Extended Applications

In "What is a Fold Monopole?", we briefly explored the use of a folded monopole that was self-resonant but which also used a linear extension. The result, as expected, involved an increase in both the resistance and the inductive reactance at the source or feedpoint. The folded monopole continued its normal antenna function in terms of radiation, with a small increase in gain due to the increased overall length.

In the first episode of this 2-part examination of short folded monopoles, we explored the properties of complete antennas, that is, folded monopoles that used equal-length legs. We saw a progression of properties from physical lengths of 10 through 90 degrees. The progression may have held some surprises for those not used to folded monopole behavior. At very short lengths (up to 30 degrees or so), the source resistance was very low, lower than for an equivalent linear monopole. In the 50- to 60-degree region, the source resistance became very high, with an accompanying set of peaks for inductive and capacitive reactance--and a narrow zero-crossing length between them. Only as the folded monopole exceeded about 70 degrees did the source impedance curves return to behaviors that we associated with linear monopoles adjusted for the impedance transformation that is inherent to the folded structure.

In this item, we shall combine the two ideas into a single exploration. We shall look at short folded monopoles from 10 through 90 degrees with linear extensions. One goal will be to see what patterns of antenna performance emerge from the exercises.

One might well wonder whether the exercise might be simply the satisfaction of idle curiosity. We do not normally hear of extended short folded monopoles among the many classes of antennas used by amateur or commercial interests. Just as a rose by any other name would smell as sweet, so an antenna by any other name would radiate just as well. There are a number of structures composed of extended short folded monopoles that we have managed to re-name--and sometimes, to misunderstand as a result of the different name. In the vagaries of labels lie many roads to misconception.

Consider the left-hand side of **Fig. 1**. The sketch shows a grounded tower fed for one of the lower amateur
bands by what we call a shunt feed system. We connect a wire parallel to the tower. The top end connects to the
tower so that the wire length combined with its distance from the tower allow--so we usually say--coupling to the
tower. We strive for a length that will yield a feedpoint impedance we can easily match to coaxial cable using
the simplest network for lowest losses. The wire length usually emerges from experience, and AWG #12 is popular
for the purpose. One instruction set that I read suggests that if the feedpoint impedance is not within a
desirable range, we should change the spacing from the tower until the impedance is acceptable.

On the right in **Fig. 1**, we have a short folded monopole that places its top wire at a height which is
not the full length of the return wire. The return wire happens to be a tower structure that is very wide. Hence, we obtain
a very sizable step-up in impedance relative to a linear wire of the same length. Since the tower goes on above the
folded monopole, we anticipate that the feedpoint impedance will show an increase, if we assume that the folded
monopole portion is self resonant. If the folded monopole section is shorter than resonant, then our work so far leaves
the impedance unknown. So the sketch has added a network at the feedpoint in case we need it to effect a match with
the main feedline.

The perspective that we took in the right portion of the sketch makes clear that the fed wire is as much a part of the
radiating structure as the tower. Its function is not simply to couple energy to the tower. Rather, its function is to
form with the tower a single radiating element. The 2-wire portion of the structure effects an impedance transformation
relative to the tower alone--if base fed--but the radiating currents are a joint function of both wires. Of course,
between the left and right sides of **Fig. 1**, we find no difference in the structure outline. The only differences
appear in the labels for the structure's parts.

The left part of **Fig. 2** shows a generalized sketch of a gamma matched element. The most common occurrence of
the match these days is for the driven elements of Yagi parasitic arrays in which we wish to connect all
elements to the boom. Ordinarily, the impedance of the element without the gamma match is lower than the desired
value, usually a value well below the 50-Ohm impedance of standard coaxial cable. We call the portion of the
gamma match that parallels part of the element length the gamma rod. We short the end to the element in a position
that yields the desired impedance at the new feedpoint. By a judicious selection of rod diameter, rod spacing from
the element, and rod length to the connection, we can sometimes produce a purely resistive 50-Ohm impedance. If
there is a reactance, we strive to make it inductive so that a simple series capacitor will compensate. Note that
we normally consider the gamma rod to be a part of a matching network and not part of the radiating element.

However, if we redraw the upper half of the sketch and terminate it at ground (instead of at a grounded boom), we
obtain the sketch on the right of **Fig. 2**. In this case, the fed wire or rod becomes one wire of a 2-wire folded
monopole, with an extension beyond the folded structure limit. The ground forms--if we wish to think in these terms--an
image of the upward or physical portion of the antenna. The gamma match turns out to be a short folded monopole with
an extension. As such, both wires in the folded structure make up the radiating element until we reach the
extension. From our work with full folded monopoles and their linear equivalents, we know that the equivalent diameter of the
folded portion of the antenna is much larger than the diameter of the extension along. Hence, every gamma-matched
element contains at least a small imbalance. The related Tee match overcomes the imbalance by using a folded monopole
on each side of the boom.

As a consequence of these instances of short folded monopole applications--whatever the preferred labels--the behavior of short folded monopoles with extensions becomes more than an idle exercise. It holds some possibility of improving our understanding of certain structures that combine impedance transformation and radiation. As well, we might develop some techniques that would be applicable to real antenna planning exercises.

Oue basic work will follow the pattern on the first episode. We shall place the folded monopoles over perfect ground and use lossless wire in order to eliminate some complex variables. In a real planning situation, we would put into our models the material conductivity of the proposed wire and the best estimate of real ground conditions. As well, our models would include the actual radial system beneath the folded monopole.

Since we need some usable increment between modeled structures, we shall again use the physical height of the structures
in degrees, where 360 degrees is 1 wavelength. We shall explore structures in 10-degree increments at 3.5 MHz. **Table 1**
provide a convenient correlation between the degree markers and the equivalent height in feet at the test frequency.
At 3.5 MHz, a wavelength is about 281.02'.

We shall create models using an implementation of MININEC 3.13. The program that I am using is Antenna Model, which incorporates a considerable number of correctives to overcome some MININEC shortcomings. Since all of our models will use different diameters for the fed and the return wires, NEC (-2 or -4) will not yield results that pass Average Gain Test (AGT) muster. As we shall eventually see, even MININEC's more ready handling of junctions between wires having dissimilar diameters has limits. However, we shall be able to create some usable models within those limits. If you try to replicate the models using a different implementation of MININEC, expect to find some variance in the output reports. If the implementation does not include an accessible AGT score, you may simply have to guess at the reliability of the model that you create.

The project itself is simple, although long and occasionally tedious. **Fig. 3** shows its general outlines.
I shall create a series of short folded monopoles for each test case. Since the most common cases of short folded
monopole applications involve return wires that are fatter than the fed wire, the models will all follow this pattern.
The folded monopoles will appear in 10-degrees steps, from 10 through 90 degrees. To each folded monopole that is
shorter than 90 degrees, I shall attach to the return wire--using the same wire diameter as the return wire--a series of
extensions in 10-degree steps. Each series will progress until the total element length is 90 degrees.

Obviously, one might carry the progressions of folded monopoles beyond 90 degrees or the extensions beyond 90 degrees. However, my goal is not to replicate every possible structure we might use. Rather, it is only to elicit the patterns of behavior of the resulting antennas, with special attention to the feedpoint impedance. We would have to end somewhere, and there is little point in becoming totally lost in a morass of excessive data. Indeed, the data that we shall observe is complex enough for one episode.

**Case 1: D1 = 0.1", D2 = 0.5", Space = 12", 2 Wires**

Our study cases can begin with a structure that we examined in the first episode. It consists of two wires spaced 12" apart. The fed wire will be 0.1", corresponding to AWG #10 wire that is midway between the wires used in amateur and commercial practice. The return wire is 0.5" in diameter to give us a sense of standard 2-wire shunt feeding of an existing mast. I have selected this starting point because the AGT scores are generally very good to excellent within MININEC despite the difference in element diameter. At a resonant length of 67.08', the reported source resistance is about 209 Ohms, compared to a calculated value of 210 Ohms.

In the present context, we shall look at short monopoles in 10-degree increments. To each of these folded monopoles, we shall add a 0.5" diameter extension in 10-degree increments. The minimum length for each portion of the following data will be the height of the simple folded monopole. However, every folded monopole will end up with a height of 90 degrees. When we later speak of the data, we may use expressions such as "20-50" to designate a line from the table. The first number indicates the height of the folded monopole portion of the antenna, while the second number reports the total height that includes the extension, if any.

The data includes a report of the AGT, the source resistance and the source reactance. In addition, there are entries
for the reported gain broadside to the pair of wire and edgewise to the wires. In the latter case, the maximum gain value
appears as a measure of the pattern's circularity or ellipticalness. **Table 2** records the data for the present 2-wire
case.

Except for the shortest lengths of both the folded monopole and the extension, the AGT scores are excellent. Therefore, the table makes no adjustments to the reported values. The gain values generally accord with those for folded monopoles that form the complete structure of the entire length. In the last episode, we notes the losses that accompany relatively short structures when we translate our perfect wire into real materials. In practical terms, there is very little difference in the numerical performance and virtually no operational real difference in gain performance among any of the various structures when the total height exceeds perhaps 60 degrees or so.

The impedance progressions that follow on each folded starting point exhibit interesting patterns. We may use the 10-10 through 10-90 series as a sample. The reactance increases very slowly but steadily. However, as it cross the resonant region (between 80 and 90 degrees total height), we do not find resonance. Instead, we find a reversal of the direction of change of reactance. The resistance for all total length up to 80 degrees is too low to be useful. However, the rate of increase climbs so that with a 90-degree total height, we achieve a matchable pair of resistance and reactance values. If we track the 20-n and the 30-n series of models, we find the same pattern for both the resistance and the reactance, with an adjustment for a new starting value set that emerges from the new length of the folded section.

Above a folded length of 40 degrees the pattern appears to change. We seem to find more rapidly changing resistance and reactance values. However, we are entering the region in which a a full folded monopole would experience rapidly changing impedance values. The extension portion of each structure has the effect of increasing the folded monopole length by a small amount with each step. Small changes of total length yield large changes in resistance and reactance. Between 40-80 and 40-90, we see a reversal in the inductance, suggesting a narrow resonant region. For the 50-degree folded structure, total height between 70 and 80 degrees records a similar reactance zero crossing. When the folded structure is over 60 degrees high, the antenna begins past the cross-over point and shows predominantly capacitive reactance. However, the 80-90 case yields another matchable impedance combination.

One of the oddities of matching practices that uses short folded monopole structures is the variability
of practice. Gamma matches for Yagi elements tend to use the shortest practical folded section that will effect
the desired impedance transformation. In contrast, tower shunt feeding tends to use the longes folded
structure that will get the job done. See Chapter 6 of *The ARRL Antenna Book*, 20th Edition, and Chapter 9 of ON4UN's
*Low-Band DXing*, 2nd Edition, for samples of tower shunt feeding. Gamma and related matching systems
appear in Chapter 23 of the ARRL book. In fact, neither Yagi practice nor tower practice seems to take note of
the other way of achieving the same goal.

Although our case study is not itself very realistic relative to either HF Yagis or to MF/HF towers, we may use
it as a way to explore a technique for surveying a more complete range of options when using short folded
structures to effect impedance matching. We can create graphs of the impedance reports. **Fig. 4** handles
the reported resistance values for our sample. The X-axis records the total height of the structure, while the individual
lines represent different heights for the folded portion of the antenna.

I have cut off the Y-axis for multiple reasons. I arbitrarily set a 500-Ohm limit to the upper end
of the resistance range. The decision in any real case would rest on an estimate of the highest resistance
value that might be acceptable. The range should be great enough to show the rate of resistance change from
one step to the next. However, it should not be so high as to obscure how close to an ideal value of resistance
the modeled value comes. In this case, we might be concerned with 50 Ohms as a target value. **Fig. 5**
shows a similar treatment for the reported reactance values.

The reactance values included in the graph range from -j100 Ohms to +j500 Ohms. Most short monopole impedance transformation system seek an inductive reactance (or zero reactance) at the feedpoint to allow matching with only high-Q capacitors. The selected range lets us see both the recorded reactances at the sampling points and the relevant rates of change to the adjacent sampling points.

The combination of the two graphs allows us to select candidates for implementation. In most cases, we shall find few viable candidates, since we are likely to be working with an existing grounded mast or tower. However, in the exercise, we are free to note any viable combinations. In the present case, the resistance table offers a number of combinations that show (by the graph's definition) usable values with modest rates of change in resistance to the next sampling point. However, the reactance graph reduces the number of candidates. Within the constraints of the exercise, total height values between 80 and 90 degrees combined with folded heights between 10 and 20 degrees offer useable combinations with relatively low rates of change. The longer folded structures that showed promise in terms of their resistance reports in this region tend to disqualify themselves due to the high rate of reactance change between sampling point. Any network that we might use to produce a final resistive impedance of 50 Ohms would likely have at best a very narrow bandwidth.

Our accumulation and exploration of data shows us how we can use the information as the basis for planning installations. However, the structure that we used is relatively unrealistic. It appears because the models are highly reliable as measured by the AGT values (which are a necessary but not sufficient condition of model adequacy). Perhaps a more realistic scenario might be useful as a second exercise.

**Case 2: D1 = 0.1", D2 = 8.8", Space = 36", 2 Wires**

Real towers that we might use as a shunt-fed vertical antenna vary in face size. We may use a modest tower with a 12" face dimension. For simplicity in the models, we may use the standard AM BC equivalence and multiple the face by 0.74 to obtain an 8.8" diameter wire that approximates the tower. (An actual planning session should model the tower structure as exactly as possible.) This new diameter forms the return wire for the folded structure and the extension above and beyond the folded structure. We may retain the 0.1" diameter fed wire as a realistic value.

The next step is to determine a workable space between the wires of the folded section. Despite MININEC's
superiority in handling junctions of wires having different diameters, it will show limits to its reliability. We
not only have a radical difference in wire diameters, but as well, we have two wires that are fairly closely spaced.
I sampled variety of spacing values and return-wire diameters using a 30-degree folded structure and an 80-degree
total height to see what AGT scores might emerge. The results appear in **Table 3**.

For any set spacing, the AGT values degrade as we increase the diameter of the return and extension wires. In some circles, AGT's are considered excellent if they fall between 0.995 and 1.005. They are usable between 0.990 and 1.010. Beyond this latter range, the data becomes questionable. Even within the usable range, we should adjust the data by virtue of the AGT score if we are developing (meaningful and comparative) progressions of values, especially if the AGT value changes from one sample to the next. For the projected diameter of the return and extension wires in the models that we shall run, the minimum spacing for adequate AGT scores is 36" or 3'. This value tends to coincide with commercial practice for folded assemblies, so I shall use it in amassing a data collection.

AGT scores will tend to improve for longer structures and degrade for shorter total antenna heights. Therefore, we should adjust the reported values to arrive at the best approximation of a final value. Because we are dealing with a folded structure, we must reverse the normal procedure set. Ordinarily, we convert the AGT score into a "dB' value (=10 log AGT) and subtract it from the reported gain. (An AGT less than 1 results in a negative dB value, which increases the reported gain when we do the subtraction.) Experience with the full folded monopoles in previous studies suggests that we must add the AGT-dB to the reported value to obtain gain values that are reasonable in terms of their consistency with values that emerge from models showing an ideal or very-nearly ideal AGT value. We normally adjust impedance values by multiplying the reported number by the AGT itself. However, folded structures appear to require that we divide the report by the AGT in order to obtain values that coincide with calculated impedance transformations.

With these cautions and conditions, we may proceed to model our erstaz tower and its shunt wire as a series of 2-wire
short folded monopoles and extensions. We shall use the same increments that we used for the initial case. **Table 4**
shows the amassed adjusted data. However, we must add one more reservation. The standard impedance transformation
equation for resonant folded dipoles results in an impedance of about 614 Ohms. The resonant version of our new
model is 65.286' high and reports an adjust resistance of 574 Ohms. The difference is about 7%. We cannot be truly
definitive in assigning a source to the difference. However, the end wire is now 3' long, almost 5% of the total folded
monopole height. As well, the impedance ratio is about 17:1, a very large ratio indeed.

Within the limits of our case study, the gain values are completely normal (with the usual reservations about the very shortest folded and total height values). Broadside gain values at a total height of height of 90 degrees coincide very closely with corresponding values for the smaller and narrower model of Case 1. The edgewise gain values provide a measure of the degree to which the 2-wire structure ovalizes the pattern.

The significant differences between the values in **Table 4** vs. those in **Table 2** appear in the resistance
and reactance columns. Between the two tables, we note a large difference in both the return/extension wire diameter
and the spacing between wires. Therefore, we shall expect to see differences in the impedance values for each increment of
folded structure.

Between folded structures heights of 10 and 30 degrees, perhaps the biggest surprise may be that we see the same general pattern of values that we experienced with Case 1. The resistance values for Case 2 are consistently about 1/3 the level of those for Case 1. However, the reactance values for each increase in the return wire length are comparable between the two cases. The parallel extends even to the decrease in inductive reactance that occurs in the total height interval between 80 and 90 degrees. The amount of decrease for the 8.8" example is somewhat less than for the 0.5" return wire, but it is equally distinct.

As we increase the height of the folded structure, the parallels remain, but with reservations. For the narrower structure, the reactance zero-crossing first appeared with a folded structure that was 40 degrees high. With our more widely spaced model, the folded structure reaches 60 degrees before we encounter the first zero crossing. If the total height for Case 2 is 90 degrees, we find nearly identical inductive reactance values for folded heights between 50 and 90 degrees. The shorter the folded structure within this range, the lower the resistance value.

The general trends give us a picture of both consistency with the earlier models and of adjustment for the new
values of return/extension wire diameter and spacing. In order to translate those general trends into a more
adequate planning venue, we may graph both the resistance and the reactance values. Since we do not have a real tower
around which to plan, we may use that same limits applied to the graphs for the earlier case. **Fig. 6** shows
the relevant resistance values.

With respect to resistance, the 20- and 30-degree folded structures show perhaps the most promise when used with total heights between 80 and 90 degrees. Especially notable is the relatively slow rate of change in resistance with changes in height over this region. These conditions suggest that variables in the physical structure relative to the model will be manageable in terms of field adjustments toward the final antenna.

**Fig. 7** shows the corresponding reactance graph. It tends to confirm the initial judgment of the promise
offered by the 20- and 30-degree folded structures with higher extensions. With the shorter folded structures, the
inductive reactance increases with the length of the folded monopole for any given total height. However, it remains
manageable. Long folded structures might yield workable values of inductive reactance at a total height of
90 degrees, but the rate of change between 80 and 90 degrees total height is very steep.

We may note in passing that the resistance curves for all lengths of folded structure show a downward trend between 80 and 90 degrees. Although we are working with a simple straight tower (equivalence) in these models, it is fairly easy for typical amateur towers to exceed 90 degrees in electrical length without passing the 70' mark of our 90-degree tower. Most shunt-fed amateur towers hold one or more Yagi antennas at the top. These structures tend to form rudimentary and imperfect top hats that increase the effective electrical length of the tower considerably. Hence, a 90-degree physical tower may easily become 100 or 110 degrees electrically. The consequences lie outside the limits set on this exercise, but we can expect to find lower resistances and variations in the reactance. If the tower is too tall electrically, we may easily find a shift back into capacitive reactance. Within modest electrical height increases relative to the study limits, we need to study all potential folded structure heights (or shunt lengths). The longest folded structures in conjunction with the longest total heights tend to show very high rates of change in resistance and reactance with small changes in total height. The result is normally a very narrow operating bandwidth for any given set of matching components.

**Case 3: D1 = 0.1", D2 = 8.8", Space = 36", 3 Wires**

One possibility, rarely explored by amateur installations but regularly used commercially, is to provide multiple
fed wires. **Fig. 8** shows the configurations that we have and shall explore here. Both of our earlier
sample cases used 2-wire construction. However, 3-, 4-, and 5-wire construction is feasible, assuming that it might
increase the number of options available for shunt feeding a tower or other applications of folded monopole
structures.

In these notes, we shall take up just two of the added options: 3-wire and 5-wire configurations. The 3-wire models will use a pair of 0.1" diameter fed wires on opposite sides of the central 8.8" tower-equivalent return wire and extension. To ensure reasonable AGT values, we shall retain the 36" spacing between the fed wires and the return wire. All of the procedures for adjusting values according to the AGT scores will also apply to this case. The only modeling difference lies in the need for having 2 sources which are, in effect, in parallel relative to the overall structure. If we bring these source together, the composite source impedance will be composed of resistive and reactive components that are each half the value of the values for the individual fed wires.

The data for the 3-wire assemblies appear in **Table 5**. Although the simple folded monopoles in the
earlier study ("What is a Folded Monopole") all produced circular azimuth patterns at resonant lengths, we find elongated
edgewise patterns in these models, likely due to the very large diameter difference between the fed wires and
the return wire. However, as we increase the total height of the antenna to 80 degrees for any height of folded structure,
the azimuth pattern becomes circular. The more symmetrical structure of the 3-wire models also shows a slight
improvement in AGT values relative to the 2 wire models.

As we have done for the other cases, we shall break the discussion of impedances values into 2 parts for Case 3. The first set of values involves folded structures that are 10 through 30 degrees high. The general trend that we discovered for the earlier cases applies to the 3-wire models. For any folded structure, as we increase the height of the extension, the source resistance slowly rises until we pass the 80-degree total height mark. Then the resistance declines. Interestingly, over this range of folded structures, we do not find very significant differences in the source resistance between 2-wire and 3-wire models. The reactance also slowly increases as we increase the total length of models with 10- through 30-degree folded structures. However, the inductive reactance is considerably lower for the 3-wire models than it was for the 2-wire counterparts.

When the folded structure exceeds about 40 degrees, the resistance and the reactance change more rapidly in 2-wire models than with shorter folded structures. In corresponding 3-wire models, the resistance tends to change more slowly than in 2-wire models with the same height characteristics. The first reactance zero-crossing occurs in 50-80, with the 60-n series of models showing capacitive reactance at all total heights except 90 degrees. When the folded structure exceeds about 70 degrees, the 2-wire and 3-wire source resistance values become very comparable. However, the reactance values of the 3-wire models appear to be almost uniformly shifted in the direction of inductive reactance.

The pattern of similarities and differences between 2-wire and 3-wire structures can naturalize us to the performance
behaviors, but we require more detailed analysis to see if we have developed any manageable matching potentials. **Fig. 9**
provides the resistance data for source values up to 500 Ohms. If we can manage source resistance values up to about
250 Ohms, then the graph suggests that we may use some taller folded structures (70 and 80 degrees) in addition to
the shorter 20- and 30-degrees structure suggested as possibilities for 2-wire structures--so long as we use a
relatively high total structure (>70 degrees).

Whether any of these potentials has a usable or manageable reactance requires that we examine the graph in
**Fig. 10**. The reactance values at a height of 90 degrees for the tower are well within the range of most
networks. However, the rate of change for the reactances associated with the taller folded structures is somewhat
steep as the value shift from capacitive to inductive between total heights of 80 and 90 degrees. The more
rapid the change in reactance with smaller height changes, the narrower the bandwidth will be for any particular
set of matching component values in basic networks. Nevertheless, the slow rate of resistance changes may
effect an improvement in operating bandwidth for the taller folded structures.

Since 3-wire systems are not very much more difficult to install than 2-wire systems, they may prove useful in a number of applications.

**Case 4: D1 = 0.1", D2 = 8.8", Space = 36", 5 Wires**

Developing a data set for 5-wire structures with 4 fed 0.1" wires and an 8.8" diameter return/extension wire requires far more effort to model than to explain. It does not matter what name we give to the structures: caged monopoles, skirted monopoles, or multi-wire folded monopoles. Central to the modeling is providing a symmetrical arrangement of the fed wires and providing each fed wire with a source. The net or parallel source impedance of the antenna will be 1/4 the value that appears on any single leg. MININEC lacks any facility for paralleling sources, so the calculation must be external to the program.

**Table 6** provides the adjusted data gathered for the series of 5-wire models. Increasing the symmetry of the
structure provides another slight improvement of AGT values. As well, the 4 wires circularize the azimuth patterns,
as indicated by the identical gain values in both the broadside and the edgewise columns. Once we pass very low levels
of total height, the gain for the system does not vary significantly regardless of the number of wires.

Adding two wires to the 3-wire assembly does not greatly change the net source resistance values relative to 3-wire models when both use shorter (10- through 30-degree) folded structures. Indeed, for shorter folded sections, all three series of model (cases 2 through 4) show similar resistance values. The more significant change for shorter folded structures occurs in the level of inductive reactance. The 5-wire models show between 2/3 and 3/4 the level of inductive reactance for each step of total height for any of the shorter folded structures.

As we increase the folded structure to a height of 40 degrees or more, we find a significant difference in antenna impedance behavior relative to 3-wire models. Model 40-80 shows the first reactance zero crossing, an event that required a 50-80 combination with 3-wire models. With folded structures between 50 and 60 degrees, all of the reactance values are capacitive, including the value for a 90-degree total height. Only with folded structures at least 70 degrees high do we find an inductive reactance with a 90-degree total antenna height. However, almost all of the reactance values are quite low, suggesting the potential for broader bandwidth matching systems.

In the category of source resistance, **Fig. 11** reveals that the 5-wire assembly offers us new candidates
for folded structures in terms of manageable values. In addition to the 20- and 30-degree folded structures, we
may add 60-90 degrees, with total lengths equal to or longer than the folded structure.

With a total height of 90 degrees, **Fig. 12** informs us that almost any of the resistance candidates will
suffice in terms of feedpoint reactance. As we lower the total height to 80 degrees, even the tallest folded structures
show less steep curves than for any of the preceding models series. Even a 60-degree folded structure will
work well with an 80-degree total height if we can handle a moderate amount of capacitive reactance.

The 5-wire short folded monopole with extensions expands the number of options available to the application of folded structures to grounded vertical towers. These notes have not explore antenna lengths greater than 90 degrees, so we cannot say off hand whether the advantages of multiple feed wires continue with taller towers.

**Matching and Planning**

In the course of these notes, I have noted that most amateurs who feed existing towers for use on one or more of the lower bands prefer to arrive at an assembly that provides inductive reactance. In many cases, the operator will sacrifice operating bandwidth for the inductive reactance. Indeed, they prefer to arrive at a source resistance that is less than 50 Ohms along with the inductive reactance. We may fairly ask why this custom prevails.

**Fig. 13** provides part of the answer. Under ideal conditions, we can effect the required matching to a
coaxial cable with a simple series capacitor, if the antenna feedpoint shows a near-50-Ohm resistive component along
with inductive reactance. The upper left sketch shows the condition. If the impedance is less than 50 Ohm resistive and
has inductive reactance, then we may use the 2-capacitor matching scheme at the upper right. Since the scheme is a
simple L-network, it is not clear why the label "omega" match persists, since nothing in the network resembles
the Greek letter in either upper or lower case forms. For many combinations of impedances with under 50 Ohms resistance
and an inductive reactance, the system at the lower right will also work. However, it does not always yield the
most desirable values (usually meaning the lowest values) of capacitance in either the series or the parallel leg.

For general matching with resistances above 50 Ohms, we normally require the L-network configuration shown at the
lower left in **Fig. 13**. The sketch shows perhaps the most familiar form of the L-network, often used with
horizontal long-wire antennas. However, it functions very well with impedance that are near to 50 Ohms with various
levels of inductive or capacitive reactance. Tower shunt feeders have in the past rejected this configuration--and the
impedances that require its use--because they have preferred to match entirely with capacitors. One may match a
a given impedance over a narrow operating bandwidth with fixed weatherproofed capacitors at the base of the antenna.
Vacuum variables can provide fairly weatherproof remote service to vary the match.

The desire to remotely match an antenna for upper MF and lower HF amateur service makes sense if we consider some of the impedance values that appear in the literature. One set of values involved a resistance of 17 Ohms and a reactance of 580 Ohms. Even if we had a resonant condition, the SWR would begin at 3:1 relative to 50 Ohms and become progressive worse with increasing reactance. With the very high reactive component, the SWR is in the hundreds.

An alternative offered by multi-wire folded structures is a reduction in the reactance to levels that may not require remote matching. Some of the 5-wire models showed resistance values in the 90s as the total height approached 90 degrees. The inherent SWR relative to a 50-Ohm line is under 2:1 with those conditions. If we raise the reactance to perhaps 100 Ohms (capacitive or inductive, the SWR climbs to about 4.3. If we use 100' of low loss cable (such as LMR600) and reserve matching for inside the operating room, we lose about 1/3 dB. A simple L-network at or near the operating position will effect the required match with little or no concern about the durability of components as the weather passes through its many potentially destructive cycles.

The possibly attractive alternative, of course, rests on the numbers yielded by the sample models, with all of the
qualifications and reservations recorded along the way. Making such a system work in a specific application requires
far better modeling, along with considerable preliminary field effort. At a minimum, a proper model should include
all of the details shown in **Fig. 14**. The tower needs full modeling, as do the specific wires to be used as fed wires
in the folded portion of the structure. Not only should the model include any extension of the tower, but as well, it
should include any mast and beam antenna at the top. In addition, the model should specify the materials for each wire
within it, with different values for material conductivity wherever they occur. Only then will the model accurately
reflect the above-ground structure and its equivalent electrical length. Of course, the many junctions of wires having
different diameters will force the use of MININEC, since a NEC model has a very high probability of being unreliable.

The below-ground structure has equal importance. A buried radial system deserves below-ground modeling in NEC-4. If we try to substitute the MININEC ground with a set of specifications for conductivity and relative permittivity, we would obtain the impedance for a perfect ground. To resolve the incompleteness of one system without the other, the modeler can first model the antenna structure as a whole in MININEC. Then he or she can develop a simplified substitute model have essentially the same characteristics, but using throughout a single wire diameter. (In many cases, this phase of the effort may require the most ingenuity.) Finally, one may transfer the model to NEC-4 for completion with the buried radial system to be used in practice.

Of course, Murphy's Law tells us that the individual who bypasses this process and uses initial estimates will spend long days in the field adjusting and readjusting the system because reality and the initial estimates are far apart. Equally, someone who goes through the entire process will conclude that the initial estimates proved to capture reality as well as the most detailed model. Such is the lot of shunt feeders.

The brief account of detailed planning requirements serves to reinforce my initial notes to the effect that these case studies only establish the interesting patterns of short folded monopole and extension behavior. They do not provide precision guides to building such structures. However, patterns can be useful in familiarizing us with the territory so that what we encounter has fewer surprises. Surprise on the battlefield is an effective offensive weapon. Surprise with antennas is usually simply offensive.