Monopole antenna

 ( Antennas ) 

The wave travels along the element at a velocity close to the speed of light $c$. The distance the wave travels in one period $T\; =\; 1/f$ is the wavelength $\backslash lambda$ where

$\backslash lambda\; =\; \{c\; \backslash over\; f\}$

• The current reflects from the top with a 180° ($\backslash pi$ ) phase change: At the top of the element, the total current must be zero because there is no place for it to go, making this point a current node (zero) of the standing wave. So the upward and downward traveling waves must have equal but opposite amplitude there, $i\_\backslash text\{up\}(h,\; t)\; =\; -i\_\backslash text\{down\}(h,\; t)$, The upward current wave is said to "reflect" from the top end of the element with opposite phase.
• The current reflects from the ground plane with no phase change: The downward wave travels down the element, through the feedline to the transmitter and back, and at the bottom reflects from the ground plane to become the upward wave. The ground plane, which can be modeled as a large capacitor plate connected to the ground conductor of the feedline, acts as a current sink, its voltage is approximately zero regardless of the current into it. Therefore the element has a voltage node (zero) and a current antinode (maximum) there. Since the voltage waves must be equal and opposite at the ground plane, $v\_\backslash text\{up\}(0,\; t)\; =\; -v\_\backslash text\{down\}(0,\; t)$, and there is a sign change due to the opposite directions of the currents, the upward and downward current waves are always equal in amplitude there, they are in phase

:$i\_\backslash text\{up\}(0,\; t)\; =\; -C\; \{dv\_\backslash text\{up\}(0,\; t)\; \backslash over\; dt\}\; =\; -C\; \{d-v\_\backslash text\{down\}(0,\; \backslash over\; dt\}\; =\; i\_\backslash text\{down\}(0,\; t)$

The sine wave repeats every $2\backslash pi$ radians (360°). So for resonance the total phase change $\backslash Phi$ during a round trip along the antenna element, including the $\backslash pi$ (180°) phase shift at the top, must be $2\backslash pi$ or an integral multiple of it

$\backslash Phi\; =\; 4\backslash pi\{h\; \backslash over\; \backslash lambda\}\; +\; \backslash pi\; =\; 2\backslash pi\; m\; \backslash qquad\; m\; \backslash in\; 1,\; 2,\; 3,...$

$h\; \backslash approx\; \{\backslash lambda\; \backslash over\; 4\},\; \{3\backslash lambda\; \backslash over\; 4\},\; \{5\backslash lambda\; \backslash over\; 4\},...$

(The resonant lengths are actually slightly shorter than this, see End effects section below.) For a given length $h$ the corresponding resonant frequencies $f\_\backslash text\{n\}$ are

The lowest resonant frequency, $f\_\backslash text\{0\}$, at which the antenna is a quarter-wavelength ($\backslash lambda/4$) long, is called the fundamental resonance, while the higher resonances, which are multiples of the fundamental, are called .

These are sometimes called the series resonant frequencies because near these frequencies the antenna acts similar electrically to a LC circuit.stated for dipole in stated for dipole in Because the feedpoint at the bottom of the antenna is a voltage node (minimum) and current antinode (maximum), at these frequencies the input impedance, equal to the ratio of voltage to current, is a minimum. For a $\backslash lambda/4$ monopole it is 36.5 ohms (as shown below).

$h\; \backslash approx\; \{\backslash lambda\; \backslash over\; 2\},\; \backslash lambda,\; \{3\backslash lambda\; \backslash over\; 2\},\; 2\backslash lambda,...$

These are sometimes called parallel resonances or antiresonances because the antenna acts similar to a LC circuit (antiresonance) tuned circuit.stated for a dipole in stated for a dipole in When fed at the bottom, due to the current node and voltage antinode there the antenna has a very high input resistance, which is difficult to calculate. For a hypothetical infinitely thin element it would be infinite, so there would be no input current. For a typical finite thickness monopole element it is around 700 - 3000 ohms depending on thickness. It also has a very high rate of change of reactance with frequency about the resonance point, which gives the antenna a narrower bandwidth than at the series resonances.

To reduce the impedance enough to match a transmission line, either an impedance matching circuit or shunt feed must be used. An advantage is that since it acts as a dipole the current in the ground system is low, so ground losses are minimized; for thin antennas a ground plane is not needed at all.

In practice monopoles are mainly used at the two lowest resonant frequencies; where the element is one quarter of the wavelength long ($\backslash lambda/4$), the quarter-wave monopole, or one half of the wavelength long ($\backslash lambda/2$), the half-wave monopole, because their radiation patterns consist of a single lobe in horizontal directions, perpendicular to the antenna axis. Higher are little used since they have more complicated radiation patterns consisting of multiple lobes directed at angles into the sky with nulls (directions of minimum radiation) between them, resulting in locations with no reception.

This is due to the shape of the electric field (fringing field) at the top end of the element ( A) which spreads out in a fan ( see diagram). This adds capacitance and reduces the inductance at the end. Due to this ability to store more charge per unit length, near the top the standing wave current profile ( I(z), red line) differs from a sine wave, decreasing faster with height. When approximated as a sine wave ( blue line), this is equivalent to the node of the standing wave ( N) occurring not at the top of the antenna but some distance above it.The effect of this on the antenna is similar to if the current wave traveled along the element at a phase velocity $v\_\backslash text\{p\}$ that is lower than the speed of light $c$, as in a transmission line. Some sources describe it this way: ; . However this is not a physically accurate description; the phase velocity is not constant along the element, as in a transmission line. So the resonant length of the element ( h) is shorter than a multiple of one quarter of the free space wavelength $\backslash lambda\; =\; c\; /\; f$ from the previous section.

The thicker the element is, the larger the end capacitance and the shorter the resonant length.

Another common way of saying this is that the resonant frequencies depend on the electrical length of the element (length in wavelengths of the current in the conductor), not the physical length (length measured in wavelengths of the radio wave in free space). The electrical length of a linear antenna is longer than its physical length, so the resonant frequencies are lower than would be calculated from its physical length.

From the equations $R\_\backslash text\{R\}(h)$ and $X\_\backslash text\{R\}(h)$ above, a thin monopole exactly one-quarter free space wavelength long, $h\; =\; .25\backslash lambda$, fed at bottom, has an inductive input impedance of

$Z(h\; =\; \{\backslash lambda\; \backslash over\; 4\})\; =\; R\_\backslash text\{R\}\; +\; jX\_\backslash text\{R\}\; =\; \{\backslash eta\; \backslash over\; 8\backslash pi\}\; \backslash text\{Cin\}(2\backslash pi)\; +\; j\{\backslash eta\; \backslash over\; 4\backslash pi\}\backslash big2\backslash text\{Si\}(\{\backslash pi\; =\; 36.54\; +\; j21.25$ ohms

In addition, anything which adds capacitance to the antenna element, such as the presence of grounded objects or high permittivity dielectric like insulating coatings or supporting electrical insulators near the end of the element will further decrease the resonant length.

These are collectively called "end effects". A widely used rule of thumb is that, due to these effects the resonant length $h$ of a quarter-wave monopole antenna is about 5% shorter than its nominal length of $\backslash lambda/4$ from the previous section, or for $h$ in metersin units of feet    An empirical formula for the actual resonant length of the quarter-wave monopole as a function of element length-to-diameter ratio $\backslash alpha\; =\; h/2b$ is

$h\; =\; 0.24\backslash lambda\{\backslash alpha\; \backslash over\; 1\; -\; \backslash alpha\}$

As can be seen from the reactance graph in the impedance section, at the half wavelength resonance the length/diameter ratio and other end effects have a much larger influence on the resonant length.

In the rest of the article, when the resonant length of a monopole is mentioned, it is assumed to include this correction.

Like a vertical dipole antenna, a monopole has an omnidirectional radiation pattern: it radiates equal power in all directions perpendicular to the antenna axis. The radiated power varies with elevation angle, with the radiation dropping off to zero at the zenith on the antenna axis. It radiates vertically polarized radio waves, with the electric field parallel to the element.

A monopole can be visualized (see diagram) as being formed by replacing the bottom half of a vertical dipole antenna (c) with a conducting plane (ground plane) at right-angles to the remaining half. If the ground plane is large enough, the radio waves from the remaining upper half of the dipole (a) reflected from the ground plane will seem to come from an image antenna (b) forming the missing half of the dipole, which adds to the direct radiation to form a dipole radiation pattern. So the pattern of a monopole over a perfectly conducting, infinite ground plane is identical to the top half of a dipole pattern.

See the gallery of radiation patterns. Up to a length of a half-wavelength ($\{\backslash lambda\; \backslash over\; 2\}$) the radiation pattern has a single donut-shaped lobe with maximum radiated power in horizontal directions, perpendicular to the antenna axis. As the length is increased above $\{\backslash lambda\; \backslash over\; 4\}$ the lobe flattens, radiating less power at high angles and more in horizontal directions.

Above a half-wavelength the pattern splits into a horizontal main lobe and a small second conical lobe at an angle of 60° elevation into the sky. However the horizontal radiated power and gain keeps increasing and reaches a maximum at a length of five-eighths wavelength: $\{5\; \backslash over\; 8\}\backslash lambda\; =\; .625\backslash lambda$ (this is an approximation valid for a typical thickness antenna, for an infinitely thin monopole the maximum occurs at $\{2\; \backslash over\; \backslash pi\}\backslash lambda\; =\; .637\backslash lambda$) The maximum occurs at this length because the opposite phase radiation from the two lobes interferes destructively and cancels at high angles, leaving more power to be radiated in horizontal directions.

Above $.625\backslash lambda$ the high angle lobe gets larger, becoming the main lobe, and the horizontal lobe rapidly gets smaller, reducing power radiated in horizontal directions, so very few antennas use lengths above this. At the 4th harmonic, $h\; =\; \backslash lambda$, the horizontal lobe disappears and all the power is radiated in the high angle lobe. As the antenna is made longer, the pattern divides into more lobes, with nulls (directions of zero radiated power) between them.

The general effect of electrically small ground planes, as well as imperfectly conducting earth grounds, is to tilt the direction of maximum radiation up to higher elevation angles and reduce the gain. When mounted on the Earth, due to the finite resistance of the soil the portion of the ground wave propagating horizontally in contact with the ground is attenuated exponentially and vanishes at long distances, so in the (far field) radiation pattern the radiated power declines smoothly to zero at the horizon (zero elevation angle).

With an asymmetrical ground plane, such as a whip antenna mounted on a car’s bumper, the pattern will no longer be omnidirectional, but will have stronger horizontal radiation on the side with the larger ground plane area.

The gain figures given in the table above are never approached in practice; they would only be achieved if the antenna was mounted over an infinite perfectly conducting ground plane. The ground plane is part of the antenna, and the gain is highly dependent on its size and conductivity. An artificial ground plane a wavelength or more in radius is equivalent to a infinite plane, but for smaller planes, which are often used at high frequencies, the gain will be 2 to 5 dBi lower, because some of the horizontal radiated power will diffraction around the plane edge into the lower half space. Similarly over a resistivity Earth ground the gain will be lower due to power absorbed in the Earth.

For electrically short monopoles below $\backslash lambda/4$ the gain decreases slowly; it is 4.76 dBi at $\backslash lambda/20$. As the length is increased to a half-wavelength ($\backslash lambda/2$), the gain increases to about 1.7 dB over the $\backslash lambda/4$ gain. Since at this length the antenna has a current node at its Antenna feed, the input impedance is very high.

The gain continues to increase up to a maximum of about 3 dB over a quarter-wave monopole at a length of five-eighths wavelength ($.625\backslash lambda$) so this is a popular length for ground wave antennas and terrestrial communication antennas. The radiation resistance drops to about 53 ohms at that length. Above $.625\backslash lambda$ the horizontal gain drops rapidly because more power is radiated at high elevation angles in the second lobe.

As mentioned, the radiation pattern of the monopole is the same as the top half of the dipole pattern. At any point above the ground plane the time average power density (Poynting vector) $\backslash widehat\{S\}$ in watts per square meter of radio waves emitted by a monopole is twice that of a vertical dipole antenna $\backslash widehat\{S\}\_\backslash text\{d\}$ of twice the length

$\backslash widehat\{S\}\; =\; 2\backslash widehat\{S\}\_\backslash text\{d\}$

For a radio antenna what is of interest is the radiation pattern in the far field region, far enough from the antenna so the induction fields have died out. The Fraunhofer diffraction equation below is accurate when $r\; \backslash gg\; h$, $kr\; =\; \{2\; \backslash pi\; r\; \backslash over\; \backslash lambda\}\; \backslash gg\; 1$ and $kh^2\; \backslash ll\; 4\backslash pi\; r$, that is at distances from the antenna $r$ much greater than the element length and the wavelength. From the radiation pattern of a dipole given in the literature the far field electric field radiation pattern of a thin ($hk\; \backslash ll\; 1$) monopole mounted over a perfectly conducting infinite ground plane is

where

$h$ is the height of the element

$k\; =\; \{2\backslash pi\; \backslash over\; \backslash lambda\}\; =\; \{2\backslash pi\; f\; \backslash over\; c\}$

$\backslash eta$ is the impedance of free space, 376.74 ohms

$I\_\backslash text\{0\}$ is the feed current at the bottom of the antenna

$r$ is the distance from origin of the coordinate system at the base of the antenna to the reception point.

$\backslash theta$ is the angle with respect to the positive z axis, the axis of the element. Since the ground plane reflects the radio waves, this equation only gives the radiation field for the field is zero for $\backslash pi/2\; \backslash le\; \backslash theta\; \backslash le\; \backslash pi$

$j\; =\; \backslash sqrt\{-1\}$ is the imaginary unit

The average power density in watts per square meter radiated by the monopole isfrom

• Series or base feed - This is the most common type, the type discussed above, in which the feedline is connected between the base of the monopole and the ground plane. For the quarter-wave $\backslash lambda/4$ monopole and odd harmonics the input impedance is a minimum, 36.8 ohms for a quarter-wave monopole. For the half-wave $\backslash lambda/2$ monopole, the impedance is very high, requiring a matching transformer.
• Shunt feed - One side of the feedline is connected to ground, and the other to a point along the antenna element, and the base of the element is grounded. The part of the element between the feedpoint and ground acts as a shorted stub. Since the impedance is zero at the base and increases continuously to a very high value, 800 - 4000 ohms at a height of $\backslash lambda/4$, any input impedance between these values can be realized by choosing the correct feed height on the element.

* Gamma match - a shunt feed with a capacitor in the feedline connecting to the element.

• Folded monopole - A monopole can also be fed at the top, by grounding the base of the element, mounting a parallel conductor next to it, attached at the top, and feeding this conductor at the bottom. Because of their proximity the two elements are coupled so the current and voltage are the same in each. The folded monopole has a radiation resistance of 4 times the base fed monopole.

Below a quarter wavelength the radiation resistance of a monopole decreases approximately with the square of the ratio of length to wavelength, p.66 eq.2-19

$R\_\backslash text\{R\}\; \backslash approx\; \{\backslash eta\backslash pi\; \backslash over\; 3\}\backslash Big(\{h\; \backslash over\; \backslash lambda\}\backslash Big)^2\; =\; (394\; \backslash text\{\Omega \})\; \backslash Big(\{h\; \backslash over\; \backslash lambda\}\backslash Big)^2\; \backslash qquad\; h\; \backslash ll\; \{\backslash lambda\; \backslash over\; 4\}$

$R\_\backslash text\{IN\}\; =\; R\_\backslash text\{R\}\; +\; R\_\backslash text\{L\}$

$P\_\backslash text\{IN\}\; =\; I\_\backslash text\{IN\}^2\; R\_\backslash text\{IN\}$

$P\_\backslash text\{IN\}\; =\; I\_\backslash text\{IN\}^2\; (R\_\backslash text\{R\}\; +\; R\_\backslash text\{L\})$

$P\_\backslash text\{IN\}\; =\; P\_\backslash text\{R\}\; +\; P\_\backslash text\{L\}$

$P\_\backslash text\{R\}\; =\; I\_\backslash text\{IN\}^2\; R\_\backslash text\{R\}\; =\; \{\backslash eta\backslash pi\; \backslash over\; 3\}\backslash Big(\{hI\_\backslash text\{IN\}\; \backslash over\; \backslash lambda\}\backslash Big)^2\backslash quad$ and $\backslash quad\; P\_\backslash text\{L\}\; =\; I\_\backslash text\{IN\}^2\; R\_\backslash text\{L\}$

$e\_\backslash text\{A\}\; =\; \{P\_\backslash text\{R\}\; \backslash over\; P\_\backslash text\{IN\}\}\; =\; \{R\_\backslash text\{R\}\; \backslash over\; R\_\backslash text\{R\}\; +\; R\_\backslash text\{L\}\}$

Another disadvantage of electrically short monopoles is that as the antenna is made shorter and the radiation resistance decreases, the capacitance decreases and so the capacitive reactance increases. The low resistance in combination with the capacitance of the antenna and inductance of the required loading coil gives the antenna a large Q factor; this means it has a narrow bandwidth, which reduces the data rate that can be transmitted or received. Antennas in the VLF band often have a bandwidth of only 50 to 100 hertz. The Chu-Harrington limit gives the minimum Q factor for a small antenna.

sometimes include a circular structure of radial rods at the top of the mast; this is called a 'top hat'. At lower frequencies in the LF and VLF bands larger top loads are used. The T antenna consists of a vertical wire driven at the bottom, rising to attach to the center of a horizontal top load wire insulated at both ends, supported by masts. Multiple parallel top load wires can be used to increase capacitance. The largest top loaded antenna is the umbrella antenna, consisting of a monopole mast radiator with many diagonal top load wires radiating symmetrically from the top, anchored to the ground through insulators. To tune out the high capacitive reactance and make the antenna resonant a large loading coil is required in series with the feedline at the base of the antenna.

At low frequencies, due to the high capacitance and low radiation resistance, the top loaded monopole has a very narrow bandwidth. This may limit the width of sidebands and thus the data rate that can be transmitted. High power transmitting antennas in the VLF band typically have $Q$ of several hundred and bandwidths less than 100 Hz. The energy stored in the antenna, stored alternately as an electrostatic field in the top load and a magnetic field in the loading coil, is hundreds of times the energy input from the transmitter each cycle. The voltage at the ends of the top-load wires is very high, $Q$ times the feed voltage, and may be hundreds of kilovolts, requiring very good insulation. The antenna must be tuned to resonance with the transmitter using a variometer coil.

• Antenna types
• Dual-band blade antenna
• Electrical lengthening
• Signal strength

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