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**Introduction to Antennas**

Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: E:

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Recommended textbook Constantine A. Balanis, Antenna Theory: Analysis and Design, 3rd Edition, Wiley-Interscience, 2005; ISBN: X Chapters 1 & 2

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Antennas An antenna can be thought of as a transition / transducer device Two ways of describing antenna operation Field point of view Circuit point of view

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Antenna examples Wire antennas Monopoles Dipoles Arrays

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**Antenna examples Aperture Antennas Reflectors Lenses Horns Patches**

Planar inverted F

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**Antennas Most antennas are resonant structures**

Narrowband Size is inversely proportional to frequency of operation Travelling wave antennas also important Wideband Size dictates lowest frequency of operation 1000 ft diameter; 50 MHz to 10 GHz chip size = 2 x 1 mm2; 60 GHz antenna

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**How does it work? – radiation**

Imagine and electron (red) with its lines of force (green) moving from left to right.

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**How does it work? – radiation**

If the electron moves with a constant velocity the lines “move” with it ...

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**How does it work? – radiation**

... just like this.

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**How does it work? – radiation**

What happens if the electron motion changes suddenly? Remember, change of motion is another word for acceleration.

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**How does it work? – radiation**

B A Imagine a test charge A close to the electron. The delay is negligible, so it sees the electric field line inside the sphere. If the test charge (now at B) is far away, the delay means the “news” that the electric fields have changed has not reached the test charge yet. Lines cannot be discontinuous – they need to stretch. The lines of force acquire a “kink” because they can only start or finish on charges. Sphere grows with time (i.e. delay increases with distance)

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**How does it work? – radiation**

Here’s a picture of many lines of force: there is a spherical shell of stretched lines of force, moving outwards from the accelerated charge at the speed of light, dividing the region of space that “knows” about the change of motion of the charge (inside the sphere) from the region of space that hasn’t yet “found out”.

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**How does it work? – radiation**

Here’s a movie of how it all works for all the electrons shaking in a short conductor, vertically positioned and the electric fields they generate. Source: MIT Open Courseware

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**How does it work? – radiation**

And here is a slightly simplified view showing how loops of line of force close in on themselves and become an entity in their own right, a wave carrying energy away from the antenna. Source: MIT Open Courseware

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Here’s a picture of the sensitivity pattern in 3D of your average television antenna. The “hotter” the colour the strongest the lines of force, or equivalently the energy transmitted, and by necessity (the principle of reciprocity applies), the receive sensitivity of the antenna to waves coming from each direction in space. Antennas – TV aerial Radiation of power in space can be controlled by carefully arranging the patterns of electron motion This is the same as their sensitivity to received signals from different directions in space

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**Fundamental antenna parameters**

Radiation pattern; radiation power density; radiation intensity Beamwidth; directivity; sidelobe levels Efficiency; gain Polarisation Impedance Bandwidth Vector effective length and equivalent area Antenna temperature

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Radiation pattern A mathematical and/or graphical representation of the properties of an antenna, usually the radiation intensity vs. spatial direction coordinates sufficiently far from the antenna Is polarisation specific Spherical polar coordinates are always used Source: C.A. Balanis©

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Radiation pattern Linear pattern Polar pattern Source: C.A. Balanis©

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**Radiation pattern Linear pattern E plane is plane of electric field**

H plane is plane of magnetic field If field direction not known, do not use E or H plane Source: C.A. Balanis©

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**Omnidirectional antenna radiation pattern**

H-plane E-plane λ/2 dipole antenna radiation pattern Source: C.A. Balanis©

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**Radiation pattern definitions**

Isotropic antenna Radiates equally in all directions in space; physically unrealisable Omnidirectional antenna Radiates equally in all directions in one plane only; e.g. dipoles, monopoles, loops, etc. Directional antenna Radiates strongly in a given direction; has a principal or main lobe, the maximum of which point in the direction of the antenna’s boreside Can you guess what is meant by front-to-back ratio?

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**Field regions Reactive near-field Radiative near-field (Fresnel)**

Phases of electric and magnetic fields are often close to quadrature High reactive wave impedance High content of non-propagating stored energy near the antenna Radiative near-field (Fresnel) Fields are predominantly in-phase Wavefronts are not yet spherical; pattern varies with distance Radiative far-field (Fraunhofer) Electric and magnetic fields are in-phase Wavefront is spherical; field range dependence is e-jkr/r Wave impedance is real (Eθ/Hφ = 120π = 377 Ω) Power flow is real; no stored energy Field regions have no sharp boundaries Source: C.A. Balanis©

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**Reminder on angular units**

Steradians For the whole sphere, Radians Source: C.A. Balanis©

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**Radiation power intensity and density**

Poynting vector Time-averaged Poyting vector Radiation power density Radiation intensity Total radiated power

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Directivity

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Directivity Isotropic antenna Current element L << λ

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Directivity Half wave dipole L = λ/2

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**Beamwidth Current element L << λ**

The half-power angles in E-plane are given by, Halfwave dipole – a similar numerical calculation for the two roots of

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**Beamwidth vs. directivity**

The narrower the beamwidth of an antenna, the bigger its directivity For a single main beam antenna where ΩA is the main lobe half power beam solid angle Kraus approximation for non-symmetrical main lobes Tai & Pereira approximation for non symmetrical main lobes Source: C.A. Balanis©

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**Antenna efficiency, ηant**

In an antenna, we experience reduction in radiated power due to Reflection at the input terminals (impedance mismatch) Ohmic conductor losses (c) in the antenna conductors Dielectric losses (d) in the antenna dielectrics The latter two are grouped under the term antenna radiation efficiency Typical antenna efficiency values Dipole ηant ~ 98% Patch antenna ηant ~ 90% Mobile phone PIFA ηant ~ 50% Source: C.A. Balanis©

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Antenna Gain Antenna Absolute Gain

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Bandwidth Many properties vary with frequency and deteriorate in value from their optimum values: Pattern bandwidth Directivity/gain Sidelobe level Beamwidth Polarisation Beam direction Impedance bandwidth Input impedance Radiation efficiency

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Polarisation Antenna polarisation refers to the orientation of the far-field radiated electric field vector from the antenna A vertical dipole radiates a vertical electric field A horizontal dipole radiates a horizontal electric field A general (e.g. horn) antenna with a vertical aperture electric field radiates a vertical electric field in the E-plane and H-plane only; everywhere else the electric field vector is inclined to the vertical and changes with angular direction

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**Polarisation The polarisation of an electromagnetic wave can be**

Linear (as in all previously discussed examples) Circular (e.g. using a helical antenna to transmit) Elliptical (e.g. circular after reflection from a lossy interface) Circular and elliptical polarisations have a sense of rotation Positive helicity (or right hand, clockwise) Negative helicity Source: C.A. Balanis©

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Polarisation Source: C.A. Balanis©

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**Polarisation Linearly polarised uniform plane wave (E0x and E0y real)**

Circularly polarised uniform plane wave (+/- corresponding to positive/negative helicity) Elliptically polarised uniform plane wave (+/- corresponding to positive/negative helicity; E0x and E0y real)

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Polarisation The radiation pattern performance of antennas is often specified in terms of its co-polar and cross-polar components Detailed mathematical definition is Ludwig’s 3rd definition of cross-polarisation (A. Ludwig (1973), “The definition of cross polarization,” IEEE Transactions on Antennas and Propagation, 21(1)) Co-polar radiation pattern of an antenna is measured with a suitably polarised probe antenna which is sensitive to the “wanted” polarisation Cross-polarised pattern is measured for linear polarisation by rotating the probe antenna by π/2 around the line joining the two antennas, or for circular/elliptical polarisation by changing the probe antenna helicity sign

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**Impedance Transmitting operation Receiving operation**

generator (Zg = Rg + jXg) receiver (Zrx) RL XA Rr Rg Xg Vg a b Ig RL Thevenin equivalent circuit (suitable for electric radiators, e.g. monopole, dipole, etc.) a Va Ia Rrx Rr Xrx b XA Ig Gg Bg Gr GL BA a b Norton equivalent circuit (suitable for magnetic radiators, e.g. loop, etc.) Grx Brx Gr GL BA a b Ia

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**Impedance The antenna operation is characterised by an impedance ZA**

An equivalent radiation resistance, Rr A loss (ohmic and dielectric) resistance, RL A reactance, XA When connected to a generator, usually via a transmission line, the usual transmission line and circuit theories apply Radiated power Maximum power transferred from generator to antenna (maximum power transfer theorem) Half of generator power is consumed intenally, other half is shared between antenna losses and antenna radiation

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Impedance

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Radiation efficiency We have come across radiation efficiency before, but now we express it in circuit theory equivalent terms Describes how much power is radiated vs. dissipated in the antenna

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**Antenna effective length**

The voltage at the antenna terminals is determined from the incident field The effective length is a vector When taking the maximum value over θ,φ this becomes For linear antennas Source: C.A. Balanis©

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**Effective aperture area Ae**

This is usually assumed to refer to the co-polar radiation pattern on the boreside of an antenna The antenna effective aperture area is defined as a ratio PT is the power delivered to a matched load in W Wi is the incident wave power density in Wm–2 Ae is the antenna effective aperture area in m2 For any passive antenna we can invoke the principle of reciprocity to show that

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**Antenna aperture efficiency**

For all aperture antennas This allows us to introduce the concept of antenna aperture efficiency For aperture antennas For wire antennas where the physical aperture is taken to be the cross sectional area of the wire

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**Friis free-space transmission**

From your propagation lectures, assuming matched antennas, This expression is a statement of the principle of conservation of energy coupled with the notions of antenna gain and antenna effective aperture area

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**What next? Attempt the tutorial sheet on antennas**

Next lectures on link budgets

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TC303 Antenna & Propagation

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