Antennas: from Theory to Practice 5. Popular Antennas Yi HUANG Department of Electrical Engineering & Electronics The University of Liverpool Liverpool L69 3GJ Email: Yi.Huang@liv.ac.uk This is a general rule, but it may need modification for certain situation.

Objectives of this Chapter To examine and analyse some of the most popular antennas using relevant antenna theories, to see why they have become popular, what their major features and properties (including advantages and disadvantages) are, and how they should be designed.

Classification of Antennas Wire-Type Antennas Aperture-Type Antennas Dipoles Horn and open waveguide Monopoles Reflector antennas Biconical antennas Slot antennas Loop antennas Microstrip antennas Helical antennas Linearly polarised antennas Circularly polarised antennas Element antennas Antenna array Narrow-band Broad-band Transmitting Receiving

Evolution of a dipole of total length 2l and diameter d 5.1 Wire Type Antennas Dipole Antennas Evolution of a dipole of total length 2l and diameter d

Current distribution of dipoles Current distribution along an open transmission line is: Thus the current distribution on the dipole is

Radiation pattern of dipoles In the far field:

Input impedance of dipoles

Electrically short dipoles When the dipole length is much shorter than a wavelength (< l/10), it can be called an electrically short dipole The input impedance can be approximated as Radiation pattern is E() = sin The directivity is D = 1.5 (1.76dBi)

Half-wavelength dipole The most popular dipole Radiation pattern: E() = cos[(/2)cos ]/sin Radiation resistance: 73  Directivity: 1.64 (2.15 dBi) The input impedance is not sensitive to the radius and is about 73 Ω which is well matched with a standard transmission line of characteristic impedance 75 Ω or 50 Ω (with a VSWR < 2). Its size and radiation pattern are suitable for many applications

Example 5.1 Solution on pages 135 - 137 A dipole of the length 2l = 3 cm and diameter d = 2 mm is made of copper wire (s = 5.7  107 S/m) for mobile communications. If the operational frequency is 1 GHz, a). obtain its radiation pattern and directivity; b). calculate its input impedance, radiation resistance and radiation efficiency; c). if this antenna is also used as a field probe at 100 MHz for EMC applications, find its radiation efficiency again, and express it in dB. Solution on pages 135 - 137

Some popular forms of dipole antennas

Monopole Antennas Half of a dipole antenna mounted above  l Half of a dipole antenna mounted above the earth or a ground plane Normally one-quarter wavelength long almost the same feature as a dipole, except the 37 radiation resistance, higher gain, a shorter length, and easier to feed! Based on the Image Theory Ground

Effects of the ground plane Its size and material property of can change the radiation pattern (hence the directivity) and input impedance.

An example

Some popular forms of monopole antennas

Duality Principle System 1 System 2 Duality means the state of combing two different things which are closely linked. In antennas, the duality theory means that it is possible to write the fields of one antenna from the field expressions of the other antenna by interchanging parameters: System 1 System 2

Loop Antennas For a short dipole Thus for a small loop

Directivity of a loop

Current distribution of a resonant loop

Radiation pattern of a one wavelength loop – this is very different from that of a short loop!

Radiation patterns of loops with various circumferences

Input impedance of loops

Helical Antennas It may be viewed as a derivative of the dipole or monopole, but it can also be considered a derivative of a loop.

Normal mode Helix It may be treated as the superposition of n elements, each consisting of a small loop of diameter D and a short dipole of length s, thus the far fields are They are orthogonal and 90 degrees out of phase; The combination of them gives a circularly or elliptically polarised wave. The axial ratio:

When the circumference is equal to the axial ratio becomes unity and the radiation is circularly polarised.

Axial Mode Helix The axial (end-fire) mode occurs when the circumference of the helix is comparable with the wavelength (C = pD ≈ l) and the total length is much greater than the wavelength. This has made the helix an extremely popular circularly-polarised broadband antenna at the VHF and UHF band frequencies The recommended parameters for an optimum design to achieve circular polarisation are:

The normalised radiation pattern: Half power beamwidth: 1st null beamwidth:

The directivity: The axial ratio Radiation resistance

Example 5.2 Design a circularly polarised helix antenna of an end-fire radiation pattern with a directivity of 13 dBi. Find out its radiation resistance, HPBW, AR and radiation pattern. Solution on pages 150 - 152

Radiation patterns Which is better?

Yagi-Uda Antennas

The driven element (feeder) is the very heart of the antenna The driven element (feeder) is the very heart of the antenna. It determines the polarisation and centre frequency. For a dipole, the recommended length is about 0.47l to ensuring a good input impedance to a 50 Ω feed line. The reflector is longer than the feeder to force the radiated energy towards the front. The optimum spacing between the reflector and the feeder is between 0.15 to 0.25 wavelengths. The directors are usually 10 to 20% shorter than the feeder and appear to direct the radiation towards the front. The director to director spacing is typically 0.25 to 0.35 wavelengths, The number of directors determines the maximum achievable directivity and gain.

Log-periodic Antennas

The antenna is divided into the so called active region and inactive regions. The role of a specific dipole element is linked to the operating frequency: if its length, L, is around half of the wavelength, it is an active dipole and within the active region; Otherwise it is in an inactive region and acts as a director or reflector as in Yagi-Uda antenna The driven element shifts with the frequency – this is why this antenna can offer a much wider bandwidth than the Yagi-Uda. A travelling wave can also be formed in the antenna. The highest frequency is basically determined by the shortest dipole length while the lowest frequency is determined by the longest dipole length (L1).

Antenna design This seems to have too many variables. In fact, there are only three independent variables for log-periodic antenna design. the scaling factor: the spacing factor: the apex angle:

In practice, the most likely scenario is that the frequency range is given from fmin to fmax, the following equations may be employed for design Another parameter (such as the directivity or the length of the antenna) is required to produce an optimised design.

Example 5.3 Solution on page 160 Design a log-periodic dipole antenna to cover all UHF TV channels, which is from 470 MHz for channel 14 to 890 MHz for channel 83. Each channel has a bandwidth of 6 MHz. The desired directivity is 8 dBi. Solution on page 160

5.2 Aperture-Type Antennas They are often used for higher frequency applications (> 1GHz) than wire-type antennas.

Fourier Transform and Radiated Field

How to link the aperture E field to the radiated field Directivity:

Near field and far field

Example 5.4 Solution on pages 166 - 168 An open waveguide aperture of dimensions a long x and b along y located in the z = 0 plane. The field in the aperture is TE10 mode and given by Find i). the radiated far field and plot the radiation pattern in both the E and H planes; ii). the directivity. Solution on pages 166 - 168

Horn Antennas Horn antennas are the simplest and one of the most widely used microwave antennas – the antenna is nicely integrated with the feed line (waveguide) and the performance can be easily controlled. They are mainly used for standard antenna gain and field measurements, feed element for reflector antennas, and microwave communications.

Pyramidal Horn Design To make this horn, we must have i.e.

The directivity: We can therefore obtain the design equation This equation in A can be solved using numerical methods. For the optimum design, use a first guess approximation

Example 5.5 Solution on pages 172 - 173 Design a standard gain horn with a directivity of 20 dBi at 10 GHz. WR-90 waveguide will be used to feed the horn. Solution on pages 172 - 173

Reflector Antennas Reflector antennas can offer much higher gains than horn antennas and are easy to design and construct. The most widely used antennas for high frequency and high gain applications in radio astronomy, radar, microwave and millimetre wave communications, and satellite tracking and communications. The most popular shape is the paraboloid – because of its excellent ability to produce a pencil beam (high gain) with low sidelobes and good cross-polarisation characteristics

Paraboloidal and Cassegrain reflector antennas

Antenna design The reflector design problem consists primarily of matching the feed antenna pattern to the reflector. The usual goal is to have the feed pattern about 10 dB down in the direction of the rim, that is the edge taper = (the field at the edge)/(the field at the centre) ≈10 dB. Directivity: Half-power beamwidth

Offset parabolic reflectors It reduces aperture blockage while maintaining acceptable structure rigidity

Radiation patterns in E and H planes

Slots Antennas They are very low-profile and can be conformed to basically any configuration, thus they have found many applications, for example, on aircraft and missiles.

Slot waveguide antenna array: widely used for radar Equivalent circuit Slot waveguide antenna array: widely used for radar

Equivalence Principle: for field analysis The radiated field by the slot is the same as the field radiated by its equivalent surface electric current and magnetic current which were given by where E and H are the electric and magnetic fields within the slot, and is the unit vector normal to the slot surface S For a half-wavelength slot, its equivalent electric surface current JS = ˆn × H = 0, the remaining source at the slot is its equivalent magnetic current MS = −ˆn × E (it would be 2MS if the conducting ground plane were removed using the imaging theory).

Babinet’s Principle The field at any point behind a plane having a screen, if added to the field at the same point when the complementary screen is substituted, is equal to the field at the point when no screen is present. Apply this to antennas: Since the impedance for a half-wavelength dipole is about 73 ohms, the corresponding slot has an impedance of

Self-complementary antennas – frequency independent This type of antenna has a constant impedance of

Microstrip/Patch Antennas Ease of construction and integration, relatively low cost, compact low profile configuration and good flexibility Typical applications for 1 - 20 GHz

Operational principles To be a resonant antenna, the length L should be around half of the wavelength. In this case, the antenna can be considered as a l/2 transmission line resonant cavity with two open ends where the fringing fields from the patch to the ground are exposed to the upper half space (z > 0) and are responsible for the radiation. This radiation mechanism is the same as the slot line, thus there are two radiating slots on a patch antenna. As a resonant cavity, there are many possible modes (as waveguides), thus a patch antenna is multi-mode and may have many resonant frequencies.

Radiation pattern

Main properties Directivity Input impedance Bandwidth for VSWR < 2

Antenna design Optimised width: Resonant freq.: Length:

Example 5.7 Solution on pages 189 - 191 RT/Duroid 5880 substrate ( and d = 1.588 mm) is to be used to make a resonant rectangular patch antenna of linear polarisation; a). Design such an antenna to work at 2.45 GHz for Bluetooth applications; b). Estimate its directivity; c). If it is to be connected to a 50 ohms microstrip using the same PCB board, design the feed to this antenna; d). Find the fractional bandwidth for VSWR < 2. Solution on pages 189 - 191

5.3 Antenna Arrays Motivations: to achieve desired high gain or radiation pattern, and the ability to provide an electrically scanned beam. It consists of more than one antenna element and these radiating elements are strategically placed in space to form an array with desired characteristics which are achieved by varying the feed (amplitude and phase) and relative position of each radiating element; The main drawbacks are the complexity of the feeding network required and the bandwidth limitation (mainly due to the feeding network)

A typical antenna array of N elements

Pattern Multiplication Principle Since the total radiated field for an array is the summation of the fields from each element where An is the amplitude, n is the relative phase, Ee is the radiated field of the antenna element, and AF is called array factor. Thus the radiation pattern of an array is the product of the pattern of individual element antenna with the (isotropic source) array pattern.

Example Total array Total array element AF AF element

For a uniform array of a constant d and identical amplitude (say 1) Thus The normalised antenna factor of a uniform array:

AF: N = 20, d = l and 0 = 0

AF: N = 10, d = l and 0 = 0

AF: N = 10, d = l/2 and 0 = 0

AF for N = 10 and d = l/2, and 0 = 450

Phased Array The maximum of the radiation occurs at  = 0 That is: Normally the spacing d is fixed for an array, we can control the maximum radiation (or scan the beam) by changing the phase 0 and the wavelength (frequency) – this is the principle of phase/frequency scanned array

Broadside and End-fire Arrays An array is called a broadside array if the maximum radiation of the array is directed normal to its axis (q = 00); while it is called an end-fire array if the maximum radiation is directed along the axis of the array (q = 900).

The radiation pattern, SLL, HPBW, and gain for four different source distributions of eight in-phase isotropic sources spaced by l/2; there are trade-offs!

Element mutual coupling The interaction between elements due to their close proximity is called the mutual coupling which affects the current distribution hence the input impedance as well as the radiation pattern The voltage generated at each element can be expressed as

Self-impedance: Mutual impedance:

5.4 Some Practical Considerations The differences between transmitting and receiving antennas From the reciprocity theorem, the field patterns are the same for transmitting or receiving. Antenna feeding and matching Balun (a device to connect a balanced antenna to an unbalanced transmission line) may be required. Polarisation Polarisation has to be matched from Tx to Rx. Radomes, housings and supporting structures. Affecting the antenna performance (impedance, pattern, …)