Antenna parameters Definition, general considerations and fundamental parameters

Departamento de Señales, Sistemas y Radiocomunicaciones Universidad Politécnica de Madrid

Manuel Sierra Castañer E-Mail: [email protected]

ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Outline

 Radiation fundaments  Fundamental parameters of antennas o Input impedance o Radiation patterns o Gain o Polarization  Friis Formula  Antenna noise temperature

2 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Radiation of a current source

The simplest radiation source is a liner electric element placed in a isotropic, homogeneous, infinity and lossless medium. . z  r   2     Ar  k 0A r  0J r  2    k 0 Az  0Jz  2 2 JIdSz   0 , 0 k 0   00   × dV dl dS Idl Escalar equation for Jz x y Since the scalar source can be considered an infinitesimal point source the problem has spherical symmetry and the solution is:

1 d  2 dA  2  r z ÷  k A    J 2 0 z 0 z r dr  dr 

Solving the equation for Jz = 0 (no sources), there are two independent solutions: e jk0r Physical problem for the Az1r  C1 Outwardly travelling wave radiation problem r e jk0r A r  C Inwardly travelling wave z2 2 r   C  0 J dV  0 Idl Solving the equation for non zero Jz 1 z 4  4  3 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 3

Radiation of a current source

• The fields produced by a source element are: 1     Replacing zˆ H A    e jk0r   0 A  0 Idl rˆ cos  ˆ sen  1  E  H 4 r j0 If k 0r>>1 (r>>) terms 1/r are more significant than 1/r 2 or 1/r 3

 jk0r     Idlsen   1   e  ˆ ˆ jk0r H  jk Idlsen  ˆ H   rA  A    jk  e 0 r  r  4r  0 r  4r  jk0r 2  e jIdl   jk 1  sen   k jk 1   E  jk Idlsen  ˆ   ˆ  0   ˆ  0  0   jk0 r 0 E r cos  2 3   2 3 e 4r 2k  r r  2 r r r 0    Radiated fields: E  r, H  r, E  H • The power density (Poynting vector) , depends on 1/r2 (spherical wave) and it is calculated as: 22 1 22k sen   *  SEHrIdlRe  22 232 r 4 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Radiation of an antenna

z  •Areal antenna has a current distribution supposed to Jr    be formed by infinites elements dV of current J dV j rr  P situated in a point r’.  r'  • Each infinites elements dV of current J in a point P in r the space will generate a differential of potential magnetic vector dA

 jk r r   e 0  x dAr  0 Jr dV y 4 r  r

•For the total radiated potential will be the superposition.         jk 0 r r   jk 0 r r  jk0 r r  J r e  I r e  Jre   0 s    0     0   Ar  dS Ar  dl ArdV  S   L   4 V rr  4 r  r 4 r  r

Vo l u m e Surface Wire Antenna

(diameter << ) 5 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Far field properties

•An antenna radiates, in far field: – The radiated electromagnetic wave is propagated radially in all the space directions. – The dependence of E and H with r is always one of a spherical wave e-jk0r/r. The field decreases with the distance as 1/r. – The field E and H depend with  and  because the spherical wave is not homogeneous. To analyze its variation, it is employed the spherical coordinates system.

z

 rˆ  ,

 x y 0   02 6 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Far field properties

z •The radiation fields of any antenna fulfil these general properties:

– The radiated spherical wave behave locally as a plane wave:   a fixed direction (,):    r E  rˆ E  H   H  rˆ E  H  x y – The fields E and H do not have radial components: 0   02    Ar() Arr  A A      E  0 H  0 EjrAr   r r  E  jA E H  

E  jA  E H  

– The power density that transport the wave decrease as 1/r2. If the medium have no losses, it is defined:

 1   * 1 2 2  S  ReE H  E r,,  E r,, rˆ 2 2 7 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Fundamental parameters of radiation

• Before we saw how to determine, from the Maxwell equations, the radiated electric and magnetic fields of an antenna. • Actual field expressions are more complex, so for the antenna characterization we use parameters that can be measured and are easier to analyse. • The measured parameters of an antenna follow the IEEE 145-1993 standard. • Those parameters allow to consider the antenna as ablackboxand calculate the parameters of a radio communication link. • The most important parameters are: • Input impedance • Radiation pattern • Gain • Polarization

8 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Parameters of an antenna: Impedance

• Feeding a linear antenna with a harmonic generator of frequency f, we can define a circuit model: • From the input terminals – Input impedance is generally a complex number that varies with the frequency – Input reflection coefficient V Transmission line Z  antenna I

ZantennaRjX antenna antenna

Transmitter Transmitting Generally, reactance Xantenna(f)=0, antenna at the frequency of resonance

* Zant  Zg T  Zant  Zg 9 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Impedance parameters

• The real part of the input impedance antenna is the sum of the loss resistance (associate to the energy that is dissipated) and the radiated resistance (associate to the radiated energy).

PRradiated radiation Radiation efficiency rad  PRRinput losses radation

• Others alternative parameters to the input impedance, more easy to measure in the high frequency range are: – Return losses (dB): VSWR: 1  Pref T RL(dB)  10log  20log T VSWR  Pinc 1 T • Available power of the transmitter and transmitted to the antenna:

2 1 Vg P  2 inc Ptrans  Pinc  Pref  Pinc 1 T  8 R g

•VSWRMAX should be 2  RL 9.5 dB 12% of power loss 10 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Parameters of an antenna: Radiation pattern

•In the far field – Radiation pattern of electric field F – Polarization pattern ê ê(,)= polarization pattern

0=120=free space impedance e  jk 0 r H  jk Idlsen  ˆ 0 4r e  jk 0 r E  j k Idlsen  ˆ 0 4r

When we feed the antenna with a voltage V, it is generated a current distribution (give by the Maxwell equations) that produce an electromagnetic radiation characterized by the fields E and H.

11 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Radiation parameters: radiation pattern

• It is defined as a graphic representation of the radiation properties of an antenna in function of space angular coordinates. • Plot patterns of:

– field :  arg arg, ECP, EXP, etc – power : = power density, Gain, Directivity.

• The formats that have the patterns are : – Absolute patterns: it plots the fields or power density for a delivered power to the antenna and a constant distance. – Relative patterns: like the previous ones but normalized in relation to the maximum value of the plotted function. In this case the plot are in logarithmic scale (dB). So, the power and fields plots coincide because:

S E 10log 20 log S max E max

12 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Pattern types

• Depending the application of the antenna, we classify: – Isotropic (quasi-isotropic) – Omnidirectional: Directional in one plane and isotropic in the other (symmetry revolution pattern). – Directional: concentrate fundamentally the radiation in a small angular cone: » Pencil beam: conic beam (f.e. for point to point communication) » Fan beam (f.e. base station mobile communication sectorial antennas) » Contour beam, typical for adjusted coverage in DBS systems » Beamforming, typical for security radar » Multibeam (several main lobes) – Multi-pattern: several simultaneous patterns depending on the feeding input. – Reconfigurable beamwidth antennas: when we can control the radiation pattern by a remote control depending on the communication system. Interesting for antennas in satellites. – Adaptative antennas: when the radiation pattern is instantaneously adapted to the radioelectric environment. 13 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

3D patterns

DIRECTIVE OMNIDIRECTIONAL PATTERN PATTERN

E, E , max 1 ISOTROPIC PATTERN Z DIPOLE /2 y

y

X

14 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 2D patterns

POLAR PLOTS AND BEAMWIDTH DEFINITION between half power points (at –3 dB) HPBW= Half-Power Beamwidth

Normalized field pattern Normalized power pattern Normalized pattern in [dB]

15 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Radiation pattern parameters

• Lobe: portion of the radiation pattern bounded by regions of relatively weak Main lobe radiation intensity (nulls) 0 BW-3dB – Major or main lobe: radiation lobe 5 Side lobe level (S.L.L.) containing the direction of maximum 10 radiation. 15 Side lobe – Minor lobes: any lobe except a major lobe. 20 – Side lobes: a radiation lobe in any direction Minor lobes other than the intended lobe. Usually is 25 BW adjacent to the main lobe. 30 first null

– Back lobe: a radiation lobe whose axis draws 35 an angle of aprox. 180º with respect to the 100 50 0 50 100 antenna’s main lobe. i • Side lobe level: ratio of the power density Radiation pattern 2D in dB. in the lobe in question to that of the major Cartesian plot lobe • Front to back ratio • Half power beamwidth (HPBW), first null beamwidth (FNBW) 16 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Radiation pattern: principal planes

y • For linearly polarized directive antennas it is usually enough the characterization of radiation pattern in main planes: – E-plane: the plane containing the electrical field vector and the direction of maximum radiation (YZ) – H-plane: the plane containing the x magnetic field vector and the direction of maximum radiation (XZ)

z

17 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Tridimensional representation

3D patterns in (u,v) coordinates

u  sin cos dB v  sin sin

dB

18 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Bidimensional representation

2D patterns in (u,v) coordinates

u  sin cos v  sin sin

19 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Radiation pattern planes: Polar and Cartesian representation

90 1 120 60 0

0.8

0.6 150 30 5 0.4

E 0.2 i max( E) EdB 180 0 i 10

15 210 330

240 300 20 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 270 i deg i Polar (Linear) Cartesian (dB)

20 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Examples of contour patterns

Multibeam pattern of contour beam DBS antenna from HISPASAT satellite.

antenna TVA-GOV pattern (multipattern antenna) form HISPASAT satellite.

21 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Radiation intensity

• Is the radiated power by solid angle in a determined direction. • Represents the capacity that have an antenna to radiate the energy in this direction.

• Solid angle: – Zone of the space included by a succession of radial lines with vertex in centre of a sphere. – Its unit is steradian (solid angle that includes a spherical surface r2 with a radius r). dA r2 sin d d ddd  sin   rr22 • Radiation intensity: – is the radiated power by solid angle unit. z r dA r d Sr ,,  dA U,  rSr2 ,,  r sin d d

22 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Directivity

• Directivity: D(,) – Represent the capacity that has the antenna to concentrate the radiation intensity in a particular direction. – The ratio of the radiation intensity in a given direction U, from the antenna to the radiation intensity of an isotropic antenna that radiated the equivalent total power averaged over all the directions.  P U, U, 2 Sr,, U  radiated D,   4  4r isotropic 4 UIsotropic Pradiated Pradiated The total radiated power of an antenna: 2 2 Prad  U, d  r S r,, sin dd 4 0 0 • Maximum directivity: D0. – Directivity in maximum radiation direction. – It is always greater than 1 (0 dBi).

– In dBi: 10 log D0. 23 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Gain and Efficiency

• Absolute gain: G(,), is the ratio of the intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically.  U, Sr, , G,   4  4r 2 Pin Pin

• Maximum gain: G0, gain in maximum radiation direction – It can be lower than 1 (0 dBi)

– In dBi: 10 log G0.

• Antenna Efficiency: it is the relation between gain and directivity

PGradiated 0 R  G,  R D , PDin 0

24 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Gain and Efficiency

• E.I.R.P.: Equivalent Isotropic Radiated Power

The EIRP is a figure of merit of the combined transmitter – antenna. If we divide it by 4r2 (sphere area), we obtain the power density at a distance r. The EIRP curves are plotted in dBW.

EIRP,,  G  Pin D  , P rad

GPEIRP,,   Sr,, in  W / m2 44rr22

25 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Parameters of an individual antenna: polarization pattern

• Another important element in the radiation pattern of the antenna is the polarization, that comes from its unitary vector. eeˆ,cos((,))sin((,)) ˆˆ     j (,)

• The shape and the orientation of the polarization ellipse depends on the amplitude relation  and the phases  between the electric field components.

26 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Polarization type

The polarization, that we generally achieved, is never perfectly circular of perfectly linear, but elliptic. So this implies that an antenna radiated with a desired polarization, which have an undesired orthogonal polarization. This is why we say “Copolar component (CP)” (for the desired field polarization) and “Cross polar component (XP)” (for the field polarization orthogonal to CP) .

Right hand circular polarization

Horizontal linear polarization

27 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Polarization: Co-polar and Cross-polar plots

 z EE,,   E  , 

 E   E,  ECP ,uˆ cp  EXP , uˆ xp E CP and XP components:  x  y • Linear polarization: Ludwig 3rd definition for linear components (co polar on y-axes)

EECP ,,sin,cos  E EE,,cos,sin E XP    E • Circular polarization: y

1  j ERHC ,  E ,  jE , e 2 E 1  E ,  E ,  jE , e j x LHC 2   28 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Typical CP-XP plots of a terrestrial station

29 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Polarization Loss Factor (PLF)

• Any field can be discomposes as a sum of two orthogonal components and to the direction of propagation to each other. • When a radio communication is settled down, the receiving antenna only couples the component of coincident incident field with its polarization. The polarization loss factor (PLF) is defined like the fraction of power that transports the incident wave in the polarization of the receiving antenna. This factor is calculated as the scalar product of the unitary vectors of polarization from the transmitting and receiving antenna in the link direction.

Dipoles 2 PLF eˆˆTR,, e

2 PLF = 1 PLF = cos p PLF = 0

30 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Polarization Loss Factor (PLF)

Examples: •Linear polarization: a change of 1° in the polarization orientation, causes 2 small losses in the copolar coupling.  PLF=cos (p)

•Circular polarization: perfect coupling (PLF=1) if the turn sense in polarization of the transmitting and receiving antenna are the same. Uncoupling (PLF decreasing towards 0) if they are in contrary sense.

•For linear(transmitter antenna) and circular polarization(receiver antenna): PLF=1/2 (-3dB)

31 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Dual polarization

• Nowadays because the saturation of the radio bands, the use of antennas of high polarization purity allow to duplicate the capacity of a band using both polarization, transmitting and receiving channels that occupy the same band on two orthogonal polarizations. – This is done for example in the fixed service by satellite, transmitting and receiving simultaneously orthogonal linear polarizations. – In order to avoid interferences between orthogonal channels, the radiation level crosspolar of the antennas do not have to be more than -35 dB. • We notice that the previous requirement also conditions the position (adjustment) of the polarization axes in the terrestrial station. – A misalignment of 1° in the axis direction of polarization reference (maximum admitted variation in terrestrial stations) cause small losses in the copolar coupling but coupled -35 dB of crosspolar component.

10logcos2 1º 0.001dB 10logcos2 89º  35.2dB

32 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Bandwidth

• It is the frequency range where the characteristic parameters (input impedance, reflection coefficient, radiation pattern, gain,…) fulfil specifications. – For the narrow band antennas (resonant antennas) it is usually defined in % of the resonance frequency. – For the broadband antennas, it is defined as the relation between the upper frequency of the band to the lower one, for example 2:1, 10:1 etc.

Reflection coefficient (Input impedance) for a Reflection coefficient (Input impedance) for a wide bandwidth antenna narrow bandwidth antenna • The antennas that are over a 2:1 relation for a certain specification (impedance…) they are designed based on angles and they receive the name of antennas independent of the frequency. 33 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Circuital model of an antenna in reception

In an antenna, reciprocity ZiR = ZiT •Available power of the receiving antenna:

2 1 Vca Pavailable  8 R iR Z iR Z0 ZL Vc.a • Input power at receiver:

1 2 2 Preceived  IL R L  Pavailable 1 R  2 Receiving Antenna Receiver •Reflection coefficient (Zo=ZiR):

* ZL  ZiR R  ZiR  ZL

34 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Absorption equivalent area

• If we consider the antenna as an aperture that get energy from the incident electromagnetic wave, we can define an equivalent antenna area (or effective area) as the “relation between the available power at the antenna and the power density of the incident wave”. P , A ,  available e  S ,   S ,  i P , i  available  * This definition consider perfect

Z i =Zo =ZL ZL Zo Zi coupling (PLF=1) in polarization between the incident wave and the • It is demonstrate that: antenna. 22 AGAG,, eemax44  0 Reception pattern is identical to the transmission one • Relation between the gain and the physical area for aperture antennas:

A    A 4  a: Aperture efficiency emax r a aper GA 0 r a 2 aperture ( 1) 0.5,0.8

35 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Friis Formulas: Propagation in free space

• In all radiocomunication systems, we need to establish a power balance between the transmitter and the receiver to calculate the needed power in the transmitter that allows to reach a minimum level of signal in the receiver, that is above the noise floor.

• Friis formula allows to calculate the insertion losses of a radiolink as a function function of the transmission parameters for achantenna, associated with the directions that which one see the other (Polarization Loss Factor (PLF)).

• These insertion losses are define as the ratio between the delivered power at the receiver PDR and the available power at the transmitter PAT.

36 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Transmission equation: Friis Formulas

Using the definitions of power gain and the mismatches of the impedance in Tx and Rx, a balance link can be made in conditions of free space. This equation is what it is defined as Friis Formula:

P 2 2 DRx  eeˆˆTtt,,1 Rrr   T  P  T ATx R 2 2   1,,R  GGTttRrr   4 R

Alternative Friis Formula:

PS,, A  eeˆˆ22 1 DR i e T R R

37 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Loss Factors

P 10log Delivered Rx • Radiolink insertion loss in dB:  PAvailable Tx

– Uncoupling polarization losses (PLF):  20log eˆ T , eˆ R ,

– Unmatched impedance losses: 10log 122 10 log 1 TR 

– Free space propagation losses:  4R  (relation with spherical behaviour of the  20log  transmitted wave).   

GdBy() GdB () – Power gain: TR

– Radiolink losses or Friis Formulas:

PDelivered Rx 2 2 10log 10log 1GdB 20log eˆˆ  ,  e   ,  GdB 10log 1 P TT T R R R Available Tx 38 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Antenna noise temperature

• When a power balance is studied in a radiolink, not only the signal level is important also the noise that reach the receiver. • All the bodies with a temperature different from 0K give incoherent radiation (noise). • The antenna catches the radiation of all the bodies that surround it through their radiation pattern and put it as an available noise power NAR at the receiving antenna input.

• Being NAR, the power of noise available in the antenna considering no losses, its noise temperature is defined as: – k, Boltzman cste. =1.38 10-23 (J/K) Nyquist Formula

–Bf, noise bandwidth (Hz) –T, antenna noise temperature (K) a N AR Ta  kB f

39 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Antenna noise temperature

• Based on brightness temperature TB (,) associated to the noise radiation that impinges on the antenna for the (,) direction, the antenna temperature Ta is obtained as:

TB ,  f ,d 4 1 Ta   TB ,  f , d 4 f , d a 4

The antenna noise temperature Ta depends on the antenna orientation in the atmosphere and of the frequency work.

40 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Typical values of Ta (MF, HF y VHF)

Maximum Tropical Zones

K] Atmospheric noise °

[ associated to the 100 rays/s A Antenna temperature Antenna temperature D C Cosmic noise

Minimum Poles

Frequency [MHz] Isolines of atmospheric noise at 1 MHz in dB refers to KTaB MF and HF: Noise temperature

41 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013

Typical values of Ta (MF, HF y VHF)

Noise from industrial type:

Ta Commercial zone 10log Residential zone 290 Rural zone Peaceful rural zone Galactic noise (medium)(medio)

f ()MHz Industrial type noise 42 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013 Typical values of Ta (Microwave band)

Narrow beam antennas pointing with the main lobe at an elevation  over the Atmospheric gas horizon with clear atmosphere (without absorption

Cosmic considering ground contribution) noise The atmospheric attenuation produce by the rain, the fog, etc. increase the K]

° antenna temperature as:

L 10 Ta  Tm 110 

(Tm, medium value of the atmosphere temperature and L additional atmosphere Antenna temperatureAntenna [ attenuation. Background noise

Atmosphere attenuation Additional noise temperature of the antenna Elevation L angle

Frequency [GHz] Noise temperature in microwave frequency Typical increase in the microwave range 43 ANTENNA DESIGN AND MEASUREMENT TECHNIQUES - Madrid (UPM) – March 2013