With the permission of Gary O'Neil, N3GO, the Author.

Figures courtesy of Communications Quarterly Magazine.

The enthusiasm of many of these new hams has created a great deal of activity in home brew antennas, with the J-pole high on their list of favorites.

After several weeks of reading the mail on the repeaters in my area; I discovered the discussions frequently evolve to J-poles, and became curious about why many of the comments were becoming popular and widely accepted. A number of recipes are circulating around for each of the design variations (copper tubing, 450 ohm ladder line, and TV twin-lead), each stressing the critical importance of careful measurement in order to achieve success. It seems there is a mystique associated with tuning them; an albatross the J-pole has carried since it's early beginnings.

Convinced that the J-pole should not be tricky to tune; I began my investigation with an analysis of a known working design by sifting through many of the mysterious claims to the contrary. As my research progressed, I soon became aware that the significance of my findings would be of interest to a much greater audience. Whether you consider the J-pole your friend or foe, you should find this thesis enlightening.

As a consequence of my research, I will attempt to defend the following claims regarding J-pole designs; several of which appear to counter popular opinion:

- Adjusting the feedpoint "tap" is not the proper way to tune
a J-pole.
- 300 ohms is the optimal transmission line impedance to use in the construction of J-poles.
- 300 ohm TV twin-lead is minimally susceptible to RF current induced in the feedline coaxial cable, enabling the J-pole to perform well without a balun.
- The "stub" portion of the J-pole is electrically longer than a quarter wavelength.
- The J-pole "shorting bar" can be connected to an earth ground reference if and only if a balun is employed at the antenna feedpoint.
- The velocity factor is the most critical transmission line parameter to consider when designing J-poles.
- J-poles are easy to build, and tune (even by the inexperienced). As a consequence, they are easy to reproduce.

- End-fed halfwave dipoles are the configuration of choice
over end-fed 5/8 wave antennas which can be matched by only
low impedance (likely less than 300 ohms) transmission
line and require a ground plane or counterpoise.
- A dual-band (144/440 MHz) J-pole is an inefficient design compromise and a likely poor performer on the 440 MHz band.

The "Jays" are sprouting up everywhere and in every form. The most popular of these are constructed from copper plumbing stock for rooftop and attic installations. In time, word got out that these can be constructed from TV twin-lead or open wire ladder line making convenient and transportable antennas for the traveling ham to hang on a curtain in his or her hotel room.

Many "Cookbook" designs exist for the copper tubing version, and most have met with reasonable success when attempting to duplicate them. However; J-poles carry with them a stigma of being tedious to match, with final adjustments being quite critical. This most damaging of the myths associated with J-poles will be dispelled by this presentation.

The reputation of this novel antenna has really taken a beating however, with attempts at constructing them from 300 ohm TV twin-lead. Many are convinced that a sufficiently good match of 1.5:1 or better cannot be achieved, and recommend using 450 ohm ladder line. Even those who have been successful are of the opinion that TV twin-lead designs cannot be easily reproduced.

Nonetheless, many have taken on the challenge of building J-poles from TV twin-lead for a number of excellent and valid reasons:

- TV twin-lead, not much larger than RG-58, is appealing to those of us who travel and need something compact that fits into our overnight bag.
- TV twin-lead and RG-58 slipped snugly inside 1/2 inch PVC
stock makes a durable (even attractive) installation on
the house, car, camper, boat, bicycle, etc.

**Note:**To avert getting mail about this; the size of plumbing stock (much like specifying board sizes in the lumber industry), only roughly represents the actual dimensions of the material. For example, my "GSR 1/2 inch C.T.S.C PVC" has an inside diameter just under half an inch, and an outside diameter just over half an inch. For the record, the size is not an issue in the context of this application. - 5 feet or so of scrap TV twin-lead is cheap and easy to find.
- Virtually every "successful" builder of a J-pole is
delighted with it's performance.
- J-poles look real simple; What is there to lose?

You may be be tempted to ask; "Doesn't 50 ohm coaxial cable create a mismatch if the antenna feedpoint impedance is really 73 ohms?" The answer is: "You bet!". The VSWR in this case would be a nominal 1.46:1 (73 divided by 50). Not to worry however... If we vary the dipole length slightly this impedance changes which in turn modifies the impedance presented to the transmission line until something near a 1:1 VSWR is achieved. We do this routinely by shortening our dipoles slightly to obtain something close to 50 ohms.

If making the antenna shorter than a halfwave decreases the feedpoint impedance, it follows that increasing the length increases the impedance. This trend continues as the length approaches a full wavelength. If the conductor were infinitely thin, the impedance would rise to infinity. For reasonable conductor sizes of .001 wavelengths in diameter, the impedance is something less (e.g. on the order of 3500 ohms for 12 gauge wire at 146 MHz). This behavior is illustrated well in a graph of impedance versus wavelength with respect to conductor size in the "Radiation and Propagation" chapter of The Radio Handbook [1].

Relating this to the J-pole... The center-fed full wavelength dipole can be viewed as a pair of halfwave dipoles fed in phase at their ends. Due to the wire gauge used (i.e. 20 ga.) in the manufacture of TV twin-lead, we might anticipate that our J-pole's end-fed halfwave dipole might exhibit a feedpoint impedance somewhat greater than 3500 ohms but less than infinity.

I have been unsuccessful at identifying quantitative works on the feedpoint impedance of an end-fed radiator other than the feedpoint impedance of a ground mounted vertical [2]. The impedance of a quarterwave vertical appears to be approximately half that of a center-fed halfwave dipole. If we assume this relationship between end fed ground referenced radiators and center fed radiators with twice the dimensions of it end fed cousin to remain constant for all wavelengths; then we might anticipate that the impedance of the end-fed halfwave dipole used in the J-pole will be greater than 1750 ohms (half of 3500 ohms).

I ran a quick ELNEC [3] simulation of an end-fed vertical dipole to assess what feedpoint impedance it predicted. I varied the wire size and height above ground to observe the changes, and the results appeared to vary slightly around 7000 ohms.

I used the dimensions from a 450 ohm ladder line design described by Lew McCoy W1ICP in the July 1994 issue of CQ Magazine [4], and performed a source to load evaluation to get an estimate of the load impedance he was seeing. This worked out to be around 5000 ohms. I assumed a perfect match at 146 MHz (mid-band), and a velocity factor of .88 for the 450 ohm ladder line he used in his design.

I selected 5000 ohms as the target feedpoint impedance for my analysis and design, speculating that this value should be achievable based on my analysis of W1ICP's design. I reasoned that if 5000 ohms isn't exactly right, I can compensate for the error by a slight shortening of the length of the halfwave dipole element (remember the trick used to achieve a match between 50 ohm coax and a 73 ohm dipole?)

I could have selected 7000 ohms, but doing so would put the design at risk if I were not able to achieve the higher value in practice. I made a number of assumptions when evaluating W1ICP's design, and 5000 ohms appears to be a reasonable expectation for the load impedance while allowing some margin of error during the construction process. This value lies near the midpoint of 1750 and 7000 ohms.

More importantly, we have established that the J-pole is an end-fed halfwave dipole with a very high feedpoint impedance. Now the task that remains is one of matching this impedance to our 50 ohm feedline.

There are a number of texts that cover the properties of transmission lines in detail [5], [6], [7], but the behavior relevant to the J-pole is what will be reviewed here.

A short at one end of a quarterwave section of transmission line appears as an open circuit (high impedance) at the opposite end. Therefore, a shorted quarterwave transmission line can be used to match the high feedpoint impedance of an end fed halfwave dipole.

Once this is achieved, the feedline must be attached at an appropriate point along the line to produce a match to the characteristic impedance of the feedline (e.g. 50 ohms for RG-58).

From this point, all else appears to be empirical, and iterative. Once any given design is made to work, it is carefully measured and documented. Others who dare to attempt building one, are forewarned that all dimensions must be precisely duplicated if they wish to achieve success.

I certainly can't argue with success, so I will submit that this approach does indeed work.

We start with certain assumptions or apriori knowledge that we have about the load. All we need to know at this point is the load impedance, (we are using 5000 ohms) and that it is non-reactive. It can be assumed to be non-reactive (i.e. a real impedance) because we are designing it to be a resonant antenna. Resonance is achieved when the available power is maximally radiated from a given antenna. This occurs when current flow is maximum. Current flow in an antenna is maximum when it appears as a pure resistance and the reactive components are cancelled. This occurs periodically at half wavelength intervals along any conductor of arbitrary length whether or not it is intended to be used as a radiator.

Technically speaking; the J-pole is fed at a current minima, which is considered the anti-resonant node. The antenna is nonetheless resonant in the sense that the reactive components cancel. This is analogous to series and parallel resonant circuits where resistance is minimum for series resonance and maximum for parallel resonance. In both cases, the reactive components (which are equal and opposite) cancel.

You may be thinking that the assumptions made could be incorrect and ultimately lead to errors in the final design. I will demonstrate that they can actually be off by a significant margin with little consequence. The J-pole design is remarkably immune to errors in these assumptions, and the tuning procedure I will be offering will readily compensate for measurement errors during fabrication and tolerances on the reproducibility of the measurements. Cloning to exact dimensions is hardly worth the bother.

For step 2, we select a transmission line that we wish to use for matching the antenna to our feedline. Since I favor 300 ohm TV twin-lead, this will be our selection.

Finally, we decide the feedline impedance to which we wish to have the antenna matched. The ever popular RG-58 has a characteristic impedance of 50 ohms, so our goal is to match the antenna to an impedance of 50 +j0 ohms. The +j0 term means that we want the feedline to be operating into a non-reactive load. Expressing a complex impedance in this way (called cartesian coordinates), enables us to work with the real (resistance) and imaginary (inductance and capacitance) components independently.

For the benefit of those not familiar with the Smith Chart, have no fear. I will be using these to "illustrate" how the J-pole is designed. To that end I will attempt to explain the concepts and procedures in clear terms. If you accept on faith that the Smith chart works, the graphics should enable you to visualize and better understand the design process. I have also appended a step by step procedure (and necessary calculations) to arrive at the same results without the aid of a Smith Chart.

Referring to fig 1, the end-fed halfwave dipole is shown as section (a,b) which has a dimension designated as (A). The bottom of this section (b) is the feedpoint for the antenna which we are assuming to have a terminal impedance of 5000 +j0 ohms (i.e. 5000 ohms resistance with zero ohms reactance).

The end of the halfwave dipole is connected to only 1 terminal (b) of the transmission line matching section (identified by dimension B) which may seem awkward and invalid. We can show however that terminal (c) is 180 degrees out of phase with terminal (b), and can therefore be viewed as a virtual (ground) return to complete the antenna termination by the transmission line matching section.

At this point (b,c) in fig 1, we are attempting to terminate a 300 ohm transmission line into 5000 ohms. This represents a mismatch (VSWR) of 16.67 to 1 (5000 divided by 300).

Since 300 ohm transmission line was selected for the matching section, it is prudent for us to use a Smith chart normalized to an impedance of 300 ohms ( fig 2) Dividing both the real and imaginary components of all complex impedances we wish to work with by 300 yields the complex impedance coordinates that are plotted on the normalized Smith chart. Conversely, both the real and imaginary components of any complex coordinate pair read off the normalized impedance Smith chart must be multiplied by 300 to obtain the actual impedance it represents.

We begin by first plotting the two coordinates we know (i.e. the source and load impedances.) Non-reactive impedances are located on the j0 axis which is the horizontal line crossing the center of the chart.

The load (5000 ohms) normalized becomes 16.67. This is plotted and labeled in fig 2 as (16.67+j0).

The end of the feedline where it connects to the J-pole (i.e. (d,e) in fig 1) is where the source is referenced. It is assumed to be (this is the mission of the antenna designer) matched at this point. The business end of the feedline is driven by a transmitter with a 50 ohm source impedance; thus terminating it at both ends in its characteristic impedance. This is a necessary condition for maximum power transfer from source (transmitter) to load (antenna.)

The feedline impedance at this point (the antenna feedpoint) is normalized by dividing 50 +j0 by 300, which becomes (.167+j0). This is also plotted and labeled in fig 2.

With these two points plotted, our mission is to use 300 ohm transmission line in a way that enables us to transform the load impedance (5000 ohms) into an impedance that matches our feedline (50 ohms). A process called navigating around the Smith chart is used to find a path that connects the load to the source. This analogy is meaningful in that all operations follow contour lines to move from point to point. Lines of constant VSWR are described by circles centered on the chart with a radius that represents the VSWR (frequently expressed as reflection coefficient). These contour lines are easily constructed when they are needed (using a compass), and are normally omitted from the chart.

Before we start trying various (and there are many) possible solutions to this problem, we should first recognize that we have the benefit of knowing beforehand what the solution should be.

Returning to fig 1, we see that connected between the load (dipole) and the source (feedline) is a section of 300 ohm transmission line (b,c,d,e). This section of transmission line is a series connection between the source and load. Since the length is physically very short, we can assume it to be lossless (having little DC resistance) and therefore need only consider how the reactance of the load appears as it is observed at different points along the length of the line. Specifically, we are interested in how it appears when it reaches the coaxial feedline (commonly referred to as the "tap"). Once again, this is identified as (d,e) in fig 1.

The contour representing the change that occurs, is a circle centered on the chart (which is why we normalized the chart to 300 ohms) with a radius equal to the VSWR or mismatch at the load. Coincidentally; this also happens to be the normalized impedance value of 16.67. One of the subtle, yet powerful, attributes of normalization. The circle is drawn in fig 2.

Once again in fig 1, we notice another section of 300 ohm transmission line (d,e,f,g) which is connected across the feedline at one end (d,e), and shorted at the opposite end (f,g). We can also show that the length of this section of transmission line is much less than a quarter wavelength. A transmission line is often used in this way to simulate a shunt inductor. It's inductance (and therefore its inductive reactance) increases with increasing length up to the point where it becomes greater than a quarter wavelength. At this point it would appear as a capacitive reactance.

But now we have a slightly different problem.

The Smith chart shown in fig 2 is an impedance plot, and the lines of reactance represent the paths that are followed for series connected reactive components (inductors and capacitors). We now need a way to represent these components when they are connected in shunt with the feedline.

A minor adjustment of the Smith chart will put us on the right track and enable us to evaluate the effects of parallel or shunt connected reactive components. Once this adjustment is made, we can illustrate how simply the J-pole is matched.

Fig 3 is a Smith chart, that represents admittance coordinates. In a simple minded way, this is the shunt equivalent of series impedance. It can get a bit confusing however, since the world of the Smith chart is quite literally turned upside down. The numerical values are changed and become the reciprocal of their impedance counterparts. Even the terminology is changed. The reciprocal of resistance is called conductance, the reciprocal of reactance is called susceptance and the units used are the mho (ohm spelled backward... as if that's supposed to make our lives easier.) Mathematically, this can become quite exhausting, but the Smith chart makes this child's play.

The conversion process is to first rotate the impedance chart half a turn. This now becomes an admittance chart.

Next we again plot the location of the load and source, (unless we can devise a way to rotate the chart without changing the location of the impedance points.) This is normally done with a compass and a ruler. With the compass at the center of the chart, extend the compass to each point, and mark the chart at the exact distance but diametrically opposite on the chart (i.e. at the same distance from the center but 180 degrees away). This has been done correctly if the old point, the new point and the center of the chart form a straight line, and both points are the exact same distance from the center of the chart.

I have done this for our example (Phew!) and the result is shown in fig 3. The new points have been converted to their respective admittance coordinates and are now in normalized units of mhos. Since we are working with a chart normalized to 300 ohms, the admittance chart becomes normalized to 1/300 or 3.33 millimhos (.003 +j0 mhos). I could have told you to turn the magazine upside down and stay with fig 2. That is the process normally used in practice, since there is no real need to use a second chart (or a second magazine for that matter.)

If you're having trouble keeping up with all this, don't worry too much about the numbers and concentrate on the chart manipulations. This makes the job easier.

The circle of constant VSWR is unchanged by the conversion from impedance to admittance coordinates, and this circle is again drawn in fig 3.

The effect of the shorted transmission line section can now be plotted as an inductive susceptance. This inductive susceptance must trace a line of constant conductance equal to the conductance of the source if the antenna is indeed matched at that point. The locus of points that describe the line of constant conductance equal to the conductance of the feedline is shown in fig 3. Notice that this locus of points and the constant VSWR circle intersect (at two points). I will show that a necessary condition for matching the J-pole with two transmission line sections is that these two lines intersect in the -j region.

The contours also intersect in the +j region as well, but we are not concerned with that intersection. For completeness, a shunt open circuited stub (capacitive susceptance) would be required to match from that intersection.

Moving along the transmission line, fig 1 (b,c,d,e), away from the antenna, and toward the feedline, the antenna admittance follows the circle of constant VSWR ( fig 3). This continues in a counter-clockwise direction starting from the load, until it intercepts the line of constant conductance at the point marked (6 -j7.96). This is where the feedline is connected to the J-pole fig 1 (d,e).

The point where the contour lines intercept is capacitive. This capacitance must be cancelled by an inductive susceptance equal in magnitude to the capacitive susceptance at this point in order to achieve a pure resistance (reactance free) match to the feedline.

A shorted length of 300 ohm transmission line
fig 1 (d,e,f,g) is shunted (connected in parallel) across the
feedline fig 1 (d,e). The length is
selected to provide the correct amount of inductive susceptance.
With this accomplished, the network (antenna, series connected
transmission line, and shunt connected shorted transmission line)
is thus matched to the feedline. It's really that simple. Fig 3a is provided for clarification of these
two maneuvers. Y_{Ant} represents the load (antenna)
admittance. Y_{f} represents the feedline admittance.

Fig 4 is a Smith admittance chart now normalized for 600 ohm transmission line with a plotted constant VSWR contour (VSWR = 8.33) for an end-fed halfwave dipole (0.12 mhos normalized), and the locus of constant conductance for 50 ohm feedline (12 mhos normalized). Note that the contours fail to intersect. In this situation, the end-fed halfwave dipole cannot be matched with the simple matching network just described. Popular opinion seems to support the contradictory notion that "the higher impedance the better".

The maximum impedance where the two lines intersect is found by computing the square root of the product of the feedline and antenna feedpoint impedances. In this case the square root of 50 times 5000 or 500 ohms. A quarter wavelength transmission line of 500 ohms would precisely match the halfwave dipole, and a tuning stub of any length (shorted or otherwise) would not be required.

J-poles fabricated from open wire 450 ohm transmission line appear to be favored over 300 ohm twin-lead; so what gives? The answer in part may be due to our assumptions. For the 300 ohm case just presented, I assumed an end-fed halfwave dipole impedance of of 5000 ohms (a reasonable assumption based on W1ICP's design). An analysis based on 450 ohm transmission line demonstrates that this assumption remains valid. It turns out however; that a design based on 450 ohm line is not as forgiving of errors in the assumptions.

For example, if the antenna feedpoint impedance is less than 4000 ohms, the contour pair would not intersect, and matching would not be as straight forward. For comparison, the antenna impedance would need to fall below 1800 ohms to create a condition not easily matched with 300 ohm twin-lead. Therefore the choice of 300 ohms provides a greater margin of error than higher impedances. If, on the other hand; the antenna impedance were significantly greater than 5000 ohms, the margin of error would improve in both cases with the lower impedance case maintaining the greater margin.

Additional research is required to accurately quantify the feedpoint impedance for various lengths and gauges of wire and tubing configured as end-fed radiators. Although it is clear that 300 ohm TV twin-lead is superior to higher impedance lines, my results are not sufficient to draw conclusions on the accuracy of the assumed antenna feedpoint impedance.

By "adjusting the tap", the center conductor of the feedline could attach to the matching section at a slightly different height (higher or lower on the matching section) than the braid (shield). This procedure along with some adjustment of the antenna length would introduce a third transmission line section in the model (by virtue of its non-symmetry). Perhaps, in this way, one can compensate by introducing a small (but significant) shunt resistance to achieve a match. This is lossy, and would result in reduced antenna efficiency.

If this is how 450 ohm open wire ladder line is made to work, the adjustment of the "tap" would be critical indeed.

I suspect that ladder line is favored over twin-lead because of the physical differences. Most J-pole recipes dictate adjustment of the tap to obtain good VSWR (a trial and error process). This is more easily accomplished in the open wire segments of ladder line.

The solid dielectric along the length of TV twin-lead makes it difficult to adjust the point where the feedline is attached. It is also difficult to perform many iterations of finding the precise tap point before it begins to look ugly.

It's extremely important to know the velocity factor of the transmission line used for the matching elements to accurately compute the series and shunt transmission line segment lengths. A J-pole constructed using the computed dimensions will accurately define the correct position of the "tap", making adjustments about this point inappropriate.

The optimum transmission line impedance for matching 5000 ohms to a 50 ohm feedline appears to be about 300 ohms. This can be shown by plotting contours as shown in fig 3 for normalized values of 200, and 450 ohms. A line drawn from the center of the chart to the outside rim and tangent to the contour of constant conductance (equal in magnitude to the transmission line admittance) is tangent at a point very close to the intersection of the two contours. If 200 ohm transmission line were used, the contour lines would intersect more to the left. For 450 ohm transmission line, this would occur more to the right.

The significance of this is demonstrated by varying the diameter of the line of constant VSWR. This produces the effect caused by increasing (larger diameter VSWR circle) or decreasing (smaller diameter VSWR circle) the antenna load impedance assumption.

Errors in assumed antenna feedpoint impedance (either too high or too low), causes little if any change to the computed length of the top (series) 300 ohm twin-lead matching section. A good match is nearly guaranteed with the risk of a slight VSWR degradation caused by the length error of the bottom (shorted) transmission line section.

For the 200 ohm case, the length of the top section becomes more critical. For the 450 ohm case, the length of the lower section becomes more critical. Interestingly, the total length of the overall matching section doesn't change significantly for either case; given that they have equivalent velocity factors. It is likely this attribute allows the iterative adjustment of the "tap" to be successful. The adjustment simply becomes increasingly critical as the transmission line impedance chosen deviates either side of 300 ohms.

The conductors of 300 ohm parallel transmission lines have a 6 to 1 spacing to diameter ratio in air and would seem to be the most optimal spacing for tubing versions of the J-pole. The fact that this isn't observed doesn't impact antenna performance. Smaller ratios reduce the characteristic impedance of the transmission line, and can be arbitrary to some extent since lower impedances can be used to match 5000 ohms to 50 ohms. Closer spacings simplify fabrication with the trade-off being against ease of adjustment. By virtue of its insensitivity to measurement errors, and tolerance to wide variations in antenna feedpoint impedance, 300 ohm transmission lines simply yield designs which are easier to fabricate and tune.

It's your choice whether to adjust the tap or vary the length of the dipole element. Both approaches are easily performed on designs constructed from tubing, with the latter being much simpler to perform on designs fabricated from flexible transmission lines.

As parallel conductors get closer together electrically the fields cancel more effectively and the transmission line radiates less. This can be achieved in either of two ways; 1) lower the frequency in which the transmission line is used (i.e. a given physical spacing is a proportionally smaller fraction of a wavelength with decreasing frequency), or 2) decrease the physical spacing of the parallel conductors to a smaller fraction of a wavelength at the desired operating frequency.

Total field cancellation is in fact only theoretical. For the fields to cancel completely, the parallel conductors would have to occupy precisely the same space.

An obvious benefit of using 300 ohm TV twin-lead versus higher impedance open wire ladder lines (often advertised as superior because of a false perception that it simplifies construction) is that the former radiates less at any given operating frequency. If it radiates less, the feedline itself is less susceptible to RF currents induced by fields surrounding the twin-lead. With an antenna properly matched to the feedline, the chances for unwanted feedline currents are also suppressed. These observations suggest TV twin-lead again appears to be a favorable choice.

Coaxial cable is unbalanced transmission line in that the field surrounding the center conductor is contained by the shielding properties of the outer braid. It is a single wire transmission line that utilizes the inside surface of the shield as the return signal path. The effectiveness of the shield determines the loss properties of the cable, with poor quality varieties exhibiting severe radiation losses.

When interfacing balanced and unbalanced transmission lines, there is always a danger that something will go awry. If the antenna is not matched perfectly, antenna currents will flow along the outside surface of the coax cable's shield producing "hot spots" along its length. These act as parasitic (power stealing) radiators that generally serve no useful purpose. They can sometimes degrade or enhance the antennas performance through destructive or constructive interference. In general, the energy is absorbed or otherwise dissipated. Whether routed through conduit, behind walls, under carpets etc.; the coax is generally not well positioned to be effective or beneficial as a parasitic radiator.

To cancel these ill effects, a balun (balanced to unbalanced transformer) is often employed. Alternatively; forming a small coil in the coaxial feedline at the point where it connects to the antenna, serves to electrically isolate (choke) the feedline's outer conductor from reflected energy that would otherwise propagate along the feedline and radiate.

For the purist, a J-pole would most certainly employ a balun. This is generally perceived as good engineering practice. However; if a good match is achieved, feedline currents can be kept to a minimum. Small currents induced on the feedline are sacrificed as a mismatch loss with little if any radiation pattern distortion. Both effects are negligible. A 1.5:1 VSWR for example produces a mismatch loss that reduces the effective radiated power by less than 0.2 dB (only about four percent).

Even a well designed balun introduces loss and adds complexity to the design. Good performance reports and a general sense of satisfaction from J-pole users likely contribute to the reason why baluns are rarely used.

While on this subject; I did experiment with the feedpoint to determine whether it made a difference if the center conductor were connected to the short leg or long leg of the J-pole. I anticipated that this wouldn't matter. I observed that the VSWR changed slightly, but I could net it back with a minor adjustment to the length of the halfwave dipole element. I concluded that this "fine tuning" is appropriately attributable to my inability to connect the stub at exactly the same points when reversing the connections.

A noteworthy observation however was an apparent change in feedline current. This condition (observed as VSWR fluctuations while wandering about the shack in the vicinity of the feedline) changed perceptibly with the center conductor connected to the short leg, fig 1 (d). The change was only slight when the center conductor was connected to the long leg, fig 1 (e). From that observation, I recommend connecting the coaxial center conductor to the long leg with the braid connected to the short leg. In that configuration, the J-pole appears to exhibit the best behavior with respect to unwanted feedline currents.

The reflected current on the short (unconnected) leg is controlled solely by the accuracy of the matching sections construction. The reflected current on the leg connected to the dipole element is a function of any residual mismatch to the antenna. Of course if a balun were used, the antenna feedpoint connections would be on the balanced side of the transformer. In that case, the way in which the J-pole is connected would make no difference.

Much of the literature describing J-pole construction from tubing (e.g. copper plumbing stock) recommends earth grounding at this point for roof and tower mounted applications. The J-pole doubles as a lighting rod in those applications, and serves as a low impedance shunt of static energy at levels considerably below strike potential during transient electrical storms. This results in a cone of protection with the tip of the J-pole as the apex of the cone. It is extremely important to note that a very low impedance connection to an earth ground reference is critical. Avoid making connections to cold water pipes inside the house, and connections of dissimilar metals (e.g. copper and aluminum) or you may be inviting trouble.

The shorted matching stub also performs as a low frequency bypass (or short circuit) across the antenna terminals of connected radio equipment. Protection from static discharges via the antenna port is provided if you don't practice disconnecting your antennas when your station is not in use.

By "grounding" the J-pole shorting bar, we are in effect attempting to place it at the same electrical potential as the braid side of the feedline coax. Although both points are at zero potential (voltage), the currents are out of phase with each other by 90 degrees. For two points to be electrically equivalent, voltage and current must be equal in phase as well as in amplitude.

I will use fig 1 to explain how this becomes a problem.

If both, the coaxial braid (d), and the shorting bar (f,g), are at zero potential; ground current is inhibited from flowing in the J-pole conductor between points (d) and (g). Consequently, the shorted stub at the base of the J-pole (d,e,f,g) is unable to behave as a balanced transmission line. Current flowing on the side connected to the center conductor (e,f) attempts to induce an equal and opposite current component on the side connected to the shield (g,d), but needs to create a potential difference between the points (g) and (d) to do so. This requirement conflicts with keeping them at the same potential, and the transmission lines balance is destroyed.

Because the Conductors that make up the shorted stub (e,f), and (g,d) are in parallel and in proximity to one another; and because they provide an RF current return path to the feedline at (d), current flowing in (e,f) finds it has two parallel return paths to earth ground. Hence a ground loop is created, with RF current induced in the earth ground reference return wire, as well as the outside of the feedline coaxial cable shield.

Both of these conditions are undesirable, and make the performance of the J-pole unpredictable. Both are easily corrected by introducing a balun where the feedline connects to the antenna. Without a balun, attempting to get a stable VSWR measurement much less a good match will become quite frustrating.

J-poles constructed from plumbing hardware are frequently shown with the feedline routed through the center of the tubing to isolate or shield it from the radiating portion of the antenna. This technique may prove effective at keeping RF current from conducting along the outside of the feedline shield, but it is not a balun. Electrically connecting the shorting bar to an earth ground reference attempts to force two points on the J-pole to the same electrical potential, and the two conditions just described will result.

If grounding to an earth ground reference at the antenna is not a requirement, the J-pole will work well without a balun, and routing the feedline coax through the center of the tubing may prove beneficial at reducing feedline currents, and makes a clean installation.

The velocity factor is of critical importance when using transmission lines as matching elements in order to accurately determine the physical length required to obtain desired electrical characteristics as a circuit element (i.e. inductance, capacitance or phase rotation).

The velocity factor I used in the analysis of W1ICP's design was a rough estimate with the assumption that it was between .82 (the published velocity factor for 300 ohm twin-lead), and 1.0 (free space).

The accuracy with which the velocity factor is known is perhaps the sole nemesis of most J-pole designs. Strangely enough, this appears to be the design parameter most often ignored. Due to the relatively short wavelengths at VHF and UHF frequencies, velocity factor is easily measured and I have appended a procedure for performing this task. The antenna tuning procedure can compensate for slight velocity factor errors; but to ensure predictable results, this parameter should be accurately known.

First; this manufacturer offers a moderately large selection of 300 ohm TV twin-lead products that vary in dielectric properties as well as physical construction. Physical variations range between flat solid construction (generally the lowest cost varieties) to solid jacketed foam designed for lower transmission losses. Varieties also vary in the construction of the region between the parallel conductors.

Although the dielectric constant of a given insulating materials "recipe" may be of some nominal value (.66 or .82 for solid versus foam varieties respectively), the density of the material as well as the various combinations of solid and foam dielectric used in the manufacturing process of each variety all play a role in the resultant velocity factor.

Perhaps the most significant result of my investigation was the discovery that velocity factor is neither known, nor controlled per se' in any of that manufacturers 300 ohm twin-lead products. One of the design engineers shared the results of a velocity factory measurement collected several years back in response to a customer query. He also told me that their manufacturing processes are focused on controlling the impedance and loss properties alone. He recommended that I perform these measurements on my own.

As a consequence of this discovery, one would be well advised to measure the velocity factor of 300 ohm television twin-lead targeted for use in any J-pole design.

Once again in contradiction to the belief that the higher the impedance of the transmission line used for J-pole matching the better; quite the opposite is true. The sensitivity to errors in velocity factor decreases with decreasing transmission line impedance. The proof of this can be seen by plotting three test cases on a Smith chart for impedances of 200, 300, and 450 ohms and introducing plus and/or minus 1 percent changes in velocity factor for each case.

This may be the reason that bygone era J-pole designs as well as many of the current plumbing hardware designs are closer to 200 ohms. At the price of a slight increase in sensitivity to errors in antenna feedpoint impedance (which can be varied by adjustments to its length), sensitivity to velocity factor is reduced. This trade-off appears to be reasonable.

300 ohms still remains the optimal impedance choice. Velocity factor of any given transmission line can be easily measured to a high degree of accuracy; thus reducing this error source to near zero.

Awareness of the importance of velocity factor, the use of a structured and reliable antenna tuning procedure, and a balun (if earth ground referencing is necessary) are all that is needed to guarantee reliable and repeatable success.

The velocity factor for a wide assortment of transmission lines can be found in most of the ARRL publications. Do not assume your J-pole design efforts will lead to success if you use the published numbers. Measure this on your own at any convenient frequency, but making the measurement at VHF or UHF will minimize the amount of material sacrificed for the measurement. The results vary only slightly with frequency, and are attributable to the ratio of line spacing with respect to wavelength.

A small but measurable increase in velocity factor may be observed at HF where conductor separation is a smaller fractional wavelength, and the influence of dielectric material between them is not as strong. The twin lead used in my experiments exhibited a velocity factor of 76.5 percent at 146 MHz, and 76.9 percent at 28 MHz.

I was running low on my supply of twin-lead anyway, so I decided to buy a new batch and determine how much velocity factor varies between types.

First; I discovered the local Radio Shack carried twin-lead under the exact part number of that which I purchased in Maryland some 6 or more years earlier. This meant I would be able to assess the variations from batch to batch.

Second; the measured velocity factor was exactly equal to that which I measured on my old batch to within plus or minus 0.1 percent; the limits of my ability to measure this parameter repeatably.

Recalling that the vendor I consulted informed me that only the impedance and loss parameters are controlled on their products, I was quite surprised by this "coincidence". Velocity factor is hardly a critical parameter for consumer television antenna installations, so it's unlikely Radio Shack's supplier makes any attempt at controlling its bounds.

A quick review of the transmission line equations reveals that the phase constant of any given line is a direct function of velocity factor which is the phase constant modified by the dielectric properties of the medium. The phase constant sets the conductor spacing to diameter ratio which itself must be held uniform and constant along the length of the transmission line in order to maintain the constant L/C ratio that establishes the characteristic impedance of the line.

The inference from this observation is that a tightly controlled characteristic impedance (independent of loss) must by necessity maintain some level of control over velocity factor. This seems plausible since conductor diameter and spacing is more easily held constant, and not likely varied by some criteria to establish uniform characteristics during manufacturing.

This discovery may explain why localized cookbook designs seem to gain popularity as being easy to clone, while published versions receive mixed reviews. The local clubs are using TV twin-lead obtained from a common (probably the same) source, and cloaning success is nearly guaranteed. This control is lost when the design surfaces elsewhere, and an otherwise reliable recipe gets a bad rap.

A consequence of this discovery is that those who wish to procure TV twin-lead from Radio Shack and embark on building a J-pole, should be able to do so with reasonable confidence that the velocity factor of "Super Low-Loss Foam TV Twin-Lead Cable" (Radio Shack Cat. No. 15-1174) is 0.769. The risk of my being wrong on this prediction is that you will need to measure the velocity factor of your batch and perform the calculations based on the value you obtain from your measurements.

I would like to hear from anybody who attempts to evaluate the same material and obtains more than half a percent deviation from my measurements. If you are using something other than "Cat. No. 15-1174", you should anticipate different results.

A QSL from those whose independent findings confirm or contradict those reported here will be warmly received.

For completeness, it seems reasonable to assume that velocity factor for a given brand and style of twin-lead needs to be determined only once. As long as the brand or style is not changed, the number should remain valid. Since the velocity factor is, for the most part, independent of frequency, the construction of J-poles on other bands can be scaled with good success. Those attempting to clone the G5RV or other Zepp derivative will benefit from this knowledge as well; since velocity factor is most conveniently measured at VHF or UHF, and verified at HF to minimize waste.

A small but measurable increase in velocity factor may be observed at HF where conductor separation is a smaller fractional wavelength, and the influence of dielectric material between them is reduced. The twin lead used in my experiments exhibited a velocity factor of 76.5 percent at 146 MHz, and 76.9 percent at 28 MHz.

I have done a few experiments using 3500 ohms as my estimate of feedpoint impedance on my 2 meter j-poles upon completing my analysis, and found this actually seemed easier for me to tune, so estimating on the low side for this parameter may not be a bad recommendation.

For example; I might start with something like 2000 ohms, and perform the calculations in 500 ohm increments up to 5000 ohms. This would give me pruning information so that if I were unable to tune the antenna with the dimensions established for 2000 ohms, I would prune back on the stub to the dimensions calculated for 2500 ohms, then 3000 ohms etc. Of course this would require that I tune the dipole over a broad range so that I was sure that I passed through it's resonant point (or anti-resonant point in this case) before pruning back on the stub each time.

This is a highly iterative process, and can be exhausting, but unless you have a good feel for the feedpoint impedance of your antenna some amount of trial and error may be required. I encourage you to publish any information you derive from this exercise, as it can save the rest of us from repeating the process.

This may all sound frustrating, but in reality is quite easy to manage. As for the stub length, all that is required is to determine the new velocity factor for the twin-lead when it is installed in the PVC tubing (or any dielectric for that matter) that you wish to use, then proceed with the design as in the open air case using the new velocity factor.

I ignored the contribution of dielectric loading when I first packaged one of my twin-lead J-poles, and observed no ill side affects. Antenna resonance dropped about 4 MHz from where I initially tuned it, and a slight shortening of the halfwave dipole element brought it back to 146 MHz. No special effort was required to install the antenna in the PVC tubing, no recalculating of lengths, no adjustment of the "tap", and no perceptible change in performance. This testimony to the J-poles tolerance to errors in fabrication illustrates the ease in which the design can be "cloned".

We now have a question of historical significance; the "chicken and egg" dilemma. Is the J-pole a fixed tuned end-fed vertically polarized Zepp; or is the end-fed Zepp a tunable horizontally polarized J-pole? The obscure way in which the J-pole has evolved suggests it followed the Zepp. In either case, the design and tuning procedures are identical. What's more; their designer(s) had a keen grasp of efficient antenna design criteria long before radio became a commodity, and long before Smith Charts were available to simplify such tasks.

An antenna can be constructed using 450 to 500 ohm ladder line, and neither the shorted stub nor a tuner would be required to obtain a match. This would be the minimum or root form of the Zepp. The ladder line is exactly one quarter of an electrical wavelength in this case, and unless operation is only desired over a narrow bandwidth, a balun would be recommended. The antenna tuner permits tuning over a wide range (often several bands), and is why that configuration of the Zepp is most common. Significant feedline radiation is expected when operating on frequencies where the "random wire" is not an exact multiple of half a wavelength.

In general, end-fed Zepps unlike center-fed halfwave dipoles are suitable for multiband operation on even as well as odd frequency multiples. Care must be exercised in the selection of feedline length however, to avoid lengths that are exact halfwave multiples at one or more of the desired operating frequencies. Such a condition would be difficult to tune, with the impedance presented to the tuner approaching several thousand ohms.

The physical attributes of end-fed designs also provide more installation versatility over their center-fed counterparts. For example; it can be fed and anchored at the apex of a roof, while only a single pole, tree, etc. is required at the opposite end. Compare this with a typical center-fed dipole installation.

Careful selection of feedline length might enable an 80 meter longwire (halfwave on 160 meters) to operate satisfactorily on all bands between 160 and 10 meters including the WARC bands. Not having performed a detailed analysis of such a design however; I offer no promise of performance. Care must be given to trade-offs between antenna and feedline lengths, tuner adjustment range, feedline radiation characteristics, and acceptable performance compromises between the respective bands of interests. I have done none of these, but see no glaring reason why attempting this would not prove useful. The information and analysis procedure presented here should provide a good start on such a task.

The analysis and design of halfwave J-poles and end-fed Zepps is identical. The pursuit of center-fed or multiband versions of the Zepp designs should prove to be a rewarding experience.

You can most certainly expect superior performance from any J-pole over a rubber duckie, and because it is a halfwave vertical radiator (end-fed in this case) it's performance should be exactly equal to that of a properly designed, matched, and tuned halfwave vertical dipole regardless of how it is fed. In addition, halfwave antennas don't require a ground plane or counterpoise as with quarterwave designs. As a result, radiation efficiency, and elevation angle are more easily controlled. The bottom line is that J-poles are end-fed halfwave dipoles of sound electrical design.

Rubberized and stubby "duckies", quarterwave ground planes, colinears, Yagis, LP's, et al. are separate and unique antenna designs addressing specific system requirements; that if properly designed, matched, and tuned, will meet the objectives of their respective applications. The right antenna is the one that fulfills your performance requirements most favorably.

The Ferrite Loop Antenna is wimpy if you wish to compare its performance to quarterwave or halfwave dipoles for example. Most of us are delighted with the Ferrite Loop for our broadcast band AM portables however. When you consider walking around with a 750 foot J-pole on your receiver, the sacrifice in performance becomes a reasonable compromise.

Indeed; the "ducks" are poor performers when compared to halfwave antenna systems. However; when your concerns are small size, weight, eye safety, and portability, and when you lack an available counterpoise (or ground plane) of any significance; your concern for "optimal" performance may fall considerably lower on your prioritized list of "absolutely must have" features.

In a nutshell, the J-pole is an apple, and the rubber duckie an orange. Any comparison of the two is meaningless, and would only serve to cast an unfavorable shadow on a truly elegant solution to a tough set of real world design criteria. It's popularity speaks for itself.

- is a end-fed halfwave dipole and performs as all
halfwave dipoles.
- is a fixed tuned vertically polarized variation
of the end-fed Zepp.
- uses balanced transmission line elements to obtain a match.
- can be fed by coaxial cable without a balun in many
applications.
- has a matching stub short at virtual ground potential,
but only when fed with a balun.
- short circuits low frequency high energy transients
across the the equipment antenna terminals.
- is not unreasonably sensitive to dimensional tolerances.
- does not have a critically located feedpoint tap.
- is easy to build, tune and replicate.

In addition, the following was revealed:

- Tuning a J-pole is no different than tuning a halfwave
dipole.
- 300 ohms is the optimal impedance transmission line for
J-pole matching networks.
- 500 ohms is the maximum transmission line impedance
suitable for matching end-fed halfwave dipoles.
- 300 ohm TV twin-lead minimizes the RF current induced
onto the J-pole's feedline due to the close spacing of
the parallel conductors, and thus performs well without
a balun.
- Induced feedline currents are further minimized by
connecting the feedline center conductor to the long
side of the "J", and the shield to the short side.
- The J-pole's matching "network" is electrically longer
than a quarter wavelength except for the singular case
when using 500 ohm transmission line and the shorted
stub is omitted. The series transmission line matching
section is exactly a quarter wavelength in that case.
- A balun must be used at the feedpoint of the J-pole if
the "shorting bar" is connected to an earth ground
reference. This avoids introducing ground loop currents
and maintains a balanced feed.
- The velocity factor is the most critical transmission
line parameter to consider in the design of the J-pole
matching elements. Knowledge of this parameter is
required (and easily defined) to a high degree of
accuracy.
- Published values of velocity factor are not reliable for
all brands and varieties of parallel transmission lines
for any given impedance value.
- The velocity factor appears to be held to within a tight
tolerance for any given brand and style of parallel
transmission line.
- The velocity factor of the transmission line as well as
that of the dipole element of the J-pole is reduced when
installed in PVC or other material having a dielectric
constant other than that of air.
- End-fed halfwave dipoles (Zepps), when tuned with an
antenna tuner, are superior to center-fed halfwave
dipoles when operation on even and odd frequency
multiples is desired; whereas center-fed halfwave
dipoles perform well on odd multiples only.
- Rubber duckies are an excellent antenna design when
size, weight, eye safety, portability and convenience
are the critical design criteria.
- J-poles offer a significant performance improvement over rubber duckies at the cost of size, weight, portability, and convenience.

First to my near and dear friend and mentor Dick Lodwig (W2KK) for his unwavering and limitless encouragement; for the countless times he attempted to teach me the utility of the Smith chart, and for a unique and special affinity toward Root Beer, to name but two of life's important lessons.

Next; sincere thanks to my new friend and work colleague Chet Burroughs (KE4QNG) for allowing me to serve as his "Elmer", and for asking the questions that led to my investigation into the theory behind J-poles. His energy and enthusiasm has been inspirational to me. He has enabled me to rediscover that engineering is indeed a fun and interesting occupation.

Finally; my deepest gratitude must go to my most cherished and loving partner and wife, Marie. She not only tolerated the many evenings and weekends (often well into the early morning hours) spent writing, rewriting, testing, and confirming the results presented here; but she also graciously accepted my negligence in keeping up with my chores. Her many sacrifices and extra burden over the last several months have been shouldered without reward. She shall always remain "The Wind Beneath My Wings".

- Radio Handbook, Twenty-Third Edition, Howard W. Sams & Company, 1989, pg. 20-7.
- Radio Handbook, Twenty-Third Edition, Howard W. Sams & Company, 1989, fig 18, pg. 20-11.
- ELNEC, version 2.24N, Copyright 1991, Roy Lewallen, W7EL
- CQ, The Radio Amateur's Journal, July 1994, Vol. 50, No. 7, pg. 50-51.
- The ARRL Antenna Book, Seventeenth Edition, The American Radio Relay League, 1994, Chapter 24.
- Radio Handbook, Twenty-Third Edition, Howard W. Sams & Company, 1989, Chapter 21.
- Antenna Impedance Matching, First Edition, Wilford N. Caron, The American Radio Relay League, 1994,
- The ARRL Antenna Book, Seventeenth Edition, The American Chapters 1 & 2.
- Antenna Impedance Matching, First Edition, Wilford N Caron, The American Radio Relay League, 1994, Chapter 28.

A feedpoint impedance of 5000 ohms was used as an estimate for the impedance of an end-fed halfwave dipole element for my analysis and experiments. The justification for this assumption is based on results of an analysis of a successfully matched (W1ICP) J-pole design. This value is likely an upper limit to use, and this value will be high if large conductors such as copper tubing are used.

A velocity factor of .769 for "Super Low-Loss Foam TV Twin-Lead Cable" (Radio Shack Cat. No. 15-1174) was used in my experiments. This parameter is quite critical, and should be measured if it is not known.

The impedance and admittance calculations are simplified whenever possible by ignoring the complex component when it is zero (i.e. +/- j0).

- First Normalize the Antenna Impedance to the impedance
of the transmission line used for the matching network.
**Equation A1:**ZP = ZA/Z0 ZP = the antenna impedance ZA normalized to the impedance Z0 of the transmission line used for the matching network. - Calculate the Antenna reflection coefficient (rho).
This describes the constant VSWR circle on the Smith chart. The
value is dimensionless, and represents the ratio of power
reflected from the load and returned to the source.
**Equation A2:**RHO = (ZP-1)/(ZP+1) RHO = the antenna reflection coefficient. - Convert the feedline impedance to normalized admittance.
(

**Note:**admittance is the reciprocal of Impedance.)**Equation A3**YF = Z0/ZF YF = The feedline admittance 1/ZF normalized to the admittance 1/Z0 of the transmission line used for the matching network. ZF = The characteristic impedance of the coaxial feedline Z0 = The characteristic impedance of the transmission line used for the matching network, to which all calculations are normalized.The feedline admittance can now be expressed as YF = G +j0 mhos in its complex form.

- Calculate the normalized capacitive susceptance at the
point where the circle of constant antenna reflection coefficient
(constant VSWR calculated in step 2) intercepts the line of
constant conductance equal to the feedline admittance calculated
in step 3.
**Equation A4**B = SQR((RHO*RHO*(YF+1)*(YF+1)-(YF-1)*(YF-1))/(1-RHO*RHO)) B = the capacitive susceptance that appears when looking at the feedline end of the series transmission line before connecting the shorted stub element.The equation yields two roots that differ only in sign. The negative root represents the capacitive susceptance, that is to be canceled by the shorted stub.

The conductance (G) calculated in step 3, along with this susceptance (B), defines the admittance (Y) which is plotted on a normalized admittance chart as:

Y = YF -jB mhos (G -jB) YF = the real component of the admittance (Conductance) B = the imaginary component of the admittance (Susceptance) preceded by a -j to indicate a negative or capacitive susceptance.

- Calculate the inductive reactance of the shorted stub
required to cancel the susceptance from step 4.
**Equation A5**X2 = -1/B (-1/B) X2 = the normalized (inductive) reactance of the shorted stub section.**Note:**this is the negative of the capacitive reactance we wish to cancel, and the capacitive reactance is the reciprocal of capaqcitive susceptance. - Calculate the electrical length (L2) of the shorted
transmission line (stub).
**Equation A6**L2 = ATN(X2)*(180/3.141592818#) L2 = The length of the shunt (bottom) transmission line matching section in degrees. - Calculate the impedance (Z) at the intersection of the
antenna reflection coefficient (rho), and the line of conductance
equal to the feedline admittance (YF). This is the
reciprocal of the admittance (Y) from step 4, and requires taking
the reciprocal of a complex number. The steps are shown here to
demonstrate how this operation is performed mathematically.
**Equation A7**R = YF/(YF*YF+B*B) X1 = B/(YF*YF+B*B) R = The real part of the impedance (Z = R+jX) at the intersection of the rho and G contours. X1 = The imaginary part of the impedance at the intersection of the rho and G contours. This is the inductive reactance for which the shorted stub must be designed. - Calculate the electrical length of the top transmission
line section. This is the length of transmission line required
to rotate the antenna impedance (along the line of constant VSWR)
to the coordinates of Y.
**Equation A8**L1 = 90-(ATN(X1)*(180/3.141592818)) L1 = The length of the series (top) transmission line matching section in degrees.To this point, the frequency or band of operation for which the antenna is being designed has not been considered. This means that you can build the J-pole (or Zepp) for any band you wish. By saving the calculations made thusfar, you can simply scale the results to the frequency of your choice.

- Calculate the physical length of each section of the
J-pole to complete the design. The velocity factor must be used
when calculating the physical length of the transmission line
sections (B and C in fig 1). The dimensions have been normalized
to MHz, inches, and degrees in the equation.
**Equation A9 - A in fig. 1**DIPOLE = 5606/F (Inches) F = Design center frequency in MHz.**Note:**The constant 5606 is 95 percent of the speed of light in inches for half a wavelength at 1 MHz. This is a common and widely accepted practice for terestrial based (i.e. not free space) antenna designs. The velocity factor of balanced transmissiion line is not considered here, as there are no parallel and opposing fields to be influenced.**Equation A9 - B in fig. 1**SERIES = 32.78*V*(L1/F) (Inches) L1 = The computed electrical length in degrees of the series transmission line matching section V = The velocity factor of the transmission line used for performing the match. F = Design center frequency in MHz.**Note:**The constant 32.78 is the speed of light in inches/degree/MHz.**Equation A9 - C in fig. 1**SHUNT = 32.78*V*(L2/F) (Inches) L2 = The computed electrical length in degrees of the shunt transmission line matching section - Strip the insulation from one end of the transmission line to be used for the J-pole at a length slightly greater than its width. Twist the bare wire ends together snugly and generously solder the connection. This is the short circuited end (bottom) of the J-pole.
- Measure from the short, the distance C calculated in step 9. Carefully remove only enough insulation on the edges of each side of the transmission line to bare a 1/16 inch length or so of the conductors. Take care not to nick the wires. Generously tin these exposed areas of the transmission line conductors with solder. This is where the 50 ohm coax feedline will be attached.
- Measure once again from the short circuited end (bottom) of the J-pole a distance that is the sum of distances B and C calculated in step 9. Carefully cut through the conductor (on one side only) of the transmission line at this point, and once again a quarter inch or so farther. Remove the conductor material from the quarter inch long section of transmission line that was just severed. This is the top of the short (left) side of the "J". Feel free to remove the entire length of wire above the cut, but it's not required.
- Again measure from the bottom a distance that is the sum of all three distances (A, B, and C) calculated in step 9. Cut the antenna off at this length to complete the J-pole.
- Carefully separate the shield and center conductor at one end of the feedline coax cable, snugly twist the shield into a pigtail, and tin with solder. The lead lengths should not exceed the width of the J-pole transmission line. This will allow for a stable and reliable connection. A 10 to 15 foot length of RG-58 makes makes a convenient and portable assembly. Rooftop and tower mounted J-poles will require longer runs. Keep the feedline as short as possible at VHF and UHF to minimize losses. Where maximum height is desirable, use a low loss coaxial cable for the feedline.
- Solder the shield of the coaxial feedline to the feedpoint location exposed and tinned in step 11 that is on the short (left) side of the J-pole.
- Finally, solder the center conductor of the feedline to the remaining feedpoint location, and trim excess leads that may be exposed at the connections to keep this area free from parasitics.
- Inspect all connections for sound electrical and mechanical integrity. Using vinyl electrical tape or shrink tubing; secure the coax to the twin-lead from just above the feedpoint to just below the shorted matching stub.
- Affix an RF connector to the remaining end of the coaxial cable to complete the fabrication.
- Proceed with tuning the J-pole as with any other resonant wire antenna. Measure the VSWR and shorten the length of the dipole element in small increments until a near 1 to 1 match is achieved. Adjusting the length of the dipole should be performed by first folding back the dipole element against itself at the top to avoid accidentally trimming the antenna too short. Once the correct length has been determined, the excess length can be trimmed away.

********************************************************************* Click here for the Basic program that performs the J-pole design calculations described in Appendix A. *********************************************************************Successful results, and optimal performance of any J-pole antenna design can be quickly and effortlessly obtained using the procedure described here. This procedure applies to any single element radiator antenna system, and those familiar with building and tuning dipoles, Vees, etc. will recognize the procedure immediately. ## APPENDIX B - TUNING WIRE ANTENNAS

## N3GO

The procedure ensures that the adjustments efficiently and reliably converge on an optimal match, and ensures that the antenna is not inadvertently cut too short. As a consequence, it will sometimes require several iterations for new antenna designs. Once a design has been completed, clones of that design can be cut only slightly longer than the original (to allow for tolerance errors), and the procedure will converge after only one or two iterations.

The procedure works equally well for fractional or multiple wavelength antennas as well (short verticals, 5/8 wave groundplanes, longwires, etc.), and is in no way limited only to J-poles.

RX noise bridges are available for a very reasonable price and work well on 10 meters and below. These are excellent tools for measuring an antennas impedance characteristics while not requiring transmissions to facilitate the measurements. These devices permit performance measurements at frequencies outside the amateur bands, and result in a faster convergence on the final solution. They are preferred over VSWR bridges for making antenna measurements below 50 MHz.

Alternatively, and at frequencies above about 50 MHz, reasonably priced test equipment is typically found in the form of a VSWR bridge or directional wattmeter. The transmitter must be operated in order to perform measurements with this equipment.

When making VSWR measurements be sure to restrict the transmitting limits to those for which you are licensed. Always identify your transmissions during testing using an operating mode authorized for the frequency in use. I prefer CW, since it not only facilitates making the measurements themselves, but also because CW is permitted when other modes are not.

Finally, be respectful to other users of the spectrum while you are performing these procedures. Listen first to avoid interfering with communications in progress. Use only enough power to enable you to obtain a reliable indication of VSWR.

## GETTING IN TUNE

- Measure and record the VSWR at several frequencies (3 to 5) evenly spaced across the band making sure to include the highest and lowest operating frequencies desired.
- Select the frequency where the VSWR is lowest (f
_{1}) This is where the antenna is closest to resonance.- Calculate the amount the antenna needs to be shortened (delta L) in order to make it resonant at the desired operating frequency (f
_{2}).Note:If the VSWR is lowest at the lowest frequency and increases with every increase in frequency, the antenna is too long (i.e. it is resonant at some unknown frequency below that which is desired) and needs to be shortened. The first set of measurements should always produce this result, or the antenna has been made too short. A negative value for delta L indicates the antenna needs to be lengthened by the amount calculated.(Equation B1):DL=(1-F1/F2)*(983.3/F2) DL = Length reduction (in feet) required to make the antenna resonant closer to the desired center operating frequency. (A negative number indicates a length increase is required) F1 = Frequency (In MHz) where VSWR is minimum F2 = Desired Operating Frequency (In MHz)- Shorten the antenna by the amount calculated in step 3 and repeat steps 1 through 3 until you observe that the VSWR is higher at the the end points (i.e. lowest and highest frequencies), and lower at one or more frequencies in the middle. This verifies that the antenna is now resonant at some frequency within the band.
Notes:I. A common practice is to fold back the antenna against itself by the amount calculated. Once it has been determined that the antenna has not been shortened excessively, it is then cut to this length prior to the next increment. A telescoping dipole element is recommended for J-poles constructed from tubing or plumbing stock.

II. For end-fed antennas like the J-pole, the antenna is shortened the amount calculated by folding back (or cutting) the end opposite that which is matched to the transmission line (i.e. the top). For designs like center-fed halfwave dipoles and inverted vees, the antenna is shortened half the amount calculated at each of the two dipole ends. This technique is used to maintain symmetry of the dipole about its feedpoint.

- Measure and record the VSWR at several frequencies near where it was found to be lowest within the band of interest, and determine the precise frequency where it is minimum. This is the frequency where the antenna is resonant.
- Repeat steps 2 through 5 until you are satisfied that the antenna is resonant sufficiently close to the desired operating frequency.
- Measure and record the VSWR at 3 frequencies (lowest, middle, and highest) in the desired operating range to verify that it is acceptable across the desired operating range.
- Preserve the integrity of the final dipole length by cutting off and discarding that portion of the dipole that was folded back against itself during tuning. If you wish to leave the excess material intact, secure the dimensional integrity with vinyl electrical tape.
*********************************************************************

The BASIC program included here performs the calculations in this appendix and was not included in the original manuscript.********************************************************************* ********************************************************************* Click here for the Basic program that performs the antenna tuning calculations described in Appendix B. *********************************************************************Normally, published velocity factors for typical transmission lines are nominal and errors in this parameter do not adversely influence performance of a given transmission line in most applications. However; when the accuracy of length measurements to precise fractions of a wavelength (as in the design of a J-pole) is required, it may be necessary to measure it precisely to achieve acceptable results. ## APPENDIX C - MEASURING VELOCITY FACTOR

## N3GO

Velocity factor can be anything between .6 and .95, depending on the transmission line used and doesn't appear to vary between batches from the same manufacturer for the same part number. Very low quality transmission lines may not exhibit this stability however, and should be verified if in doubt.

The following procedure is offered as a means for determining the velocity factor of your transmission line using only a dummy load, a VSWR indicator, and your transmitter. Obviously; if you own an antenna analyzer capable of performing this measurement directly, the procedure is greatly simplified, and this appendix can be ignored.

## THE SETUP

Start with a section of copper clad printed circuit board material approximately 1 inch square or slightly larger to accommodate the width of your transmission line and solder a pair of RF connectors at opposite ends. This provides a physically and electrically stable test fixture for mounting lengths of transmission line to be measured.Newcomers who wish to attempt measuring the velocity factor of their transmission line should recruit the assistance of an experienced Elmer to ensure the test fixture used is reasonably free of parasitics.

I used SMA series subminiature connectors with adapters to BNC, but only a purest would come up with an argument to suggest this is a requirement. However; care must be taken to keep leads short and connections electrically and physically stable. The use of a carefully designed test fixture ensures this is achieved.

Be sure to pay careful attention to lead lengths, line to ground spacing, and good soldering practices. If you don't have confidence in your skill or that of your Elmer, use the published velocity factor for the transmission line nearest in construction and material to compare your results. If you fail to obtain a measurement to within a few percent of the published data, you should question the quality of your measurements, and seek a second opinion. Of course the result should always yield a number less than unity. Quite simply, the velocity factor is a number that represents the ratio of a physical length of transmission line to the propagation distance in free space that exhibits an equivalent electrical delay (360 degrees per wavelength.)

A shorted length of transmission line equal in electrical degrees to an odd multiple of a quarter wavelength exhibits an open circuit impedance at its input. At even multiples however, the circuit once again appears as a short circuit. Thus, a shorted half wavelength stub will present a zero impedance at it's open end. This repeating short circuit property is used to determine velocity factor.

## MAKING THE MEASUREMENTS

- Connect an SWR bridge between a 50 ohm termination (dummy load), and a transmitter (HT) on the other. Measure the VSWR at the frequency where the velocity factor measurements are desired. Using a barrel connector in place of the test fixture in fig 5 will minimize measurement errors.
Note:The measurements described here can be made out of band if you are using a dummy load of high quality, and if your transmitter can operate out of band and at reduced power. You alone are responsible if you fail to avoid interference. If in doubt, restrict your measurements to within the limits of your operating privileges.- Measure and record the VSWR at several points near where the stub is desired to be resonant for these measurements. These will serve as the "Minimum Reference" VSWR values.
It is best to perform these measurements near the frequency where operation is desired, but for HF applications, it may be more convenient to make them at a higher frequency (e.g. two meters), then verify the results at the desired operating frequency. If higher precision is desired on HF, use the velocity factor determined at a higher frequency to provide a more precise sample size estimate for the HF measurement.

Making the measurements at VHF or even UHF will result in less waste of transmission line, since the length of a half wavelength sample becomes shorter with increasing frequency. The accuracy of the measurement at VHF or UHF should be adequate for most applications, and changes only slightly with frequency.

- For open wire transmission lines such as ladder lines which have a minimal amount of insulating material separating the conductors; use .95 or even .90 as the initial estimate of velocity factor to compute the length of the measurement sample, since these transmission lines have typical velocity factors close to unity. This will reduce the number of iterations required to determine the velocity factor precisely.
For TV twinlead, and transmission lines with a solid and continuous insulator separating the conductors, use .85 or .80 as an initial estimate.

- A sample length of transmission line equal to half a wavelength at the measurement or operating frequency is desired.
Published data for most varieties of coaxial cable may prove to be a reasonable estimate for those transmission lines, but start with a length just slightly longer than you expect, to ensure your sample doesn't start out too short.

You can always start with an estimate of 1.0 to be on the safe side, but don't get alarmed by the need to perform a few iterations of this process. For example, if the velocity factor of your transmission line is .70, you will be end up reducing a full length (half wavelength in free space) sample by 30 percent.

- Use the following formula and compute the initial length of the transmission line sample:
(Equation C1):L=(V*5901.6)/*F (Inches) L = Initial length estimate of transmission line sample in inches. V = Initial estimate of velocity factor of transmission line sample. If in doubt, use 1.0. F = Frequency in MHz where measurements are to be made.- Short one end of the transmission line sample, and connect the remaining end between the two connectors mounted on the printed circuit board test fixture. The transmission line should now be connected in series between the center pins of the connectors( fig 5.) The ground return for this connection is completed via the copper clad material to which the connector shells were soldered in the setup procedure described above.
- Connect a 50 ohm termination (dummy load) on one of the connectors of the test fixture, and an SWR bridge and transmitter (HT) on the other ( fig 5).
- Measure and record the VSWR by transmitting through this network at several points near where the stub is thought to be resonant.
- Select the frequency where the VSWR is closest to one of the "Minimum Reference" values recorded in step 3 above. This is where the stub is closest to half a wavelength. Remove the test fixture and measure the VSWR of the dummy load at this frequency to verify that the two measurements are equivalent. If not, adjust the frequency slightly in either direction and repeat this step until the measurements agree. This may occur at two nearby frequencies, and both should be recorded. Two values of velocity factor will be derived, and the measurements should be repeated at a frequency far removed to resolve the ambiguity. Only one of the first set of measurements will agree with a measurement made at the second frequency. This will occur when the dummy load in use is not a pure resistance of 50 ohms and has a finite but significant reactive component.
Note:If the VSWR is lowest at the lowest measurement frequency and increases with increasing frequency, the stub is too long and needs to be shortened. The first set of measurements should always produce this result, or the stub has been made too short at the onset.- Calculate the amount the stub needs to be shortened (or lengthened if the result is negative).
(Equation C2):DL=(1-F2/F1)*(5901.6/F1) (Inches) DL = Length change (in inches) required to make the stub resonant closer to the desired center operating frequency (A negative number indicates a length increase is required.) F1 = Desired Operating Frequency (In MHz) F2 = Frequency (In MHz) where VSWR is lowest- Shorten the stub by the amount calculated in step 10 and repeat steps 8 through 10 until you observe that the VSWR is equal to that of the dummy load (i.e. near 1:1 in most cases using a dummy load of good quality).
Note:Minimum VSWR does not need to occur at the desired operating frequency for the purpose of determining velocity factor. However; the frequency where the VSWR most closely matches the "Minimum Reference" VSWR must be determined as precisely as possible.- Measure and record the VSWR at several frequencies near where it was found to be lowest, and determine the precise frequency (F2) where it is equivalent to that of the dummy load alone. This is the frequency where the stub is equal to an electrical half wavelength.
Note:If two frequencies are found that meet this criteria, the calculations that follow will need to be performed for both measured values. In addition; this same exercise will need to be repeated at a second frequency (using the larger computed velocity factor for the initial velocity factor measurement in Equation C1). Two of the four measurements should be very close to the same value, while the remaining two are considerably different and unique. The value that is consistent for both measurement exercises is the true velocity factor, and the ambiguity is thus resolved.- Using the frequency (F2) derived in step 12, and the physical length (L) of the stub (as measured from the connector center line to the shorted end); calculate the velocity factor (V) of the transmission line.
(Equation C3):V=(F2*L)/5901.6 (Inches) V = Measured (actual) Velocity factor of the transmission line sample. F2 = Frequency(s) where the VSWR of the transmission line sample matches that of the dummy load alone when measured at the same frequency. L = The measured physical length (in inches) of the shorted transmission line sample used to perform the above electrical measurements.Note:The computed velocity factor (V) should be a number less than 1.0, and will typically be within the range of 0.6, and 0.9 in most cases. A computed value outside this range should be questioned, and the measurements repeated to ensure the result is repeatable.If the Minimum Reference VSWR occurred at two nearby frequencies; repeat Steps 1 through 13 at a measurement frequency far removed (a few percent) from the initial test frequency to resolve the ambiguity.

It is also wise to verify the accuracy of the computed value, by attempting to construct a stub at a frequency slightly higher than where the current sample is resonant. This will require a shortening of the sample and will minimize waste. This exercise should produce a new stub length that resonates very close to where you predict.

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The BASIC program included here performs the calculations in this appendix and was not included in the original manuscript.********************************************************************* ********************************************************************* Click here for the Basic program that performs the velocity factor calculations described in Appendix C. *********************************************************************