= ft.  X VF= physical length.
  here goes    462/50.2=9.2031872 Ft.  x .94= 8.6509959 Ft  or 103.81195 inches.  From the looks of that, a standard CB whip is close to a halfwave verticle...... so each leg of the dipole is half that for 51.9 inches a leg.... 52 works fine!   I make my error from the correct result instead of "compounding it as it's  figured.  I have two lengths of 1/2" PVC that I slipped the wire into.  A four way connector (as a "t") was used to join the arms.   The pvc "t" connector allowed the used of other lengths of pipe to be used as a mast.
  rg8x coax was slipped up thru the four way and appropriate sides of the coax were attached to each leg of the dipole and wapped with electricians tape.   The dipole was fed directly.  There are debates raging about the effectiveness and loss problems associated with using a BALUN at uhf and up frequencies.  SWR measured at the transmitter was 2.1-1. 
   Stations were heard, but no contacts  were established with the dipole.  To be fair, it was operated leaning against my truck and only the one time during some initial swr measurements........
QUAGI  antenna was introduced in qst for the 440 band.  Tiny antennas cause a lot of mechanical physical length building problems.   So,  an experimentally minded amateur combined two antenna types and eleiminated a number of problems, and created an antenna of noticeable gain as well.    Notably, the original antenna uses the quad element as the DE and reflector with the yagi as a director.  
   While watching Tv in CN76, (Klipsan Beach, Wa) The stations started  fuzzing in an out with different programs fighting for the channel.  checking channel 3, sure enough, News radio, UPN20 (DENVER CO?) was coming in strong.  Channel 3 is unused in klipsan area. A call on the dipole quickly netted a response.  The swr was infinite? outside I discovered the dipole had fallen and shorted the driven side to ground.   Standing there, I realized I had two half "tennas" which would easily and quickly blend to one two element affair.  So, two dipole support arms were slid into the boom with the wire dipole taped onto the horizontal arms. The spacing had been pre-drilled and figured so no new figuring or building was necessary.
   How did it work?  Still, a 2.1 .1 Swr.   Forward power appears  be a solid 100 watts on peaks.   Using an mfj  989c tuner (yup, they work on 6) I brought the SWR down to test direct and matched feed.  
   Setting the antenna on the ground, with the dipole end supported on a sawhorse,  I made numerous 6 qsos.  No one could hear a difference between matched or direct feed.   I also could not tell an audio or measured signal difference between the two feeds.     Later when I set the antenna facing straight up the swr measured  1.7.1.  
    The chief difference is the driven element..  The quad design has more capture area, but the combination of the two seems to mimic the best qualities of both.  I think I even remember reading that in The Antenna Handbook.  So, with only two elements, theoretically the quagi will have a gain which compares favorably to a 3 element yagi and compare  a 2 el quad.  Topping off the advantages is the shorter boom length.  I think a 3 el quagi is just around the corner!  

Two holes are drilled @ 90degs. First at the boom end, the second 3" back 
A hole saw makes the job sweet! Not having the proper size, I enlarged and rounded the hole with my trusty moto-tool  
The cross member is 7/8" sch 40 pvc.  A snug fit holds the member in place.  The second hole is drilled and ready for the magic of the moto tool.
AUGUST  2000
Intended as a reflector, DIAMOND becomes the driven element.  The  front (not shown) yagi-dipole becomes the DIRECTOR.  To achieve the higher gain, there is a trade off.  Theory suggests the pattern is "squeezed"  by the  yagi director.  The supports slip snugley into the holes in the boom. 
Up close and personal!   This spacing is a little bit far apart, but it works and does not adversly affect  performance.   When the annna is mounted, the wire element supports the pvc arms resulting in no sag!
These pictures are my humble attempts at explaining the QUAGI I built. They should serve as a platform to build from.  I am working on a 4 element version.  There comes a point where size weight and gain must make some compromises.   The material I am using (free) is very heavy compared to aluminum and limits a workable size.  I do plan on building this with lightweight aluminum, but in the spirit of HOMEBREW, I will do my very best to SCROUNGE the parts.   My best scores have recently been at garage/yard sales where cable and satellite owners are junking their FM TV antennas.   Most of the time, The "garage sailors"  will ask me to "PLEASE HAUL THAT JUNK AWAY!"
2 opposing 90 deg supports.
See any power outlets in the spruce trees?
Some of the source I have look for supports have been,
  old fiberglass fishing rods---
  Bicycle pole flags
  tent poles
  bamboo the neighbors have grown and thrown away.....Can you Imagine?

  Cheaps things at garage sales that even resemble usable support arms.