Literature about multi-wire monopoles is fraught with odd labels for the structures. We can find terms like *folded monopole*, *folded isopole*, *caged monopole*, and *skirted monopole*. If we can find legible diagrams for what the labels
label, we are in for something of a surprise: they all refer to the same class of antenna. However, some engineers prefer to
reserve the title of *folded monopole* for an antenna with only 2 wires. Others apply the term more generally to all or most
multi-wire monopole systems. To the best of my knowledge, the *skirted monopole* terminology arose when the outer wires
served as a means for detuning the monopole--usually a tower--from its sensitivity to interact with nearby (near-field) AM BC
transmitting antennas. Hence, detuning skirts are common on urban cell towers. However, we can also feed the skirt on a
transmitting tower and obtain a measure of impedance transformation and control that turns out to be useful. We might speculate
that the expression *caged monopole* arose as a somewhat more politically correct than the term *skirted monopole*.
Regardless of the humor we may make out of the terminological morass, we are left with a basic question.

Is the multi-wire skirted or caged monopole a folded monopole or isn't it?

Let's start at some sort of beginning by looking at some forms of multi-wire monopoles. **Fig. 1** shows a few of the
many possible configurations. On the far left is a standard 2-wire folded monopole. It forms a touchstone for all that
follows. At this stage, I shall note only one interesting property of the standard folded monopole. Edgewise to the wires,
we find a very tiny (and operationally insignificant) asymmetry to the antenna's gain. For ordinary wire spacing, the
differential might be up to 0.04 dB in models, favoring the feedpoint side of the antenna. The broadside gain is the average of
the edgewise gain values. Next to the 2-wire folded monopole is a 2-wire folded monopole with an extension on the return-wire
side. (In practice, it makes no difference whether the extension connects to the fed wire or to the return wire if
the connecting wire is short enough as a function of a wavelength.) I drew the antenna in the manner shown because it
shows the relationship of a folded monopole with an extension to a gamma or omega matched tower used by some amateurs on
40 meters. If we assume that the antenna would be self-resonant without the extension, then with the extension, we find an
increase of both the resistive and the inductive components of the feedpoint impedance. If the fed wire length does not result
in a self-resonant antenna without the extension, then we usually call the added fed wire a *matching line*. The preferred
term here is a function of what we are trying to achieve more than it is a difference in the electrical performance
of the antenna. Like all folded elements, we shall find both a transmission line function and a radiating function
within the folded section.

The sketches jump to 4- and 5-wire structures. However, a 3-wire monopole system is both possible and interesting. If we
place wires on opposite sides of a return wire/tower and if we feed both new wires in parallel, we obtain a rudimentary
caged or skirted system. Like the more complex 4- and 5-wire systems in **Fig. 1**, it produces a symmetrically circular
azimuth pattern. In fact, within very narrow limits--largely a function of the fact that the more complex cage systems
tend to result in slightly shorter antennas when they are self-resonant--the gain of all types of caged, folded, or skirted
monopoles is the same. (Some models of these antennas have shown more deviant values, but they usually correct to the
basic value when adjusted for the average gain test (AGT) score of the model.) Over perfect ground using lossless wire,
the entire set of self-resonant monopoles show a median gain of 5.15 dBi, with less than about +/-0.04 dB variation.

The two sketches on the right of **Fig. 1** differ in only one small way. The 5-wire monopole uses one or more
wires that circle or girdle the outer wires only. In large installations, the connecting wires serve an important mechanical
goal to help rigidify the cage of very long out wires. Also note that the sketches show a set of connecting wires at the
base with a single feedpoint between the wire and ground. (We shall presume that all return wires in the figure return to
ground.) In theory and in practice, the single feedpoint can result in slightly different current magnitudes and phase
angles along the outer wires. The connecting wires create short circuits along the structure that tend to equalize currents
along the outer wires.

We may replace the energy source with a network and change the system function from radiation to tower detuning. There are numerous techniques that allow engineers to use essentially the same caging wires to detune a tower from most frequencies within the upper MF range. Some techniques may involve modifications to the cage of wires as well as to the base network. Tower detuning via skirts has become a fairly routine and commonplace engineering service. Its necessity and profitability has increased with the proliferation of cell-phone and other UHF/microwave towers that now pervade urban, suburban, and rural landscapes.

For our purposes, we may bypass the detuning role of skirts and cages in order to address more directly our initial question: are they forms of folded monopoles? To approach an answer, let's begin by seeing what makes the 2-wire folded monopole so special.

**The Folded Dipole and the Folded Monopole**

Hardly a soul among those interested in antennas does not know about the folded dipole. Unfortunately, what many folks know is
only a tiny piece of the story. If we parallel two identical wires at a reaonably close and constant spacing, if we connect the
ends and feed one of the wires, and if we bring the antenna to resonance, then the feedpoint impedance on the selected fed
wire is 4 times the impedance of a linear resonant dipole. There is much more to the folded dipole story than this, and I have
tried to tell some of it in "**Unfolding the Story of the Folded Dipole**".

Part of the story involves the fact that a folded dipole and a linear dipole have the same gain and pattern. Another
part of the story involves the fact that a folded dipole is two devices in one. It is a dipole and has radiating currents that
almost exactly parallel the radiating currents of a linear dipole in both magnitude and phase angle. The folded dipole
is also a transmission line (or, counting from the feedpoint, two transmission lines with a common starting point)
with a relatively constant current magnitude and phase angle (that is 90 degrees out of phase with the radiating
current). John Kuecken showed how to separate the two currents in *Antennas and Transmission Lines* (pp. 224 ff).

Perhaps the most significant part of Kuecken's account is that he describes the technique in connection with the
*hairpin monopole* (another name for the folded-monopole list of aliases). The technique applies equally both to
folded monopoles and to folded dipoles, since the former is simply half the latter if terminated in a perfect ground or
in a ground plane the approximates a perfect ground. If we make the folded structure self-resonant using a perfect
ground and lossless wire, a dipole will show about 72 Ohms for a feedpoint or source impedance (resistive, of course),
while a linear monopole will show 36 Ohms. Folded versions of the two will shows 288 and 144 Ohms, respectively under
suitable conditions. **Fig. 2** shows the correlation of the two antennas and their linear roots.

The "suitable conditions" clause of the folded antenna impedance report presumes that the two wires in the folded structure
have the same diameter. As well it presumes that the two wires are close enough to form a transmission line rather than simply
an open loop or open half-loop. Unfortunately, too many amateurs are unaware that we may effect other impedance transformations
by varying the diameters of the two conductors, or the spacing between them, or both. **Fig. 2** hints at that wider
range of potentials by designating the wire spacing as s, the diameter of the fed wire as d1, and the diameter of the
return wire as d2. How these dimensions (all in the same unit of measure) go together to effect an impedance transformation
appears in the following equation.

If d1 and d2 are equal, then the right side of the expression in () is 1, and to that number we add 1, to get 2, which squares to 4 as the value of R, the ratio. Hence, the most common case of a folded dipole multiplies the linear dipole impedance by 4. A folded monopole meeting the same conditions does likewise. Next, let's make the return wire diameter go to an infinitesimal value. We cannot let it go to zero or we cannot have a return wire, but an infinitesimal diameter will suffice to leave us with a wire, but one that reduces the d2-diameter and right side of the expression in () to a value insignificantly different from zero. Within the () we now have a value of simply 1, which squares to 1. This condition sets the minimum transformation in a folded dipole or monopole. In other words, a folded mono-/di-pole cannot transform an impedance downward from the linear value--only upward. On the other hand, making the return wire very small drives the denominator on the right side of the expression in () toward zero, increasing the value of the fraction to an indefinitely high value. For most antenna work, resulting ratios (R) greater than 10:1 are seldom encountered. However, we often find conversion ratios above 4:1, especially in gamma-match structures, where the gamma rod is considerably thinner than the main element to which it attaches.

**Fig. 2** also labels the end wires that must be part of any real folded antenna. I note these wires because they
do have an effect on the physical version of what we calculate from the equation. The wires must be short enough that
their effect is relatively insignificant. However, their effect is real and shows up in computer models of folded
dipoles and monopoles. One easy way to see the effect is to create a resonant model of a folded dipole using wires
having different diameters. Now alternately use the fat wire or the thin wire diameter for the end wires and recheck the
required length for resonance. You may also wish to look at the current tables available in NEC and MININEC for additional
confirmation of the effect of end wires. To make the effect more vivid, use a lower frequency with a fairly wide physical
spacing (such as 3' at 3.5 MHz) and use enough total segments so that the end wires have multiple segments.

If we create a multi-wire cage around the center wire, we can achieve two different orders of phenomena. Of we place the source on the center wire, then the set of cage wires (any number from 2 upward for a total folded antenna count of 3 upward) increases the impedance transformation ratio. We rarely encounter this situation. However, users of cages around a central mast or tower in the upper MF and lower HF regions often feed the cage wires in parallel, allowing the fat center wire to serve as the return wire. This practice serves a number of ends. First, it allows the central tower a direct connection to ground. Not only does this move simplify the tower's mechanical structure, it also is an important safety measure. Second, using the central mast or tower as the return wire results in an impedance transformation ratio that is lower than 4:1. By choosing the correct number of wires for the cage or skirt and feeding them in parallel, we can obtain an impedance that is higher than a monopole's 36-Ohm value over perfect ground but much lower than the 4:1 value of 144 Ohms. Indeed, a 4-wire cage provides a value that is very close to 50 Ohms, virtually ideal for coaxial cable.

**The Root of the Issue**

The problem that we encounter with both physical antennas and their NEC models is that the resultant impedance does not coincide with the basic folded dipole/monopole equation. The resultant impedances that we encounter when connecting parallel sources together for a caged or skirted monopole do not answer to any simple relationship to the 2-wire folded monopole (or dipole). As a consequence, some engineers hesitate to identify the caged or skirted monopole with the 2-wire monopole.

We might initially treat caged monopoles in a variety of ways. For example, we might consider the structure to be a version of a coaxial monopole in which the return wire forms a center conductor, with the outer wires forming the outer conductor corresponding to the braid on an ordinary coaxial cable. However attractive this picture may be, we also must recognize that the outer wires leave mostly empty space. In addition, if we apply the 2-wire equation to this situation, then the value of d1, the fed wire, becomes identical to the value of 2s, that is, twice the spacing between conductors. The common log of 1 is zero, resulting in an impedance transformation of 1. Hence, a resonant monopole under this treatment would show a 36-Ohm impedance. However, cage monopoles show a higher impedance, with the actual value being partially a function of the number of wires.

Alternatively, we may model various samples of cage monopoles and, with due attention to AGT scores, arrive at reasonable estimates of the resulting impedance. We quickly discover a factor that the coaxial treatment cannot take into account directly. For any given return wire (d2) diameter, as we change the diameter of the outer wires, the resultant antenna impedance will change. The coaxial treatment can use only one value for d1, taken just now to mean the overall outside diameter of the cage system. It is possible to obtain from the basic equation an impedance that is equal to the modeled (or field tested) value by using a selected value of diameter for d1. However, this treatment is initially ad hoc. It involves varying the diameter of d1 until the impedance value matches the modeled or field value. If we survey enough values, then we might use some form of regression analysis to arrive at correlations that would be usable for almost any (practical) combination of center diameters, spacing values, and cage-wire thicknesses. Nevertheless, regression analysis is an excellent tool for establishing a mathematical correlation to a set of curves derived from observation, but it does not provide an explanation of the correlation. The equations would not necessarily fit any set of known electrical foundation equations to provide a seamless continuum between 2-wire and multi-wire folded dipoles.

The absence of a means of direct derivability that might ensure that cage monopoles are a variety of folded monopole--or that might provide sufficient reason to withhold the connection--does not mean that we must give up on the problem. There may be other alternatives yet to be explored. Any such alternative must recognize that the presence of multiple fed wires that do not surround the center conductor or return wire will present disturbances to a strict correlation. Indeed, perhaps part of the past thinking that wishes to claim that a cage monopole is not a folded monopole has looked too strictly at what a cage does not do and too little at what it does do. Granted, a cage lacks the solidity to form a true coaxial surface. However, let us suppose that each fed wire forms with the central return wire a 2-wire folded dipole. Under this supposition, we can expect the fed wires to interact or mutually couple. The degree of interaction would vary with the diameter of the center return wire, the spacing, the diameter of each out fed wire, and, of course, the relative diameters of the fed and return wires. Despite the variables, we should still be able to detect a pattern of values that we can trace to the results of a 2-wire folded monopole.

**A Test and Its Limitations**

Within certain limits, we may set up a fairly simple modeling test. For the test we shall use a series of
monopoles, as shown in **Fig. 3**. Each monopole will be resonant at a given test frequency. Since we shall
use lossless wire and perfect ground to minimize the number of extraneous variables, virtually any frequency will
do. My test frequency will be 3.5 MHz. When modeling each test structure, the monopole will be resonated
to within +/-j0.1 Ohm.

The outer wires will have a constant diameter, 0.1". I shall vary the diameter of the center or return wire in steps. Since a zero diameter is not possible, I shall use 0.1-Ohm as the minimum return wire diameter. The remaining steps will be linear: 0.25", 0.5", 0.75", and 1". I shall end the progression at this point for modeling reasons. As the diameter of the center conductor increases, the AGT score departs ever further away from the ideal value. Using NEC-4, the value becomes unreliable more quickly than with MININEC (using a suitably corrected implementation of the public domain version 3.13), but both programs eventually fail to yield very usable results. However, we shall be able to track the requisite results over the range of selected values and arrive at some preliminary conclusions. The procedure is no less and perhaps no more approximate than the industry-standard practice of using single wire substitutes for complex geometries that more adequately reflect open tower structures. The AM BC industry regularly uses a wire radius of 0.37 times the face dimension of a triangular tower and 0.56 times the face of a square tower.

Besides varying the diameter of the return wire, the test models will also vary the center-to-center spacing between the return wire and the fed wire(s). I shall use spacing values of 12", 24", and 36". The top wires will use a diameter of 0.1", the same used for the fed wire. Each top wire will use a segment length of 1' (12"). The vertical wires will use 60 segments each, a value that produces segment lengths between about 0.9 and 0.95 of a foot. The very small disparity between the top-wire segment lengths and the vertical wire segment lengths does not jeopardize current calculations in NEC 4.1, since the feedpoint is in the lowest segment of each outer vertical wire. Tests using segment lengths that are as a close to 12" as possible result in variations of the feedpoint impedance by no more than 0.02 Ohm relative to either the resistive or reactive component.

One aspect may be unique to these test models, although it is a common modeling practice. The uniqueness is the attention that we shall give to it. Most NEC modelers attempt to supply the model with a single feedpoint to end up with an overall impedance for the structure. There are a number of ways in which we can perform the feat. We might elevate the ends of the fed wires and provide shorting wires between legs ends. Then we may run a single wire to ground and place a source on this wire. Alternatively, we may run transmission lines to a remote wire and place a source on it. If we select a near-zero length for the transmission line lengths (which are independent of the actual distance to the remote wire), we effectively connect the four base segments in parallel.

In MININEC we must--and in NEC, we may--simply place sources at the ground end of each fed wire. Of course, the number of sources will be one less than the number of vertical wires in the model. A 5-wire cage monopole will have 4 sources. Since the impedance values for all of the sources will be identical, the net impedance will be the resistance and the reactance at each source divided by the number of sources. This derived value will be the same as the one we would produce by using the transmission-line technique of paralleling the sources. What differs is that we shall have--and pay close attention to--the source impedances of the individual fed wires.

The test will include 2-wire folded monopoles, even though we may calculate the impedance transformation ratio from the standard equation. We shall be as interested in how close the fit may be between the model and the equation result as for any other form of folded monopole. A series of monopole models of lossless wire over perfect ground yields a resonant impedance of 36 Ohms. Hence, the reference impedance for each new combination of return wire diameter (d2) and spacing (s) will be 36 Ohms times the equation-based ratio. We shall be comparing the modeled impedance values for each fed wire with the reference impedance value.

The test will initially yield reported values of source impedance. As well, each test will have an AGT score. Over perfect ground, the ideal AGT is 2.000, although the value is 1.000 in free space. The free-space equivalent of the ideal perfect-ground AGT is simple 1/2 the perfect-ground value. I shall use this free-space equivalent value in test reports, since it plays an important role in arriving at a usable impedance value. One reason for resonating the folded monopoles to such close tolerances is to allow us to use the AGT score to arrive at reasonably reliable values of resistive impedance.

However, with folded structures, we must alter NEC manual procedures somewhat. For a linear element--whether a dipole or a monopole--we normally multiply the AGT times the reported impedance to arrive at a corrected source impedance. The correction is most reliable when the impedance is virtually resistive. With folded dipoles and monopoles, we must reverse the correction procedure. To arrive at the usable impedance value, we must divide the reported impedance by the AGT score. As a matter of course, we shall also report the net impedance of the structure. More significant for our interests will be the ratio of the adjusted or corrected impedance value for each leg to the calculated 2-wire impedance for a folded monopole having the wires and spacing applicable to a single fed wire and the center return wire.

**Some Test Results**

**Table 1** provides the results for the series of modeling tests that I just described. The table lists 5 test
sequences, each of which uses a different diameter for the inner, center, or return wire. The first column lists the
3 steps of spacing. The second column tells us the total number of vertical wires in the assembly. The number of fed
wires is 1 less than the total. The third column lists the height in feet of the resonated skirt-fed monopole. The
"Raw R" column lists the NEC 4.1 source resistance value before correction. The "Raw X" column provides a record of
how close the model came to perfect resonance. The final column of raw data lists the AGT score using hemispherical
increments of 5 degrees.

The remaining columns list the operations performed on the raw NEC data. The adjusted source resistance per leg results from dividing the raw resistance by the AGT score. The net source resistance appears in 2 columns, the first dividing the raw leg resistance by the number of source, the second dividing the adjusted leg resistance by the number of sources. The final column lists the ratio of the adjusted leg resistance to the calculated 2-wire impedance.

The resonant antenna height has only suggestive utility beyond showing the trends that confirm the propriety of model construction. As we increase the number of wires or the diameter of the center return wires, or the spacing between any fed wire and the return wire, the resonant height decreases over perfect ground. Although the trends are true, the exact resonant height of an actual folded monopole will vary somewhat with the ground quality and the number of radials forming the ground system. The AM BC standard of 120 quarter-wavelength radials with shorter intervening radials remains applicable to all monopoles, whether linear or folded. With respect to the source impedance of an assembly, such a system best replicates perfect ground. (Of course, the overall ground quality plays a significant role in determining the far field patterns for the antenna.

The AGT values provide an indication of the reason for halting the systematic modeling venture with a 10:1 ratio between the return wire and each of the fed wires. As we increase the diameter of the return wire, the AGT score decreases. By a 10:1 ratio, the score reaches 0.915. Beyond this value, I would not fully trust the reliability of the reported data, even when applying the corrective to the per-leg source resistance value. The impedance transformation ratio for a 2-wire system is largely a function of the physical properties of the folded monopole. Hence, the use of a large diameter tower (or its equivalent 3- or 4-face open tower) with standard wire sizes for the fed cage structure becomes problematical from a modeling perspective. 0.1" diameter wire approximates AWG #10, a value that falls about halfway between AWG #12 and #14, popularly used by radio amateurs, and AWG #6, sometimes used by commercial installations.

The net adjusted source resistance columns indicate one reason why cage-fed or skirt-fed monopoles are finding proponents. As we add fed wires (symmetrically, of course) to a center return wire, the net source impedance of the parallel-fed outer wires brings down the overall source impedance. With equal-diameter wires for the fed and return legs, we have the familiar 4:1 up conversion of the impedance for each leg. As we increase the return wire diameter, the source impedance in each leg increases in step with standard expectations from the 2-wire equation, although we cannot obtain a precise number for more than a 2-wire system. Nevertheless, when we parallel the leg sources, the net impedance decreases as we increase the number of fed outer wires. For any given combination of fed and return wire sizes, increasing the spacing decreases the net impedance. However, for any number of fed sources, increasing the return wire diameter increases the impedance. A 5-wire (4-source) cage indicates impedances that are close to optimal for direct coax feeding with either no matching or minimal matching requirements. Construction variables relative to both the cage and the return mast or tower, along with ground and radial system conditions will modify the values shown. Nevertheless, the trends are useful in system planning, even if NEC-4 models may fail to be reliable at the return structure diameter that might be used. For example, a triangular tower with a 12" face might show an equivalent diameter of 8.88", which--even with 36" spacing--would yield models of very dubious reliability.

For any given spacing and return-wire diameter, the per-leg source resistance shows a relatively tight
grouping of values as we move from a 2-wire to a 5-wire folded monopole. About 50 Ohms separates the lowest
from the highest value in each group. The variations within each group tend to suggest the level of
mutual coupling among the fed wires and other interactions. Data patterns alone do not provide the details
of the complex interactions. However, *the close proximity of the values within each group relative to the
calculated impedance value for a 2-wire folded monopole strongly indicates that each fed wire and the return
wire form a 2-wire folded monopole, modified in impedance performance by the interactions.* If each pair
of wires in a complex multi-wire monopole forms a folded monopole, then we may legitimately call the entire
structure, regardless of the number of cage or skirt wires, a folded monopole.

We may regroup the final columns of values that show the ratio of calculated to modeled values of per-leg
source resistance and graph them by reference to the spacing between the fed wire and the return wire. **Fig. 4**
shows the results for a spacing of 12". Each line represents one of the folded-monopole systems. The X-axis
shows the increase in the return wire diameter. Note that the lowest value (0.1") is not a true linear increment relative
to the other increments on the graph.

The 2-wire graphed line establishes that using corrected per-leg impedance values yields models that are always well within 1% of the calculated value of impedance. The per-leg values for 3-wire systems are always below those for 4-wire and 5-wire monopoles. For a spacing of 12", the lowest per-leg value is about 0.83 of the calculated 2-wire value. In contrast, the highest value is about 1.4 times the calculated value. Although these limits are fairly wide, each curve shows a much narrower range of departure from the calculated value, which the 2-wire curve indicates.

As we increase the spacing to 24", as shown in **Fig. 5**, the ratio of calculated to modeled adjusted per-leg
impedance increases, except for the 2-wire model. It continues to show its tight correlation to the calculated
impedance value. Perhaps only the effects of requiring a top wire prevent the ratio from reaching 1 to 1. The
ratio values for the larger folded monopoles show slight increases for all of the more complex
assemblies. Interestingly, about half of the data points fall above the 1:1 ratio lines, and half below it.

The graph for a spacing of 36" between the return wire and each fed wire appears in **Fig. 6**. The overall
grouping has all of the properties that we saw in the preceding graphs. However, the majority of data points now
fall above the 1:1 ratio line. The differences among the 3 graphs are not great, but they are noticeable as a function
of the increased spacing.

Perhaps more interesting than the differences are the similarities among the graphs. For each size of folded-monopole assembly, regardless of spacing, the curve shapes are regular and similar. (Even the 2-wire curve shows a very slight drop in value as we increase the diameter of the return wire.) As well, the values within each graph show a relatively tight clustering around the calculated impedance value. 5-wire systems show the highest level of departure from the calculated value, a fact that appears to coincide with the closer proximity of the fed wires to each other. Determining the effects of mutual coupling would require a different sort of study from the present effort. In each case, I have resonated the total folded monopole system in order to arrive at as pure a resistive impedance as feasible. Interactive analysis of the wires might require a study using a set of fixed-length wires.

Neverthless, the data shows that caged and skirted monopoles have their roots in 2-wire folded monopoles and are
an extension of the basic structure. The variations are insufficient to deny the use of the term *folded monopole*
as a generic label for all such structures.

In many ways, however, settling the terminological preferences of engineers has only been a pretext for the true point of these notes. Too many amateurs are unfamiliar with the general properties of folded monopoles, both simple and complex. These notes represent one small attempt to fill the void and to acquaint the amateur with the range of labels that he or she might encounter in basic reading about these antennas. A secondary goal has been to show the nature and the limits of modeling these antennas using NEC-4. AGT values for NEC-2 versions of the models would be even worse. We might extend the range of the sampling of return-wire diameters by using a well-corrected version of MININEC 3.13, but even that program will eventually show less reliable results before we reach the tower dimensions that we might encounter in reality.

Nevertheless, the trends shown in these notes may be useful in establishing realistic expectations from multi-wire folded monopole assemblies. The data shown here cannot eliminate the need for extensive field adjustment, but they may go some distance toward reducing the time involved.

* Updated 12-06-2005. � L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for
publication in print or any other medium without permission of the author.*