unit 2 fundamental parameters of antennastsc.unex.es/~tabo/rog/rog_tema2_02.pdf · radiación y...

Radiación y ondas guiadas – J.M. Taboada 1

Escuela Politécnica U

niversidad de Extrem

adura

UNIT 2 Fundamental parameters of antennas




adura Transmitting and receiving antennas

� An antenna is the part of a transmitting or receiving system, specifically designed to radiate or receive electromagnetic waves.

� A transmitting antenna is a dispositive that allows the energy transition between a transmitter and the free space.

� A receiving antenna is a dispositive that allows to gather the energy from free space to a receiver.

Tx

Transmitter

Waveguide

Antenna

Free-space spherical wavefronts

Rx

Receiver

Waveguide

Antenna

Incoming plane wavefronts




adura Radio communications

� The combination of a transmitting and a receiving antenna allows the setup of a radiolink.

� Advantages of radio-links with respect to transmission lines or optical fiber: � It allows point to point links in a very easy way.

� It does not require lines to be tended.

� Terminals may be portable. � Disadvantages:

� Strong attenuation with the distance and atmospheric propagation.

� The transmitting antenna puts electromagnetic pollution on the environment. � The receiving antenna gathers noise and interference from the environment, in addition

to the desired signal.




adura Types of antennas




adura Types of antennas




adura Examples of antennas




adura Examples of antennas

� Optical nano-antennas




adura Antenna fundamental parameters

� To describe the performance of an antenna, definitions of various parameters are necessary. We will follow the IEEE Standard Definition of Terms for Antennas (IEEE Std 145-1983).

� Most important parameters:

� Input impedance

� Radiation pattern � Antenna directivity

� Antenna gain

� Polarization




adura Antenna input impedance

� Antenna offers an impedance to the transmission line.

� Equivalent transmission circuit.

i

i i i

VZ

IZ R jX

�

� �

0g g g

g

Z R jX

X

� ��

Tx Transmitter

Antenna V

I Z0

Z0 ~

ZL = Zi

Zg

Vg




adura Antenna input impedance

� The real part of the input impedance of a transmission antenna is the sum of the loss resistance and the radiation resistance.

� Radiation efficiency:

Rr

V

Rloss

jXi

I




adura Alternative parameters

� Easier parameters, more suitable for measurement and work at high frequencies: reflection coefficient, standing wave ratio (SWR), or relación de onda estacionaria (ROE), and power return PR coefficient:

� We are assuming that the incident power is the available power from the transmitter (Pg). This implies that the transmitter is perfectly matched to a lossless transmission line. In other case, losses and/or mismatch should be considered.

Pincident = Pg (available power from the transmitter), whenever the transmitter is perfect matched to a lossless transmission line

Z0 ~

Zi

Rg

Vg




adura Radiation pattern

� A radiation pattern is a graphical description of the directional properties with regards to the spatial angular coordinates

� Usual radiation pattern diagrams: � Field strength: |E|, E� , E��

� Power: <S>, Gain, Directivity

� Usual formats: � Absolute diagrams: showing fields or power densities for a given delivered power to

the antenna and at a constant distance

� Relative diagrams: absolute diagrams normalized with regards to the maximum of the represented function. Typically logarithmic scales apply, in which case the field and power diagrams are coincident, since:




adura Coordinate system




adura 3D diagrams

Pencil directive pattern

Omnidirectional pattern




adura 2D diagrams

� They are cuts of 3-D diagrams:

Normalized field strength pattern (natural units)

Normalized power pattern (natural units)

Normalized pattern (logarithmic units, dB)




adura Polar and rectangular patterns




adura Contour patterns




adura Examples




adura Examples




adura Radiation pattern parameters




adura Radiation pattern parameters

� Lobe: portion of the diagram delimited by regions with lower radiation

� Main (major) lobe: contains the maximum radiation direction � Secondary (minor) lobes: non-main lobes

� Side lobes: adjacent to the main lobe

� Back lobe: in the opposite direction of the main lobe � Secondary lobes level (SLL): level of the main secondary lobe with regards to the level of

the main lobe

� Main lobe beamwidth (half-power beamwidth, HPBW): defined by the 3dB drops

� First null beamwidth (FNBW): defined by the first two nulls at both sides of the maximum radiation direction

� Front/back ratio: ratio between the main lobe and the back lobe strengths

2.25FNBW HPBW�




adura Main planes

For directive antennas linearly-polarized

antennas, it is usually enough to known the 2-D diagrams on the main planes:

� E-plane: contains electric field vector E and the maximum radiation direction (yz in this example)

� H-plane: contains the magnetic field vector H and the maximum radiation direction (xz in the example)




adura Solid angle

� Region of the space delimited by a sequence of radial lines whose vertex is located at the center of a sphere

� The SI units of solid angle is the steradian (solid angle delimiting a soherical surface r2 with radius r)




adura Radiation intensity

� Average radiated power, or power density: it is the average radiated power per surface unit.

� Radiation field intensity: it is the power radiated from an antenna per unit solid angle (angular power distribution).

� Radiated power:

Isotropic antenna




adura Directivity

� Directive gain (or directivity), D(�, �): Ratio of the intensity radiated in a given direction to the radiation intensity of a theoretical isotropic antenna (which evenly distributes power in all directions) radiating the same amount of total radiated power.

� Directivity D0:

� Directive gain in the maximum radiation direction � The meaning of the directivity is the gain in the radiation intensity in the maximum

direction compared to the isotropic antenna (with uniform radiation of power in all directions of the space).

� Values in dBi (dB with regards to the isotropic radiation): 10log D0

� It is always greater or equal to 1 (0 dBi)




adura Power gain

� Power gain, G(�, �): Ratio of the intensity in a given direction to the radiation intensity that would be obtained if the input power to the antenna were radiated isotropically.

� The power gain is closely related to the directivity. � It takes into account the radiation efficiency, as well as the directional pattern.

� Gain (G0): Power gain in the direction of maximum radiation.

� Values in dBi (dB with regards to the isotropic radiation): 10log G0

� It might be lower than 1 (0 dBi) � Radiation efficiency:

� Usually the radiation efficiency is close to 1




adura PIRE

� Equivalent isotropically radiated power (EIRP), potencia isotrópica radiada equivalente (PIRE): EIRP of an antenna A in a given direction d is the total power that an isotropic antenna would need to radiate to produce the same power density in the direction d as the antenna A. EIRP takes into account both the transmitter and the gain of the antenna.

� The EIRP curves are usually specified in dBW




adura Directivity vs. beamwidth

� Normalized field pattern:

� Beam solid angle:

� Relation with directivity:

� In directive “pencil” diagrams:

� In omnidirectional diagrams:

being the half-power (3 dB) beamwidths




adura Polarization

� Polarization of an antenna is the polarization of the radiated wave.

� Polarization of a radiated wave is defined as the figure traced as a function of time by the extremity of the vector of the radiated field at a fixed location r0 of the space, as observed from the antenna along the direction of propagation.

v̂RE

I�ER�E

IE




adura Linear polarization

� Under any of the following conditions:

� �

�

� The trace of the electric field is a line.

ad

ad

0R �E

v̂RE

I�ER�E

IE

0I �E||R IE E

v̂




adura Circular polarization

� The following conditions are met simultaneously :

� �

� The trace of the electric field is a circumference.

ad

ad

R I�E E

v̂RE

I�ER�E

IE

( 0)R I R I� � �E E E E

RE

I�Ev̂




adura Elliptic polarization. Case 1.

� Elliptic polarization with: .

� Ellipse major and minor axes are coincident with the real and imaginary directions of the

electric field phasor .

( 0)R I R I� � �E E E E

IE

RE

IE

REv̂

v̂




adura Elliptic polarization. Case 2.

� Elliptic polarization with:

� We introduce a phase offset as:

� Then we proceed with using case 1.

IE

REv̂

0R I� E E

IE

RERb

Ib




adura Rotation

� We must calculate the direction of rotation. The temporal evolution of the wave is as follows:

� Then: � : Positive rotation (right rotation) � : Negative rotation (left rotation)

v̂REv̂

I�E

v̂R�E

v̂IE

0t � / 4t T� / 2t T� 3 / 4t T�

:

:




adura Polarization loss factor (PLF)

� PLF or factor de pérdidas de polarización (FPP): In general the polarization of the receiving antenna will not be exactly the same as the polarization of the incoming wave. This is known as polarization mismatch.

� The amount of power extracted by the receiving antenna will not be maximum due to the polarization loss factor.

� The PLF is defined as the fraction of the total power that transports the incoming wave in the polarization of the receiving antenna

� For circular polarization:

� PLF = 1 for same rotation direction

� PLF = 0 for opposite rotation direction � For linear to circular polarization:

� PLF = 0.5 (-3 dB)

aaa

nnn




adura Bandwidth

� Frequency range where the characteristic parameters of an antenna (input impedance, SWR, beamwidth, SSL, etc.) fulfill the prescribed specifications.

� For narrowband antennas (resonant antennas) it is usually specified in percentage with respect to the resonant frequency:

� For broadband antennas it is usually specified as a ratio between the upper and lower

frequency. For example 2:1 (one octave), 10:1 (one decade), etc.:




adura Antenna in reception

� When an incident wave impinges on an antenna, the antenna absorbs a portion of the transported power and transfers it to the receiver.

� The antenna behaves like a sensor, interacting with the wave and the receptor. There are parameters related to the interaction with the receptor, as well as parameters related to the electromagnetic interaction with the incoming wave.

� Given the antenna is passive, the circuital parameters in transmission and reception are exactly the same.

� With regard to the electromagnetic interaction parameters, a new important parameter is defined that characterizes the power reception capabilities of the antenna: the equivalent absorption area.




adura Antenna in reception

� An locally plane wave Ei, Hi provided by a far away transmitting antenna impinging on a (receiver) antenna will induce electric current density I, which in turns will generate a voltage Vca in the antenna fed terminals.

Rx Receiver

Antenna Vca

I

Pincident




adura Circuital parameters of a receiving antenna

� The impedance of a receiving antenna is the same as the input impedance of that antenna in transmitting mode: ZiR = ZiT.

� We are assuming that the incident power is the available power on the receiving antenna

(Pincident). This implies that the receiver is perfectly matched to a lossless transmission line (ZL = Z0). In other case, losses and/or mismatch should be considered.

iR iR iRZ R jX� �

� Available power in the receiving antenna:

� Delivered power to the receptor:

Z0 ~

ZL

ZiR

Vca

Receiver Antenna




adura Equivalent absorption area

� Considering the receiving antenna as an aperture absorbing energy from an incident electromagnetic wave, the antenna equivalent area (or effective area) is defined as the ratio of the available power in the terminals of the antenna to the power density of the incident wave.

� Let us assume that the antenna is illuminated by a plane wave (Rx and Tx y far field) and perfect polarization matching:

� It is related with the antenna gain for aperture antennas:

� And it is related with the physical aperture area as:

Aperture efficiency Note that the transmitting and receiving patterns are identical

Z0 ZL

Vca ZiR




adura Friis transmission equation

� The Friis equation relates the power received to the power transmitted between two antennas separated by a distance r:

� In general:




adura Friis transmission equation

� The Friis equation relates the power received to the power transmitted between two antennas separated by a distance r:




adura Loss and gain factors

� Insertion losses in the radiolink:

� Polarization mismatch losses:

� Impedance mismatch losses:

� Free-space propagation losses:

� Power gains:




adura Radar range equation.

� Power density impinging on the target:

� Reflected radiation intensity:

� Radar cross section (RCS, ): area intercepting the amount of power which when scattered isotropically produces at the receiver the same density than the actual target

� Reflected power density arriving the receiving antenna:

� Available power in the receiving radar antenna:




adura Radar cross section (RCS)

� O sección equivalente radar (SER): area intercepting the amount of power which when scattered isotropically produces at the receiver the same density than the actual target.

� It can be monostatic or bistatic, depending on the position of the transmitting/receiving antenna.

� A rigorous definition will involve the polarization. So we have for different RCS components: hh, hv, vh, vv .




adura Antenna noise temperature.

� All bodies at a temperature different from 0ºK are sources of incoherent radiation (noise).

� A given antenna gathers these noise radiations from all bodies surrounding it, throughout its radiation pattern, and integrate them into a noise power available at the antenna terminals: NavailableR.

� k: Boltzman constant: 1,38 10-23 (julio/K)

� Bf: noise bandwidth (Hz)

� Ta: antenna noise temperature

� From a systems point of view, the noise temperature of an antenna is the actual temperature of a resistance equal to the radiation resistance of the antenna generating the same amount of noise power.





� From a physical point of view, the noise temperature of an antenna can be obtained as a function of the bright temperature of the radiation impinging on the antenna in each direction of the space, as:

� When the main beam of the antenna points to a uniform region of the space with constant temperature TB = T, the noise temperature of the antenna can be considered as Ta = T.





� In low frequency the predominant noise is mainly the atmospheric noise, related with lightnings (100 per second approx.)

� From 25 to 30 MHz the cosmic noise from external sources becomes important. Apart from the atmospheric and cosmic noise, whose origin is natural, we must also have into account industrial noise.

� In microwave frequency bands the noise temperature of directive antennas depend on the observation angle of their main beam. For antennas that are not pointing to intense noise sources, such as the sun or planets, noise is generated by the absorption of atmospheric gases. Noise increases for low elevation angles, due to the thicker atmosphere section the ray must pass through.

� The combination of cosmic noise and gas absorption noise has a minimum in range 2-4 GHz. This band is used for the exploration of deep space.

� Generally, noise increases with frequency. There are successive maximuns corresponding to the spectral lines of absorption due to resonance of different atmospheric gases (23GHz for water vapor, 55-60GHz for oxygen, etc.)





� If there are additional attenuations due to meteorological phenomena, the noise temperature of the antenna is incremented as:

with Lm the atmospheric attenuation and Tatmosph the physical temperature of the atmosphere.




adura Ta values in MF, HF and VHF bands.

Atmospheric noise isolines at 1MHz referred to kT0B




adura Ta values in MF, HF and VHF bands.




adura Ta values in microwave regime.




adura Ta values in microwave regime.




adura Noise analysis

� Without transmission line losses. Antenna efficiency equal to 1. (L=1)

availableP

availableN




adura Noise analysis

� With transmission line losses and/or antenna efficiency lower than 1 (L>1)

availableP

availableN

0/

rx ir rx availableS G P G P L� �

ir f AN KB T�

1tl

r

L L�

�

noise factor of an attenuator equivalent noise temperature of the attenuator

equivalent noise at the receptor input




adura Sensitivity

� The minimum power required at the receptor, Pdelivered R, min (sensitivity) is obtained from the minimum S/N ratio at the output:

� And we can take this to the Friis formula to calculate all the required parameters to

guarantee the minimum S/N ratio:




adura G/T parameter

� This parameter determines the quality of the tandem antenna-receptor (for L=1):

� By writing the available power as a function of the incident power density and the effective area of the receiving antenna we obtain the following expression:

� Where it is clear that for a given incident power density, the signal to noise ratio in the

receptor is proportional to the quality parameter G/T.

� Usually G/T is expressed in logarithmic units as dB(1/K) = 10log(G/T)

unit 2 fundamental parameters of antennastsc.unex.es/~tabo/rog/rog_tema2_02.pdf · radiación y...

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