# The Bandwidth Of Narrowband Biology Essay

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Antenna that can operate over large range of frequencies is know is broadband antenna. In fact the term BROADBAND is typically referred to bandwidth .bandwidth is measured in two ways let f1 and f2 be the upper and lower frequencies respectively the centre or design frequency is denoted by f3 then bandwidth will be :

Bp= %

Bandwidth is also denoted as ratio:

Br=

The bandwidth of narrowband is denoted by present using Bp while broadband antenna is denoted their bandwidth as Br. Resonant antenna has small bandwidths for example half wave dipole have bandwidths of 8 and 16%. On the other hand antennas having travelling waves rather than standing waves in them operate over large range of frequencies.

More precisely,''If impedance and patterns of an antenna do not change significantly over about an octave ( or more we call it as a broadband antenna.' Broadband antennas usually require structures that don't emphasize abrupt changes in their physical structures and dimensions involved. Smooth physical structures tend to produce patterns and input impedances that also change smoothly with frequency. This is an important key concept in broadband antennas. The broadband antenna is typically an antenna that is non resonant with constant Impudence throughout over large range of frequencies. Antenna is well match to spacing providing smooth transitions from the guided wave and input transmission line to free space wave. For example short dipole has abrupt transitions from guided wave on the transmission line to space with large reflection of energy with resonant and back and forth near a dipole before being radiated. The large energy storage before radiation. The constant impedance curved biconical is travelling wave antenna the axial mode helical antenna is also travelling wave antenna. Little energy is reflected from open end so input impedance remains same and constant over a wideband. Typically VSWR≤1.5 over a 2 to 1 bandwidth. This behavior is maintained in an array of many helices because of small mutual coupling of helices.

Types of Broadband Antennas:

TRAVELLING WAVE WIRE ANTENNAS

The concept of travelling wave antenna is referred when there are no strongly reflected waves. A travelling wave antenna acts as guiding structure for travelling waves and provides a path to waves. Whereas resonant antenna supports standing waves that limits the bandwidth of an antenna. Also very long antenna may dissipate most of the power, leading to small reflected waves by virtue of fact very small power incident on the ends.

Simplest travelling wave wire antenna is straight wire carrying a pure travelling wave referred to as travelling wave long wire antenna. A long wire is one that greater than one half wave long. The travelling wave long wire with matched load resistance is RL to prevent reflections from wire ends. A travelling wave long wire operated in the presence of an imperfect ground plane is referred as Beverage antenna or Wave antenna. Long wire is fed from coaxial wire as an practical method The vertical section of height d is assumes not to be radiated which is true for d<<L finally we assume radiative and ohmic losses along the wire are small. When attenuation is neglected the current amplitude is constant

(Z)=

Which represents an unattenuated travelling wave propagating in +z direction with phase constant β of free space.

( DIAGRAM OF TRAVELLING WAVE LONG WIRE ANTENNA)

(PATTERN OF TRAVELING WAVE LONG WIRE ANTENNA WITH 6 LAMPDA)

(V ANTENNA AND UNIDIRECTIONAL BIDIRECTIONAL)

(RHOMBIC ANTENNA)

HELICAL ANTENNA:

If a conductor is wound into helical shape and fed properly it is referred to as a helical antenna or simply helix. Helical antenna is shown in the figure if one turn of the helix is uncoiled the relationship among the various helix parameters are revealed. Symbols used to describe the helix are defined under:

D= diameter of helix (Between centers of coil materials)

C= Circumference of helix = π D

S= Spacing between turns =C tan α

α = pitch angle =

L= Length of one turn =

N= Number of turns

= length of helical coil=NL

h = height =axial length= NS

d = diameter of helix conductor.

When S=0 the helical reduce to loop antenna and when D =0 it reduces to linear antenna. A helical can be operated in two modes the normal mode and axial mode .The normal mode yields radiations that is most intense normal to the axes of the helix. This occurs when helical diameter is small compared to wavelength. The axial mode provide radiation maximum along the axes of the helix.

Normal Mode Helical Antenna:

In the normal mode of operation the radiated much in the direction normal to the helix axes, theory we emit circularly polarized waves. For normal mode of operations the dimension of helical antenna must be small as compared to A swavelength that is D<<lambda and usually L<<Lamda.Normal helical is electrically small antenna hence its efficiency is low. Since helical is small so current is constant both in phase and magnitude over its length. Far field pattern is independent of number of turns and may be obtained even by examining one turn.

The far zone electric field of ideal dipole is shown

Ñ˜ ω µ IS

Where S is the spacing between turns is the length of an ideal dipole

Where l is being replaced by S in addition by a loop and is given by:

## *

Where is substituted by for 'a'

Axial ration is defined by the ration of .

## =

By varying the D and S or only D the axial ratio attains of 0≤AR≤∞.The value of AR=0 is special case and occurs when leading to linearly polarized wave of horizontal polarization .When AR=∞, and the radiated wave is linearly polarized with vertical polarization (the helix is vertical dipole).Another special case is the one when AR is unity occurs when:

= 1

Or C=π D

When the dimensional parameters of the helix satisfy the above relation then radiated field is circularly polarized in all directions. Change of polarization state can be defined better by pitch angle of zero degree that is starting, which reduces helix to a loop antenna with linear horizontal polarization. As α increase polarization becomes elliptical. When α is such that AR=1 we have then circularly polarization. Finally when α becomes 90 degree the helix reduces to linearly polarized. To get normal mode of operation it is seen that the current throughout the length of helix is of constant magnitude and phase also. This is because that total length of helix wire is very small compared to the wavelength ( <<lamda) and is terminated properly to reduce multiple reflections. Because of the critical dependence of its radiation characteristics on its geometrical dimensions which is very small as compared to wavelength this mode of operation is very narrow and its radiation efficiency is very small. Practically, this mode is limited and less in use.

Axial Mode

Its more practical mode of operation which can be generated easily is the axial or endfire mode. In this mode of operation there is only on major lobe and maximum radiations intensity along the axes of helix. The minor lobes area are at oblique angles to the helix. For this mode the diameter D and spacing must be large fractions of the wavelength. To achieve circular polarization the circumference of the helix must be in order of < range. And spacing about S=lambda/4. The pitch angle is usually. Most often in this mode antenna is used in conjunction with a ground plane, whose diameter is least lambda/2, and is fed by coaxial line. The dimensions of helix for this mode of operation are not critical results in greater bandwidth.

Electric Magnetic Dipole:

By assuming that helical antenna geometry is represented by number of horizontal loops and vertical infinitesimal dipoles. It would then seen than seem reasonable that an antenna with only one loop and single vertical dipole represents a radiator with elliptical polarization. Circular polarization is achieved in all space if the current in each element can be controlled by dividing the available power equally between the dipole and the loop, so that the magnitude of the field intensity radiated by each is equal. This kind of antenna usually operates nearly 350 MHz and other near 1.2Ghz.This kind of antenna is very useful in UHF communications networks where considerable amount of fading may exist. In case of fading one component is affected while other communicates properly in the same manner, thus provide continuous communications. The same result would apply in VHF and UHF broadcasting. In addition to this an antenna of this kind may transmit or receive with horizontal or vertical elements, providing a convenience in the architectural design of receiving antenna.

Yagi-Uda Array of Linear Elements

A very practical radiator in HF (3-30 MHz), VHF (30-330 MHz) and UHF (300-3000 MHz) Ranges in yagi-uda antenna. This antenna consists of number of linear dipole elements. One of them is energized directly by a feed transmission line while other acts as parasitic radiators whose currents are introduce by mutual coupling. The common feed element in such kind of antenna is folded dipole. TV antenna is the example of yagi-uda antenna. To achieve the endfire beam formation the parasitic elements in the direction the beam are somewhat smaller in length than the feed element. Normally the driven element resonant with its length slightly less than lambda/2 while the length of directors will be about (.4-.45lambda). Directors are not necessary that they should be of same length and diameters. Separation between the directors should be (0.3-0.4 lambda) and is not necessary to keep it constant for designing purpose. A significantly drop in gain is noticed as we increase spacing greater than 0.3 lambda.

As the length of each director is small as compared to resonant length the impedance of each is capacitive and current Induces emf. Similarly impedance of reflectors is inductive and phases of the current lags those of induced emf's. Total current is not determined only by their length but also by the spacing present between the elements. Properly space elements and length less than lambda/2 acts as directors because current is similar in elements with equal progressive phase shifts which will reinforce the field of energized elements towards the directors. The yagi-uda structure supports the travelling wave whose performance is determined by the current distribution in elements and phase velocity if travelling wave. The major role of reflector is played by the first element next to the one energized and very little in the performance of yagi-uda is gained if more than one reflector is used. However considerable improvement is achieved if more directors are added to array. A certain limitation in addition of directors to array is that the amount of current that is distributed is reduced. Usually most antennas have about 6-12 directors. However many arrays are designed to have 30-40 directors. Array length of order 6*lambda have been mentioned. The radiation characteristics that are usually of interest in yagi-uda array antenna are forward and backward gains, input impedance, bandwidth front to back ratio magnitude of minor lobs. Length and spacing of elements have great influence on characteristics. Analytical based ferulae determines the different characteristics. Yagi-uda antenna has low input impedance and narrow bandwidth on the order of about 2%, Improvements on both has been made on the expense of others. A trade off or compromise has to be done, that depends on particular design. One way to improve the input impedance without affecting the performance of other parameters is to use an impedance setup element as a feed such as folded dipole.

(DIAGRAMS + RADIATION PATTERNS)

Spiral Antenna

Spiral antenna yields very high bandwidths and they are known as broadband antennas.

Equiangular Spiral Antenna

Equiangular spiral curve is shown and its equation is denoted

r =

Where is the radius of for=0 and 'a' is constant controlling the flare angle rate of the spiral. The spiral in the figure is right handed. Left handed spiral is generated by negative value of 'a' or by simply turning over the spiral of figure. The four metallic regions in spiral have their own equation.

= (Region no 1)

(Region no 2)

(Region no 3)

(Region no 4)

(Diagrams of equiangular spiral + planner equiangular spiral antenna for self complementary case )

The impedance pattern and polarization of the planner equiangular spiral antenna remain nearly constant over wide range of frequencies. The feed point at the center the overall radius and flare angle affect the performance .The flare rate factor 'a' is more conveniently represented through expansion rate

which is increase factor of the radius for one turn of the spiral :

## = = = .

A typically value of is 4 and then from equation a=0.221. The frequency at the upper end of operating band is determined by the feed structure.

The minimum radius is about a quarter wavelengths at for an expansion ratio of 4. A nearly equivalent criterion is a circumference in the feed region of 2π. The low frequency limit is set by overall radius R which is roughly a quarter wavelength at . So the circumference of the circle that is enclosing the spiral can be used to set the low frequency limit through C=2π=lambda l.

Consider a one and one half turn spiral with a=.22 so the maximum Radius R=r(φ=3π) == 8.03 . This is equal lambda l/4 where lambda l is wavelength at low band edge frequency. At the feed point r=r(φ=0)= and this is equal lambda/4 where lambda u is the wavelength at upper edge so the bandwidth is = lambda l/ lambda u = 8.03 This 8:1 bandwidth is typically : however bandwidth of 40:1 can be achieved.

The radiation pattern of planner equiangular spiral antenna is bidirectional with two wide beams broadside to the plane of spiral. The polarization of radiation is close to circular over wide range of angles. Out to as far from broadside .The sense of polarization is determined by sense of flare angle of the spiral.

Archimedean Spiral Antenna

This is another kind of spiral antenna. This antenna as are many spiral antenna is easily constructed using printed circuit techniques. Equation of two spiral antenna is given by:

r = and (φ-π)

The Archimedean spiral is linear proportional to the polar angle as compared to exponential for the equiangular spiral. The geometry of Archimedean antenna defines well the principle in frequency independent antennas. Band description of radiation is defined by active region responsible for radiations. Currents exist in a transmission line mode and fields cancel out in far field region. The active region occurs on that portion of the antenna that is one wavelength in circumference for curved structures or has half wavelength long element in antennas with straight wires or edges. Beyond the active region currents are small having lost power to radiations in active region. Active region moves around the antenna with frequency.

The arms are feed out of phase at points and. This is represented with oppositely direction of current arrows. The current is inward from arm no 1. So phase shifts from the feed to A are identical, preserving the current directions. The active region where circumference is one wavelength contains path points label A or B. It can be assumed that current distribution is almost same in this region. Phase however shifts as the travelling wave moves along the arms. Since the circumference electrically large in active region , phase must be accounted for. The phase shifts between and between because of path difference lambda/2. Now it is determined that points and are in phase. This in phase situation causes reinforcement of electrical fields in broadside direction, giving maximum radiations. Resistive loads are added to prevent reflection from the ends due to remaining travelling waves. Second important aspect is state of polarization; Archimedean spiral antenna is associated with circular polarization property. In active region points that are one quarter turn around the spiral are out of phase. For example the phase ar point lags that at point by. In addition the currents are orthogonal in space. The current magnitudes are also nearly equal.

The spiral produces broad main beam perpendicular to the plane of spiral. Most of application requires a unidirectional beam. This is created by backing the spiral with ground plane; most common approach is to use a metallic cavity behind the spiral forming a cavity backed Archimedean spiral antenna. This introduces fixed length thereby altering true frequency independent behavior. This problem is solved by loading the cavity with absorbing material to reduce resonant effects this however introduces loss.

(REDUCE SPIRAL IN SIZE + BANDWIDTH CAVITY BACKED ARCHIMEDEAN SPIRAL ANTENNA)

Sleeve Antenna

A sleeve monopole antenna is shown in the figure feed from a coaxial transmission line. The sleeve exterior behaves as an element which is radiating and the interior acts as outer conductor of the feed coaxial line. In general the length of sleeve may be any portion of the total length of the monopole. From zero to where sleeves constitutes the entire radiating portion of antenna. In general the length of sleeve is almost to the height of monopole. This is due to the fact that the current at virtual feed point changes only slightly as the overall monopole height varies from lambda/4 to lambda/2. The first sleeve monopole resonance occurs at frequency where the monopole length l+L. The remaining design variable is l/L. It has been found experimentally that a value of l/L=2.25 yields optimum radiations patterns about 4:1 band. The factor l/L has little effect for l+L<<lambda/2 since the current on outside of the sleeve will have approximately the same phase as on the top portion of monopole itself. However for long electrical lengths ration of l/L has very significant effect on radiation pattern.

(DIAGRAMS AND RADIATION PATTERNS OF SLEEVE MONOPOLES)

Pattern bandwidth

4:1

l + L

Lambda/4 at low end of band

l/L

2.25

D/d

3

VSWR

Less than 8:1

Log Periodic Antennas

A planner log-periodic consists of a metal strip whose edges are specified by angle α/2. However in order to specify the length from origin to any point on the structure a distance characteristic must be included. In spherical coordinate system (r, the shape of the structure can be written as

## )

It is evident from above equation that values of θ are repeated whenever the logarithm of radial frequency ln (ω) = ln (2πf) differs by 2π/b. The performance of the system is then periodic function of logarithm of the frequency si we call it log-periodic antenna. A specific configuration is shown it consists of two coplanar arms geometry .The pattern is unidirectional towards the apex of the cone formed by the two cone and it ids linearly polarized. The pattern of this antenna is not totally frequency independent the amplitude variations of certain design are very slightly so practical they are frequency independent.

Log periodic antennas were discovered while studying the current distribution on log periodic surface structures. This shown there is strong current concentration at or near edges of the conductors. Thus if we remove part of a surface that is linear to form a wire antenna it should not seriously degrade the performance of the antenna. To verify this wire antenna with geometrical shape similar to pattern formed by the edges of the conducting surface was built and it was investigated that performance of the antenna was identical to that of edges. If wires or edges of the plates are linear the geometry reduce to trapezoidal tooth log periodic structures with no losses in operational performances , there are numerous practical shapes of log periodic antennas with very less loss and efficient performance.

For uniform periodic teeth we define the geometrical ratio of the log periodic structures as under:

τ =

And width of antenna slot is:

X =

If are two frequencies are one period apart they are related to geometrical ratio as under:

τ =

While

If we talk about the performance of the antenna it comes to know that it is the function of α, β, τ, X. In general these structures perform planner and conical structures.

Major difference is that log periodic antennas are linearly polarized instead of circularly polarization. Some characteristics of cavity backed linearly polarized flush mount log-periodic slot antenna are: VSWR-2:1; Eplane beam width. H-plane beam width is. The maximum diameter of cavity is about 2.4in.(6.1cm) the depth is 1.75in (4.445cm), and weight is(.14kg)

Dipole Array Log-Periodic Antenna:

Most common and easily recognizable log-periodic structure is dipole array structures. It consists of sequence of side by side parallel linear dipoles forming a coplanar array. Although it is much similar to yagi-uda antenna but still there are lot of differences. Directivities are similar to yagi-uda (7-12db) they are achievable and maintained over much bandwidths. There are many differences between them. Geometrical dimensions of yagi-uda elements () spacing () diameter and even gap spacing at dipole centre of log periodic array increases logarithmically as defined by inverse of geometrical ratio.

## = === ====

Another factor that is associated with dipole array is spacing factor σ and is defined by:

σ =

Straight lines through dipole end meet to form an angle 2α which is characteristic of frequency independent structures.

Constant dimensions are used because it is not easy to bend the wires up to desired length or spacing or gapping, so normally minor factors don't limit the performance.

While in yagi-uda only one element is directly energized by the feed while other element are always in parasitic mode. If elements are closely spaced then phase progression of the current is to the right.

The radiated single log periodic array is linearly polarized and it has horizontal polarization when plane of antenna is parallel to the ground. However bidirectional patterns and circular polarization can be achieved by phasing multiple log periodic dipole arrays. Though structure is periodical but it always does not mean to give very large range of frequencies or it behave like broadband antenna however a good bandwidth can be achieved by varying the parameters through repetitive cycling process.

DIAGRAMS OF DIPOLE ARRAY LOG PERIODIC ANTENNA AND RADIATION PATTERNS