The J-pole Theory
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The theory that the antenna is the most important part of your station has lead me to realize that you could study antennas for the rest of your life, and hardly scratch the surface. In order to completely understand antennas, and transmission lines, you will need a thorough understanding of impedance, reactance, velocity factor, and enough math skills to be a professor. The study I am undertaking here, is about just one antenna, and although the facts learned apply to many others, we are looking for a vertical, omni-directional antenna that is broad enough to cover the whole band, and has enough gain to be useful for simplex. Most new Hams start out with a hand-held and a rubber duck, and then usually go on to a quarter wave ground plane. Some may go so far as to stick a 5/8 on top of a pie plate, and some even get a half wave hot-rod. This is a natural progression, but when faced with getting some high gain that will really get out there, most will opt for a directional beam antenna. Most often, antenna gain is described as compared with a half wave dipole, but in this case I will use the quarter wave ground plane as a reference to zero gain as we are talking about vertical omni antennas. For instance, a half wave vertical can be stated as having 3db of gain over a quarter wave. Now comes the Collinear. By stacking half wave sections, one over the other, fed in phase, we can have as much as 3db of gain per section over a quarter wave. We can feed the sections in phase by inserting a quarter wave phasing loop between the half wave sections. The loop will shift the phase of the first half wave section 180 degrees, and feed the second section in phase with the first. Three half wave sections fed in this manner, will produce 9db of omni directional gain. There are commercially made antennas that will do this, but only the most expensive will have an SWR that is 1 to 1 across the band. I dont mean to single out any brand, but most Cushcraft verticals will not offer an acceptable match at the bottom of the band without adjustment, and sometimes not at all. The lower part of the band is important if you wish to take advantage of all modes such as SSB and CW on the 2 meter band. A collinear J-pole will match 1 to 1 across the band, and give you about 9db of omni-directional gain for about $25.00. Yes, you will have to add the cost of quality coax as you would with the most expensive antenna. The collinear J-pole will radiate 1000 watts with no sweat. If you run it at 100 watts, it will have an effective radiated power of 800 watts. The design criteria begins by stating that the j-pole is an end-fed vertical zepp antenna, that is matched to the transmitter output impedance by a series tuned section of transmission line. Most published J-pole designs have been derived by making the series section, or J section, a quarter wave length long, and although in most cases, this will match, the actual length needed to match 4000 ohms to 50 ohms, is considerably longer. The tuned section is described as the series section above the coax attachment point and the shunt section below. The following must be known. The antenna feed-point impedance, the transmitter impedance, the characteristic impedance of the tuned section, and the velocity factor of the tuned section, the latter being the most critical. Some assumptions must be made here. An accurate antenna analyzer will tell you what the feed-point impedance is, but not until the antenna is built. Experimentation has lead me to believe that the feed-point impedance is between 3500 and 4000 ohms, and is the least critical part of the over-all formula. The velocity factor of open transmission line constructed from tubing, although stated in most publications as being .80, is actually .86, or 86 percent. The best characteristic impedance for the tuned section is a trade off between how broad or sharp the tuning will be. Raising the impedance will raise the Q of the circuit, and cause the tuning to be sharp. Again, experimentation has shown that a characteristic impedance of 300 ohms is about middle of the road between ease in tuning and a 1 to 1 SWR. This is also supported by calculations on a Smith Chart, but I will spare you the added complication of learning to understand Smith Charts, as it is a college course in it self. Now that we have the input parameters, we can begin our calculations.
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J-pole Design Facts
Matching section impedance: Zo = 276logb/a 146.0 mhz
Where as: Zo = characteristic impedance b = center to center distance of conductors a = radius of conductor
Outside diameter of ½ copper tubing is .625 Spacing for Zo of 300 ohms is 3.825.
Phasing Loop impedance:
The phasing loop must equal ½ wavelength in total length in order to shift the phase 180 degrees so that the 2nd collinear section of the antenna will be fed in phase with the first. This also follows true for the 3rd collinear section.
Outside diameter of #6 copper wire is .162, radius = .081. Outside diameter of #8 copper wire is .1285, radius = .06425.
#6 copper wire spaced 1 will have a Zo of 301 ohms. #8 copper wire spaced at .800 will have a Zo of 302 ohms.
A ridged, unsupported parallel tuned section, such as the J-section, or phasing loop Will have a velocity factor of about .86, or 86%, and must be considered when determining the electrical length of the section.
The Halfwave Formula:
To express the length in inches, the figure 5905 is substituted for 492. For ½ copper tubing, .625 O.D., a K factor of .958 is used. For #6 or #8 wire, a K factor of .955 is used.
½ wave in inches = 5905 x k.958 146.0 mhz
The length of the halfwave radiators is 38.750.
The top collinear section is made from a tapered whip using a K factor of .95 And is 38.423 in length. Phasing loop length:
The formula is: 5905 x k .955 146.0 mhz
The phasing loop length is 38.625. Add 2 for attachment.
As demonstrated by the, calculations page, a feed point impedance of 3500 ohms will require a series tuned section of 300 ohm characteristic impedance, 19.786 long, with the 50 ohm coax attachment at 2.750 from the shunt end. A Velocity factor of .85 was used for this calculation. If a feed point impedance of 4000 ohms is used, the section will be 19.797, with the coax at 2.750. It can be seen from this that the feed point impedance has little effect on the length of the section. If you assume a bit faster velocity factor however, such as .875, the changes have a much broader affect For example, in the case of the 3500 ohm feed point impedance, if you use a velocity factor of .875, the tuned section will be 20.369 long, with the 50 ohm coax at 2.830. I am assuming for this design, a feed point impedance of 4000 ohms, and a velocity factor of .86. The series tuned section is 20.029, with the coax feed point at 2.782 from the shunt end.
A balun is not required at the feed point unless the antenna is grounded at its base.
The antenna must be matched in the clear. As with all VHF antennas, the higher you can get it, the better it will perform.
Insulators must be made to go in between the collinear sections. The phasing loops will connect the sections around the insulators which must be made to maintain the 1 spacing of the loops.
When cutting the tubing to length for the matching section and the radiating sections, pay attention to subtracting the correct amount to make up for the elbows and tees.
The phasing loops may be bent circular around the antenna for a more balanced look, or they may be left straight out at 90 degrees.
Once it is carefully constructed and clear coated with a good brand of clear acrylic, it should perform for years without maintenance. This antenna will dissipate 1000 watts with room to spare. |
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