Some Basic Properties

In "What is a Folded Monopole?", we examine some basic properties of resonant folded monopoles using 2, 3, 4, and 5 wire construction. When resonant, modeled folded monopoles show a clear relationship between the reported source impedance and the calculated impedance using the classical equation.

R is the ratio between the impedance of the new folded antenna and the impedance of a resonant linear antenna that otherwise has the same design. The equation applies equally to folded dipoles and to folded monopoles. Where the diameters of both the fed wire (d1) and the return wire (d2) are the same, the ratio is 4:1. The new impedance follows a very simple equation:

Since the feedpoint (or source) impedance (Zlinear) of a linear monopole over perfect ground is 36 Ohms, the resonant feedpoint impedance of a folded monopole (Zfolded) is 144 Ohms. If the fed wire is fatter than the return wire, then the impedance ratio is less than 4 but always greater than 1. If the return wire is fatter than the fed wire, then the impedance ratio is always greater than 4.

The basic principles in our initial foray into folded monopoles neglected a very important aspect of folded monopole use.
Many antenna builder use lengths that are shorter than the resonant length. For very short to moderate folded monopole lengths,
(where the resonant length might be considered long), the feedpoint impedance will show an inductive reactance. In that
property, a short folded monopole bears a resemblance to a transmission-line shorted stub. However, the stub and the
antenna have some important differences, crudely marked in **Fig. 1**.

The two structures are similar in that the properties are dependent on the diameter of the wires and on the spacing between wires. The letters s, d, d1, and d2 designate these fundamentals that make performance dependent to a significant degree on physical properties of the structure. The folded monopole requires a ground (or a suitable ground plane) in order to operate. The energy source is normally positioned in series with the lower end of one wire (d1) and the ground. In contrast, the shorted stub uses no ground. Rather, the energy source is placed across the two wires of the transmission line opposite the shorted end. As a consequence, the shorted transmission-line stub does not radiate (if properly constructed and isolated from influences that would create imbalance between the lines). It ideally shows only transmission-line currents, which are equal in magnitude and opposite in phase at points along the line that are equidistant from the energy source. The folded monopole radiates and therefore exhibits both transmission-line currents and radiation currents.

At this point, we have to choose a direction for analyzing the behavior of short folded monopoles. We might legitimately turn to a mathematical treatment of the structures. However, my goal is not to replicate texts on the subject, but rather to familiarize you with the patterns of short folded monopole behavior. Therefore, my chosen route of analysis is modeling some selected folded monopoles to develop some patterns in the behavior. The method will be effective in showing some of the variables that influence the behavior, while also developing some rational expectations of them. We shall choose our modeling software to fit the structure that we are modeling. For our first two case studies, NEC-4 is adequate to the task, although we shall pay close attention to the Average Gain Test (AGT) score (where 1.000 is ideal) in order to adjust numbers as needed.

Since we shall not be dealing in resonant antenna lengths, we need an increment of folded monopole length to use for our samples. One convention used in the AM BC industry is to list antenna lengths in electrical degrees, where 1 wavelength equals 360 degrees. We may adopt this convention for physical lengths even though we know in advance that 90 degrees physical is longer than the resonant physical length that we would call 90 degrees electrical length. We shall survey folded monopoles every 10 degrees at a standard test frequency of 3.5 MHz for the entire exercise. To reduce the number of variables, we shall use lossless or perfect wire along with a perfect ground. As well, in this initial investigation, we shall work only with 2-wire folded monopoles.

**Case 1: d1 = d2 = 0.1", s = 12"**

We may begin with a folded monopole structure already explored in the earlier item. We shall form a set of folded monopoles where both wires have a diameter of 0.1" and the spacing is 12" between them (center-to-center). The use of 0.1" diameter wire is not accidental. It roughly corresponds to AWG #10 wire, which falls between two practical extremes. Amateurs often used AWG #14 or #12 wire for such structures due to its availability and relatively low cost. Commercial installations may use wire that approximates AWG #6 (0.16").

At a resonant length of 67.25', the modeled impedance is 143.5 Ohms, compared to the calculated value of
144 Ohms. When we model the antennas in the collection in 10-degree increments, we end up with a set of
performance values such as those shown in **Table 1**.

Besides showing the length of each model in degrees and feet, the table lists the source resistance and reactance of each model. It also lists the AGT in terms of the score and the gain adjustment in dB (where the adjustment value is subtracted from the reported value). Because all but the 10-degree scores are very close to 1.000, the table makes no adjustments in this case.

There is much to note in the tabular data. We might begin with the gain values, which we show in terms of the
gain broadside to the plane of the 2 wires and in terms of the maximum gain in line or edgewise to the 2 wires.
Maximum gain occurs in the direction of the feedpoint. There is always at least a slight difference in the 2
values, but as we make the folded monopole shorter, the differential becomes very noticeable. **Fig. 2**
compares the elevation patterns for 10-degree and 30-degree versions of the antenna. In each case, the plots
overlay the patterns broadside and edgewise to the wires. The shorter antenna shows a large difference that almost
completely disappears by the time the antenna is 30 degrees long.

One way to make sense of the remaining data in the table is to contrast it to corresponding data for an
equivalent linear monopole. Therefore, I created a model of a monopole that showed a resonant length of
67.25', the resonant length of the folded monopole. The model required a wire diameter (d) of
2.75" to achieve this goal. **Fig. 3** shows a sketch of the 2 antennas.

I then sampled the antenna in 10-degree intervals to produce a table comparable to the one for the folded monopole.
The results of this exercise appear in **Table 2**. The columns in this table exactly parallel those of **Table 1**.

Both tables list the gain of the antenna over perfect ground using 3 different wire compositions: perfect or lossless, copper, and aluminum. Copper has a bulk resistivity of about 1.7E-8 Ohms/meter (corresponding to a conductivity of about 5.8E7 S/m). Aluminum's resistivity is about 4E-8 Ohms/m (conductivity about 2.5E7 S/m). Antenna modeling programs adjust the material losses for frequency and skin affect in actual calculations. Hence, the gain values for perfect or lossless wire would reappear at any frequency, but the gain values will vary a bit as we change frequency if we use copper, aluminum, or any other real wire material.

**Fig. 4** compares the gain values from the tables for all sampled lengths. The values for the 2.75"
linear monopole are for aluminum only, since the differences between pefect wire and the worst case used in the
sample are so small. However, with wires that are only 0.1" in diameter, the material losses of copper and aluminum
are exceptionally significant as we reduce the overall length of a folded monopole. Below a length of about
50 degrees, the thin-wire folded monopole shows a rate of gain decrease that may question the practicality of
using such a thin, short structure as an antenna without specific needs that make the highly reduced gain
acceptable as a trade-off.

At resonant length, the folded monopole may rival the linear monopole, but at very short lengths, the very low source radiation resistance becomes only s small fraction of the total source resistance. The wires are too thin to overcome the resistive losses of the material and of skin effect. With real wire, the 10-degree folded monopole shows less than 1% power efficiency. For the shortest thin-wire folded monopoles in the sample, the use of phosphor bronze or stainless steel would increase losses even further.

The monopoles that we have examined are over perfect ground. Placing them over real (lossy) ground will
further reduce the gain available (as well as raising the elevation angle of maximum radiation). **Table 4**
provides a rough guide to the amount of further gain reduction we are likely to experience over three levels
of ground quality. Very good soil has a conductivity of 0.0303 S/m and a relative permittivity of 20. Average
soil uses a conductivity of 0.005 S/m and a relative permittivity of 13. Very poor soil uses a conductivity
of 0.001 S/m with a relative permittivity of 5. These widely diverse soil types may let you approximate the
additional losses of your local soil by rough interpolation. The radial systems use 0.1" wire buried 1'
below the ground surface in the NEC-4 models.

The table is only a first-order estimation device, not a precise gauge. For increased accuracy, you would need to model a proposed short folded monopole using both the actual material ad the actual ground conditions at the proposed site--along with a model of whatever buried radial system the antenna might use.

Linear monopoles have gained some renown for their low feedpoint resistance values when they are very short. However,
if you compare **Table 1** with **Table 2**, you will discover that the feedpoint resistance of the
folded monopole does not catch up to the feedpoint resistance of the linear monopole until we reach a total length
of about 40 degrees for both antennas. **Fig. 5** compares the feedpoint resistance values for both antennas across
the span of surveyed heights.

The linear monopole resistance values show a smooth progression from 10- through 90-degree lengths, reaching a final value of about 41 Ohms. However, the folded monopole shows a very large spike in values between 50 and 60 degrees. The actual peak value is much higher than the largest graphed value, since the peak occurs at a height of about 57 degrees. Then the resistance value decreases rapidly so that between 80 and 90 degrees, it shows an expected slight rise with increasing length in this region. Even at 90 degrees, somewhat beyond resonance, the resistance is 164 Ohms, about 4 times the linear value for the same length.

The peaking of the resistance value accompanies a peaking of the the reactance value in folded monopoles.
**Fig. 6** graphs the reactance for both the folded and the linear monopole as we increase the length from
10 to 90 degrees.

The linear monopole shows a smooth curve that traces the decreasing capacitive reactance as the antenna lengths increases toward resonance. Since the 90-degree length is long relative to resonance, the curve smoothly proceeds into the region of inductive reactance. In contrast, the folded monopole shows very high values of reactance at 50 and 60 degrees. One may interpolate a sudden shift in reactance type at about the length at which the resistance reaches its maximum value. Of course, at this point, we would find a very small region of height at which the reactance would be nearly zero. However, that specific height is unlikely to be achieved in any practical installation. Even if achieved, a slight temperature change would alter the antenna height enough to throw the reactance into a high value region--either inductive or capacitive, depending on the direction of the temperature shift.

The very high value of resistance and the sudden shift of reactance from inductive to capacitive are typical behaviors of horizontal antennas as they pass the 1-wavelength mark or of ideal vertical monopoles as they pass through the 1/2-wavelength mark. However, the folded monopole is less than 0.16-wavelength long.

**Fig. 6** contains reactance values for one extra case: a shorted transmission-line stub constructed according
to the same wire diameters and spacing values that we used for the folded monopole. I arbitrarily cut off the table
at +j5000 Ohms since the reactance value of a shorted stub increases without limit at exactly 90 degrees.
**Table 3** shows the calculated values of the stub's reactance at the line lengths that correspond to the
folded monopole's lengths in the survey.

The table rests on calculating the characteristic impedance (Zo) from the physical dimensions of parallel
wires, as indicated in **Fig. 1**. One common equation for the calculation uses common logs.

However, there is a more precise equation that uses natural logs.

For the case in point, the impedance is high enough (657.22 Ohms) that the two equations yield essentially the same results.
The more precise equation becomes essential where the wire spacing is very close. Our 12" spacing is not close for
0.1" diameter wires. To calculate the inductive reactance of the stub, we may use another common equation. The
*l* term represents the line length in electrical degrees (or radians).

The shorted transmission line that uses 0.1" diameter wires and a 12" spacing has a calculated characteristic impedance (Zo) of 657.22 Ohms. For any given length, the inductive reactance is a direct function of the Zo value, and that value always apears as the inductive reactance at a length of 45 degrees for lossless lines.

I note these equations only to supply the basis for the tabular and graphical results shown. They suffice to show that the source impedance behavior of the short folded monopole--at least for the sample used here--is quite unlike the behavior of a linear monopole and the behavior of a shorted transmission line stub. To test these behaviors and to check for any variability, we need at least one more sample.

**Case 2: d1 = d2 = 0.5", s = 12"**

As a check on our work, let's sample a second folded monopole through the same total height steps. In this case, we shall increase the wire diameter to 0.5", a 5-fold increase over the initial sample folded monopole. The increased wire diameter applies to all parts of the antenna and so will have no effect on the impedance transformation ratio. The resonant impedance of a modeled antenna was 143.1 - j0.1 Ohms at a height above perfect ground of 66.81' (or 99.3% of the height of the resonant version of the first model).

Although the use of fatter wires with a 1' spacing does not change the folded monopole impedance transformation ratio,
it does change the characteristic impedance of the line if used in a shorted stub configuration. The new Zo is
464.17 Ohms (compared to 657.22 Ohms for the version using 0.1" diameter wires). For reference, **Table 5**
presents the calculated inductive reactance values for the sampled lengths of the stub in 10 degree increments. The
45-degree entry allows a quick reference to the line Zo.

Except for the lowest 2 heights (10 and 20 degrees), the NEC-4 models of the antenna produce excellent AGT values. Hence,
they require no adjustment in the tabular data. **Table 6** provides the information gathered from the test runs
using the same format and column entries that we used for the thinner model.

To facilitate comparisons, I also created a linear monopole over perfect ground. I selected an element diameter that would achieve resonance at the same height (66.81') as the folded monopole in question in order to develop a relatively fair comparator. The required diameter was 5". The diameter is 1.8 times the diameter (2.75") of the comparison linear monopole used for the folded monopole with 0.1" elements. Both folded monopoles use the same center-to-center wire spacing. The exercise establishes that finding an equivalent linear monopole diameter to a given folded monopole structure requires attention to the wire diameter as well as to the wire spacing of the original folded structure.

**Table 7** shows the linear monopole data, again using the format established earlier. Of course, the linear
monopole requires only one gain figure, since the pattern is uniform in all azimuth directions. Our initial comparisons will
be internal to the new sample. We shall make cross-sample comparisons a bit later.

The relative gain values appear in **Fig. 7**. Since the gain of the linear monopole varies so inconsequentially
over the range of real materials, the aluminum gain curve suffices as a substitute for 3 overlapping lines. The pattern
of gain deficiencies with real materials for the folded monopole below a length of about 50 degrees reappears in this
graph and in the tabular data. However, the 5-fold increase in folded monopole wire diameters shows up as a
significant reduction in the deficiency level.

In **Fig. 8** we find the comparison of linear and folded monopole source resistance values. The linear monopole
resistance increases in a regular (but not linear) fashion. In contrast, the folded monopole shows a very sharp
peaking of resistance at about 60 degrees. The positions of the adjacent resistance values suggests that the true peak may be
at a length very close to 60 degrees.

**Fig. 9** tracks the progression of reactance values. One line shows the inductive reactance of a shorted
transmission-line stub. As I did earlier, I cut off the Y-axis arbitraily, since the 90-degree reactance value
increases without limit. (The tables show an exceptionally high but not limitless value for 90 degrees due
to computer conventions for avoiding errors.) In contrast, the linear monopole shows a continuous, regular decrease in the
capacitive reactance as the antenna grows toward its resonant height. Of course, at a physical height of 90
degrees, the antenna is slightly long relative to resonance, and so we find an inductive reactance.

The reactance curve for the folded monopole shows peak values of reactance at 50 and 60 degrees, with a transition region between them. The actual transition region is very small, as the reactance on either side climbs to values much higher than those recorded at the sampling points. In the length region that is about +/-10 degress either side of resonance, the reactance curve shows a seemingly normal curve that moves from capacitive to inductive as we pass through the resonant folded monopole length.

**A Tentative Comparison of Two Folded Monopoles**

We have looked individually at two folded monopoles that use the same 12" center-to-center wire spacing. The only difference between them is the diameter of the wires: 0.1" vs. 0.5". Hence, the impedance transformation ratio for both monopoles at a resonant height is the same: 4. Since a linear monopole using either wire diameter--or using the equivalent diameters in the comparators--has a resonant impedance of 36 Ohms (+/- 0.03 Ohm), we expect a resonant folded monopole impedance of 144 Ohms. The thin and think folded monopoles show 143.5 and 143.1 Ohms, respectively. We may consider these values to be very much on target, given the fact that our basic impedance transformation equation does not take into account the diameter or the length of the end wires. The models cannot exist without taking these end-wire factors into account.

When we look at short folded monopoles using the same basic structure, we have to recognize that we cannot expect a precise equivalence. The length increments use the physical length of the structure, not the electrical length relative to the resonant length. The 0.1" antenna was resonant at a length of 67.25', while the 0.5" version resonated at 66.81'. However, the lengths are less than 1% apart, which minimizes any differentials in this area of concern.

For a sample of the gain differential, **Fig. 10** compares the modeled maximum gain edgewise to the wires for
both folded monopoles using copper wire. The thinner-wire folded monopole shows a 7-dB gain deficit compared to the
fatter-wire model at the shortest length. As we increase the length of the folded monopole, the gain difference
decreases in a smooth curve so that by the time we reach a length of 50 or 60 degrees, the differential disappears
(depending on our standard of when a differential is too small to be notable). The root source of the differential
lies in skin effect. In small loop antennas, builders commonly use the largest practical conductor (sometimes round,
sometimes flat) to reduce to the lowest possible level any losses due to the resistivity of real materials. The losses
of the linear monopoles suggest that a wire diameter of well over 2" may be needed by folded monopoles shorter than
about 50 degrees in order to reduce these losses effectively. Unfortunately, such diameters are not practical
for NEC-4 models.

**Fig. 11** superimposes the source resistance and the reactance curves for the two folded monopoles. Due to the
paucity of sampling points, the peak values appear to coincide. However, such curves can be somewhat misleading if
we seek more than general guidance. Let's look at each folded monopole.

*0.1" Model*: A series of models using finer length gradiations set the height at which the reactance passes
through zero at about 42.321' or 54.215 degrees. The resistance in the immediate length region rose to 19540 Ohms.
The length of the folded monopole was about 62.9% of a resonant version or about 0.157-wavelength electrically.

*0.5" Model*: A similar series of models produced a height of 44.270' or 56.711 degrees at which the
reactance passed through zero. At this height, the source resistance report was 10480 Ohms. However,
the source resistance peaked (10510 Ohms) at about 44.235' or 56.667 degrees. The zero-reactance model was
about 66.26% of a resonant version of the antenna or about 0.166-wavelength electrically.

We may note several interesting items about these numbers after observing an significant caution. The numbers derive from models that show an ideal AGT score, but which remain subject to all of the limitations to which the antenna modeling software (NEC-4) is subject. Hence, the numbers are useful for comparisons, but not necessarily for trying to build a short, resonant, very-high impedance folded monopole.

The thinner-wire folded monopole shows a much higher peak source resistance than the fatter-wire model. In fact, the ratio of peak source resistance values is 1.86:1. Although the tests did not specifically seek out the peak values of reactance that occur on the limits of the transition region, the thinner folded monopole appeared to reach values at least 1.6 times higher than the thicker model in the sequence of test model height. In both cases, the transition region was about 2 degrees of height, 56-58 degrees for the 0.5" model and 53 to 55 degrees for the 0.1" model. The transition region includes heights at which the initial peak inductive reactance value begins to decrease and--at the opposite end--the height at which the capacitive reactance increases toward but does not reach its peak value.

The height at which the folded monopoles pass through zero reactance seems initially counter-intuitive, since we might expect the folded monopole using fatter element wires to pass that point at a shorter height in keeping with the slightly shorter height of a 1/4-wavelength resonant version. As well, the 0.5" model's slight difference between the zero-reactance height and the maximum source resistance height may also seem somewhat counter-intuitive to our understanding of high-impedance resonant points. In both cases, the most likely candidate to serve as the source of these interesting results is the end wire. The potential corner coupling of the 0.5" model might account for both phenomena. However, the models are not self-explanatory in this regard. As well, we cannot say from the model alone whether the phenomena is an artifact of modeling or a real phenomena. Models that mix wire diameters at angular junctions quickly become unreliable in NEC (both -2 and -4).

The differences in behavior between the two folded monopoles using equal legs, but of a different size for each model, are small. More significant is the general behavior trends that show the progression of antenna behavior with increasing length. First, the very low source resistance of shorter lengths (up to and perhaps beyond 30 degrees) results in a very lossy structure when using real materials of even the finest quality. Second, the very high impedance resonance in the 54- to 56-degree region is notable for both its potentials and its limitations relative to using a short folded monopole. The short folded monopole acts neither like a shorted transmission line nor like a short linear monopole.

**Short Folded Monopoles with Dissimilar-Diameter Legs**

Many folded monopoles make use of an existing structure for one leg and add a wire for the second leg. At resonant 1/4-wavelength sizes, we expect the monopoles to closely approximate calculated values of source impedance. We can do some initial modeling to see what happens as we sample shorter lengths, but we cannot do so reliably within NEC. We must turn to a version of MININEC. For the following examples, I used Antenna Model, a highly corrected version of MININEC 3.13. Fortuitously, the program provides AGT scores as a matter of course.

To limit the stresses upon the limitations of the core, we may restrict our initial investigation of folded monopoles
with unequal leg diameters to only 2 leg sizes: 0.1" and 0.5", the sizes that we used in the first two cases. As
shown in **Fig. 12**, the top wires for the new cases will use the thinner wire size. The black dots represent the
location of the model source. In NEC, we generally construe the source location to be along or at the center of the
lowest segment in the relevant leg. In MININEC, the source is at the junction of the leg with the ground.

The ratio of leg diameters is 5:1. However, the equation that calculates the impedance transformation does not use that ratio directly, but incorporates the leg diameter within a ratio with twice the space between legs and then takes the common log of both space-diameter ratios. Hence, the resonant linear monopole source resistance becomes (by calculation) about 210 Ohms when we feed the thinner leg and about 105 Ohms when we feed the fatter leg. The proximity of modeled impedances to the calculated ones becomes a second test (in addition to the model's AGT) of the reliability of the reported data on the short folded monopoles.

**Table 8** provides the data for the version of the folded monopole with the source located on the thinner
wire, Case 3. The table omits information on gain values for real wire materials, since that information would largely
parallel the data for Cases 1 and 2. The perfect-ground gain data generally parallels the corresponding information
for folded monopoles with equal-diameter legs. However, the broadside-to-edgewise gain differential is slightly greater.
Although the impedance information for the shortest length appears quite reasonable and the AGT is only slightly
off ideal, the gain data appears to need further study before we accept it at face value. In the following notes,
gain will not be our main focus.

**Table 9** presents the comparable data for Case 4, which feeds the 0.5" leg of the folded monopole. Although
the AGT scores are virtually ideal (at least through 3 decimal places), the gain data is subject to further scrutiny.
However, the broadside-to-edgewise gain values more closely parallel those we obtained from the first two cases.

Whatever the reservations we may apply to the gain data, the most significant data resides in the resistance and reactance columns of the tables. Like the equal-diameter cases, both of the new cases shows exceptionally low source resistance values at the shortest lengths. The tables provide an entry for the resonant length information. In both new cases, the modeled resonant impedances are within 1/2 of 1% of the calculated values.

The curiosity of the folded monopoles with unequal leg diameters appears clearly in **Fig. 13**. When we
feed the thinner wire, the source resistance peaks close to 60 degrees, or higher than either of the length
values that we found in the first two models with equal-diameter legs. In contrast, when we feed the fatter leg,
the length that shows peak source resistance is closer to 50 degrees. This length is shorter than we found for the
first two cases.

Due to the very high peak resistance values, the lower source resistance values form almost stright lines, forcing us back to the tables for the interesting properties. When we feed the thinner leg of the folded monopole, we discover a very rapid increase in impedance, beginning at a thousandth of an Ohm and climbing in a span of about 0.16 wavelength to an exceptionally high value. Predicting the source resistance of a physical version of the short Case-3 folded monopole would be a daunting task at best. Even temperature changes might yield significant resistance excursions at the feedpoint unless we use a wideband or a lossy matching network. Case-4 monopoles fair no better for lengths from 10 to 50 degrees. However, the region from 60 through 90 degrees shows a much slower rate of resistance change from one step to the next. Unfortunately, this region also shows consistent capacitive reactance.

**Fig. 14** overlays the reactance curves for the two new cases. In general outline, the curves follow the pattern
established by te first two cases that use equal-diameter legs. However, the transition regions call for some special
attention. Cases 3 and 4 both show that the transition region occurs between lengths of 50 and 60 degrees. Within that
10-degree span, the two new structures differ considerably. By tracking the level of the 50- and the 60-degree peak values,
we can obtain a fairly close approximation of the difference. For example, if we feed the thinner wire (Case 3), then
the capacitive reactance at 60 degrees is close to -j3000 Ohms, but the inductive peak at 50 degrees is only a little
over j1000 Ohms. The zero-crossing point must therefore occur much closer to the 60-degree mark.

In contrast, in we feed the fatter wire (Case 4), the inductive reactance peaks at about j8000 Ohms at the 50-degree level. By 60 degrees, the capacitive reactance is about -j1000 Ohms. By the same reasoning, we must conclude that the zero-crossing point for this configuration is not much above 50-degrees physical length.

More generally, we see a widening of the possible range for reactance transitions and resistance peaks with these cases than when we simply change the diameter of equal-diameter versions of the folded monopole. A thin-fed wire to fat-return wire situation tends to push the transition point to a higher length level. In contrast, a fat-fed wire to a thin-return wire pushes the zero-crossing point to a lower total fold monopole height.

**Some Tentative Conclusions**

Modeling demonstrations do not yield proofs of performance. However, from the general trends that we have observed with our four case studies, we may draw some conclusions that we may think of as reasonable expectations of folded monopole performance.

1. At very short lengths (up to 30 to 40 degrees), 2-wire folded monopoles of any description show very low source resistance values. The values are lower than we obtain with linear monopoles of the same height. In fact, it is in this region that we find the closest coincidence between folded monopole and shorted transmission-line stub behavior with respect to the inductive reactance. When we translate the models to real types of wire, material losses alone are sufficient to create very high gain deficits. Below a total height of about 30 degrees, the losses may be high enough to jeopardize the utility of the structures for communications.

2. Between heights of 50 and 60 degrees, we find a transition region in which the resistance rises to a very high peak value. In the same region, the reactance peaks both inductively and capacitively, with a very small height region in which it crosses the zero point. The behavior closely resembles the behavior of center-fed linear horizontal antennas as they they approach 1 wavelength or of linear monopoles as they approach 1/2 wavelength. In folded dipoles, the behavior occurs with lengths between 0.14 and 0.17 wavelength.

3. Although the region of peak values between 50 and 60 degrees dominates graphs of the folded monopole's feedpoint performance, the entire span from 40 to 70 degrees shows rapid changes in both resistance and reactance with only small changes in folded monopole height. These behaviors can make the matching of a folded monopole in this height region a very finicky task. In all cases, one must experimentally determine if the settings used will be stable through the entire set of environmental conditions that the antenna may face.

4. The most stable region of folded monopole performance occurs at physical lengths between about 70 and somewhere above 90 degrees. In virtually all cases, resonance will occur at physical heights between 80 and 85 degrees. Within the overall region, the resistance changes per unit of height change are relatively small. Reactance changes are likewise small and follow the normal progression from capacitive reactance below resonant length to inductive reactance above resonant length. Therefore, matching networks and wide-band impedance transformers will tend to show the same performance characteristics that they display when used with linear antennas.

5. For every resonant folded monopole, there is a linear monopole of some diameter that will resonate at the same length. The required diameter for the linear dipole is a mutual function of both the wire diameters and the wire spacing of the folded monopole. Since the equivalent linear monopole will be very large relative to the diameters of the wires within the folded monopole, it will exhibit far lower losses with real materials than the folded monopole using the same real materials, especially at very short lengths. However, the folded monopole may offer a considerable total weight reduction relative to the linear monopole, especially at longer, more stable overall heights.

In the tables, the numbers recorded are overly precise relative to the general reliability of the models with respect to reality. My reason for recording the reported modeling data in these terms was to ensure accurate graphing. At best, these notes serve as a general guide to reasonable expectations from folded monopoles. By omitting real ground types and real materials from the calculations, the notes do not qualify as guides to building a physical antenna. Nonetheless, the consistency of the general trends may provide some insight into short folded monopole behavior.

In the cases that we have explored in this set of notes, both legs of the short folded monopoles used the same length, and the top wire shorted the upper end of the structure. However, short folded monopoles often find application where the return wire is longer than the fed wire. We have learned to name such applications, but it is less clear that we have developed any reasonable expectations of behavior. Therefore, we have another trail to explore through the forest of folded monopoles.

**Apprendix: A supplementary Exercise in Current Analysis**

The exercises that we have explored in developing some basic properties of folded monopole antennas focused upon antenna gain and the feedpoint impedance as guides. There is an alternative approach that may provide additional insights into the behavior of short and long folded monopoles. We may analyze the currents in the legs of the folded monopole into two component currents, often called radiation currents and transmission-line currents. At any point along the length of the folded monopole, the sum of the two current magnitudes and phase angles (one on each leg) result in the radiation curreent, while the difference yields the transmission-line current, assuming that we set up the model wires for the legs in parallel fashion, that is, counting from the ground up (or the top down) for both legs. See the Antenna Modeling series of articles, #123, for details of how to set up the calculations. Although NEC output files list the currents in terms of both real and imaginary components and of magnitude and phase angle, EZNEC current tables list only the magnitude and phase angle. Thus, the first step is convert the given values to real and imaginary components, then to perform the additions and subtractions, and finally to reconvert the values back into magnitudes and phase angles. A repetitive spreadsheet is, of course, the most convenient method for automating the required machinations.

If we perform the operation on a resonant folded monopole at 3.5 MHz, we obtain some interesting results. For the subject antenna using 0.1"-diameter elements and a separation of 1', the resonant length is 67.25 or 86.15 degrees. For comparison, let's also set up a resonant linear monopole of the same length. The linear monopole must have a diameter to 2.75" to be resonant at the prescribed physical length. For simplicity, we shall set both antennas against a perflect ground and use perfect (or zero-loss) conductors. NEC, of course, will provide a direct reading of currents on the linear monopole because it has no currents that we can analyze as transmission-line currents.

The results of the exercise appear in **Table 10**.
On the left, the first four current magnitude and phase columns provide
magnitude and phase-angle values from the EZNEC current table every 5
segments along the antenna's length from the ground upward. The next
two columns provide the analyzed radiation current (Irad) magnitude and
phase angle for each increment of antenna length. The final two columns
list the analyzed transmission-line current (Itl) magnitude and phase
angle. To the right are the current values for the linear monopole
model.

Except for the 60th segment, the radiation current magnitude values for both antennas are virtually identical. The slight aberration in the last value is a function of the folded monopole top connecting wire. Minimum current occurs at its center. As well, the pattern, although not the precise values, of radiation current phase is the same for both antennas. With respect to transmission-line currents on the folded monopole, the magnitude values increase from the ground toward the top. However, the phase angle of these currents is the same all along the antenna and 90 degrees out of phase with the feedpoint current. We would see similar results from a folded dipole counting from the feedpoint outward to the antenna end.

Next, let's examine a short folded
monopole, perhaps one that is 20 degrees (15.612') long. We may not
only perform a similar analysis (using each of the 12 segments in the
model), but as well we may again compare it with the corresponding
2.75"-diameter linear monopole of the same length. The results appear
in **Table 11**.

The linear monopole on the right displays a
normal progression of currents from the ground upward, despite the very
short length of the antenna. However, the folded monopole shows
something entirely different, due to the fact that the overall length
falls well below the critical region (between 40- and 60-degree
lengths) in which the antenna transitions from transmission-line-like
behavior to antenna-like behavior. (See **Fig. 6**, which shows the
reactance of a comparable transmission line, a folded monopole and a
linear monopole to see more vividly the critical transition length
region.) At the very short length of 20 degrees, the folded monopole
shows far higher current magnitude in the transmission-line column than
in the radiation column. Because the two wires, treated as a
transmission line, are almost perfectly out of phase with each other,
the net phase angle is zero and constant along the short length. The
minuscule radiation current magnitude is accompanied by a minimal
phase-angle shift that only become apparent at the top of the folded
monopole.

Applying the current analysis to the modeled current values for the short folded monopole yields an impression that the short folded monopole is likely to be a relatively poor radiator. In some applications, it might actually be superior to the short linear monopole once we add to the single element the requisite loading coil at a plausible level of Q. Nevertheless, below the critical transition length region, the short folded monopole principally acts like a shorted transmission line rather than like an antenna.