# stacking antenna and broadside collinear gain increase

**Endfire Broadside and Collinear Antennas**

There are three primary types of arrays, collinear, broadside, and end fire.

Collinear describes two or more things

arranged in a straight line. Extended double Zepps and two half waves in phase

are examples of collinear arrays. A 5/8th wave radiator, which developes gain when placed over an infinite ground plane through ground reflection image, is also a collinear.

The 5/8th wave is collinear with the ground reflection image.

Broadside is used to describe pattern in relationship to spatial area

occupied by the array. While a collinear array is a broadside array, the term

broadside is generally reserved for non-collinear arrangements.

End fire arrays are arrays with elements arranged in a row, running in the direction(s) of maximum

radiation. Yagi antennas, W8JK arrays, and log periodic dipole arrays are all

end fire arrays. They fire in the direction of the boom through the plane

of the elements.

## Gain

Before analyzing

stacking (broadside) or collinear antennas, we

really should

understand how antenna systems produce gain. There is a common “Ham-myth” that doubling the number the number of elements doubles

field strength (3dB more gain). This actually isn’t true. Doubling the number of

elements, or even doubling array size, can change gain almost any amount. While

there are isolated cases where a size or element number change might result in

3db additional gain, it is through coincidence rather than science. To

understand this, we have to understand what causes “gain”.

When a fixed power level is coupled into an antenna, all energy not lost as

heat is radiated as an electromagnetic field. This radiation is unevenly

distributed in space, much like a volume of air in a rubber balloon. The

creation of new or deeper nulls, in angles and directions initially having significant

radiation, forces energy into narrower directions. This increases level in those

areas at the expense of radiation in other direction, much like squeezing a

balloon with our hands will cause a balloon to expand in certain directions at

the expense of others. It is this squeezing of the radiation into a smaller

spatial area that causes a “gain” increase. A newly

created null or a deeper null removes energy from null areas, forcing that energy in

what we hope are more useful or desirable directions. In other words, because applied transmitter power is constant,

energy formerly radiated in areas of * significant radiation *moves to

enhance field strength in

other directions.

This effect is not from increased element number area or physical array size. The gain increase is actually caused by

redistribution of energy, because of the new, wider, or deeper null areas. When

a cancellation of radiation removes power from areas with significant radiation,

the pattern becomes narrower. This is an increase in directivity. When directivity increases without significantly increasing heat losses,

“gain” has to increase.

Null forming is caused by the relative phase and level relationship between two or more sources of radiation at different points in space around an array. If we arrange elements over space, phasing the elements in a way that forces

a null where there is very little energy, there will not be much pattern directivity or gain change. This

is because the system is attempting to remove energy from an area already lacking significant

energy. The reward is small, because there is little energy to redirect to more

useful angles or directions. An example of this is the

quad element, as height is

varied. When a horizontally polarized full-wave quad element is placed 1/2λ

above ground, or multiples of 1/2λ above ground, quad gain over a dipole is

minimized or can even be negative. This is because the quad element is trying

to force a null in an area that already has a deep null from ground reflection. Conversely, when the

quad element is compared to a dipole , each at 3/4λ high (which produces a strong overhead radiation lobe from ground reflection), or if a quad element is compared to a dipole in free space, quad element gain over a

dipole is maximized. This is because, under the latter conditions, the

dipole had significant energy where radiation from the quad’s second current

maximum forces a null.

This effect is

sometimes called * pattern*. Before

multiplication

antenna modeling

software was

commonly available,

we often used

pattern

multiplication to

estimate patterns

and gain. Pattern multiplication remains a useful tool, helping us visualize why

or how a particular array behaves in a certain way.

We should always consider patterns caused by spacing and

phasing, including earth reflections, when planning optimum spacing. At lower heights optimum

spacing will often vary as element mean height above earth, or null points created by

original cells making up an array, vary. We should never assume a certain spacing always

produces optimum gain, or that

effective

aperture somehow sets optimum broadside or collinear spacing. In fact, doubling an antenna’s size almost never doubles antenna gain (3dB).

I’ve added graphs

from Jasik’s ** Antenna Engineering Handbook** throughout this article. These graphs show theoretical

maximum gain of short, lossless, dipole elements

when arranged end-to-end

(Collinear) or

parallel above or next to each

other (stacked

broadside). These graphs represent the maximum possible theoretical or mathematical gain

of array elements having a single current maxima at or near the center, such as a dipole or center fed 5/8th wave element.

## Collinear

Gain

First we have the

end-to-end or *collinear
*element

placement gain.

The “Relative Spacing In Wavelengths” in the graph (fig 5-22) above is the

*current-maximum*

spacing of the

elements, not element “tip” or “center” spacing.

Gain for two collinear 1/2λ (or

shorter) dipole elements peaks with ~0.9λ

(wavelength) spacing.

Radiation is caused by current, and so areas of maximum current are where radiation

primarily occurs. With a

1/2λ dipole in

each element, the

dipole center spacing

below would be 0.9 – .25

-.25 = 0.4λ. The overall array length would

be .9 + .25 + .25 = 1.4λ

With two

dipoles placed end-to-end at the center with almost no end spacing, spacing of current

maximums (S) would be

.25+.25=.5λ. Overall length would be

twice that of a single dipole, or 1λ. Maximum theoretical gain for this spacing is found

on the graph above,

at the crossing of

the vertical 0.5

RELATIVE SPACING IN WAVELENGTHS and

intersection of

“curve 2” (the two-element curve), as ** just under 2dB over a single**Gain

element.

of two half waves in phase with close end-spacing is always less than

2dB over a single element in ANY

collinear antenna using 1/2λ or shorter

elements with very small element end spacing (D).

Despite what is commonly claimed in Ham-myths, we see simply doubling the

number of elements and doubling array length does

**guarantee a gain increase of 3dB!**

*not*Obtaining 3dB gain by doubling the number of collinear elements from one to

two requires a significant size increase over double-size. A ** collinear** two-element antenna, using half-wave dipole

elements, has

3dB gain over a single dipole when dipole current maxima spacing (S) is .75λ. This is .25λ

D, or 1.25λ overall L in the case of 1/2λ dipole elements, for 3dBd gain. Keep in

mind 3dB is not the maximum obtainable gain for two elements. Maximum

theoretical

gain is about 3.25dBd, and for 1/2λ dipole elements, occurs at about 0.9λ

S current maxima spacing, or 1.45λ L overall length. If the elements were 5/8th wave, the result would actually be less gain! This gain loss occurs from the addition of areas with out-of-phase currents in the 5/8th wave element.

Doubling gain

again (3dB

more gain, for a total of ~6dB), over the two-element case, requires

a minimum of ** four** collinear elements.

In this case array length would be

2.75λ, or 5.5 times the overall

length of the initial dipole.

A four or more element collinear array can produce over 6dBd gain

by a current maxima spacing over 0.75λ. If,

for example, the array

has 0.95λ

current maxima spacings,

a four element array

would have an optimum

gain of 6.7dB. This would result in an overall physical length of 3.35λ.

Again, this does not follow the “double elements is 3dB more gain” myth. Now the

gain is 6.7dBd, it has 4 (or more) times the elements, and has 6.7 times the

length of the initial dipole. To obtain 6.7dB gain over a dipole, the array had

to be 6.7 times the dipole length! To obtain 6 dB over a dipole, the array

length had to be 5.5 times the dipole length.

The more elements the

array has, the further individual

elements must be

spaced for optimum

gain. Doubling physical size while doubling the number of elements does not

double collinear gain.

**EXAMPLE OF COLLINEAR**

Using EZNEC, we see the gain of a lossless dipole in freespace is 2.14 dBi.

Adding a second collinear element with close end-to-end spacing, which

doubles antenna size, we have:

We now have 3.71-2.14 = 1.57dBd gain. We doubled antenna size, but gain

increased only 1.57 dB. Looking at Jasik’s collinear gain graph, we find

very close agreement. Current maximum spacing “S” in the model is 0.5λ, and maximum

theoretical gain predicted in Jasik’s graph is about

1.75dB:

Increasing spacing S to 0.9 wavelengths should produce maximum gain for two

lossless collinear dipole elements. EZNEC shows, for full-size dipoles:

We now have 5.37-2.14 = 3.23 dBd gain. This is in close agreement with

Jasik’s graphs. ** 3dB gain increase requires 2.6 times antenna area**,

increase

and this is with simple dipoles. Generally, as individual elements or cells (groups) of

elements making up an array become more directive, optimum spacing distance

increases.

### Earth Influences on Azimuth-focused Gain

When an antenna with azimuthal or compass-heading directivity increase is

placed above earth, pattern multiplication and gain is not largely affected by

earth. It is still possible to nearly obtain full theoretical gain at any

height. This is because the earth is not trying to force a null where the array

is also trying to create a null.

## Broadside Arrays

Broadside array usually describes elements

or cells or elements placed parallel

and one above the

other. The graph below shows * OPTIMUM*,

or maximum possible gain

not the actual

gain an array might

have. The graph below is for

*1/2*λ

*dipole*

elements (or shorter) in

freespace. Stacked Yagis

would, in general, require wider

spacing to produce

maximum possible gain, and almost always produce less than the theoretical

maximum gain increase shown below. This is because a Yagi generally has a

significant null off the antenna’s forward lobe. The differently located nulls,

or reduced energy level in areas where dipoles normally have significant

radiation, change optimum broadside stacking distance.

Optimum broadside

stacking distance

increases with more

directive elements

or cells. This is

why a pair of multi-element

Yagi’s stacked

requires wider

spacing for the same gain increase than a pair

of dipoles, and why

** less** maximum

stacking gain is

possible with the Yagi than we might

obtain with stacked

dipoles. Think of it

this way, if the

antenna is already

narrow there is less

unwanted energy

available to move to

the main lobe. Again, this shows doubling the number of elements or size does not double the gain.

Here is the

optimum gain graph

for dipoles in

freespace:

We can see

maximum gain occurs

at .675λ stacking

height. The stacking

gain is 4.8db, not

3dB as we often see

claimed. Again the

more elements the

narrower the

pattern, and the

narrower the pattern

the wider spacing

must be between

elements for maximum

gain.

### EZNEC Comparison

Here is the freespace EZNEC plot of two stacked (broadside) dipole elements:

Compared to a lossless dipole in freespace, gain is 5.96 – 2.14 = 3.82 dBd.

This agrees with the graph from Jasik.

### Earth Influences on Elevation Patterns

The presence of earth influences optimum stacking distance. This is because

the earth is trying to force a null in the same area or areas that elevation

stacking is also influencing. The earth can be considered a second element, and

before computer modeling, this influence was often visualized and calculated by

using fields from an imaginary “image antenna” placed down in the earth. The

“image antenna” was not something that actually existed, but was a tool for

calculating elevation patterns in the presence of earth. If we search old

textbooks and handbooks, the image antenna often appeared.

If we have a lossless dipole at 1/2λ over

perfect earth, we have this basic gain:

For a single lossless dipole, 1/2λ over

perfect earth, gain is 8.4 dBi. Now let’s watch when we stack the dipoles at the

same 1/2λ wave stack spacing:

The system now has 10.91 – 8.4 = 2.51 dBd gain. Freespace stacking gain was

3.82 dBd, stack gain is about 1.3 dB less.

Moving the dipole to 3/4λ height, we have

the following dipole pattern and gain:

This is 8.05dBi gain, now with significant energy where the stack would

force a null. Adding the second broadside element, in the stack, we have:

Gain is now 11.31 dBi, or 3.26 dBd (dipole at 3/4λ).

### Summary

I hope these

graphs help dispel

the myth that

doubling number of elements, or doubling array size, doubles

gain (3dB gain). Things are not that simple, and things almost never follow that

rule.

1.) Doubling

elements or array

size does not

guarantee doubling (3 dB more) gain. That’s a myth, because it is almost never

true.

2.) The narrower initial

antenna pattern is,

the wider stacking

distance generally becomes for

maximum gain

improvement. This does, in some very rough way, relate to

effective aperture.

3.) Optimum

stacking distance

for gain is

virtually never 1/2λ, it is

almost always wider.

4.) Optimum

stacking distance

can be very wide for

arrays with multiple sharp-pattern

antennas, or cells, in the array.

5.) Maximum gain

occurs only when a

null is forced in

an area that formerly contained significant energy

levels. If the original element or cell of elements has a null where the

stacking distance tries to force a new null, maximum gain increase is reduced.

6.) Height above

ground affects

antenna pattern, and

because of that,

height also affects optimum

stacking distance.

7.) Determining optimum stacking height or distance requires a model that

includes earth, as well as feed line and conductor losses.

## Feed Systems

The optimum feed system is generally a distributed or branching type of feed

system. There are many articles suggesting feed systems, so I’ll only point out

a few places where caution should be applied.

One error is using long lengths of 75-ohm line to co-phase two 50-ohm

elements. An odd-quarter wavelength 75-ohm line transforms impedances because

the line is mismatched, and has standing waves. If the line is lossless with a

perfect 50 0j ohm load, the 75-ohm SWR all along the 75-ohm line is 1.5:1. This

means, at odd-quarter wave distances, line impedance becomes 1.5*75 = 112.5 0j

ohms. Two of those impedances in parallel are 56.25 ohms. Unfortunately, the

required coaxial cable physical length means elements must ether be less than

1/2λ apart, or we must use longer feed lines from

the Q-sections to element centers.

Many articles make the Q-section longer than

λ/4, such as 3λ/4 or 5λ/4. We should be careful doing this, for two reasons:

- Losses increase because mismatched sections

are longer - Bandwidth decreases because there are

multiple mismatched sections in series

Consider the case of a line 5λ/4 wavelengths

long. Such a line has five 90-degree sections in series. If frequency changes

2%, it causes a 2% error in each λ/4 section. Errors in each of the five

sections add, and now the total line error is 10%. The Q-section not only has

additional loss, it also has reduced bandwidth.

Using a 50-ohm section from each element to its

respective Q-section, so each Q section only needs to be λ/4 long, will always

increase bandwidth and often decrease losses. It is also not difficult to

implement. My 6-meter Yagi stack uses 50-ohm equal length lines to the

Q-sections, which are only λ/4 long. Length of the 50-ohm sections does not

matter, so long as they are equal, because the 50-ohm sections are matched, and

essentially have a 1:1 VSWR. If I make a velocity factor error, or change

frequency, or have 75-ohm line losses, errors and/or problems are 5 times less!

I’m not forced to have feed lines between the

antennas that can only be changed in multiples of λ/2, such as λ/4, 3λ/4, 5λ/4,

and so on. I can use two equal length 50-ohm feed lines that are any physical length

that reaches, with the only attention to detail the quarter wavelength 75-ohm

Q-sections. This greatly reduces cable cutting errors because the long

lines are matched, and only need to be equal lengths of the same cable stock.

## Where do we use

stacking and

collinear gain most

effectively?

We use broadside

stacking and

collinear gain most

effectively in

Curtain Arrays like

the Lazy H antenna.

You can read more

about Curtain

Antenna Arrays on my

**
Sterba Curtain
Lazy-H antenna page**.

## Arrays over Earth

Unless we remove energy from an area that had significant energy, antennas

cannot produce gain. If an antenna has a wide area with no radiation at all, and

we designed a system to force a null totally within that same area, there would

be no gain at all. The pattern must be narrowed to increase gain, and it must be

narrowed in a way that does not increase heat losses faster than it concentrates

electromagnetic radiation.

Earth focuses energy in the elevation plane, creating one or more nulls in

elevation pattern. Height above earth, as well as quality of earth, controls the

nulls formed by earth reflections. For somewhat flat earth, nulls formed by the

presence of earth are all in the elevation plane of the pattern. In most cases,

azimuthal beamwidth, or compass directivity, is largely unaffected by antenna

height. For this reason, azimuth pattern multiplication, or gain increase by

focusing in what we consider “compass direction”, is largely unaffected by

height above earth or changes in stacking spacing. We saw this above in the

relationships between actual gain with height or vertical spacing of the antenna

or antennas, and gain changes with changes in horizontal spacing or area

occupied by the antenna elements.