Antenna fundamentals

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Antenna and its fundamentals ANTENNA and its Fundamental Parameters Antenna is actually device that can sense the electromagnetic waves and can transmit the electromagnetic waves. The origin of antenna: [R1] The first experiments that involved the coupling of electricity and magnetism and showed a definitive relationship was that done by Faraday somewhere around the 1830s. He slid a magnetic around the coils of a wire attached to a galvanometer. In moving the magnet, he was in effect creating a time-varying magnetic field, which as a result (from Maxwell's Equations), must have had a time-varying electric field. The coil acted as a loop antenna (a small loop antenna often used as receiver having low resistance and high reactance) and received the electromagnetic radiation, which was received (detected) by the galvanometer - the work of an antenna. Just think about when TV or television first came on to the market. All that was out there for communication in the home was the radio. There wasn't even antennas needed before television. After television came the antenna market. People wanted their TV to have the best picture. Next came more channels which meant more directions for TV signal. That's when the rotor came into place to rotate the antenna system. Then to even make television better we put TV's in several rooms. To keep the picture quality good at all locations came amplification of the antenna system. Types of antenna: [R2] 1. Yagi-Uda Antenna , 1920s: 1

Transcript of Antenna fundamentals

Page 1: Antenna fundamentals

Antenna and its fundamentals

ANTENNA and its Fundamental Parameters

Antenna is actually device that can sense the electromagnetic waves and can transmit the electromagnetic waves.

The origin of antenna: [R1]

The first experiments that involved the coupling of electricity and magnetism and showed a definitive relationship was that done by Faraday somewhere around the 1830s. He slid a magnetic around the coils of a wire attached to a galvanometer. In moving the magnet, he was in effect creating a time-varying magnetic field, which as a result (from Maxwell's Equations), must have had a time-varying electric field. The coil acted as a loop antenna (a small loop antenna often used as receiver having low resistance and high reactance) and received the electromagnetic radiation, which was received (detected) by the galvanometer - the work of an antenna. Just think about when TV or television first came on to the market. All that was out there for communication in the home was the radio. There wasn't even antennas needed before television. After television came the antenna market. People wanted their TV  to have the best picture.  Next came more channels which meant more directions for TV signal. That's when the rotor came into place to rotate the antenna system.  Then to even make television better we put TV's in several rooms. To keep the picture quality good at all locations came amplification of the antenna system.

Types of antenna: [R2]

1. Yagi-Uda Antenna , 1920s:

The Yagi antenna was invented in Japan, with results first published in 1926. The Yagi-Uda antenna or Yagi Antenna is one of the most brilliant antenna designs. It is simple to construct and has a high gain, typically greater than 10 dB. The Yagi-Uda antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz), although their bandwidth is typically small, on the order of a few percent of the center frequency.

Figure 01: Yagi-Uda Antenna

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2. Horn antennas , 1939:

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies. They often have a directional radiation pattern with a high gain , which can range up to 25 dB in some cases, with 10-20 dB being typical. Horn antennas have a wide impedance bandwidth, implying that the input impedance is slowly varying over a wide frequency range. The bandwidth for practical horn antennas can be on the order of 20:1 (for instance, operating from 1 GHz-20 GHz), with a 10:1 bandwidth not being uncommon.

3. Antenna Arrays , 1940s :

An antenna array (often called a 'phased array') is a set of 2 or more antennas. The signals from the antennas are combined or processed in order to achieve improved performance over that of a single antenna. The antenna array can be used to

increase the overall gain provide diversity reception cancel out interference from a particular set of directions "steer" the array so that it is most sensitive in a particular

direction determine the direction of arrival of the incoming signals to maximize the Signal to Interference Plus Noise Ratio

(SINR) Figure 02: Antenna Arrays

:

Figure 03: Cell-tower Antenna Array. These Antenna Arrays are typically used in groups of 3 (2 receive antennas and 1 transmit antenna).

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4. Parabolic Reflectors :

The most well-known reflector antenna is the parabolic reflector antenna, commonly known as a satellite dish antenna. Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization. They also have a reasonable bandwidth, with the fractional bandwidth being at least 5% on commercially available models, and can be very wideband in the case of huge dishes (like the Stanford "big dish" above, which can operate from 150 MHz to 1.5 GHz). The basic structure of a parabolic dish antenna is shown in Figure 04 . It consists of a feed antenna pointed towards a parabolic reflector. The feed antenna is often a horn antenna with a circular aperture. Figure 04: Basic Design

Figure 05: parabolic reflector antenna(satellite dish antenna)

5. Patch Antennas , 1970s:

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board. Microstrip antennas are becoming very widespread within the mobile phone market. Patch antennas are low cost, have a low profile and are easily fabricated. The top view of simp;e patch anteena is shown in the figure 06.

Figure 06: Top View of Patch Antenna

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Antenna Fundamentals: [R3]

Before we can design an antenna we must understand the basics of antennas, which are the fundamental parameters that characterize an antenna. Suppose one day you are walking down the street and a kind but impatient person runs up and asks you to design an antenna for them. "Sure", you quickly reply, adding "what is the desired frequency, gain, bandwidth, impedance, and polarization?"

The Fundamental parameters of antenna are given below

1. Frequency 2. Frequency Bands3. Radiation Patterns4. Field Regions5. Directivity6. Efficiency & Gain7. Beams width & Side lobes8. Impedance9. Bandwidth10. Polarization of Waves11. Polarization of Antennas12. Effective Aperture13. Fiirs Transmission Formula14. Antenna Temperature

1) Frequency:

Frequency is one of the most important concepts in the universe and to antenna theory. Antennas function by transmitting or receiving electromagnetic (EM) waves. An "electromagnetic wave" is an electric field that travels away from some source (an antenna, the sun, a radio tower, whatever). A traveling electric field has an associated magnetic field with it, and the two make up an electromagnetic wave. The universe allows these waves to take any shape. The most important shape though is the sinusoidal wave, which is plotted in figure 07. EM waves vary with space (position) and time. The spacial variation is given in figure 07, and the temporal (time) variation is given in figure 08.

Figure 07: A Sinusoidal Wave plotted as a function of position.

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Figure 08: A Sinusoidal Wave plotted as a function of time.

The equation that relates frequency, wavelength and the speed of light is given by;

C= f λ

Basically, the frequency is just a measure of how fast the wave is oscillating. And since all EM waves travel at the same speed, the faster it oscillates the shorter the wavelength. And a longer wavelength implies a slower frequency

2) Frequency Bands:

In general, waveforms are not made up of a discrete number of frequencies, but rather a continuous range of frequencies. No matter what information you want to send, that waveform can be represented as the sum of a range of frequencies. Since every piece of information in the universe can be decomposed into sine and cosine components of varying frequencies by the use of ‘Mathematical Technique Fourier Transforms’, we always discuss antennas in terms of the wavelength it operates at or the frequency we are using.

By the use of modulation (which in a nutshell shifts the frequency range of the waveform to be sent to a higher frequency band), the waveforms can be relocated to separate frequency bands. As an example, cell phones that use the PCS (Personal Communications Service) band have their signals shifted to 1850-1900 MHz. Television is broadcast primarily at 54-216 MHz. FM radio operates between 87.5-108 MHz.

The Bandwidth of a signal is the difference between the signals high and low frequencies. For instance, a signal transmitting between 40 and 50 MHz has a bandwidth of 10 MHz. This means that the energy of the signal is contained between 40 and 50 MHz (and the energy in any other frequency range is negligible).

We have table of frequency bands along with the corresponding wavelengths. From the table, we see that VHF is in the range 30-300 MHz (30 Million-300 Million cycles per second). At the very least then, if someone says they need a "VHF antenna", we should now understand that the antenna should transmit or receive electromagnetic waves that have a frequency of 30-300 MHz

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Frequency Band Name

Frequency RangeWavelength

(Meters)Application

Extremely Low Frequency (ELF)

3-30 Hz10,000-100,000

kmUnderwater

Communication

Super Low Frequency (SLF)

30-300 Hz 1,000-10,000 kmAC Power (though not a

transmitted wave)

Ultra Low Frequency (ULF)

300-3000 Hz 100-1,000 km

Very Low Frequency (VLF)

3-30 kHz 10-100 km Navigational Beacons

Low Frequency (LF) 30-300 kHz 1-10 km AM Radio

Medium Frequency (MF)

300-3000 kHz 100-1,000 m Aviation and AM Radio

High Frequency (HF)

3-30 MHz 10-100 m Shortwave Radio

Very High Frequency (VHF)

30-300 MHz 1-10 m FM Radio

Ultra High Frequency (UHF)

300-3000 MHz 10-100 cmTelevision, Mobile

Phones, GPS

Super High Frequency (SHF)

3-30 GHz 1-10 cmSatellite Links, Wireless

Communication

Extremely High Frequency (EHF)

30-300 GHz 1-10 mmAstronomy, Remote

Sensing

Visible Spectrum400-790 THz

(4*10^14-7.9*10^14)

380-750 nm (nanometers)

Human Eye

Table: Frequency Bands

3) Radiation Pattern:

A radiation pattern defines the variation of the power radiated by an antenna as a function of the direction away from the antenna. This power variation as a function of the arrival angle is observed in the antenna's far field.

As an example, consider the 3-dimensional radiation pattern in figure 09, plotted in decibels (dB) .

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Figure 09: Example radiation pattern for an Antenna.

This is an example of a donut shaped or toroidal radiation pattern. In this case, along the z-axis, which would correspond to the radiation directly overhead the antenna, there is very little power transmitted. In the x-y plane (perpendicular to the z-axis), the radiation is maximum. These plots are useful for visualizing which directions the antenna radiates.

Standard spherical coordinates are used, where ‘θ’ is the angle measured off the z-axis, and ‘Ø’ is the angle measured counterclockwise off the x-axis as shown in Figure 10.

Figure 10: Angle measured of z-axis ‘θ’  & x-axis ‘Ø’ 

In short we can say that the radiation pattern is a plot which allows us to visualize where the antenna transmits or receives power.

4) Field Regions:

The fields surrounding an antenna are divided into 3 principle regions: Reactive Near Field. Radiating Near Field or Fresnel Region. Far Field or Fraunhofer Region.

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The far field region is the most important, as this determines the antenna's radiation pattern. Also, antennas are used to communicate wirelessly from long distances, so this is the region of operation for most antennas.

a. Far Field (Fraunhofer) Region:

The far field is the region far from the antenna, as you might suspect. In this region, the radiation pattern does not change shape with distance (although the fields still die off as 1/R, so the power dies off as 1/R^2). Also, this region is dominated by radiated fields, with the E- and H-fields orthogonal to each other and the direction of propagation as with plane waves.

If the maximum linear dimension of an antenna is D, then the following 3 conditions must all be satisfied to be in the far field region:

R= (2D2/ λ) Equation: 1

R››D Equation: 2

R›› λ Equation: 3

The first and second equation above ensure that the power radiated in a given direction from distinct parts of the antenna are approximately parallel (see figure a). This helps ensure the fields in the far-field region behave like plane waves. Note that >> means "much greater than" and is typically assumed satisfied if the left side is 10 times larger than the right side. The Rays from any Point on the Antenna are Approximately Parallel in the Far Field as shown in figure 11.

Figure 11. Rays from Antenna in Far Field.

Near a radiating antenna, there are reactive fields that typically have the E-fields and H-fields die off with distance as ‘1/R2’ and ‘1/R3’. The third equation above ensures that these near fields are gone, and we are left with the radiating fields, which fall off with distance as ‘1/R’.

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The far-field region is sometimes referred to as the Fraunhofer region, a carryover term from optics.

b. Reactive Near Field Region:

In the immediate vicinity of the antenna, we have the reactive near field. In this region, the fields are predominately reactive fields, which means the E- and H- fields are out of phase by 90 degrees to each other (recall that for propagating or radiating fields, the fields are orthogonal (perpendicular) but are in phase).

The boundary of this region is commonly given as:

Equation: 4

c. Radiating Near Field (Fresnel) Region:

The radiating near field or Fresnel region is the region between the near and far fields. In this region, the reactive fields are not dominate; the radiating fields begin to emerge. However, unlike the far field region, here the shape of the radiation pattern may vary appreciably with distance.

The region is commonly given by:

Equation: 5

5) Directivity:

Directivity is a fundamental antenna parameter. It is a measure of how 'directional' an antenna's radiation pattern is. An antenna that radiates equally in all directions would have effectively zero directionality, and the directivity of this type of antenna would be 1 (or 0 dB). Directivity is technically a function of angle, but the angular variation is described by its radiation pattern. An antenna's normalized radiation pattern can be written as a function in spherical coordinates:

F (θ , Φ)

Mathematically ‘directivity’ formula is given by:

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Equation: 6

The numerator is the maximum value of F (the magnitude of the radiation pattern), and the denominator just represents the "average power radiated over all directions".

6) Antenna Efficiency and Gain:

a. Antenna Efficiency:The efficiency of an antenna relates the power delivered to the antenna and the power radiated or dissipated within the antenna. The losses associated within an antenna are typically the conduction losses (due to finite conductivity of the antenna) and dielectric losses (due to conduction within a dielectric which may be present within an antenna).

The antenna efficiency (or radiation efficiency) can be written as the ratio of the radiated power to the input power of the antenna:

Equation: 7

Equation [7] is sometimes referred to as the antenna's radiation efficiency. The total efficiency of an antenna is the radiation efficiency multiplied by the impedance mismatch loss of the antenna.

Equation: 8

ML = antenna's loss due to impedance mismatch, ‘εR’ is the antenna's radiation efficiency.

b. Antenna Gain

The term ‘Gain’ describes how much power is transmitted in the direction of peak radiation to that of an isotropic source. Gain is more commonly quoted in a real antenna's specification sheet because it takes into account the actual losses that occur.

Gain (G) can be related to directivity (D) by:

Equation: 9

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7) Beam widths and Side lobe Levels:

In addition to directivity, the radiation patterns of antennas are also characterized by their beam widths and side lobe levels.

Consider the radiation pattern given by:

Equation: 10

This pattern is actually fairly easy to generate using ‘Antenna Arrays’. The 3-dimensional view of this radiation pattern is given in Figure 1.

Figure 12: 3D Radiation Pattern.

The polar angle measured off z-axis plot is given by:

Figure 13: Polar Radiation Pattern. The main beam is the region around the direction of maximum radiation. The main beam

in Figure 2 is centered at 90 degrees. The side lobes are smaller beams that are away from the main beam. These side lobes are

usually radiation in undesired directions which can never be completely eliminated. The side lobes in Figure 2 occur at roughly 45 and 135 degrees.

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The Half Power Beam width (HPBW) is the angular separation in which the magnitude of the radiation pattern decrease by 50% (or -3 dB) from the peak of the main beam. From figure 2, the pattern decreases to -3 dB at 77.7 and 102.3 degrees. Hence the HPBW is 102.3-77.7 = 24.6 degrees.

Another commonly quoted beam width is the ‘Null to Null Beam width’. This is the angular separation from which the magnitude of the radiation pattern decreases to zero (negative infinity dB) away from the main beam. From Figure 2, the pattern goes to zero (or minus infinity) at 60 degrees and 120 degrees. Hence, the Null-Null Beam width is 120-60=60 degrees.

Finally, the ‘Side lobe Level’ is another important parameter used to characterize radiation patterns. The side lobe level is the maximum value of the side lobes (away from the main beam). From Figure 2, the side lobe level (SLL) is -14.5 dB.

8) Antenna Impedance:

An antenna's impedance relates the voltage to the current at the input to the antenna. If impedance of an antenna is given by:

Z= x+ jy Equation: 11

The real part of an antenna's impedance ‘x’ represents power that is either radiated away or absorbed within the antenna. The imaginary part of the impedance ‘y’ represents power that is stored in the near field of the antenna (non-radiated power). An antenna with a real input impedance (zero imaginary part) is said to be resonant.

9) Bandwidth:

Bandwidth is another fundamental antenna parameter. This describes the range of frequencies over which the antenna can properly radiate or receive energy. Often, the desired bandwidth is one of the determining parameters used to decide upon an antenna. For instance, many antenna types have very narrow bandwidths and cannot be used for wideband operation. There are also other criteria which may be used to characterize bandwidth.. The bandwidth is often specified in terms of its Fractional Bandwidth (FBW).

10) Polarization - EM Waves :

Polarization of Plane Waves:

Polarization is one of the fundamental characteristics of any antenna. The main types of antenna polarization are:

a. Linear Polarization:

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A plane electromagnetic (EM) wave is characterized by travelling in a single direction (with no field variation in the two orthogonal directions). In this case, the electric field and the magnetic field are perpendicular to each other and to the direction the plane wave is propagating as shown in Figure 14.

A linearly polarized wave does not need to be along the horizontal or vertical axis. For instance, a wave with an E-field constrained to lie along the line shown in figure would also be linearly polarized.

Figure 14: Locus of E-field amplitudes for a linearly polarized wave at an angle.

The E-field in Figure could be described by Equation (12). The E-field now has an x- and y- component, equal in magnitude.

Equation: 12

In Equation (12) the x- and y-components of the E-field are in phase( they both have the same magnitude and vary at the same rate).

b. Circular Polarization

Suppose now that the E-field of a plane wave was given by Equation (13):

Equation: 13

In this case, the x- and y- components are 90 degrees out of phase. If the field is observed at (x,y,z)=(0,0,0) again as before, the plot of the E-field versus time would appear as shown in figure 15.

Figure 15: E-field strength at (x,y,z)=(0,0,0) for field of Eq. (13).

The E-field in Figure 15 rotates in a circle. This type of field is described as a circularly polarized wave. To have circular polarization, the following criteria must be met:

The E-field must have two orthogonal (perpendicular) components. The E-field's orthogonal components must have equal magnitude. The orthogonal components must be 90 degrees out of phase.

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c. Elliptical Polarization:

If the E-field has two perpendicular components that are out of phase by 90 degrees but are not equal in magnitude, the field will end up Elliptically Polarized. Consider the plane wave travelling in the +z-direction, with E-field described by equation (14):

Equation: 14

The locus of points that the tip of the E-field vector would assume is given in figure .

Figure 16: Tip of E-field for elliptical polarized wave of Eq. (14).

The field in figure,travels in the counter-clockwise direction, and if travelling out of the screen would be ‘Right Hand Elliptically Polarized’. If the E-field vector was rotating in the opposite direction, the field would be ‘Left Hand Elliptically Polarized’.

11) Polarization of antenna:

The polarization of an antenna is the polarization of the radiated fields produced by an antenna, evaluated in the far field. Hence, antennas are often classified as "Linearly Polarized" or a "Right Hand Circularly Polarized Antenna".

This simple concept is important for antenna to antenna communication. First, a horizontally polarized antenna will not communicate with a vertically polarized antenna. Due to the reciprocity theorem, antennas transmit and receive in exactly the same manner. Hence, a vertically polarized antenna transmits and receives vertically polarized fields. Consequently, if a horizontally polarized antenna is trying to communicate with a vertically polarized antenna, there will be no reception.

12) Effective Area (Effective Aperture):

A useful parameter calculating the receive power of an antenna is the effective area or effective aperture. Assume that a plane wave with the same polarization as the receive antenna is incident upon the antenna. Further assume that the wave is travelling towards the antenna in the antenna's direction of maximum radiation (the direction from which the most power would be received).

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Then the effective aperture parameter describes how much power is captured from a given plane wave. Let ‘W’ be the power density of the plane wave (in W/m^2). If ‘P’ represents the power at the antennas terminals available to the antenna's receiver, then:

Hence, the effective area simply represents how much power is captured from the plane wave and delivered by the antenna. This area factors in the losses intrinsic to the antenna (ohmic losses, dielectric losses, etc.).

A general relation for the effective aperture in terms of the peak gain (G) of any antenna is given by:

Equation: 15

13) Friis Transmission Formula:

The Friis Transmission Equation is used to calculate the power received from one antenna (with gain G1), when transmitted from another antenna (with gain G2), separated by a distance R, and operating at frequency f or wavelength lambda.

Derivation of Friis Transmission Formula

To begin the derivation, consider two antennas in free space (no obstructions nearby) separated by a distance R:

Figure 17: Transmit (Tx) and Receive (Rx) Antennas separated by R.

Assume that “PT” Watts of total power are delivered to the transmit antenna. For the moment, assume that the transmit antenna is omnidirectional, lossless, and that the receive antenna is in the far field of the transmit antenna.

The power ‘P’ of the plane wave incident on the receive antenna a distance ‘R’ from the transmit antenna is given by:

P= PT / 4πR2 Equation: 16

If the transmit antenna has a gain in the direction of the receive antenna given by “GT” , then the power equation above becomes:

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P= (PT / 4πR2 ) × GT Equation: 17

The gain term factors in the directionality and losses of a real antenna. Assume now that the receive antenna has an effective aperture given by ‘AER’. Then the power received by this antenna (PR) is given by:

Equation: 18

Since the effective aperture for any antenna can also be expressed as:

Equation: 19

The resulting received power can be written as:

Equation: 20

This is known as the ‘Friis Transmission Formula’. It relates the free space path loss, antenna gains and wavelength to the received and transmit powers.

14) Antenna Temperature:

Antenna Temperature ‘TA’ is a parameter that describes how much noise an antenna produces in a given environment. This temperature is not the physical temperature of the antenna. Moreover, an antenna does not have an intrinsic "antenna temperature" associated with it; rather the temperature depends on its gain pattern and the thermal environment that it is placed in. Antenna temperature is also sometimes referred to as Antenna Noise Temperature. An antenna's temperature will vary depending on whether it is directional and pointed into space or staring into the sun.

For an antenna with a radiation pattern given by ‘R(θ,Ø)’ the noise temperature is mathematically defined as:

Equation: 21

The noise power received from an antenna at temperature ‘TA’ can be expressed in terms of the bandwidth (B) the antenna (and its receiver) are operating over:

Equation: 22

In the above, K is Boltzmann's constant (1.38 * 10^-23 [Joules/Kelvin = J/K].

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Refrences:

[R1]: http://www.antenna-theory.com/intro/history.php

[R2]: http://www.antenna-theory.com/

[R3]: http://www.antenna-theory.com/basics/main.html

Pictures: http://www.antenna-theory.com/

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