1 Decibel 2 Transmission lines SWR 3 Antenna

1. Decibel 2. Transmission lines, SWR 3. Antenna properties 4. Some common antennas Tiiti Kellomäki, OH 3 HNY

The decibel

Decibel scale • All circuits either amplify or attenuate power. A = Po/Pi = 100000 B = Po/Pi = 0. 0002 • As the power ratios can be very large or very small, it is handy to use a logarithmic scale, the decibel scale. A(d. B) = 10 log Po/Pi = 10 log 100000 = 50 d. B B(d. B) = 10 log Po/Pi = 10 log 0. 0002 = – 37 d. B • Positive decibel readings indicate gain and negative values attenuation.

Decibel calculation • Multiplication of power ratios corresponds to addition of decibel values. • If the first block amplifies by 3 d. B and the second one attenuates by 10 d. B, the whole circuit has an effect of – 7 d. B, or the output is one fifth of the input. Po/Pi = Po/Pa ∙ Pa/Pi = 2 ∙ 0. 1 = 0. 2, or – 7 d. B.

Decibel units of measure • Decibel readings always mean power related to some known level, e. g. input power, carrier power, or noise level. • A commonly used d. B unit is d. Bm "decibels over one milliwatt". One watt in d. Bm is 10 log 1 W / 1 m. W = 10 log 1000 = 30 d. Bm. • One milliwatt is no more than one milliwatt, hence the ratio is one and 1 m. W in d. Bm is 10 log 1 = 0 d. Bm.

Rules of thumb • Negative decibels are for attenuation, positive for amplification. • Adding 0 d. B is the same as multiplying by one. • Adding 10 d. B is multiplication by 10. • Adding 3 d. B is multiplication by 2. • 7 d. B = 10 d. B – 3 d. B, or 10·½ = 5. • 24 d. B = 10 d. B + 10 d. B – 3 d. B, or 10· 10/2/2 = 250.

Transmission lines

Transmission lines • Because the wavelength of a RF signal is short (say, 80 m to 23 cm in your normal frequency range, or millimeters), cable lengths are large in terms of wavelengths. • Signal voltage level varies rapidly in time and space. • Wires must be thought of as transmission lines.

Characteristic impedance • Characteristic impedance tells the ratio of voltage to current (or electric to magnetic field) on the line. • On a 50 -ohm line, a 1 -volt signal will be a 20 -milliampere signal. • This impedance is not related to loss. • 50 ohms is most often used in amateur radio. 75 -ohm coaxial cable is used in tv networks.

Mismatch • If the characteristic impedance of the transmitter, the cable, and the antenna are not the same, power is not delivered properly. • Power is reflected in every impedance discontinuity. • At some points, the forward and reflected voltages will add, and at some points cancel each other. Hot and cold spots are formed on the cable.

Standing wave ratio • Standing wave ratio is the radio of the maximum and minumum voltage on the line. • SWR = 1 means that there is no standing wave, thus no reflections, and all the power is delivered properly. • SWR = 2 means that 10 % of the power is reflected at the end. • SWR = 3 means that 25 % of the power is reflected at the end. • SWR = ∞ means that no power is delivered to the load. • To avoid reflections, impedance can be matched so that the transmitter sees a 50 -ohm load.

Coaxial cable • Coaxial cable is formed of two coaxial tubes. • Between the outer and the inner conductor there is some dielectric material. • All electric and magnetic fields are inside the cable. • Coaxial cable is not affected by nearby metallic objects or slight bending. • 50 -ohm coax is the most common transmission line used by radio amateurs.

Two-wire lines • The electric and magnetic fields of a two-wire transmission line spread into the surroundings of the line. • Two-wire lines radiate and cannot be used above HF. • Nearby metallic objects affect the performance of twowire lines. • In twinlead, there is insulating material between the wires. Its characteristic impedance is often 240 or 300 ohms. • Open wire is essentially air-insulated and of 450 ohms.

Symmetry in transmission lines • If one of the conductors on a line can be thought of as a ground, the line is unbalanced. • Coaxial cable is unbalanced. • If the lines are identical, the line is balanced. • Two-wire lines are balanced. • Symmetrical antennas need to be connected to symmetrical lines or else a balun (balanced-tounbalanced transformer).

Antennas

Antennas • Antenna is the part of an electromagnetic system that either transforms energy from current and voltage into electromagnetic radiation or vice versa. • An antenna has the same properties regardless of whether it is used as a transmitting or a receiving antenna.

Antenna as a load • When an antenna is connected to a transmitter, the radio sees it as a load, an impedance. • The antenna input impedance is strongly dependent on frequency. • At resonance the impedance is real (resistance). • Antenna bandwidth may be defined as the bandwidth where the reflected power due to impedance discontinuities is sufficiently small, or in other words, the SWR is small enough (say, 2 or 3).

Some useful antenna properties • Radiation pattern is a plot of radiated power in different directions. • An isotropic antenna radiates equally in all directions. • Directivity tells how efficiently the antenna radiates in the maximum direction, compared to the isotropic antenna (d. Bi). • Directivity can also be expressed in d. B compared to a half-wave dipole (0 d. Bd = 2 d. Bi).

Some useful antenna properties • Gain is the same thing but multiplied by efficiency. It is the property of a real antenna. • Gain is also expressed in d. Bi or d. Bd. • Efficiency tells the ratio of radiated power to power delivered to the antenna. If the efficiency is 73 %, 27 % of the delivered power is lost as heat because the antenna is made of lossy materials. • If the directivity is 10 d. Bd and efficiency 50 %, the gain is 10 d. Bd – 3 d. B = 7 d. Bd (one half of the original).

Dipoles • • A half-wave dipole is the simplest antenna. The dipole is commonly used in HF. You need a balun to feed it properly. A half-wave dipole has an input impedance of 73 ohms, so you can connect it directly to a 50 -ohm radio. The bandwidth covers any one HF band. The half-wave dipole gain is 2 d. Bi = 0 d. Bd (small). A dipole can be of any length, e. g. l, 2 l… Dipoles are balanced.

Monopoles • A monopole is half a dipole used with a ground plane. • The monopole and its mirror image form a dipole. • Common sizes are l/4 (gain 0 d. Bd), 5 l/8 (gain 2 d. Bd), ½l and one l. • The longer the monopole, the higher the gain. • Monopoles are commonly used in HF, VHF, UHF, and in handheld devices. • Monopoles are unbalanced.

Images of monopoles and dipoles 5 l/8 radiation pattern folded dipole l/4 radiation pattern dipole radiation pattern

Loops • The most common loop size is one wavelength. • The loop radiates in the direction of the hole. • Loops are used in HF. • The exact shape of the loop is not important, just set up some wire in trees. • The loop has a small gain, 1 d. Bd. • Loops are balanced.

radiator Yagis boom directors • The Yagi-Uda antenna is a dipole with some reflector additional elements. • The (half-wave) dipole part radiates, behind it is a long reflector element, and in front are one or more directors. • The yagi is a directive antenna with a gain of 2 to 20 d. Bd. • To achieve more gain, the number of elements must be increased.

Yagis • Yagis are used in HF above 14 MHz, and up to 1200 MHz. • Yagis need to be carefully designed and fed. • Two or more yagis can be stacked in order to achieve gain: – if you place them side by side, the horisontal lobe will narrow, – one upon the other narrows the vertical lobe.

Quads • A quad is like a yagi but formed of loops instead of dipoles. • You can place loops of different sizes within each other without problems. • Quads are used in HF and VHF. • A quad may have a gain of 4 to 10 d. Bd.

Helices • A helix can be used in two ways: – if the diameter is small compared to a wavelength, the helix will radiate like a dipole, – if the diameter is a large fraction of a wavelength, the helix radiates axially and its polarisation is circular. • The former type is used in handheld radios. • The latter is used in UHF and up.

Reflector antennas • To achieve large gains, reflector antennas can be used. • The diameter of the reflector must be several wavelengths. • Reflector antennas are used in microwave frequencies, SHF. • A gain of 30 d. Bi may be achieved.

Exam questions You are constructing a 432 MHz transmitting antenna. Which one is correct? • ? 43 cm half-wave dipole • ? 34 cm half-wave dipole • ? 43 cm 5/8 -wavelength monopole • ? 34 cm monopole and ground plane

Exam questions You are constructing a 432 MHz transmitting antenna. Which one is correct? • – 43 cm half-wave dipole • + 34 cm half-wave dipole • + 43 cm 5/8 -wavelength monopole • – 34 cm monopole and ground plane

More exam questions Coaxial cable has the property • ? not to radiate because the electromagnetic field stays inside the cable • ? its characteristic impedance is affected by the distance between the conductors • ? it can be mounted on a metallic roof • ? it can be bent with a sharp radius (minimum radius 5 D)

More exam questions Coaxial cable has the property • + not to radiate because the electromagnetic field stays inside the cable • + its characteristic impedance is affected by the distance between the conductors • + it can be mounted on a metallic roof • – it can be bent with a sharp radius (minimum radius 5 D)

Questions? • Feel free to ask further questions. • Check the nice antenna books at the club room: – ARRL Antenna Book – Antennisuunnittelu-kurssin pruju – Simple and Fun Antennas for Hams