# Communication Systems/Antennas

## Antennas

The purpose of an antenna is to collect and convert electromagnetic
waves to electronic signals. Transmission lines then guide these to the
receiver front end.

The relevant electric fields associated with an antenna are extremely
complex and have the general form:

$$E = j30\beta ^2 Idz\left( {\frac{j}{{\beta r}} + \frac{1}{{\left( {\beta r} \right)^2 }} + \frac{1}{{\left( {\beta r} \right)^3 }}} \right)\sin \theta e^{ - j\beta r}$$

where *Idz* = moment of differential current element in rms amp meters

$$\beta  = \frac{{2\pi }}{\lambda }$$

:   

    :   *r* = distance in meters

The near field or Fresnel region consists of three fields.

The electrostatic (*1/r^3^*) and inductive (*1/r^2^*) fields fall off in
intensity quite quickly. The far field or Fraunhoffer region consists
entirely of the (*j/r*) radiated field. This article will only consider
this radiated field.

Although most antennas are simply a piece of bent wire, their
interaction with electromagnetic fields is quite complex, and a whole
array of terms is needed to characterize them:

::\**Beamwidth*: the angle defines by the radiation pattern where the
signal strength drops 3 dB of its maximum value in a given plane.

::\**Polarization*: the plane of electric field polarization with
respect to the earth.

::\**Gain*: a figure of merit used to quantify the signal capturing
ability of the antenna. It is closely related to directivity and
beamwidth.

::\**Effective area*: a measure of the antenna's ability to collect
energy. It is related to gain by the expression:
$A = \frac{{G\lambda ^2 }}{{4\pi }}$.

::\**Input impedance*: The impedance, which is necessary in the receiver
for maximum power transfer to occur.

::\**Radiation resistance*: the ratio of the power driving the antenna
to the square of the current driving its terminals.

::\**Bandwidth*: the usable frequency band associated with the antenna.

Before any antenna can be selected, the center frequency and operating
bandwidth must be known. In general, the higher the operating frequency,
the smaller the antenna. Antenna gain is always measured against a known
reference such as an isotropic source (*dBi*) or a half wave dipole
(*dBd*).

  Antenna Type       Typical Gain \[*dBd*\]
  ------------------ ------------------------
  Dipole             0
  Omni               0
  Gain Omni          3 --- 12
  Mobile Whip        -0.6 to +5.5
  Corner Reflector   4 --- 10
  Log Periodic       3 --- 8
  Horn               5 --- 12
  Helix              5 --- 12
  Microstrip Patch   3 --- 15
  Yagi               3 --- 20
  Panel              5 --- 20

Increasing antenna gain by 3 dB generally requires increasing the size
by a factor of 2-3 or by reducing the beamwidth. Vertical omni
directional antennas and collinear arrays are used for line-of-sight
communications with ground-based mobile units. Sectoring can be
accomplished by panel antennas. Fixed point-to-point links generally use
a yagi or parabolic dish.

Antennas exhibit reciprocity, which means they have the same gain
whether used for transmitting or receiving.

### Isotropic Radiators

An isotropic source radiates energy equally well in all directions.
Stars are isotropic radiators. Our sun is an extremely powerful
radiator, broadcasting 64 Megawatts per square meter of surface.
Although it is not possible to construct isotropic radio antennas, the
concept provides useful analytical tools.

The power density as a function of distance from an isotropic source is
easily calculated. It is simply the total energy broadcast, divided by
the area it passes through, in this case, a sphere.

$$P_{DI}  = \frac{{P_t }}{{4\pi r^2 }}$$ watts/m^2^

Isotropic gain is also called absolute gain. Antennas gains with respect
to isotropic gain are specified in units of dBi. Antenna gains can also
be specified with respect to a half wave dipole or a short vertical
antenna. The gain of a half-wave dipole is 1.64 dBi, and that of a
dipole is 2.15 dBi.

### Non Isotropic Radiators

Virtually all types of antennas are non-isotropic sources. That is that
they tend to radiate more energy in a particular direction.

:   

    :   ![](non_isotropic_radiator.gif "fig:non_isotropic_radiator.gif")

Because of this non-uniform energy distribution, the antenna appears to
have a gain (*G~t~*) (if broadcasting the same power) relative to an
isotropic radiator along its principal axis and a loss in other most
directions. The power density along the antenna axis is given by:

$$P_D  = \frac{{P_t G_t }}{{4\pi r^2 }}$$ watts/m^2^

The receiving antenna attempts to collect this radiated energy through
an effective area (*A~eff~*). The received power is therefore:

$$P_r  = \frac{{P_t G_t }}{{4\pi r^2 }}A_{eff}$$ watts

It would seem reasonable to conclude that the effective area is simply
the physical size of the antenna. Fortunately, this is not the case, and
very small antennas are possible.

It has been determined that there is a relationship between effective
area, transmitted wavelength and antenna gain:

$$\frac{{A_{eff} }}{{G_r }} = \frac{{\lambda ^2 }}{{4\pi }}$$

Therefore, the received power can be expressed as:

:   

    :   $P_r  = P_t G_t G_r \left( {\frac{\lambda }{{4\pi r}}} \right)^2$
        watts

Recall that: $\lambda  = \frac{c}{f}$

If *f* is expressed in MHz, *c* in meters per second, and *r* in km,
then the received power in dB can be expressed as:

$$P_r  = P_t  + G_t  + G_r  - \left( {32.45 + 20\log r + 20\log f} \right)$$
dB

### Electric Field Strength

If the power density of an electromagnetic wave is known, the field
strength can be obtained from:

$$E = \sqrt {Z_0 P_D }$$

where:

$$Z_0  = \sqrt {\frac{\mu }{\varepsilon }}  = \sqrt {\frac{{4\pi  \times 10^{ - 7} }}{{8.854 \times 10^{ - 12} }}}  = 120\pi$$
(for free space)

Therefore the field strength at one meter is:

$$E_o  = \sqrt {120\pi \frac{{P_t G_t }}{{4\pi r^2 }}}  = \sqrt {30P_t G_t }$$
volts/m

## Antenna Types

Antennas come in a bewildering array of shapes and sizes however, they
can be divided into two broad categories : Marconi and Hertzian.

Marconi antennas are electrically unbalanced and a require a ground
plane. Hertzian antennas are electrically balanced and do not require a
ground plane. Depending on one\'s point of view, it is possible to
consider one type the subset of the other. This will become clearer
later on.

## Marconi Antenna

Marconi antennas are usually 1/4 wavelength long and require a path to
ground. The ground plane itself acts as a reflector of energy, and
combines with the directly radiated wave to create the overall radiation
pattern. If the ground is dry or otherwise a poor conductor, a copper
grid is generally laid out on the ground. The impedance of a 1/4
$\lambda$ Marconi antenna is 36.6 $\Omega$.

:   

    :   ![](1_4_wave_marconi_antenna.gif "1_4_wave_marconi_antenna.gif")
        !100 px

Notice that a Marconi antenna could be considered as a dipole antenna
with one of the poles buried in the ground. The ground acts as a
reflector to create the appearance of an buried antenna in the same way
that a mirror creates the appearance of someone behind the glass.
Increasing the antenna length has a significant impact on the radiation
pattern:

:   

    :   ![](Marconi_antennas.gif "fig:Marconi_antennas.gif")

### Helical Antenna

Most Marconi antennas operate in the broadside mode, which means that
the bulk of the signal radiates off the side of the wire. However it is
possible to modify the antenna to operate in the end fire mode:

:   

    :   ![](Helical_antenna_principle.png "fig:Helical_antenna_principle.png")

## Hertzian Antenna

Hertzian antennas do not require a path to either ground or a ground
plane. The simplest antenna of this type is the elementary doublet. It
is a hypothetical antenna where the instantaneous current magnitude is
constant along its length.

:   

    :   ![](elementary_doublet.gif "fig:elementary_doublet.gif")

The radiation pattern for this antenna is donut shaped, with the antenna
rod running through the hole. The bulk of the energy is radiated at
right angles to the rod and nothing off the ends.

:   

    :   ![](doublet_radiation_pattern.gif "fig:doublet_radiation_pattern.gif")

This antenna is often used as a reference instead of an isotropic
radiator, since close approximations of it can be constructed. Other
antennas can be considered as being composed of a series of doublets.

The field strength at any distance and angle can be calculated from:

$$E = \frac{{60\pi LI}}{{\lambda r}}$$

Where

:   

    :   *L* = doublet length in meters
    :   $\lambda$= wavelength in meters
    :   *I* = current in amps (rms)
    :   *r* = distance in meters

### Dipole Antenna

A dipole is sometimes referred to as a Hertzian dipole. Since it has a
relatively simple construction and its radiation characteristics are
well defined, it is often used as the standard to which all other
antennas are compared.

The dipole radiation pattern is shaped like a slightly flattened donut.

:   

    :   ![](dipole_pattern.gif "fig:dipole_pattern.gif")

The simplest antenna is the dipole. The relationship between antenna
current and electric field is given by:

$$E_\theta   = j\eta \frac{{e^{ - j\beta r} }}{{2\pi r}}I\frac{{\cos \left( {\frac{{\beta L\cos \theta }}{2}} \right) - \cos \left( {\frac{{\beta L}}{2}} \right)}}{{\sin \theta }}$$

where:

:   

    :   *E* = electric field strength
    :   $\theta$ = angle from antenna axis (in radians)
    :   *I* = antenna current (rms)
    :   $\eta$ = intrinsic impedance (377 $\Omega$)
    :   *L* = antenna length
    :   *r* = distance

A ½ $\lambda$ dipole has an impedance of about 70 $\Omega$. To increase
this impedance and more closely match the characteristics of a twin lead
cable, the dipole may be folded. A ½ $\lambda$ folded dipole has an
input impedance of about 280 $\Omega$, and is used as the driving
element in many other types of antennas.

Most TV receivers are equipped with two indoor antennas, one to cover
the VHF band and the other the UHF band. The most common VHF antennas
are the extendible monopole and vee dipole colloquially known as the
rabbit ears. These are available with either a 75 $\Omega$ or 300
$\Omega$ impedance and have a typical gain of -4 dB with respect to a ½
$\lambda$ dipole. The vee dipole has a lower input impedance than a
straight dipole of the same length, but under some conditions, it can
exhibit a higher directivity due to the reduction of sidelobes.

The common UHF antennas are the circular loop and triangular dipole.
They typically have a 300 $\Omega$ impedance. The dipole version
sometimes has a reflecting screen to improve the gain and directivity.

### Halfwave Dipole

The radiation pattern of the half wave dipole is very much like a donut.

:   

    :   ![](half_wave_dipole_pattern.gif "fig:half_wave_dipole_pattern.gif")

The distribution of voltage, current, and impedance resemble:

:   

    :   ![](half_wave_dipole_current.gif "fig:half_wave_dipole_current.gif")

By increasing the length of the dipole, the donut tends to flatten out
and then explodes into complex multi lobed shapes.

### Folded Dipole

:   

    :   ![](Antenna-folded-dipole-diagram.png "fig:Antenna-folded-dipole-diagram.png")

folded dipole antenna has high input impedance as compared to ordinary
dipole.

### Loop Antenna

The entire UHF band can be received on a single 20.3 cm diameter loop.
The circumference varies from one wavelength at 470 MHz to 1.7
wavelengths at 806 MHz. The directivity is about 3.5 dB. The mid band
gain is 3 dB higher than a ½ $\lambda$ dipole, but falls off to about
1 dB at either end.

:   

    :   ![](loop_antenna.gif "fig:loop_antenna.gif")

Loop antennas that are much smaller than wavelength they are attempting
to catch, exhibit a null in the direction of the loop axis. This makes
it suitable for radio direction finding equipment. If the loop size is
increased, it begins to generate a lobe across the axis and in line with
the feed.

### Triangular Dipole (Bowtie)

:   

    :   ![](bow_tie_antenna.gif "fig:bow_tie_antenna.gif")

The bowtie antenna is formed of two triangular sheets connected to a
transmission line and provides a 3 dB gain over a simple dipole. It can
also be constructed of a wire mesh if the spacing is less than 1/10
wavelength. The input impedance is a function of length and flare angle.
For television applications, the flare angle a is between 60^o^ and
80^o^. If the antenna is mounted ¼ $\lambda$ in front of a reflecting
surface, the gain increases to approximately 9 dB. Stacking two of them
vertically one wavelength apart, increases the overall gain to about
12 dB.

If the receiver is located at a great distance from the broadcast tower,
it is often necessary to use an outdoor antenna. These often have a gain
of 15 dB. Placing the antenna on a tall mast also increases the received
signal strength by as much as an additional 14 dB. A further improvement
occurs because these antennas have a greater immunity to interference,
due to their complex structure.

Most outdoor antennas are a combination of two antennas \[UHF and VHF\]
in a single structure. The VHF antenna is generally a log-periodic
dipole array. The UHF antenna may be an LPDA, Yagi-Uda, corner
reflector, parabolic reflector, or triangular dipole array with
reflecting screen.

### Log Periodic Dipole Array \[LPDA\]

This antenna is called a log periodic array because the impedance
variations across the usable band are periodic functions of frequency.
The high impedance version is mounted on an insulated boom and feed by a
balanced cable. The average domestic antenna of this type has a gain of
about 4.5 dB in the low VHF band, rising to 7 dB in the high VHF band.

:   

    :   ![](log_periodic_antenna.gif "fig:log_periodic_antenna.gif")

$$\tau  = \frac{{X_n }}{{X_{n + 1} }} = \frac{{L_n }}{{L_{n + 1} }} = \frac{{s_n }}{{s_{_{n + 1} } }} = \frac{{d_n }}{{d_{n + 1} }}$$
\-- Typically $0.7 \le \tau  \le 0.95$

$$\alpha  = \tan ^{ - 1} \left( {\frac{{1 - \tau }}{{4\sigma }}} \right)$$
\-- Typically $10^0  \le \alpha  \le 45^0$

$$\sigma  = \frac{{d_n }}{{2L_n }}$$

:   

    :   Bandwidth:
        $B = \frac{{f_{high} }}{{f_{low} }}\left( {1 + 7.7\left( {1 - \tau } \right)^2 \cot \alpha } \right)$

```{=html}
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:   

    :   Number of dipoles:
        $N = 1 + \frac{{\ln B}}{{\ln \frac{1}{\tau }}}$

Most CATV applications use a 75 $\Omega$ unbalanced configuration,
because it is more compatible with their cable feeds and equipment.

:   

    :   ![](unbalanced_coax_feed.gif "fig:unbalanced_coax_feed.gif")

Two parallel conducting booms form a low impedance transmission line.
Phase reversal between dipoles is obtained by alternate attachment to
the booms.

An UHF LPDA can be constructed from V-shaped dipoles. The dipoles are
used in their ½ $\lambda$ and 3/2 $\lambda$ modes and eliminate the need
for higher frequency dipoles.

### Yagi Uda Antenna


:   

    :   ![](yagi.gif "fig:yagi.gif")

The dipole is typically 0.40 to 0.50 wavelengths long. The reflector is
normally 0.55 wavelengths long and placed anywhere from 0.1 to 0.25
wavelengths behind the dipole. The reflector spacing has no effect on
the forward gain, but does influence the front to back ratio and input
impedance.

The directors are normally 0.4 to 0.45 wavelengths long and are spaced
at 0.3 to 0.4 wavelengths in front of the dipole. An antenna will
usually have 6 to 12 directors.

### Parabolic Reflector


:   

    :   

## Antenna Arrays

By combining several radiating elements together, the overall radiation
pattern can be modified to suit a particular application. In some cases
the antennas must be manually steered, but in other cases they can be
electronically steered using phase shifting between elements.

:   

    :   !200 px
        ![](PAVE_PAWS_Radar_Clear_AFS_Alaska.jpg "PAVE_PAWS_Radar_Clear_AFS_Alaska.jpg"){width="200"}

The array factor is the increase in field strength in an array when
compared to a single element radiating the same power:

:   

    :   ![](Array_side_view.gif "fig:Array_side_view.gif")

$$AF = \left| {\frac{{\sin \left( {\frac{{n\varphi }}{2}} \right)}}{{\sqrt n \sin \left( {\frac{\varphi }{2}} \right)}}} \right| \vdots \quad \quad \quad AF_{\max }  = \sqrt n$$

:   

    :   Where:

$$\varphi  = \frac{{2\pi }}{\lambda }s\cos \left( \theta  \right) + \alpha$$

:   

    :   = phase difference between radiated fields from adjacent
        elements

:   

    :   *n* = number of radiating elements
    :   *s* = element spacing in wavelengths
    :   $\alpha$ = current phase shift between elements
    :   $\theta$ = angle from array axis

### Broadside Array

If all of the elements are fed in-phase, there will always be a
broadside radiation pattern. However, depending on the relative spacing,
an end fire pattern can also be created.

:   

    :   ![](Broadside_wavefront.gif "fig:Broadside_wavefront.gif")

The radiating elements in the above illustration can be placed such that
they reinforce one another along the array axis, or not. An end fire
pattern is recreated when they reinforce.

By varying the space or phase shift between the elements, the size and
direction of the side lobes can be adjusted between these two extremes.
Increasing the number of radiating elements increases the overall array
gain.

:   

    :   ![](Array_factor_1.gif "fig:Array_factor_1.gif")

Determining the array factor is sometimes relatively straightforward. By
definition, the signal strength for a broadside array is a maximum when
$\theta$ = 90^o^ and a minimum when $\theta$ = 0^o^

Since the array factor is a maximum when $\varphi$ = 0^o^ we can
determine the current phase shift $\alpha$, required to create a
broadside radiation pattern for a given frequency or element spacing:

$$\varphi  = \frac{{2\pi }}{\lambda }s\cos \left( \theta  \right) + \alpha$$

$$0 = \frac{{2\pi }}{\lambda }s\cos \left( \theta  \right) + \alpha$$

$$\alpha  = 0$$

:   

    :   Therefore the array factor for a broadside array is:

$$AF = \left| {\frac{{\sin \left( {\frac{{n\varphi }}{2}} \right)}}{{\sqrt n \sin \left( {\frac{\varphi }{2}} \right)}}} \right|\quad {\rm{where}}\quad \varphi  = \frac{{2\pi }}{\lambda }s\cos \left( \theta  \right)$$

$${\rm{generally}}\quad s = \frac{\lambda }{2}\quad \quad \quad {\rm{therefore}}\quad \quad \quad \varphi  = 2cos\left( \theta  \right)$$

Each element may have its own feed or there may be a single feed:

:   

    :   ![](Broadside_feed.gif "fig:Broadside_feed.gif")

This form of antenna is often deployed in vertical stacks, with a
reflector spaced 1/4 wavelength behind the curtain. This broadband
dipole curtain array is the standard antenna for 100 to 500 kW
short-wave broadcasting stations.

:   

    :   ![](Broadside_array.gif "fig:Broadside_array.gif")

CBC Radio International operates eight curtain arrays at Sackville NB.
Three have an output power of 100 kW and five have an output of 250 kW.
They are tunable over the range of 4.9 to 21.7 MHz. Signals are beamed
to Africa, Europe, Latin America, The Caribbean, the USA, and Mexico.

### Endfire Array

If all of the elements are positioned in such a way that the combined
wave fronts reinforce along the array axis.

:   

    :   ![](Endfire.gif "fig:Endfire.gif")

Calculate the array factor is relatively straightforward. The signal
strength is a maximum when $\theta$ = 0^o^ and a minimum when $\theta$ =
90^o^

Since the array factor is a maximum when $\varphi$ = 0^o^ we can
determine the value of $\alpha$:

$$\varphi  = \frac{{2\pi }}{\lambda }s\cos \left( \theta  \right) + \alpha$$

$$0 = \frac{{2\pi }}{\lambda }s\cos \left( 0 \right) + \alpha$$

$$\alpha  =  - \frac{{2\pi }}{\lambda }s$$

:   

    :   The array factor for an end fire array is:

$$AF = \left| {\frac{{\sin \left( {\frac{{n\varphi }}{2}} \right)}}{{\sqrt n \sin \left( {\frac{\varphi }{2}} \right)}}} \right|\quad {\rm{where}}\quad \varphi  = \frac{{2\pi }}{\lambda }s\left( {\cos \left( \theta  \right) - 1} \right)$$

$${\rm{generally}}\quad s = \frac{\lambda }{4}\quad \quad \quad {\rm{therefore}}\quad \quad \quad \varphi  = \frac{\pi }{2}\left( {cos\left( \theta  \right) - 1} \right)$$

Varying the spacing for a 6-element array produced the following
patterns:

:   

    :   ![](Broadside_patterns.gif "fig:Broadside_patterns.gif")

### Phased Array

By varying the phase shift between elements, a beam or multiple beams
can be pointed towards a given direction. This forms the basis of the
large electronically steered radar system currently being deployed.
Collectively theses systems are known as phased arrays.

:   

    :   !300 px

The PAVE PAWS early warning radar for example has 1792 active crossed
dipole antennas on a 102-foot face. Each face can scan 120^o^ in azimuth
and 80^o^ in elevation. The array has a range of 300 miles and can
produce multiple beams, which can be redirected in milliseconds.

## Further reading

-   Wifi/Building an antenna

