Antenna Def[1]

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FrequencyThe basics of sinusoids (sine and cosine waves), wavelength, frequency and the speed of light.

More Advanced Frequency InformationA discussion on how all waveforms in the universe are made up of the sum of sinusoids(simple waves) This helps explains why in antenna theory we always discuss wavelengthand frequency no matter what signal (information) we want to transmit.

Frequency Bands No discussion on antenna fundamentals is complete without a real-world list of frequency bands.

Radiation PatternThe radiation pattern for an antenna is defined on this page. We have 3D graphs of realantenna radiation patterns, with a discussion on isotropic, omnidirectional and directionalradiation patterns. Radiation patterns are of the utmost importance in the discussion of antenna basics.

Field RegionsThe introduction to antennas continues with a discussion of Field Regions. The Far Field,

Near Field and Fresnel Regions for an antenna is presented.

DirectivityDirectivity is fundamental to antennas. It is a measure of how "directional" an antenna'sradiation pattern is.

Efficiency and Antenna GainAn antenna's efficiency is a measure of how much power is radiated by the antennarelative to the antenna input power. The subject of Antenna Basics also includes adiscussion of Antenna Gain, which is real power radiated in a particular direction.

Beamwidths and Sidelobes
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An antenna's radiation pattern in the far field is often characterized by it's beamwidth andsidelobe levels. This introduction to antenas illustrates this with an example.

ImpedanceAntenna Impedance is presented as the ratio of voltage to current at the antenna'sterminals. Low- and High-Frequency models are presented for transmission lines. Thefundamentals of antenna theory requires that the antenna be "impedance matched" to thetransmission line or the antenna will not radiate. The concept of VSWR is introduced as ameasure of how well matched an antenna is.

Bandwidth

The bandwidth of an antenna is the frequency range over which the antenna radiates. The bandwidth can be defined in different ways; this page presents an introduction to antenna bandwidth.

Polarization of WavesAll electromagnetic plane waves have an associated polarization. The antenna concepts of Linear, Circular and elliptical polarization are presented.

Polarization of AntennasAntennas are also classified by their polarization; this defines the type of plane wave

polarization the antenna is most sensitive to. This is a fundamental antenna concept.

Effective ApertureEffective aperture is a basic antenna concept that is a measure of the power captured by anantenna from a plane wave. Effective aperture can be expressed as a function of the

antenna gain and the wavelength of interest.

Friis Transmission EquationFriis Transmission Formula is the most fundamental equation of antenna theory. Thisequation relates transmit power, antenna gains, distance and wavelength to received

power. This page is a must-read for those interested in antenna theory.
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Antenna TemperatureAntenna Temperature is a property of an antenna and the environment it operates in. It is ameasure of the noise received by the antenna due to thermal (or temperature) effects.

Why do Antennas Radiate?The antenna basics section concludes with a discussion of Why Antennas Radiate. Theidea here is to explain the physical concepts that produce radiation in terms of electronsflowing on a wire.

Antenna Factor

The Antenna Factor is used by RF or EMC antenna engineers to describe the requiredelectric field strength that produces 1 Volt at the terminals of an antenna. Alternatively,the Antenna Factor concept specifies what the received voltage is in the presence of anelectric field. It is defined mathematically as:

Technically, the above definition is a little ambiguous. For instance, if the terminals of theantenna are short circuited, the received voltage is always zero, so the Antenna Factor isnot defined. Hence, the Antenna Factor has an implied impedance associated with theantenna terminals, most commonly 50 Ohms. However, sometimes an "open circuit"antenna factor is discussed, which is the available voltage for an antenna with an opencircuit (no receiver or load attached). The basic concept of antenna factor with a terminal(port, receiver or load) impedance is shown in Figure 1.
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Figure 1. Graphical Illustration of Antenna Factor, with Antenna Terminated in a Load(which represents the Receiver).

In the above Figure, the E-field is shown as part of a propagating wave (which isn'tneccessarily the case). The antenna receives the field at a voltage shows up at itsterminals, the circles shown in Figure 1. The receiver impedance (or the load, or ameasuring device such as a network analyzer) is shown connected to the antennaterminals. The ratio of the incident field strength to the output voltage is the AntennaFactor.

The above equation for the Antenna Factor assumes that the polarization of the E-fieldand the antenna are matched (no polarizatoin mismatch loss).

The axial ratio is the ratio of orthogonal components of an E-field. A circularly polarizedfield is made up of two orthogonal E-field components of equal amplitude (and 90 degreesout of phase). Because the components are equal magnitude, the axial ratio is 1 (or 0 dB).

Axial RatioThe axial ratio for an ellipse is larger than 1 (>0 dB). The axial ratio for pure linear

polarization is infinite, because the orthogonal components of the field is zero.

Axial ratios are often quoted for antennas in which the desired polarization is circular. Theideal value of the axial ratio for circularly polarized fields is 0 dB. In addition, the axialratio tends to degrade away from the mainbeam of an antenna, so the axial ratio may beindicated in a spec sheet (data sheet) for an antenna as follows: "Axial Ratio:


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BalunsA Balun is used to "balance" unbalanced systems - i.e. those where power flows from anunbalanced line to a balanced line (hence, balun derives from bal ance to un balanced). As

an example, consider a coaxial cable connected to a half-wave dipole antenna shown inFigure 1.

Figure 1. An unbalanced transmission line (coaxial cable) connected to a dipole antenna.

In Figure 1, a coaxial cable is connected to a dipole antenna. For a dipole antenna tooperate properly, the currents on both arms of the dipole should be equal in magnitude.When a coaxial cable is connected directly to a dipole antenna however, the currents willnot neccessarily be equal. To see this, note that the current along a transmission lineshould be of equal magnitude on the inner and outer conductors, as is typically the case.Observe what happens when the coax is connected to the dipole. The current on the center conductor (the red/pink center core of the coax, labeled IA) has no where else to go, somust flow along the dipole arm that is connected to it. However, the current that travelsalong the inner side of the outer conductor ( IB) has two options: it can travel down thedipole antenna, or down the reverse (outer) side of the outer conductor of the coaxial cable(labeled IC in Figure 1).
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Ideally, the current IC should be zero. In that case, the current along the dipole armconnected to the outer conductor of the coax will be equal to the current on the other dipole arm - a desirable antenna characteristic. Because the dipole wants equal or

balanced currents along its arms, it is the balanced section. The coaxial cable does notnecesarily give this however - some of the current may travel down the outside of theouter coax, leading to unbalanced operation - this is the unbalanced section.

The solution to this problem, however you come up with it, is a balun. A balun forces anunbalanced transmission line to properly feed a balanced component. In Figure 1, thiswould be done by forcing IC to be zero somehow - this is often called choking the currentor a current choke.

There are many baluns that have been developed to choke off the outer current and restore balanced operation. Some of the most popular methods are described in the following pages.

Bazooka BalunsThe principle of operation of a Bazooka Balun is presented on this page. This balun addsa short-circuited sleeve around the coaxial cable, which somewhat resembles a bazooka,giving it the name.

The fundamental features of a Bazooka Balun are shown in Figure 1.

Figure 1. Bazooka or Sleeve Balun.

An equivalent diagram of this balun is shown in Figure 2.
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Figure 2. Equivalent Representation of Sleeve Balun.

The green sleeve in Figures 1 and 2 acts as a transmission line, that is short circuited at theend. From Gauss's law, it is (basically) true that the current on the inside of the outer armof the bazooka (green line) must be the opposite of that flowing on the outside of the coax(grey line). Hence, the current IC actually sees a short-circuited transmission line. If thelength L of the sleeve is chosen to be a quarter-wavelength (at the desired frequency of operation), then the impedance that the current IC sees is infinite (this is the principle of ashort-circuited quarter-wave transmission line - see the impedance page for a brief introduction to transmission line theory).

Since the impedance is infinite for traveling down outer side of the coaxial cable, the

current flowing out of the inner conductor (red/pink line) must be equal to the currentflowing out of the outer conductor (grey line). Consequently, we have balanced operation,and the sleeve has successfully given balanced operation to an inherently unbalancedtransmission line.

Cross PolarizationCross polarization (sometimes written X-pol, in antenna slang) is the polarizationorthogonal to the polarization being discussed. For instance, if the fields from an antennaare meant to be horizontally polarized, the cross-polarization in this case is vertical

polarization. If the polarization is Right Hand Circularly Polarized (RHCP), the cross- polarization is Left Hand Circularly Polarized (LHCP). See also Polarization .

This term arises because an antenna is never 100% polarized in a single mode (linear,circular, etc). Hence, two radiation patterns of an antenna are sometimes presented, theco-pol (or desired polarization component) radiation pattern and the cross-polarizationradiation pattern.
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The cross polarization may be specified for an antenna as a power level in negative dB,indicating how many decibels below the desired polarization's power level the x-pol

power level is.

Decibels (dB)Many parameters related to antennas are measured in decibels; for instance, gain is oftenspecified in decibels, written as 10 dB. Or maybe the minimum received power for anantenna system to work is specified as -70 dBm (decibels relative to a milliWatt). Or thetransmit power of your cell phone is given as -3 dB.

Why is this? Why don't they just tell you how much power is transmitted in Watts or thegain of an antenna in regular (linear) units?

The decibel system is used when quantities can vary by massive amounts. The Richter

scale for earthquakes is also on a scale similar to decibels, because the magnitude of earthquakes can vary from barely perceptible with sophisticated equipment to earthquakesthat demolish vast amounts of land. As an example, lets look at power received by anantenna relative to power transmitted.

Suppose we have an antenna transmitting 50 Watts of power, with a gain of 2 (=3 dB) inthe direction of a receive antenna with a gain of 2 (=3 dB). Suppose the antennas areseparated by 20,000 kilometers (as is the typical orbit of a gps satellite). The GPSsatellites operate at a frequency of 1.575 GHz. How much power is received?

Using the Friis Transmission Equation and the fact that wavelength equals c/f , we cancalculate the received power to be:

Of the 50 Watts transmitted, about 2.3e-16% of that power gets through. Incidentally, thismight seem frighteningly small, but yes, antenna systems can operatte with this much

power. So be patient with the GPS unit in your car, it is doing a good job.
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Antenna engineers (all engineers actually) don't like to use linear units when the quantitiescan vary by such large amounts. Its real tough to picture in your head the difference

between 1e17 and 1e18. To work around this, we use the decibel system. Its a simplelogarithmic transformation - units in linear are easily converted via:

Hence, the above quoted value of 1.149e-16 Watts is equal to -159.4 decibels, written-159.4 dB.

To give a cemented idea on the conversions, a table of linear to decibel levels is presented.

Table I. Conversion between Linear Units and Decibels. Linear Value dB Value

1e-10 -100 dB

1e-9 -90 dB1e-6 -60 dB

1e-3 -30 dB

1e-1 -10 dB

0.5 -3 dB

1 0 dB

10 10 dB

100 20 dB

1e3 30 dB

1e6 60 dB

Another common unit is dBm. This means "decibels relative to a milliWatt". In this case,we are talking about power, and the power is just specified in milliWatts instead of Watts.So:

1 W = 1000 mW = 0 dB = 30 dBm

Or

0 dBm = -30 dB = 0.001 W = 1 mW

Another common variation on dB in antenna theory is dBi which means "decibels relativeto an isotropic antenna". This just specifies the gain of an antenna relative to the isotropicgain, which is 1. So really nothing changes...:

Gain of 10 dB = Gain of 10 dBi


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The reason people specify dBi sometimes is that other relative values are sometimesspecified, like dBd. This means "decibels of gain relative to a standard half-wave dipoleantenna". The gain of a half-wave dipole is 2.15 dBi. So:

Antenna with a gain of 10 dBi = 10 dB = 7.85 dBd

Gain of half-wave diple antenna = 2.15 dBi = 0 dBd

Another nice feature of decibels is they make multiplication problems become addition, asseen on the decibel math page.

DesenseDesense is the degradation in sensitivity due to noise sources, typically which are

generated by the same device the radio is in. An example will make this clear.

Suppose we are looking at a certain frequency (let's say UMTS Band V, channel 9162)and the sensitivity of the receiver is -110 dBm. For illustration, we will assume we aretalking about a smartphone, with memory chips, an LCD display, a camera, etc. Thismeans that a reliable data link can be maintained when the receive power is -110 dBm andhigher. If the received power is lower (-111 dBm for instance), the bit-error-rate (BER)will not be acceptable.

You should read the page on Total Isotropic Sensitivity (TIS) . TIS is basically the

sensitivity of the receiver-antenna system, integrated over all possible angles.

Now, let's say we connect an antenna to the receiver, and the antenna efficiency is -3 dB.What do you think the Total Isotropic Sensitivity should be? You would expect themeasured TIS (average sensitivity) to be -110 dBm - (-3 dB) = -107 dBm.

Let's say you measure a TIS of -107 dBm when no other processes on your phone arerunning (so the camera is off, the screen (display) is off, no background applications arerunning). To see how the receiver is affected by other electronics, let's say you turn on amemory intensive application. This application is having the memory send signals back

and forth to the CPU during your measurement. You again run the sensitivitymeasurement, and this time you measure TIS = -97 dBm.

What happened? You just lost 10 dB of sensitivity. This 10 dB loss is known as desense .How did this happen? Well, the electric signals between the CPU and the memory areoperating at a relatively low frequency (maybe a few hundred MHz), but a harmonic of these signals will be at the same frequency as where we are measuring sensitivity. Theelectric signals to the memory are on transmission lines , but even transmission lines act as
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(very poor) antennas. And, we now have a very clean path to the receiver: that is thesmartphone's own antenna, the job of which is to collect as much energy as possible.Hence, the antenna receives energy, even if it is the onboard noise source we don't want itto receive. And because the sensitivity of the receiver is so low (-100 dBm means 10^-10mW sensitivity), the small power from the transmission lines to the memory will benoticed. This effectively increases the noise level - and since the sensitivity is a functionof the Signal to Noise Ratio (SNR), we have a loss in sensitivity. This is illustrated inFigure 1:

Figure 1. Illustration of Noise Power Collected By the Receiver

Sources of Desense

The desense discussed above pertained to the memory. This is a common source of WIFInoise in computers. Desense can come from pretty much anything your computer,smartphone or whatever does:

Hard DriveCameraScreen (LCD, monitor, whatever)MemoryPeripherals plugged into your device: USB, ethernet, whatever In military aircraft, other out-of-band transmitters cause desense

In general, any process or feature on a device can be checked for desense by ensuring it isoff during the initial sensitivity (TIS) measurement, and then re-running the sensitivitymeasurement with the process on.


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Mitigation of Desense

Desense mitigation is a must-do for modern devices. Desense can be reduced by findinghow the noise energy is being radiated, and then doing everything possible to reduce that.For instance, in memory, there are pins that go up to the memory chip, and these act assmall inefficient antennas. By shielding the pins or reducing their length, the radiationefficiency (and hence the radiated power) of the lines can be reduced.

Another technique is to try to keep lines symmetric. That is, if a signal is travelling oneway on a wire, the return path should be near the forward path and a mirror image of thefirst line. This will help to cancel the radiated fields from the current flowing on the wire.

If you kill the antenna (by reducing the antenna efficiency), you will reduce the noise power to the receiver. However, since you are interested in maintaining a wireless link (and therefore want to maximize the SNR), killing the antenna will reduce your signal asmuch as the noise so nothing gained.

In general, the process of desense mitigation is (1) trying to find the noise source (whichoften is a harmonic of a lower frequency noise source), and (2) finding the mechanism for radiation or coupling to the antenna (which directs the noise power to the receiver). If oneor both of these links can be reduced, the desense will be improved.

Acceptable levels of desense are application specific. Sometimes 10 dB of desense isgood, other times, 3 dB is considered too much.

E-planeThe E-plane is any plane that contains the E-field and the direction of maximum radiationfrom the antenna. As an example, consider a short dipole , the electric fields are given by:

This states that in the x-y plane, the E-fields are vertically oriented (negative z-direction).See Figure 1 below.
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Figure 1. Fields at a point along the y-axis from a short dipole.

The fields at a point along the y-axis are shown in Figure 1. The E-field is oriented in thenegative z-direction, the direction of propagation at the point is the +y-direction (also thedirection of maximum radiation in this case), and the H-field is oriented in the negative x-direction.

The E-plane is any plane that contains the E-field and the direction of maximum radiation.Hence, the E-plane in this case is any plane that contains the z-axis (xz plane, yz plane,etc). The E-plane cut is not unique in this case, but a plot of the radiation pattern given in

the E-plane would be a function of the polar angle ( ), which is measured off the z-axis.

See also H-plane .

H-planeThe H-plane is a plane that contains the H-field and the direction of maximum radiationfrom the antenna. As an example, consider a short dipole , the magnetic fields are given

by:

This states that in the x-y plane, the H-fields are horizontally oriented (in the x-y plane).See Figure 1 below.
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Figure 1. Fields at a point along the y-axis from a short dipole.

The fields at a point along the y-axis are shown in Figure 1. The E-field is oriented in thenegative z-direction, the direction of propagation at the point is the +y-direction, and theH-field is oriented in the negative x-direction. The direction of maximum radiation is

broadside from the antenna.

The H-plane is any plane that contains the H-field and the direction of maximumradiation. Hence, the H-plane in this case is the x-y plane. See also E-plane .

Effective Isotropic Radiated Power (EIRP)EIRP is Effective Isotropic Radiated Power , also called the Equivalent Isotropic Radiated

Power . In antenna measurements, the measured radiated power in a single direction (thatis, for a fixed and ) is known as the EIRP.

Typically, for an antenna radiation pattern measurement, if a single value of EIRP isgiven, this will be the maximum value of the EIRP over all measured angles.

EIRP can also be thought of as the amount of power a perfectly isotropic antenna wouldneed to radiate to achieve the measured value.
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As an example, suppose the radiated power is measured for an arbitrary antenna. Supposethe peak power is measured at = =90 degrees, and the value is EIRP = 20 dBm = -10dB = [0.1 W = 100 mW]. Then a perfectly isotropic antenna radiating 20 dBm would

produce the same measured power for the peak angles of our antenna.

The EIRP can be related to the power transmitted from the radio ( P_t ), the cable losses(possibly including antenna mismatch) L, and the antenna gain (G) by:

[Equation 1]

Often the cable losses L can be neglected, as they are generally a small fraction of a dB.

Total (full 3D) Measurements from a Single-Point (single-direction) Measurement

If the peak EIRP and the directivity (D) are known for an antenna, then the Total RadiatedPower (TRP) can be found from the equation:

TRP = EIRP - D [Equation 2]

In this manner, if the directivity and peak angle for an antenna are known in advance, themeasurement time can be greatly reduced by using equation [2].

See also Effective Isotropic Sensitivity (EIS) .

Effective Isotropic Sensitivity(EIS)EIS is the Effective Isotropic Sensitivity . In antenna measurements, the measuredsensitivity in a single direction (that is, for a fixed and ) is known as the EIS.

Typically, for an antenna system (antenna + transmission line + receiver + associatedelectronics) sensitivity measurement, if a single value of EIS is given, this will be theminimum value of the EIS over all measured angles.

If the EIS value was measured for an antenna system with an isotropic antenna, then theEIS would be the same as the Total Isotropic Sensitivity (TIS) .

Total (full 3D) Measurements from a Single-Point (single-direction) Measurement

If the minimum EIS and the directivity (D) are known for an antenna, then the TIS can befound from the equation:
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TIS = EIS + D [1]

In this manner, if the directivity and peak angle for an antenna are known in advance, themeasurement time can be greatly reduced by using equation [1]. This is particularly

important for sensitivity measurements, which take much longer than power measurements.

See also Effective Isotropic Sensitivity (EIRP) and TIS .

Electric Field (E-Field)Electromagnetic waves are made up of Electric Fields (often called the E-field) andmagnetic fields . What is an E-field?

Technically, the E-field at a point in space is a measure of how strong the force would beon a unit point charge (a small sphere with an electric charge of 1 Coulomb on it). Hence,the units of the E-field are Newtons/Coulomb [N/C]. These units are equivalent toVolts/meter [V/m], which is what the E-field is commonly quoted in (for instance, 10V/m).

The E-field is a vector quantity - this means at every point in space it has a magnitude anda direction. For instance, lets say an E-field exists in space given by:

This is the E-field of a plane wave travelling in the +z-direction, and the E-field is linearly polarized and 'points' in the y-direction ( k is the wavenumber ). The amplitude of the waveis A Volts/meter.

At time t =0 and z =0, the E-field is A Volts/meter in the +y-direction. This means that aunit point charge (1 Coulomb) at this location would experience a force of A Newtons inthe +y-direction.

The electric field also relates to voltage - a stronger E-field incident upon an antenna willinduce a larger voltage difference across the antenna's terminals. However, except for lowfrequencies, the relationship between E-fields and Voltage is not simple (the voltage is a

potential which is subject to different definitions). At d.c., when the fields are static (novariation with time), the E-field and voltage V are related to each other by:
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The electric field associated with a point charge with a positive charge point away from itat every location; the fields associated with a pont charge with a negative charge pointtowards it.

Electric Flux Density (D-Field)The Electric Flux Density (usually written as the vector quantity D) is often used inelectromagnetics. While we won't give it a rigorous definition here, it can be sufficientlyunderstood for the purposes of antenna theory as being proportional to the Electric Field .The proportionality constant depends on the medium being analyzed, and is known as the

permittivity :

The electric flux density has units of charge/area (Coulombs/meter-squared or [C/m^2]).The permittivity is often frequency -dependent, and is sometimes anisotropic (implying the permittivity depends on which direction the fields are in):

In the most general case the E-field is related to the the electric flux density by a 3x3matrix, which is also frequency-dependent.

The only other major result in relation to the electric flux density involves the continuitiyof fields across boundaries. Consider two materials as shown in the figure below.
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The normal component of the electric flux density will be discontinuous at the boundary by an amount equal to the surface charge density , which has units of charge/area(Coulombs/meter-squared). This can be written mathematically as:

This relation holds at every point along the interface of a material discontinuity (mediumchange).

Folded BalunsThe principle of operation of a Folded Balun is presented on this page (this balun issometimes called the quarter-wavelength balun). This balun draws a cancelling currentfrom the central arm of the coax that cancels any current that travels down the outer sleeveof the coaxial cable - thus eliminating the unbalanced condition.

This balun is tricky to understand. Personally, I had to stare at it, then go to sleep, wakeup, think about it some more, then it made sense. I will attempt to describe the operationhere.

Note that the current on inner conductor of the coaxial cable contributes to the current thatflows on the outer conductor. This could be cancelled by tying the inner conductor to theoutside of the coaxial cable (because the current on the inner conductor is 180 degrees outof phase), which would cancel any net flow of current down the outer side of the coaxialcable. However, this would short-circuit any antenna connected to the coaxial cable, andthus we would have no radiation. The goal however, is to find a way to tie the currentfrom the center cable of the coax to the outer shield such that the outer current iscancelled.

The folded balun is shown in Figure 1. The green line (which will be made of a cylindricaltube of the same dimensions and material as the main coax) is connected from the reddipole arm (that is connected to the center conductor) to the outside of the coaxial cable, adistance L from the end. If L is chosen to be a quarter-wavelength at the frequency of
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operation, then just as is the case for the bazooka balun , the impedance seen by this arm isinfinite (due to the properties of transmission line theory and the quarter wavelength line).Hence, the first thing we need to note is that adding this balun does not affect theimpedance of the dipole antenna - this means that if we can get the correct voltage to theantenna, it will radiate properly.

Figure 1. Folded Balun - the green line represents a cylinder of the same dimensions asthe grey (main) coax.

Now, lets try to figure out why this will achieve balanced operation. Enlarging Figure 1and showing all of the currents on the coaxial cable and balun (and getting rid of the other

half of the dipole antenna because it does not need to be illustrated here), we have Figure2. I've introduced another current, ID, which travels along the balun.
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Figure 2. Zoomed In on a Folded Balun with all Currents Shown.

We are going to have to understand all of the currents shown in Figure 2. The current IAis what travels down the center of the coaxial cable and onto the red arm of the dipole.The current IB is what flows on the inside of the outer shield of the coaxial cable andfeeds the other dipole arm (not shown). The coaxial cable is a lossless transmission line -this means that the currents IA and IB are equal in magnitude but 180 degrees out of

phase. That is, IA = - IB.

The current IC is what travels down the outside of the coaxial cable - this is the currentthat we would like to choke off. How large is IC? To determine this, we note that whenthe current IB travels to the end of the coaxial cable, it can either travel down the greydipole arm (of Figure 1) or down the outside of the coaxial cable. The current IC willdepend on what the impedance is looking down the outside of the coaxial cable relative tothe impedance of the dipole arm. Lets call the impedance of the path on the outside of thecoaxial cable as Zg .

The current ID must travel in the opposite direction to that of the current IC, because it isfed by the current IA, whereas IC is fed by IB. Here is the important observation. What isthe magnitude of ID? The answer is - it must be equal to IC. Why? The answer lies in thefollowing two observations:

First, note that the voltage on the inner conductor (pink line) is out of phase with thevoltage on the outer conductor (grey line) - but they are of equal magnitude. Hence, if theattachment point of the balun to the red dipole arm (green to red connection in Figure 2),is made close to the center conductor, then the voltage at the balun connection point and


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the voltage at the connection between the outer conductor and the grey dipole arm areequal in magnitude but out of phase.

Second, at the point of attachment of the balun (the green-red connection in Figure 2), theimpedance viewed down towards the outside of the coaxial cable must be equal to Zg .This is because the balun is made of the same shape and material as the main coaxialcable. Consequently, the impedance viewed down the balun and onto the main coax must

be the same as that for the current IC.

Hence, if the voltages are equal in magnitude and out of phase, then the currents willcancel in the region below the balun. Consequently, balanced operation is restored.

This concept will probably take a few reads to make sense. Draw yourself some diagramsand work through it, and you will understand what is going on.

Note that because this balun requires a quarter-wavelength section to work properly, it isinherently narrowband. Away from the design frequency, the balun will no longer be aquarter-wave long and the properties described here will degrade.

Fractional Bandwidth (FBW)The fractional bandwidth of an antenna is a measure of how wideband the antenna is. If the antenna operates at center frequency fc between lower frequency f1 and upper frequency f2 (where fc=(f1+f2)/2 ), then the fractional bandwidth FBW is given by:

The fractional bandwidth varies between 0 and 2, and is often quoted as a percentage(between 0% and 200%). The higher the percentage, the wider the bandwidth.

Wideband antennas typically have a Fractional Bandwidth of 20% or more. Antennas witha FBW of greater than 50% are referred to as ultra-wideband antennas.

Front-to-Back RatioThe Front-to-Back Ratio is a parameter used in describing directional radiation patterns for antennas. If an antenna has a unique maximum direction, the front-to-back ratio is theratio of the gain in the maximum direction to that in the opposite direction (180 degreesfrom the specified maximum direction). This parameter is usually given in dB.

The Infinite Balun
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In the case of a coaxial cable feeding an antenna, a balun is used to choke (eliminate or reduce) thecurrents flowing on the outside shield of the coaxial cable.

The idea of an Infinite Balun is to use the currents flowing on the outside of the coaxial cable as partof the antenna. In this case, we won't need to choke the current at all; we just need to align the cable

with where we want the current to flow on our antenna.

As an example, consider the spiral antenna . The spiral antenna has two equal arms, which needs fedin the center (center conductor of the coaxial cable to one arm, and the ground or shield of the cableto the second arm of the spiral). For spiral antennas to work properly, we need balanced currents oneither arm of the spiral.

Suppose we try to run the cable up to the spiral antenna from below, as in Figure 1:

Figure 1. A Spiral Antenna Fed With a Coaxial Cable from Below.

In Figure 1, the spiral has two arms the blue and the green. The center conductor of the coaxial cable(red wire) is attached to the blue arm. The outer conductor of the coaxial cable (black) is attached tothe green arm of the spiral antenna.

For the antenna of Figure 1 to work properly, the current on the outside of the coaxial cable (black region) must be choked. This could be done with a bazooka balun ; however, this balun is farelynarrow bandwidth. Since spiral antennas are extraordinarily wideband, a better balun needs used.

The solution is to use the coaxial cable's outer conductor as one arm of the spiral antenna. In thissense, the current can flow on the outside of the coaxial cable, so that the unbalanced operation becomes desirable (current flows on both arms). Remember: current exiting a coaxial cable views theoutside of the coaxial cable as a comletely independent surface from the inside surface (where thecurrent is flowing in the transmission line mode). Hence, when the coaxial cable "opens up" (i.e.

begins to feed an antenna), the current has no problem flowing on the outside of the coaxial cable.

The infinite balun uses the coaxial cable as one arm of the spiral, as shown in Figure 2:
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Figure 2. The Infinite Balun Used With The Spiral Antenna.

In Figure 2, the black coaxial cable leaves the radio (transmitter and receiver). The coaxial cable

wraps around and forms one arm of the spiral antenna. The center conductor of the coax (shown inred) attaches to the other arm of the spiral antenna (shown in Blue).

Why does this work? Imagine current flowing down the transmission line, a forward travelling waveon the inner conductor and the opposite on the inside surface of the outer shield of the coaxial cable.Once the coaxial cable ends (the center conductor is exposed and connected to the blue arm), thecurrent on the center conductor of the coaxial cable must travel to the blue arm of the spiral antenna.

Now, when the current flowing on the inside of the outer shield of the coaxial cable is exposed(where the shield is broken at the feed point), the current has nowhere to flow except the outside of the coaxial cable. Hence, the current must travel down the outside of the coaxial cable, whichhappens to double as the black arm of the spiral antenna.

This balun works wonderfully. It has no bandwidth problems and is a very clever design. In addition,since the spiral antenna is a good radiator, the currents die off quickly as the spiral winds away fromthe center. Hence, terminating one arm of the spiral (the coaxial cable) to the radio does not affect the

performance.

This balun can be used whenever a separated ground region is available to merge the coaxial cableoutside shield with one region of the antenna. Care must be taken when exiting the coaxial cable from


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the structure, so that the lead of the coaxial cable to the radio (transmitter/receiver) does not detune or negatively affect the antenna.

Intrinsic ImpedanceThe intrinsic impedance is a property of a medium - an area of space. For a vacuum(outer space) or for wave propagation through the air around earth (often called 'freespace'), the intrinsic impedance (often written as or Z ) is given by:

=

This parameter is the ratio of the magnitude of the E-field to the magnitude of the H-field for a plane wave in a lossless medium (zero conductivity):

This relation can be derived directly from Maxwell's Equations . For a general medium

with permittivity and permeability given by , the intrinsicimpedance is given by:

For a medium with a conductivity associated with it, the intrinsic impedance is given by:

When the conductivity is non-zero, the above intrinsic impedance is a complex number,

indicating that the electric and magnetic fields are not in-phase.

The intrinsic impedance of free-space has nothing to do with the electrical impedance of an antenna. Also, there is no reason to have the impedance of an antenna match theintrinsic impedance of free space (no mismatch loss occurs).

Magnetic Field (H-Field)
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Electromagnetic waves are made up of Electric Fields (often called the E-field) andMagnetic fields (also known as H-fields). What is an H-field?

The H-field is a vector quantity (has a magnitude and direction) and is measured inAmps/Meter [A/m]. Recall that the E-field points away from a positive point charge. AnH-field curls (or wraps) around a wire of moving charge, as shown in Figure 1. Hence, H-fields are associated with moving electric charges.

Figure 1. H-field associated with a static current.

There are no isolated magnetic charges as of 2008, so an H-field can't be defined as aforce per unit magnetic charge in the way an E-field can be defined. However, magneticdipoles do exist (magnets) which have a positive and negative end (or North and South).The magnetic field lines travel away from the North side and terminate on the south side.
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Figure 2. H-field lines associated with magnetic dipole.

The H-field is orthogonal to the direction of propagation in a plane wave, as well as perpendicular to the E-field. It is the interaction of the E-field with the H-field in spacethat allows for wave propagation.

Magnetic Flux Density (B-Field)The Magnetic Flux Density (or B-field) is related to the magnetic field (H ) by the

permeability (written as of the medium where the fields are observed:

The magnetic flux density has units of magnetic charge/area (Webers/meter-squared or Wb/m^2, also known as a Tesla (T)). The permeability is often frequency -dependent, andis also sometimes anisotropic (which means the permeability is a function of whichdirection the fields are in):

In the most general case the H-field is related to the the magnetic flux density by a 3x3matrix, which is also frequency-dependent.

Recall that the electric field can be defined in terms of a "force per unit electric charge".Further, note that magnetic fields are associated with moving electric charges. The
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magnetic flux density can be defined in terms of a force per unit charge moving at unitvelocity. An emperical law relating the speed of an electric charge ( u ), the magnitude of the charge in Coulombs ( q), the magnetic flux density B), and the associated magneticforce ( F ) can be written as:

In the above equation, the represents the cross product for vectors. This shows that if the charge is moving in the +x-direction, and the magnetic flux density is in the +y-direction, the charge will experience a force in the +z-direction. If the charge is moving inthe same direction as the magnetic field, no force will be felt by the charge.

Maxwell's EquationsMaxwell's Equations are a set of four vector-differential equations that govern all of electromagnetics (except at the quantum level, in which case we as antenna people don'tcare so much). They were first presented in a complete form by James Clerk Maxwell

back in the 1800s. He didn't come up with them all on his own, but did add thedisplacement current term to Ampere's law which made them complete.

The four equations (written only in terms of E and H , the electric field and the magneticfield ), are given below.

In Gauss' law, is the volume electric charge density, J is the electric current density (inAmps/meter-squared), is the permittivity and is the permeability .

The good news about this is that all of electromagnetics is summed up in these 4equations. The bad news is that no matter how good at math you are, these can only besolved with an analytical solution in extremely simple cases. Antennas don't present avery simple case, so these equations aren't used a whole lot in antenna theory (except for numerical methods, which numerically solve these approximately using a whole lot of computer power).
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The last two equations (Faraday's law and Ampere's law) are responsible for electromagnetic radiation. The curl operator represents the spatial variation of the fields,which are coupled to the time variation. When the E-field travels, it is altered in space,which gives rise to a time-varying magnetic field. A time-varying magnetic field thenvaries as a function of location (space), which gives rise to a time varying electric field.These equations wrap around each other in a sense, and give rise to a wave equation.These equations predict electromagnetic radiation as we understand it.

MultipathMultipath is the arrival of a transmitted signal at a receive antenna from multiple pathsdue to reflections. The reflections can occur from the ground, trees, buildings, people, or whatever is around. As an example, see Figure 1. The dominant signal is often the Line of Sight (LOS) signal, which is the direct path from the receiver to the transmitter. The other arriving signals (due to reflections) are known as multipath. In some situations(particularly in urban environments), there is no line of sight signal, and all received raysare from multipath. Multipath causes significant variation in received signal - sometimesthe multipath reinforces the received signal, but often it subtracts from it (a phenomenonknown as fading). See also diversity reception .

Figure 1. Example of multipath.

PermeabilityPermeability is a property of a medium or a region of space. On this page, I'm

going to give its meaning as it relates to antenna theory, with only a smallexplanation on the physics behind it. The permeability, as we saw relates themagnetic flux density to the electric field . The permeability is given in units of Henries/meter; since Henries relates to inductance, a material with a higher

permeability can be thought of as storing more magnetic energy.

The permeability of a vacuum (or free space) is given by:
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This is roughly the permeability of air on Earth. Suppose now we are looking at amagnetic material (for instance, iron). This material will affect the magnetic field

because the magnetic moments of the molecules that make up the material alignthemselves in the direction of an external magnetic field. In addition, thesemagnetic moments tend to remain even after the external field is turned off,leading to a permanent magnetization of some materials. The permeability of amedium is typically specified by a relative permeability:

Materials are characterized as diamagnetic (relative permeability slightly less than1.0), paramagnetic (relative permeability slightly more than 1.0), and

ferromagnetic (high value for relative permeability, that also exhibits hysteresis).A table of common materials and their relative permeabilities is presented below.

Material Relative Permeability

Gold 0.999996

Mercury 0.999997

Water 0.99999

Air 1.000004

Aluminum 1.00002

Cobalt 255

Nickel 600

Steel 2000

Iron 4500

Finally, as mentioned on the page on permittivity , the permeability also affects thespeed of propagation of an electromagnetic wave in a medium with a relative

permeability given as , and also its corresponding wavelength:

In the above, c is the speed of wave propagation in the medium and is the speedof light in free space (or a vacuum); also is the wavelength of a wave at
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frequency f in the medium, the wavelength at the same frequency in a vacuumwould be .

PermittivityPermittivity is a property of a medium or a region of space. On this page, I'm going togive its meaning as it relates to antenna theory, with only a small explanation on the

physics behind it. The permittivity, as we saw relates the electric flux density to theelectric field . The permittivity is given in units of Farads/meter; since Farads relates tocapacitance, a material with a higher permittivity can be thought of as storing moreelectrical energy.

The permittivity of a vaccum (often called free space) is given by:

The above is roughly the permittivity of air on earth. Suppose we have some other dielectric medium (glass, rubber, wax or other non-conducting material). The permittivitydescribes how an electric field is affected within a medium. The E-field tends to polarizethe molecules within the material, which make up a net electric field that opposes theapplied E-field. As a result, the total E-field is less than it would be in a vacuum. Thiseffect is quantized in terms of the permittivity - which can be anisotropic (directiondependent) and frequency dependent.

As an antenna engineer, the permittivity affects the speed of propagation of a wavethrough a medium and also its wavelength. The permittivity of a medium is most oftengiven as a relative permittivity:

The speed of wave propagation in a given medium is given as:

Hence, if a medium has , then the speed of wave propagation in the medium will be half as fast as in free space (1.5*10^8 m/s). As a result of the speed being slowed, thewavelength of a plane wave decreases in size as well (the frequency remains constant):
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The above fact is often used in antenna-miniaturization: since resonant antennas are often

a half-wavelength in size, if they are placed in a medium with a higher permittivity therequired length decreases and hence the antenna will be smaller.

Permittivity alters the direction of travel of a wave incident upon a medium through snell'slaw. In addition, the reflection and transmission coefficients of a wave travelling from onemedium to another is influenced by the permittivity.

Reciprocity

reciprocity is one of the most useful (and fortunate) property of antennas. Reciprocitystates that the receive and transmit properties of an antenna are identical. Hence, antennasdo not have distinct transmit and receive radiation patterns - if you know the radiation

pattern in the transmit mode then you also know the pattern in the receive mode. Thismakes things much simpler, as you can imagine.

Antenna QThe Q of an antenna is a measure of the bandwidth of an antenna relative to the center frequency of the bandwidth. If the antenna operates over a band between f1 and f2 withcenter frequency fc=(f1+f2)/2 , then the Q is given by:

Antennas with a high Q are narrowband, antennas with a low Q are wideband. The higher the value of Q, the more sensitive the input impedance is to small changes in frequency.

ResonantAn antenna is said to be resonant if its input impedance is entirely real, i.e. Zin = R + j*0.

In this case the voltage and current are in phase at the antenna's terminals. This propertymakes the impedance matching of an antenna to a transmission line and receiver easier, asthe imaginary part of the impedance does not need tuned out.

In addition, when viewing the frequency plot of S11 for an antenna, there is often a largedecrease in the magnitude of S11 around the resonanct frequency, indicating that power isradiated well around this frequency.
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S-ParametersS-parameters describe the input-output relationship between ports (or terminals) in anelectrical system. For instance, if we have 2 ports (intelligently called Port 1 and Port 2),then S12 represents the power transferred from Port 1 to Port 2. S21 represents the power transferred from Port 2 to Port 1. In general, SNM represents the power transferred fromPort N to Port M in a multi-port network.

As an example, consider the following two-port network:

In the above Figure, S21 represents the power received at antenna 2 relative to the power input to antenna 1. For instance, S21=0 dB implies that all the power delivered to antenna1 ends up at the terminals of antenna 2 (which isn't physically possible). If S21=-10 dB,this implies that 1 Watt delivered to antenna 1 (or 0 dB), ends up as -10 dB at antenna 2,or 0.1 Watts.

In practice, the most commonly quoted parameter in regards to antennas is S11. S11represents how much power is reflected from the antenna. If S11=0 dB, then all the power is reflected from the antenna and nothing is radiated. If S11=-10 dB, this implies that if 3dB of power is delivered to the antenna, -7 dB is the reflected power. The rest was"accepted" by the antenna. This accepted power is either radiated or absorbed as losseswithin an antenna. Since antennas are typically designed to be low loss, the majority of the power delivered to the antenna is radiated.

As an example, consider the plot of S11 in the following figure:


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The above would typically be measured using a network analyzer, which can plot S11.The above figure shows that the antenna radiates best at 2.5 GHz, where S11=-10 dB.Further, at 1.5 GHz the antenna will radiate virtually nothing, as S11 is close to 0 dB. The

bandwidth can also be determined from the above figure. If S11 is to be


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The units of SAR are W/kg, or equivalently, mW/g. The SAR limit in the US for mobile phones is 1.6 W/kg, averaged over 1 gram of tissue. In Europe, the SAR limit is 2.0 W/kgaveraged over 10 grams of tissue. It is typically harder to achieve the US specificationthan the Europe spec, so if the phone meets the US spec it will typically also meet theEuropean spec.

Measuring SAR

To obtain official SAR measurements, the DASY system by SPEAG is used. This isshown in Figure 1:

Figure 1. The DASY SAR Measurement System.

In Figure 1, there is a hollow tub that the yellow robot moves the measuring probe into.

The tub is formed in standardized shapes, which replicate the shape of the human head.The tub that the probe is measuring for Figure 1 simulates the left side of the human head.The DUT is the device-under-test (the mobile phone) is placed directly on the edge of thetub, and transmits at maximum power continuously. The probe is moved through the headregion by the yellow robot arm, performing the averaging in Equation [1].

To simulate the conductivity and density correctly, the tub is filled with a fluid that hassimilar properties to human tissue. The fluids are frequency-dependent, so a standardized


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fluid for a measurement at 1800 MHz will be different from the correct fluid for measuring SAR at 900 MHz.

The SAR must be measured on both the left and right side of the head as shown in Figure1. Even though geometrically the measurements are fairly similar, the results can be verydifferent due to the chaotic nature of the near field. The SAR values quoted for a mobile

phone are the highest value of SAR measured for any frequency the phone operates in,from both the left and right side of the head.

Lowering SAR

SAR is critical to antenna design, because if the SAR is too high the antenna must bechanged. Typically, if the SAR is too high the transmit power is lowered, which directlyyields lower SAR. However, since there are minimum transmit power specifications for mobile devices, the SAR cannot be dropped indefinitely.

As a result, the antenna positioning is critical. The antennas for mobile phones aretypically on the bottom of the phone, to keep the radiating part of the phone as far as

possible from the brain region.

Other methods for dropping the SAR include impedance matching changes and parasiticresonators which will disturb the antenna's radiation pattern (hopefully lowering SAR).

Spherical CoordinatesUnderstanding Spherical Coordinates is a must for the practicing antenna engineer. Youare probably familiar with Cartesian Coordinates - a position (point P ) can be specified bya triplet like (x,y,z) where x is the distance from the origin to the point along the X-axis,and so on (see Figure 1). Spherical coordinates use a different coordinate system, one withspherical symmetry, which makes it very useful in engineering and physics in certain

problems.

Figure 1. A point P defined in the Cartesian Coordinate System.


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The point P could be specified relative to the same origin in a different coordinate system.Spherical coordinates utilize three distinct coordinates:

R - the magnitude of the distance between the origin and the point (always positive)

- angle between the z-axis and the vector from the origin to the point (ranges from 0 to180 degrees)

- angle between the x-axis and the projection of the point onto the x-y plane (rangesfrom 0 to 360 degrees)

Any point specified in Cartesian coordinates as (x,y,z) can be re-expressed in sphericalcoordinates via the following transformation:

The above might look complicated, but after you've worked with it for a while it makes alot of sense. The point P =(0,6,5) can be evaluated in spherical coordinates as:

The coordinates are illustrated in Figure 2:


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Spherical coordinates are popular for antennas, because we often are only interested in theantennas response in a particular direction, not how far away something is (radiation

patterns die off as 1/R^2 for all antennas in the far field). In Cartesian coordinates, 3variables need specified to determine the direction from the origin, and it is not intuitive.For spherical coordinates, once it is understood, the polar angle and the azimuth angle

can be readily used.

For practice, make sure the following table makes sense. I give a set of rectangular coordinates on the left, and the corresponding spherical coordinates on the right.

Table I. Conversion of Cartesian Coordinates to Spherical (these should all makesense).

Cartesian (X,Y,Z) Spherical (R, , ) [angles in degrees](1, 0, 0) (1, 90, 0)

(0, 1, 0) (1, 90, 90)

(-1, -1, 0) (1.414, 90, 225)

(0, 0, 1) (1, 0, 0) [note: not unique here - could be anything. Why is that?]

(1, 1, 1) (1.73, 45, 45)

(0, 0, -1) (1, 180, 0) [ not unique again]

(0, 0, 0) (0, 0, 0) [ and could be any number!]

(-5, 0, 0) (5, 90, 180)(2, -4, -4) (6, 153, -135)

That is an overview of spherical coordinates. They come up a lot in the study of electromagnetics and physics, and can aid in understanding and solving of certain

problems. They arise in antenna engineering most often in regards to radiation patterns ,which specify how an antenna radiates vers
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Total Isotropic Sensitivity (TIS)Total Isotropic Sensitivity (TIS) is a commonly quoted specification in the mobile phoneindustry. This, like Total Radiated Power (TRP) is a parameter that depends on theantenna and the receiver (or radio) that make up the communication link. To define TIS,we will start by understanding receiver sensitivity.

Sensitivity

The sensitivity of a receiver is the smallest amount of power that can be input to thereceiver, such that the receiver can still maintain reliable communication. As an example,suppose the threshold Bit-Error Rate (BER) is 2.0%. This means that data can betransmitted reliably as long as the BER


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Suppose the initial power was -60 dBm (dBm= decibels relative to a milliWatt) and theresultant BER was 0.001%. We will again take the BER threshold to be 2%. The power would be lowered, say to -61 dBm, and the process repeated. At -90dBm suppose theBER was 1.9%. The power would then be dropped to -90.5 dBm, and suppose the BER was 2.03%. The resultant sensitivity of the receiver would be recorded as -90 dBm,

because this is the lowest power at which reliable communication was measured. Sincethe sensitivity is measured via wires instead of over the air as described below, this typeof receiver sensitivity measurement is known as the conducted sensitivity of the receiver.

Total Isotropic Sensitivity

Total Isotropic Sensitivity, or TIS, is a measure of the average sensitivity of a receiver-antenna system, when averaged over the entire 3-dimensional sphere. The result will bestrongly related to the antenna's radiation pattern , as we will see.

To determine the TIS, the system under test (the receiver/antenna package) is placed in ananechoic chamber , and the chamber antenna transmits at the system under test. The power is lowered until the BER reaches the threshold. Suppose that we did this for a fixed angle,

, and for a fixed polarization, say the . What we have just found is theeffective isotropic sensitivity (EIS) for that specific angle and wave polarization. The EISis written as:

The units of EIS are the same as that for sensitivity (i.e. power, typically measured indBm). To determine the Total Isotropic Sensitivity, we need to also measure the phicomponent of the polarization, which for this specific angle would be written as:

The Total Isotropic Sensitivity is the EIS components averaged over the entire sphere of

angles:

[1]
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The averaging in equation [1] may seem slightly peculiar. Some reflection on this willclear things up. Since the EIS should be very small to contribute to the integral, we needterms such as 1/EIS contributing to the integration. If we were integrating over the spherewithout taking the reciprocal, the angles for which the sensitivity was very poor (highvalues for sensitivity) would dominate the integration. As a result, the equation is invertedso that the smaller numbers (good sensitivity) are weighted correctly.

As you can imagine, since the sensitivity measurement is an iterative measurement, andsince we must measure both polarizations over the entire sphere, this measurement tendsto take a very long time.

Because of how long the measurement takes, you might ask if we can simply use thereceiver sensitivity along with the antenna's radiation pattern in order to simplify this

process. Since when we change polarizations or angles, the only variable is the antenna, itseems we should be able to account for this using just the antenna's radiation pattern?

Well, the answer is no. The first, and primary reason is that the antenna is picking upnoise from all the electronics that make up the system under test that the receiver wouldn'totherwise be exposed to. As an example, on mobile phones, the antenna receives energyfrom the memory and the phone's screen, which is delivered directly to the receiver. Thisdesensitization of the receiver is known as desense . Since the antenna picks up addednoise that the receiver otherwise wouldn't be exposed to, and since the antenna'sefficiency is always less than 1, the TIS will always be worse (higher) than the receiver'sconducted sensitivity.

Also, as noted on the TRP page , the non-ideal impedance of the antenna will also affectthe receiver. Commonly this causes a further degredation to the receiver's performance.

It should be clear from this page that the TIS is a function of the antenna, the receiver module, and the noise environment in which the measurement is performed in (the noiseenvironment includes the ambient noise [thermal], and the self-generated noise from theassociated electronics).

See also Effective Isotropic Sensitivity (EIS) .

Total Radiated Power (TRP)Total Radiated Power (TRP) is a measure of how much power is radiated by an antennawhen the antenna is connected to an actual radio (or transmitter). TRP is an activemeasurement , in that a powered transmitter is used to transmit through the antenna. Thetotal received power is calculated, and the result is the Total Radiated Power.
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As an example, suppose that a transmitter outputs 20.0 dBm of power (or 100 mW, seedecibels ) when connected to a 50 Ohm load. Suppose the total received power in the far field is measured to be 17.0 dBm (which can be measured in an anechoic chamber , seemeasuring radiation pattern . The resultant TRP is 17.0 dBm.

Now the above paragraph might seem so stupid that you are asking yourself "isn't this justthe same thing as measuring the antenna efficiency ? Why can't we just figure out thetransmit power of the radio, and then substract out the antenna efficiency to get the TotalRadiated Power?"

The above objection is a good point. The answer is that TRP measures the radiation in anactual live system. As a result, it is a function of not just the antenna, but also theradio/transmitter and the connection between the radio and the antenna.

As an example, let's consider the previously mentioned radio that outputs 20.0 dBm of power when connected to a 50 Ohm load. We actually do not know how much power theradio will output when connected to our antenna, because the antenna impedance is notactually 50 Ohms. In fact, even though we try to design the antenna to be 50 Ohms, it willnever be exactly 50 Ohms, and can be significantly different from 50 Ohms, particularly if the antenna must work over a larger range of frequencies (large bandwidth ).

The loss of power due to the antenna being away from 50 Ohms is not just related tomismatch loss (i.e. non-matching impedance between radio and antenna) in this situation,

but rather because the radio will not put out the same power for every impedance that itconnects to. Taken to the extreme, if an open circuit or short circuit is applied across aradio terminals, the radio will output zero power. For an antenna with a VSWR of 3:1, the

power output could typically swing by 3 dB (can range between 17 and 23 dBm - yes, the power can actually be higher for a mismatched antenna!).

As a result, the only way to know how the antenna and radio system will perform as awhole is to measure the Total Radiated Power (TRP). In fact, when a cell phone iscertified by a wireless carrier (such as AT&T, Verizon, China Mobile, T-Mobile, etc),they do not specify the antenna efficiency, but rather the TRP for the cell phone as awhole. In practical use, this is the parameter that is important, and is strongly dependentupon both the antenna and the radio.

See also Total Isotropic Sensitivity (TIS) and Effective Isotropic Radiated Power (EIRP) .

VSWR (Voltage Standing Wave Ratio)For a radio (transmitter or receiver) to deliver power to an antenna , the impedance of theradio and transmission line must be well matched to the antenna's impedance . The
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parameter VSWR is a measure that numerically describes how well the antenna isimpedance matched to the radio or transmission line it is connected to.

VSWR stands for Voltage Standing Wave Ratio , and is also referred to as StandingWave Ratio (SWR). VSWR is a function of the reflection coefficient, which describes the

power reflected from the antenna. If the reflection coefficient is given by , then theVSWR is defined as:

The VSWR is always a real and positive number for antennas. The smaller the VSWR is,the better the antenna is matched to the transmission line and the more power is deliveredto the antenna. The minimum VSWR is 1.0. In this case, no power is reflected from the

antenna, which is ideal.

Often antennas must satisfy a bandwidth requirement that is given in terms of VSWR. For instance, an antenna might claim to operate from 100-200 MHz with VSWR


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Figure 1. Voltage Measured Along a Transmission Line.

In industry, VSWR is sometimes pronounced "viz-wer".

When an antenna is not matched to the receiver, power is reflected (so that the reflectioncoefficient, , is not zero). This causes a "reflected voltage wave", which creates standingwaves along the transmission line. The result are the peaks and valleys as seen in Figure 1.If the VSWR = 1.0, there would be no reflected power and the voltage would have aconstant magnitude along the transmission line.

VSWR, Reflected Power, and s11

Is a VSWR of 3 bad? How bad is a VSWR of 12? Well, there are no hard rules. In thissection, we'll try to put the VSWR number in context. Below is a table showing therelationship between VSWR, total reflected power, and (also known as s11), and totalreflected power. Note that the reflected power is simply the reflection coefficient ( )squared.

Table I. VSWR, Reflected Power, and (s11)VSWR (s11) Reflected Power (%) Reflected Power (dB)

1.0 0.000 0.00 -Infinity

1.5 0.200 4.0 -14.0

2.0 0.333 11.1 -9.55

2.5 0.429 18.4 -7.36

3.0 0.500 25.0 -6.00

3.5 0.556 30.9 -5.10


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4.0 0.600 36.0 -4.44

5.0 0.667 44.0 -6.02

6.0 0.714 51.0 -2.92

7.0 0.750 56.3 -2.50

8.0 0.778 60.5 -2.189.0 0.800 64.0 -1.94

10.0 0.818 66.9 -1.74

15.0 0.875 76.6 -1.16

20.0 0.905 81.9 -0.87

50.0 0.961 92.3 -0.35

In the above table, a VSWR of 4 has 36% of power delivered by the receiver reflectedfrom the antenna (64% of the power is delivered to the antenna). Note that a reflected

power of 0 dB indicates all of the power is reflected (100%), whereas -10 dB indicates10% of the power is reflected. If all the power is reflected, the VSWR would be infinite.

Note that VSWR is a highly non-linear function of the reflection coefficient . That is,there is very little difference in reflected power when the VSWR increases from 9 to 10;

however there is an 11% change in reflected power when the VSWR changes from 1 to 2.

In general, if the VSWR is under 2 the antenna match is considered very good and littlewould be gained by impedance matching. As the VSWR increases, there are 2 main

negatives. The first is obvious: more power is reflected from the antenna and therefore nottransmitted. However, another problem arises. As VSWR increases, more power isreflected to the radio, which is transmitting. Large amounts of reflected power can

damage the radio. In addition, radios have trouble transmitting the correct information bitswhen the antenna is poorly matched (this is numerically defined in terms of another

metric, EVM - Error Vector Magnitude).

VSWR Specs for Antennas

Often in industry, antennas are screened (pass/fail criteria) based on VSWR specifications

(VSWR specs). This is a method of measuring the antennas passively to determine if theyare properly tuned in a quick manner. The antenna is measured with a network analyzer,

and the VSWR as a function of frequency is recorded. As an example, consider thissituation where the VSWR of 5 antennas are measured and plotted, along with 4 lines that

represent the VSWR specs for this antenna (in blue):


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Figure 2. Plot of 5 antennas VSWR versus Frequency.

The VSWR specs in Figure 2 are defined by:

(1) VSWR < 3.8 for 825MHz < f < 910 MHz(2) VSWR > 4.0 for 1200MHz < f < 1400 MHz

(3) VSWR > 3.0 at f = 1.7 GHz, linearly reduced to VSWR > 2.0 at f = 1.8 GHz

(4) VSWR < 3.0 for 1860MHz < f < 2000 MHz

In Figure 2, the red VSWR curve antenna would fail the second spec, and the lightblue VSWR curve antenna would (marginally) fail the fourth specification. This is

illustrated in Figure 3:


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Figure 3. VSWR specs and the VSWR Curves.

Setting VSWR specs is a somewhat tricky job for antenna engineers. The idea is to fail theoutliers (detuned antennas or antennas with broken connectors, etc). However, it is

difficult in practice to determine what the acceptable variance is, particularly in high-volume industries where a tight spec could fail thousands of good antennas.

Note that VSWR is a measure of how much power is delivered to an antenna. This doesnot mean that the antenna radiates all the power it receives. Hence, VSWR measures the

potential to radiate . A low VSWR means the antenna is well-matched, but does notnecessarily mean the power delivered is also radiated. An anechoic chamber or other radiated antenna test is required to determine the radiated power. VSWR alone is not

sufficient to determine an antenna is functioning properly.

Wave NumberThe wavenumber is a scalar quantity that only depends on the frequency in question, andspecifies the phase change per meter for a wave. The quantity (often denoted k or sometimes as ) is given in radians/meter:


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In the above, is the wavelength of operation, f is the frequency and c is the speed of light in the given medium.

The wavenumber k shows up everywhere in antenna theory and physics. For free space

calculations, it is basically another way to represent frequency. However, because thewavelength is smaller in dielectric materials with a permittivity or dielectric constantgreater than 1, or for a material with a permeability greater than 1, the wavenumber succinctly represents the phase change of a propagating plane wave in terms of radians/meter, with 2*PI radians being one complete cycle, in all mediums. The wavenumber can also be written as:

See also the wave vector .

Wave Vector

The Wave Vector (or wavevector) refers to a vector that describes the phase variation of a plane wave, in 3-orthogonal directions (x, y, and z-axes typically). The magnitude of thewavevector is the wavenumber .

For a wave propagation in a direction described by the spherical coordinates , thewavevector k is given by:

The x-component of the wavevector, , determines the rate of change of the phase of a propagating plane wave in the +x-direction. The same definitions apply for the y- and z-directions.

The wave vector is a property of plane waves. The phase variation for a plane wave will

always be .

Hence, the magnitude of the wave vector will be equal to the wavenumber. Therefore:
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If = , then the other two components of the wave vector (ky and kz) must be zero.

2.4 GHz AntennaIts kind of funny actually. Makers of cordless phones often advertise these devices withthe main feature being "operates at 900 MHz". That is completely irrelevant from anoperational or end-user viewpoint. What does specifying the frequency in GigaHertz or MegaHertz mean?

A 2.4 GHz antenna or system is simply a device that transmits and receives at thefrequency 2.4 GHz. All devices are required to operate in a narrow frequency band.Wireless routers are forced (by government regulation) to work at 2.4 GHz. If thegovernment had said they have to work at 2.9 GHz or 1.3 GHz, it would not havemattered at all. The wireless propagation environment is different for 2.4 GHz or 1 GHz,

but for home personal wireless communications it would not matter significantly.

The only thing 2.4 GHz really tells you is that the wavelength is

c/f = (3e8 m/s)/(2.4e9 1/s) = 0.125 meters = 4.92 inches

When you plug in your home wireless router, the antennas will probably be dipoleantennas , because they receive information uniformly in the horizontal plane, and therouter won't know where your computer is located. Since dipole antennas work greatwhen they are a half-wavelength long, you could guess the antennas should be about 2.5inches long, as is roughly the case if you look at your typical router:
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There are two antennas primarily for diversity reception .

If you are trying to get free wireless internet, you could look around for a high-gaindirectional antenna at 2.4 GHz. To get this to work, you'll need to attach your router to ahigh gain antenna that is pointed towards a McDonalds or somewhere that is giving out

free Wi-Fi from their wireless LAN (or steal it from one of your neighbors who is notusing encryption - by the way, its worth taking the few minutes required and set up your routers encryption for this reason). A high gain antenna is simply an antenna that has avery directional radiation pattern, in that it receives energy most strongly from particular directions and suppresses them from other directions.

Bluetooth devices also use the 2.4 GHz band, in addition to some cordless phones andradio controlled toys. The IEEE 802.11 wireless standard specifies WLAN computer communication at 2.4 GHz.

Antenna Theory HistoryWhat is the origin of the antenna? I'm ruling out such early devices as compasses, becausewhile they in some sense receive a magnetic field, it is not an electromagnetic field. BenFranklin's kite experiment wasn't quite an antenna, as that captured lightning discharge,which is a direct current path where the energy is not transferred independent of themedium it travels. The human eye of course receives high frequency electromagnetic
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waves (light, to the layman). Technically the eye could be classified as an antenna;however since it can't transmit waves, it is really a sensor, so I'll exclude that as well.

The first experiments that involved the coupling of electricity and magnetism and showeda definitive relationship was that done by Faraday somewhere around the 1830s. He slid amagnetic around the coils of a wire attached to a galvanometer. In moving the magnet, hewas in effect creating a time-varying magnetic field, which as a result (from Maxwell'sEquations), must have had a time-varying electric field. The coil acted as a loop antenna and received the electromagnetic radiation, which was received (detected) by thegalvanometer - the work of an antenna. Interestingly, the concept of electromagneticwaves had not even been thought up at this point.

A painting of Michael Faraday. Being a great experimentalist, he naturally dabbled inchemistry, shown here.

Heinrich Hertz developed a wireless communication system in which he forced anelectrical spark to occur in the gap of a dipole antenna . He used a loop antenna as areceiver, and observed a similar disturbance. This was 1886. By 1901, Marconi wassending information across the atlantic. For a transmit antenna, he used several verticalwires attached to the ground. Across the Atlantic Ocean, the receive antenna was a 200meter wire held up by a kite [1].

In 1906, Columbia University had an Experimental Wireless Station where they used atransmitting aerial cage.

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