# Relationship between antenna length and frequency

### Frequency, wavelength, and antenna tuning - TIGHAR

There is an inverse relationship between frequency and If an antenna is a non- resonant length (as Earhart's was) it must be tuned to. An antenna must be tuned (matched) to the same frequency band as the radio system Note: The physical length of a half-wave dipole is slightly less than half a The relation between gain and directivity includes a new parameter (η) which . The example given was for a Bluetooth antenna with a frequency of MHz. The antenna length was calculated as / = m = 12cm. The author.

The majority of antenna designs are based on the resonance principle. This relies on the behaviour of moving electrons, which reflect off surfaces where the dielectric constant changes, in a fashion similar to the way light reflects when optical properties change. In these designs, the reflective surface is created by the end of a conductor, normally a thin metal wire or rod, which in the simplest case has a feed point at one end where it is connected to a transmission line.

The conductor, or element, is aligned with the electrical field of the desired signal, normally meaning it is perpendicular to the line from the antenna to the source or receiver in the case of a broadcast antenna. This causes an electrical current to begin flowing in the direction of the signal's instantaneous field.

When the resulting current reaches the end of the conductor, it reflects, which is equivalent to a degree change in phase. That means it has undergone a total degree phase change, returning it to the original signal. The current in the element thus adds to the current being created from the source at that instant. This process creates a standing wave in the conductor, with the maximum current at the feed.

The physical arrangement of the two elements places them degrees out of phase, which means that at any given instant one of the elements is driving current into the transmission line while the other is pulling it out.

Monopoles, which are one-half the size of a dipole, are common for long-wavelength radio signals where a dipole would be impractically large. Another common design is the folded dipolewhich is essentially two dipoles placed side-by-side and connected at their ends to make a single one-wavelength antenna. The standing wave forms with this desired pattern at the design frequency, f0, and antennas are normally designed to be this size.

This allows some flexibility of design in terms of antenna lengths and feed points. Antennas used in such a fashion are known to be harmonically operated.

At the resonant frequency, the standing wave has a current peak and voltage node minimum at the feed. In electrical terms, this means the element has minimum reactancegenerating the maximum current for minimum voltage.

Effective Height of Antenna, Antenna Parameters in Antenna and wave propagation by Engineering Funda

This is the ideal situation, because it produces the maximum output for the minimum input, producing the highest possible efficiency. Contrary to an ideal lossless series-resonant circuit, a finite resistance remains corresponding to the relatively small voltage at the feed-point due to the antenna's radiation resistance as well as any actual electrical losses.

Recall that a current will reflect when there are changes in the electrical properties of the material. In order to efficiently send the signal into the transmission line, it is important that the transmission line has the same impedance as the elements, otherwise some of the signal will be reflected back into the antenna. This leads to the concept of impedance matchingthe design of the overall system of antenna and transmission line so the impedance is as close as possible, thereby reducing these losses.

Impedance matching between antennas and transmission lines is commonly handled through the use of a balunalthough other solutions are also used in certain roles. An important measure of this basic concept is the standing wave ratiowhich measures the magnitude of the reflected signal. Using the appropriate transmission wire or balun, we match that resistance to ensure minimum signal loss.

Feeding that antenna with a current of 1 ampere will require 63 volts of RF, and the antenna will radiate 63 watts ignoring losses of radio frequency power.

Now consider the case when the antenna is fed a signal with a wavelength of 1. Electrically this appears to be a very high impedance. The antenna and transmission line no longer have the same impedance, and the signal will be reflected back into the antenna, reducing output.

This could be addressed by changing the matching system between the antenna and transmission line, but that solution only works well at the new design frequency. The end result is that the resonant antenna will efficiently feed a signal into the transmission line only when the source signal's frequency is close to that of the design frequency of the antenna, or one of the resonant multiples.

This makes resonant antenna designs inherently narrowband, and they are most commonly used with a single target signal. They are particularly common on radar systems, where the same antenna is used for both broadcast and reception, or for radio and television broadcasts, where the antenna is working with a single frequency.

They are less commonly used for reception where multiple channels are present, in which case additional modifications are used to increase the bandwidth, or entirely different antenna designs are used. As these antennas are made shorter for a given frequency their impedance becomes dominated by a series capacitive negative reactance; by adding a series inductance with the opposite positive reactance — a so-called loading coil — the antenna's reactance may be cancelled leaving only a pure resistance.

Then it may be said that the coil has lengthened the antenna to achieve an electrical length of 2. For ever shorter antennas requiring greater "electrical lengthening" the radiation resistance plummets approximately according to the square of the antenna lengthso that the mismatch due to a net reactance away from the electrical resonance worsens.

Or one could as well say that the equivalent resonant circuit of the antenna system has a higher Q factor and thus a reduced bandwidth [15]which can even become inadequate for the transmitted signal's spectrum.

### what is relation between antenna size and frequency?

The amount of signal received from a distant transmission source is essentially geometric in nature due to the inverse-square lawand this leads to the concept of effective area.

This measures the performance of an antenna by comparing the amount of power it generates to the amount of power in the original signal, measured in terms of the signal's power density in Watts per square metre.

A half-wave dipole has an effective area of 0. If more performance is needed, one cannot simply make the antenna larger. Although this would intercept more energy from the signal, due to the considerations above, it would decrease the output significantly due to it moving away from the resonant length.

In roles where higher performance is needed, designers often use multiple elements combined together. Returning to the basic concept of current flows in a conductor, consider what happens if a half-wave dipole is not connected to a feed point, but instead shorted out. But the overall current pattern is the same; the current will be zero at the two ends, and reach a maximum in the center.

Thus signals near the design frequency will continue to create a standing wave pattern. Any varying electrical current, like the standing wave in the element, will radiate a signal. In this case, aside from resistive losses in the element, the rebroadcast signal will be significantly similar to the original signal in both magnitude and shape.

If this element is placed so its signal reaches the main dipole in-phase, it will reinforce the original signal, and increase the current in the dipole. Elements used in this way are known as passive elements.

A Yagi-Uda array uses passive elements to greatly increase gain. It is built along a support boom that is pointed toward the signal, and thus sees no induced signal and does not contribute to the antenna's operation. The end closer to the source is referred to as the front.

Near the rear is a single active element, typically a half-wave dipole or folded dipole. Passive elements are arranged in front directors and behind reflectors the active element along the boom. The Yagi has the inherent quality that it becomes increasingly directional, and thus has higher gain, as the number of elements increases.

However, this also makes it increasingly sensitive to changes in frequency; if the signal frequency changes, not only does the active element receive less energy directly, but all of the passive elements adding to that signal also decrease their output as well and their signals no longer reach the active element in-phase.

It is also possible to use multiple active elements and combine them together with transmission lines to produce a similar system where the phases add up to reinforce the output.

The antenna array and very similar reflective array antenna consist of multiple elements, often half-wave dipoles, spaced out on a plane and wired together with transmission lines with specific phase lengths to produce a single in-phase signal at the output. The log-periodic antenna is a more complex design that uses multiple in-line elements similar in appearance to the Yagi-Uda but using transmission lines between the elements to produce the output.

We use low-loss components in our matching circuits to provide the maximum transfer of energy between the transmission line and the antenna. A high VSWR is an indication the signal is reflected prior to being radiated by the antenna.

VSWR and reflected power are different ways of measuring and expressing the same thing. A VSWR of 2. Most commercial antennas are specified to be 1. Based on a watt radio, a 1. The definition used is based on VSWR. Bandwidth is often expressed in terms of percent bandwidth, because the percent bandwidth is constant relative to frequency.

If bandwidth is expressed in absolute units of frequency, for example MHz, the bandwidth is then different depending upon whether the frequencies in question are near MHz, MHz or MHz.

The beauty of dB is they may be added and subtracted. A decibel relationship for power is calculated using the following formula. At MHz, one fourth of the power applied to one end of a coax cable arrives at the other end.

What is the cable loss in dB?

It is convenient to remember these simple dB values which are handy when approximating gain and loss: There is a relationship between gain and directivity. We see the phenomena of increased directivity when comparing a light bulb to a spotlight. A watt spotlight will provide more light in a particular direction than a watt light bulb and less light in other directions. The spotlight is comparable to an antenna with increased directivity. Gain is the practical value of the directivity.

This is known as a gain transfer technique. At higher frequencies, it is common to use a calibrated gain horn as a gain standard with gain typically expressed in dBi.

Another method for measuring gain is the 3-antenna method. Transmitted and received powers at the antenna terminal are measured between three arbitrary antennas at a known fixed distance. The Friis transmission formula is used to develop three equations and three unknowns. The equations are solved to find the gain expressed in dBi of all three antennas. Pulse-Larsen uses both methods for measurement of gain. The method is selected based on antenna type, frequency and customer requirement.

Use the following conversion factor to convert between dBd and dBi: The radiation pattern is three-dimensional, but it is difficult to display the three-dimensional radiation pattern in a meaningful manner. It is also time-consuming to measure a three-dimensional radiation pattern. Often radiation patterns measured are a slice of the three-dimensional pattern, resulting in a two-dimensional radiation pattern which can be displayed easily on a screen or piece of paper.

These pattern measurements are presented in either a rectangular or a polar format. Omnidirectional antennas radiate and receive equally well in all horizontal directions. The gain of an omnidirectional antenna can be increased by narrowing the beamwidth in the vertical or elevation plane. Selecting the right antenna gain for the application is the subject of much analysis and investigation.

Gain is achieved at the expense of beamwidth. Higher-gain antennas feature narrow beamwidths while the opposite is also true. When you tilt the basin back and forth, most of the time the water just moves back and forth with little other effect. This is like the electric field of an EM wave that pushes the electrons in the antenna to one side.

At a low frequency of tilting, the water just moves back and forth, settling at each end before the tilt reverses. At a high frequency, the water barely has a chance to move before the tilt reverses. But, if you tilt back and forth at just the right frequency, the sloshing of the water builds up and builds up until it splashes completely out of the basin. This is the resonant condition of the basin of water. You can imagine that longer basins have a lower frequency of resonance since it takes longer for the sloshing water to go from one end to the other.

It's the same with an antenna: The following is a view of the charges in an antenna that shows the sloshing of electrons at resonance the red shaded area; blue shows the magnitude of the velocity of the charges. Animation comes from the same Wikipedia article: