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Teach-In 2026 by Mike Tooley World of Wireless – An Introduction to Radio and Wireless Technology Series 12, part 5: antennas digital systems can control analog oscillators, with a particular emphasis on phase-locked loops (PLL). We also introduced digital frequency synthesis and software-defined radio (SDR). We examined different SDR solutions and show how a costeffective SDR paired with powerful software enables you to receive a wide range of radio signals at frequencies extending from HF to UHF. Our Hands-On practical project involved the construction of a modular amplitude-modulated (AM) signal source. This month, our focus shifts to antennas, covering how several popular types are built, how they work, and how well different types of antenna perform. We’ll demonstrate easy ways to construct several basic antennas gain and directional characteristics and discuss why matching them of real antennas. Fig.5.1 shows how properly with your equipment the radiation from a real antenna matters. compares with that from an isotropic Area illuminated (entire This part also explores antenna radiator. surface of the sphere) feeders and the voltage standing The isotropic radiator in Fig.5.1(a) wave ratio (VSWR). Our Hands-On radiates uniformly in all directions. project is a handy reference dipole In other words, when placed at antenna. the centre of a sphere, the antenna Serving both transmission and would uniformly illuminate the reception, antennas are essential Isotropicinternal radiator surface. While this ancomponents in all radio and wire- tenna can’t be realised in practice, less systems. A transmitting antenna it’s used as a reference for antenna turns electrical energy into electro- analysis. magnetic waves, while a receiving The real antenna in Fig.5.1(b) antenna does the reverse. According has directional properties and a to the law of reciprocity, an anten- radiation pattern that illuminates a na’s gain and directional properties much smaller area of the spherical are the same whether transmitting region. Concentrated energy radior receiving. ated in a specific direction implies The isotropic radiator is a theoreti- an apparent gain. The energy supcal antenna that serves as a reference plied to an isotropic source would for comparing and calculating the have to be correspondingly greater Un if in a orm r ll d adi ire atio ctio n ns L ast month, we showed how (a) Radiation from an isotropic radiator Area illuminated (entire surface of the sphere) Area illuminated Real antenna (a) Radiation from an isotropic radiator Ma xim um rad iat ion Un if in a orm r ll d adi ire atio ctio n ns Isotropic radiator (b) Radiation from a real antenna (energy concentrated) Fig.5.1: a comparison of an isotropic radiator (a) with a real antenna (b). 20 Practical Electronics | March | 2026 Voltage Voltage λ/2 Current Current Max. Max. Max. Max. Min. Min. Min. Min. Fig.5.2: a half-wave dipole antenna. to maintain the same field strength at a particular point. To understand how antennas work (and why they sometimes don’t work as expected), it’s important to have a basic grasp of antenna theory. Many complex antenna types are merely refinements of one or another basic form of antenna. We shall start by describing one of the most fundamental types: the half-wave dipole. Half-wave dipole antenna The basic half-wave dipole antenna (Fig.5.2) consists of a single conductor split in the centre, having an overall length equal to one-half of the signal wavelength. The split at the centre is used for the feeder connection, which may be coaxial cable or twin-feeder (explained later). An approximation of antenna length in metres can be found by dividing 150 by the frequency (in MHz) of the wave being transmitted. The relationship between the overall length of a half-wave dipole, l, (in metres) and its resonant frequency, f, (in MHz) is l = (150 ÷ f )m. In practice, because of the capacitance effects between the ends of the antenna and the ground plane, the antenna is invariably cut a lit- Feed point Feed point Min. Min. Max. Max. l /2 l /2 Fig.5.3: the voltage and current distribution in a half-wave dipole antenna. tle shorter than a half wavelength, meaning the physical length of the antenna is less than its electrical length. When determining the optimum dimensions, a correction factor, k, is applied. End effects, or capacitance at the ends of the antenna, require that we reduce the actual length of the antenna by about 4-6%, so k usually ranges from 0.96 to 0.94. At frequencies below 3MHz, k is often close to 0.96, whereas in the range of 3-30MHz, k falls to about 0.95. Above 30MHz, k is usually 0.94, or less. The formula then becomes l = (150k ÷ f )m. For VHF and UHF, where wavelengths are very short, it is more practical to work in centimetres, rather than in fractions of a metre. The length of a half-wave dipole antenna can then be calculated as l = (15000k ÷ f )cm. Current and voltage distribution Fig.5.3 shows the distribution of current and voltage along the length of a half-wave dipole antenna. The current is at a maximum in the centre and zero at the ends. Conversely, the voltage is zero at the centre and maximum at the ends. The dipole antenna in Fig.5.3 has the directional properties illustrated in Fig.5.4. Fig.5.4(a) shows the radiation pattern of the antenna in the plane of the antenna’s electric field (parallel to the ground), while Fig.5.4(b) shows the radiation pattern in the plane of the antenna’s magnetic field (vertical). In Fig.5.4(a), minimum radiation occurs along the axis of the antenna, while the two regions of maximum radiation are at 90° (perpendicular) to the two dipole elements. In the other (orthogonal) plane, Fig.5.4(b), the antenna radiates uniformly in all directions. The important conclusion from Fig.5.4 is that a horizontal dipole will have a bidirectional characteristic, whereas a vertical dipole will have an omnidirectional radiation pattern. In three–dimensional space, the combined effect of these two patterns will be a doughnut shape, Fig.5.4: horizontal/azimuth (left) and vertical/elevation (right) plots for a vertical half-wave dipole in ‘free space’. These idealised plots were made using a popular antenna modelling package. If it isn’t obvious how this relates to the antenna, refer to Fig.5.5. Practical Electronics | March | 2026 21 Voltage Voltage Current Current /2 /2 Feeder (a) Vertical dipole Fig.5.5: 3D radiation pattern produced by popular antenna modelling software. illustrated by modelling software in Fig.5.5. You will be able to verify this from this month’s Hands-On project! Note that a horizontal dipole will radiate horizontally polarised waves, whereas the radiation from a vertical dipole will be vertically polarised (recall from Part 1 that electromagnetic waves are said to be polarised in the direction of the electric field). Monopole antennas A vertically mounted dipole antenna providing omnidirectional radiation characteristics is desirable in scenarios where uniform signal coverage is required. Unfortunately, mounting a dipole in the vertical plane can sometimes have problems due to the proximity of a conductive mounting structure. An alternative solution is a vertical quarter-wave antenna in conjunction with a reflecting ground plane, effectively cutting the antenna in half, as shown in Fig.5.6. Such antennas produce an omnidirectional radiation pattern in the horizontal plane, and radiate vertically polarised signals. Practical quarter-wave antennas can be easily produced for VHF and UHF applications, but their height can become prohibitive at frequencies below 30MHz. To produce a reasonably flat radiation pattern, it is essential to incorporate an effective ground plane. At HF, the ground plane can be the Earth itself. To minimise Earth resistance and increase the efficiency of the antenna, it is often necessary to incorporate some buried Earth 22 radial conductors emanating from the grounded base of the antenna. At VHF, quarter-wave radial elements can instead be mounted at the feed point. These can be either straight or drooping, as shown in /4 Fig.5.7. The sloping arrangement in Fig.5.7(b) produces a slightly flatter radiation pattern. A typical quarterwave vertical antenna with a sloping ground plane is shown in Fig.5.8. This antenna is ideal for aircraft reception in the VHF band. Another popular alternative is shown in Fig.5.7(c). This ⅝th wave vertical offers some gain over a basic quarter-wave antenna and behaves electrically as a three-quarter-wave antenna with the incorporation of an inductor in the radiating element. (a) Vertical dipole Voltage Voltage Current Current /4 Ground Ground reflection Ground reflection Antenna gain (b) Vertical monopole Since different antenna types pro(b) Vertical monopole duce different field strength values Fig.5.6: vertical dipole and vertical for the same applied RF power level, monopole antennas. we attribute a power gain to them. To be meaningful, this power gain a quoted gain of 10dBd is equivalent is specified in relation to a refer- to 12.15dBi. Furthermore, since ence antenna, specified in decibels 10dB is a power ratio of 10:1, we (dB). Reference antennas are usually can conclude that you would have either the isotropic radiator that we to deliver ten times more power to met previously, or a standard half- a half-wave dipole antenna to mainwave dipole. tain the same field strength at a given Since the former type exists point as this example antenna. only in theory, the latter is usually It should come as no surprise quoted. When quoting antenna gain, that an antenna located on the top subscripts i (isotropic) and d (dipole) of a tall building will usually perdistinguish the two types. Due to form significantly better than one its directivity (see Fig.5.1), the half- located at ground level. To achieve wave dipole provides a gain of about the same signal level, a higher gain 2.15dB when compared with that antenna will be required if it must of the fundamental isotropic refer- be mounted at a relatively low elence. We can thus infer that 0dBd evation. Note that ‘height gain’ only = 2.15dBi. applies to an in-situ antenna and not As an example, an antenna having to a particular antenna type. Practical Electronics | March | 2026 Grou Radiating element Radiating element Radiating element λ/4 λ/4 Radiating element Radiating element λ/4 λ/4 λ/4 λ/4 λ/4 λ/4 λ/4 λ/4 Radials (4 off) λ/4 Radials (4 off) λ/4 50 Ω coaxial feeder Radials (4 off) Radials (4 off) 50 Ω coaxial feeder 50 Ω coaxial feeder 50 Ω coaxial feeder Radials (4 off) Radials (4 off) 50 Ω coaxial feeder 50 Ω coaxial feeder (b) Quarter wave vertical with drooping ground plane Fig.5.7: basic ground plane (a) Quarter wave vertical Radiating element 5λ/8with ground plane for (a) Quarter wave vertical witharrangements ground plane VHF monopole antennas. Multi-element antennas (b) Quarter wave vertical with drooping ground plane Driven element Driven element Driven element (a) Quarter wave vertical with ground plane 90° Director Director Director Reflector Reflector Reflector 180° 180° 0° 0° 180° 90° 90° Mirror Mirror Mirror Director Director Director Invented by Japa(b) Quarter wave vertical with drooping ground plane nese scientists Yagi and Uda, the Yagi Radiating element (a) beam Antenna configuration 5λ/8 array has re(a) Antenna configuration Loading coil mained extremely (a) Antenna configuration popular for use in applications such Loading coil as terrestrial TV, FM radio and long-range Wi-Fi. (a) Antenna configuration λ/4 To explain in sim(a) Antenna configuration Converging lens ple terms how the Converging lens Yagi antenna works, (a) Antenna lens configuration we shall use the Converging λ/4 Radials (4 off) analogy shown in Fig.5.9, where an 50 Ω coaxial feeder filament (b) ordinary Light analogy (b) Light analogy lamp radiates elecRadials (4 off) Converging lens tromagnetic energy (b) Light analogy Converging (c) 5/8 wave vertical with drooping ground plane in the form of vis50 Ω coaxial feeder ible light. Just like an Light source Converging len Light source antenna, the filament lamp converts electrical energy (c) 5/8 wave vertical with drooping ground plane Light source (b) Light analogy into electromagnetic ener(b) Light analogy gy. The main difference is Fig.5.8: this that we can see the energy omnidirectional quarter(b) Light analogy wave ground-plane that it produces! antenna has a gain of Ligh To concentrate the light 2.5dBi and is ideal for radiated from the filaaircraft reception at ment lamp (which would (c) Directional pattern 125MHz. otherwise radiate inpattern all Lig (c) Directional directions), we can place a (c) Directional pattern reflective mirror surface behind it. Here, the radiation is reflected while undergoing a 180° phase change, reinforcing the light on one (c) Directional pattern side of the filament lamp. (c) Directional pattern To achieve the same effect in our antenna system, we (c) Directional pattern need to place a conducting element about one quarter Fig.5.9: how a Yagi antenna works of a wavelength from the diby analogy with focusing the output pole element. This element of a light bulb (light is also a form of is referred to as a reflector, electromagnetic radiation). 0° 0° 270° 0° 270° 270° 0° und Radiating element Practical Electronics | March | 2026 23 0° 0° 0° 0° 0° (a)(a) Dipole Dipole (a) (a) Dipole and (a) Dipole and reflector Dipole and reflector and reflector and reflector reflector Driven Driven element element Driven Driven element element Driven element 270° 270° Typical Typical gain: Typical gain: Typical 3dBd Typical gain: 3dBd gain: 3dBd gain: 3dBd 3dBd Typical Typical beamwidth: Typical beamwidth: Typical Typical beamwidth: beamwidth: 90°beamwidth: 90° 90° 90°90° 270° 270°270° 90° 90° Reflector Reflector Reflector Reflector Reflector (b)(b) Three-element Three-element (b)(b) Three-element (b) Three-element Three-element Yagi YagiYagi Yagi Yagi Typical Typical gain: Typical gain: Typical 4.5dBd Typical gain: 4.5dBd gain: 4.5dBd gain: 4.5dBd 4.5dBd Typical Typical beamwidth: Typical beamwidth: Typical Typical beamwidth: beamwidth: 60°beamwidth: 60° 60° 60°60° 180° 180° 180° 180°180° 0° 0° 0° 0° 0° Director Director Director 1 Director 1 Director 1 1 1 270° 270° 270° 270°270° 90° 90° Driven Driven element Driven element Driven Driven element element element Reflector Reflector Reflector Reflector Reflector Director Director Director 2 Director 2 Director 2 2 2 180° 180° 180° 180°180° 0° 0° 0° 0° 0° (c) (c) Four-element Four-element (c) (c) Four-element (c) Four-element Four-element Yagi YagiYagi Yagi Yagi Director Director Director 1 Director 1 Director 1 1 1 Typical Typical gain: Typical gain: Typical 6dBd Typical gain: 6dBd gain: 6dBd gain: 6dBd 6dBd Typical Typical beamwidth: Typical beamwidth: Typical Typical beamwidth: beamwidth: 45°beamwidth: 45° 45° 45°45° 270° 270° 270° 270°270° 90° 90° Driven Driven element Driven element Driven Driven element element element Reflector Reflector Reflector Reflector Reflector 180° 180° 180° 180°180° Director Director Director 3 Director 3 Director 3 3 3 0° 0° 0° 0° 0° Director Director Director 2 Director 2 Director 2 2 2 (d)(d) Five-element Five-element (d)(d) Five-element (d) Five-element Five-element Yagi YagiYagi Yagi Yagi Typical Typical gain: Typical gain: Typical 7dB Typical gain: 7dBgain: 7dB gain: 7dB7dB Typical Typical beamwidth: Typical beamwidth: Typical Typical beamwidth: beamwidth: 30°beamwidth: 30° 30° 30°30° 270° 270° 24 90° 90° Director Director Director 1 Director 1 Director 1 1 1 Driven Driven element Driven element Driven Driven element element element Fig.5.10: a comparison of Yagi antennas with two, three, four and five elements. 270° 270°270° Reflector Reflector Reflector Reflector Reflector 180° 180° 180° 180°180° and it is parasitic (ie, not actually connected to the feeder). The reflector needs to be made slightly longer than the driven dipole element. The resulting direction90° 90° 90° al pattern now has only one major lobe. To further concentrate the light energy into a narrow beam, we can add a lens to the optical system. To ensure that the light emerging from the optical system is bent towards the normal line, the filament lamp must be positioned at the focal point of the lens. To achieve the same 90° 90° 90° effect in our antenna system, we need to place a conducting element on the other side of the dipole and about one quarter of a wavelength from it. Once again, this element is parasitic but, in this case, it needs to be cut slightly shorter than the driven dipole element. This element is called a director. The resulting directional pattern will now have a narrower major 90° 90° 90° lobe as the energy becomes further concentrated at right angles to the dipole elements. To improve the directional characteristics of our optical system still further, we can simply add more lenses, each time bending the light beam further towards the normal axis. The result is a parallel beam of phase-coherent light. In the same way, we can add further directors to our antenna system so that 90° 90° the 90° energy is concentrated into a narrow parallel beam. Fig.5.10 shows how the gain is increased and beam width reduced for Yagi antennas with two, three, four and five elements. As a rule of thumb, an increase in gain of 3dB will result each time the number of elements is Practical Electronics | March | 2026 Fig.5.11: the twin monopole quarter-wave VHF antennas on a Piper Saratoga 2 for navigation and VHF comms. doubled. Thus, a two-element antenna will offer a gain of about 3dBd, a four-element array will produce 6dBd, an eight-element Yagi will realise 9dBd etc. When more elements are added, additional side lobes begin to appear (see Fig.5.10). Front-to-back ratio The front-to-back ratio is defined as the ratio (expressed in dB) between the radiation from an antenna in the wanted direction to that in the opposite direction. Because the two main lobes are equal in size, a horizontal half-wave dipole antenna (Fig.5.4) has a 0dB front-to-back ratio. The five-element Yagi array shown in Fig.5.10(d) has a much larger front-to-back ratio of around 10dB. The larger the front-to-back ratio, the better an antenna is at rejecting signals and interference arriving from directions other than that of the wanted signal source. Other antenna types Many other types of antenna are in common use. Here are just a few of those you might encounter. Helical antennas are well-suited for use in portable and handheld VHF and UHF equipment. They are inexpensive, robust and reasonably small. Gains of around -1.5dBd are common. Ferrite antennas are commonly used in portable domestic MW and LW radio receivers. They comprise one or more inductive windings on a high-permeability ferrite rod or slab. The inductive winding is brought into resonance at the signal frequency by a parallel-connected tuning capacitor. Such an arrangement has directional properties – the direction Practical Electronics | March | 2026 Fig.5.12: the author’s home-built magnetic loop antenna. Used with its companion unit, it provides continuous HF coverage over 10-30MHz. of maximum sensitivity is at right angles to the axis of the ferrite rod. Printed antennas are fabricated as part of a larger printed circuit board, avoiding the need for off-board connectors and external antennas. Printed antennas are restricted to low-power applications at frequencies above 1GHz. They are found in IoT and Wi-Fi devices, mobile phones, plus Bluetooth equipment. Loop antennas (sometimes referred to as ‘magnetic loops’) are useful at frequencies below 30MHz. Their inherently low impedance necessitates the use of a matching and tuning unit. The gain and directivity of a properly matched loop can often approach that of a full-size half-wave dipole antenna. Frame antennas were commonly used in domestic receivers before the advent of the ferrite rod. Instead of an inductive winding on a ferrite rod, the coil was wound on a large (invariably rectangular) former running round the inside of the case of the receiver. As with the ferrite rod aerial, the inductive winding formed part of a tuned circuit brought to resonance at the signal frequency. Again, the aerial has directional properties. Foil, plate & telescopic antennas are used in domestic portable VHF and other receivers and, while this type of antenna may be adequate for local station reception in strong signal areas, its performance cannot rival that of an external half-wave dipole or small Yagi. The directional characteristics of such aerials are hard to predict. Corner reflectors are an alternative to the Yagi antenna that consist of two perpendicular conductive reflecting surfaces (which may be solid or perforated to reduce wind resistance). The reflecting surfaces are mounted behind a driven element (usually a half-wave dipole). Corner reflectors provide gains and beamwidths of around 10dBd and 40°, respectively. Parabolic reflectors meet the need for very high gain coupled with a directional response at UHF and microwave frequencies. A parabolic reflector is used in conjunction with a radiating element positioned at the feed-point of the reflecting surface. To provide high gain, the diameter of a parabolic reflecting surface must be large in comparison with the wavelength of the signal. Gains of up to 46dBi and beam widths as low as 5° are not unusual. Log-periodic arrays are broadband directional antennas comprising a series of elements that gradually vary in length and spacing. The elements are arranged along the supporting boom in such a way that the electrical length and spacing between elements varies logarithmically, allowing the antenna to maintain consistent performance over a wide range of frequencies. Typical applications are wideband reception and spectrum monitoring. Horns, like parabolic reflectors, are commonly used at microwave frequencies. Horn antennas can be used alone or as a means of illuminating a parabolic (or other) reflecting surface. They are ideal for use with waveguide feeds; the transition from the waveguide to the free space aperture is accomplished over several wavelengths, the waveguide being gradually flared out in both planes. Figs.5.11 to 5.14 show various antennas used in different RF applications. 25 Fig.5.13: the compact printed antenna on a 2.4GHz ESP8266 Wi-Fi module has an indoor range up to about 15m. Antenna impedance and losses Because voltage and current appear in an antenna (albeit in tiny quantities in the case of most receiving antennas), they will exhibit impedance. It’s worth remembering that impedance is the combined effect of resistance, R, and reactance, X (both of which are measured in ohms [Ω]). R remains constant while X varies with frequency. The impedance of a half-wave dipole at its design frequency is usually between 70Ω and 75Ω. At this frequency, the antenna will appear purely resistive (ie, its reactive component is zero). Fig.5.15 shows the three series-connected components that together make up the impedance of an antenna: • the DC loss resistance, RDC • the radiation resistance, RR • the reactance, X (this may be inductive or capacitive) When an antenna is operated at a frequency that lies in the centre of its passband, the off-tune reactance will be zero. We are then left with just two elements: the loss resistance and the antenna’s radiation resistance. The important point to note from this is that for minimal wasted power, the Source, E Radiation resistance, RR Loss resistance, RDC Off-tune reactance, X Fig.5.15: an antenna-equivalent circuit. 26 Fig.5.14: this large horn-fed parabolic reflector antenna supports a microwave telecommunications link between remote communities in southern Greenland. loss resistance must be very much less than the radiation resistance. looking into an infinite length of the feeder at its working frequency. Fig.5.16 illustrates this point. Feeders and cables In a feeder considered loss-free, The purpose of a feeder line is to this impedance, Z0, is determined by deliver maximum power from the the inductance, L, and capacitance, transmitter to the antenna. Ideally, a C, present in the feeder and given feeder would have no losses (no power by Z0 = √L÷CΩ. would be wasted in it), and it would The values of L and C are referred Z0 Load, Zthe 0 present a perfect match between to as the ‘primary constants’ of the Z0 a feeder. In this respect, L is the loop Load, of impedance of theZ0output stage transmitter and the impedance of the inductance per unit length, while antenna to which it is connected. C is the shunt capacitance per unit The impedance of a feeder (called length, as shown in Fig.5.17. In pracZ0 load you Load, 0 Z0 (a) Looking into the will Zsee its ‘characteristic impedance’) is tice, there will be a small amount Z0 load Zsee Load, 0 Z0 of loss resistance in the feeder, (a)impedance Looking intothat the you willseen the would be Z0 load you Load, 0 Z0 (a) Looking into the will Zsee Z Z Load, 0 0 Z (a) Looking into the load you will see 0 Z0 Z0 load you will see Z (a) Looking into the Fig.5.16: the impedances seen ‘looking’ into a transmission line. 0 (a) Looking into the load you will see Z0 Z0 infinite length of feeder you will see Z0 (b) Looking into an Z0 infinite length of feeder you will see Z0 (b) Looking into an Z0 infinite length of feeder you will see Z0 (b) Looking into an Z0 infinite length of feeder you will see Z (b) Looking into an 0 Z0 Z0 infinite length of feeder you will see Z (b) Looking into an 0 Load, Z0 Load, Z0 (b) Looking into an infinite length of feeder you will see Z0 0 (c) You will see Z0Zlooking into any length of feeder terminated with Z0Load, Z0 0 (c) You will see Z0Zlooking into any length of feeder terminated with Z0Load, Z0 Practical Electronics | March | 2026 0 (c) You will see Z0Zlooking into any length of feeder terminated with Z0Load, Z0 L’ L’ L’ L’ L’ L’ L’ L’ L’ L’ L’ L’ L L Short-circuit at the far end (a) Loop inductance Short-circuit at the far end (a) Loop inductance C’ C’ C’ C C’ C’ C’ C Open-circuit at the far end d D Fig.5.18: coaxial cable construction. (as well as many HF) applications. Coaxial cables have a centre conductor (either solid or stranded wire) (b) Loop capacitance but this can usually be ignored. surrounded by an outer conductor The characteristic impedance of a 180  109 180  109 3 that completely shields the inner 103 421800 42 Z0   conductor, Z 0  12  1.81210 1.81800 cable can be easily calculated knowing as shown in Fig.5.18. its primary constants. For example, a 100 10 100 10 The two conductors are concentric  10   10  cable with a loop inductance of 20nH separated by an insulating dielecZ  138log Z 010138log Z 0  138log 138 0.7isusually 5   138 97that 97 air or some form of 50.7  and 10    10   Z 010138log and a loop capacitance of 100pF0 can Coaxial cable tric 2 2     be determined as follows (20nH = 20 Fully screened coaxial cables are polythene. The characteristic imped× 10-9H and 100pF = 100 × 10-12F): used for feeders in VHF and UHF ance, Z0, of such a cable is given by Z0 = 138log10(D ÷ d)Ω. Table 5.1: commonly-used RF coaxial cables Here, D is the inside diameter of Characteristic Loss (db/100m) Velocity the outside conductor, and d is the Type Diameter Typical application Impedance <at> 100MHz Factor outside diameter of the inside conductor, both in millimetres. High-performance ~2.2dB 0.88 12.7mm LDF4-50 50Ω Thus, the characteristic impedance uses up to 2GHz of a coaxial cable can be calculated if General purpose LMR-400 50Ω ~3.9dB 0.85 10.3mm you know its dimensions. The charup to 2GHz acteristic impedance of a cable with RG-6 75Ω ~5.6dB 0.82 6.9mm Cable & satellite TV an insideconductor diameter of 2mm 9 9 180 109and 180an 180 10 10 3 3 3 outside conductor diameter Z  Z  Z   1.8  10   1.8 1800   10 1.8   42 10 1800  1800  42of  42 0 0 12 0 General purpose 12 12 10mm is calculated as: 100  10 100  100 10  10 RG-58 50Ω ~11dB 0.66 5.0mm up to 500MHz  10   10  10  Z  138logZ  138log Z10  0.7 97 0.7 0.7 97 Z 138log Z  138log 5 138  0 138 5 10 138 0  10 Z10 0 5138log 10  138log RG-59 75Ω ~7.4dB 0.66 6.2mm Video and0 CCTV 100  2 0  2  2  (b) Loop capacitance Open-circuit at the far end Fig.5.17: the primary constants of a feeder. RG-174 50Ω RG-213 50Ω ~22dB ~6.7dB 0.66 Forward wave Forward wave Source 0.66 Source 2.8mm Jumper leads, short cable runs 10.3mm High-power HF/ VHF transmission Load Load Reflected wave LineLine voltage, voltage, V V Reflected wave 0 0 Practical Electronics | March | 2026 Standing wave Standing wave Forward wave Forward wave Reflected wave Reflected wave Fig.5.19: a standing wave produced by a mismatch between a transmission line and the load. Velocity factor The velocity of a wave travelling in a cable or transmission line will be less than that of the wave in free space. The ratio of the two (actual velocity and velocity in free space) is known as the velocity factor. Depending on the cable construction and dielectric material, the velocity factor varies from about 0.6 to 0.95. This reduction in velocity has an impact on the wavelength in the cable. Table 5.1 provides details of commonly used RF coaxial cables. Voltage standing wave ratio (VSWR) Where the impedance of a feeder is perfectly matched to the load, all the energy delivered by the source will be transferred to the load. In this ideal state, the voltage will be the same at all points along the feeder. If the match is less than perfect, a proportion of the energy will be reflected, as shown in Fig.5.19. 27 Forward wave Source (ZS) Line voltage, V Source Source (ZS) Line voltage, V (ZS) Line voltage, V ForwardReflected wave Forward wave wave Reflected wave Reflected wave Feeder (Z0) Load (ZL) Load Load (ZL) (ZL) Line Linevoltage, voltage, Line voltage, VV V Feeder (Z0) Feeder (Z0) Standing wave Standing wave Standing wave Vmax Vmin Vmax Vmax Vmin Vmin Distance Fig.5.20: a standing wave and the resulting voltage along the length of the feeder. In this non-ideal state, the reflected wave (shown in red) will interact with the forward wave (shown in green) to produce a standing wave along the line. The line voltage will then no longer be constant at all points, but will vary with maximum and minimum values determined by the degree of mismatch. While both the forward and reflected waves are moving, the standing wave remains. The current distribution along the feeder will have a similar pattern, but the voltage maxima will coincide with the current minima, and vice versa. Fig.5.20 shows a source (transmitter) connected to a load (antenna) in an unmatched system, where measurements of the line voltage reveal the presence of the standing wave in the feeder. To understand what’s happening, it can be useful to contrast the ideal and worst-case conditions with those shown in Fig.5.20. If the system is perfectly matched to the load, only the forward wave will be present, and the feeder voltage will be constant at all points. In this condition, V = Vmax = Vmin. Distance Distance In the worst-case condition, when the line is either short-circuited or open-circuited at the load, all the energy will be reflected, and the forward and reflected waves will be identical. In this condition, the largest possible standing wave will be present in the feeder where Vmin = 0 and Vmax = 2V. The degree of mismatch is expressed by the ratio of maximum to minimum voltage along the feeder. This important quantity ratio is referred to as the voltage standing wave ratio (VSWR). Thus, VSWR = Vmax ÷ Vmin. Values for VSWR can range from 1 (perfectly matched) to infinity (worst-case). In practice, values between 1 and 1.5 are usually considered acceptable, while values above 2 usually merit investigation and indicate a need for improvement. Table 5.2 will give you some idea of the percentage of power that’s reflected for different values of VSWR. The mismatch indicated previously in Fig.5.19 corresponds to a VSWR of about 3. Baluns A balanced-to-unbalanced transformer (or ‘balun’) can be used to match a balanced antenna (such as the half-wave dipole that we met earlier) to an unbalanced coaxial feeder. These handy passive devices can be easily constructed using ferrite cores or purchased ready-made. They are usually fitted close to the antenna feed point, but they can also be integrated into the antenna. This month’s Hands-On project uses a simple balun constructed using a small toroidal ferrite core. Fig.5.21(a) shows a dipole antenna fed using a ribbon cable. Since both the feeder and the dipole are balanced, no balun is needed. In Fig.5.21(b), a dipole antenna is fed with a coaxial cable. Although this may be expedient, the mismatch between the balanced antenna and the unbalanced feeder can cause current to flow in the shield of the coaxial cable, resulting in unwanted radiation from the cable as well as the antenna. This can also distort the antenna’s radiation pattern and on receive may introduce unwanted noise and interference from nearby sources. It may also introduce unwanted noise and impact on overall performance. Fig.5.21(c) shows a balun correctly connected at the feed point of a dipole. Hands-On: Dipole reference antenna This month’s Hands-On project is a dipole antenna suitable for use across much of the VHF spectrum. It serves as a valuable reference for testing and measurement and can also be used for broadcast listening, Fig.5.21: a balun can assist when a balanced dipole antenna is used with an unbalanced coaxial feeder. Table 5.2: VSWR vs reflected power Reflected Reflected VSWR VSWR Ribbon Coaxial feeder Coaxial Coaxial Coaxial feeder feeder feeder Coaxial feeder Ribbon Ribbon feeder feeder feeder Ribbon feeder Ribbon feeder Coaxial feeder Coaxial Coaxial Coaxial feeder feeder feeder Coaxial feeder Coaxi power Ribbon feeder power (unbalanced) (unbalanced) (unbalanced) (unbalanced) (unbalanced) (balanced) (balanced) (balanced) (balanced) (balanced) (balanced) (unbalanced) (unbalanced) (unbalanced) (unbalanced)(unbalanced) (unb 0% 2.2 14.6% 1.0 1.1 0.2% 2.5 18.4% Balun Balun Balun Balun Balun 1.2 0.8% 2.7 21.1% 1.3 1.7% 3 25.0% 1.4 2.8% 4 36.0% 1.5 4.0% 5 44.4% 1.6 5.3% 6 51.0% 1.7 6.7% 7 56.3% 1.8 8.2% 8 60.5% 1.9 9.6% 9 64.0% 2.0 11.1% 10 66.9% 28 Practical Electronics | March | 2026 Fig.5.22: the internal layout of the dipole reference antenna (underside view of the lid). aircraft, marine and amateur radio in the 4m, 2m, and 1.5m bands. The antenna comprises two telescopic elements mounted on the opposite faces of a small ABS enclosure. The symmetrical internal arrangement is shown in Fig.5.22. To permit connection of the coaxial feeder, a female chassis-mounting BNC connector is attached to the lid of the enclosure, and the two telescopic antennas are secured using two M3-tapped hexagonal pillars. The balun is constructed by winding two complete turns of solid hook-up wire over the ferrite toroidal core, as shown in Fig.5.23. Start by cutting two 9cm lengths of differently coloured hookup wire before winding them together in a bifilar arrangement (wound together side-by-side) around the core; it’s important to keep the windings symmetrical and closely interleaved. The wires can then be trimmed to length ready for soldering into the enclosure. The ferrite core should be a good quality, low-loss ferrite material suitable for use at VHF. The Amidon Fair-Rite FT50-43 is ideal for this application; we used a 4.9mmthick core with inside and outside diameters of 7mm and 12.7mm, respectively. These are available from several internet suppliers. Once again, to ensure balance, it’s important to keep the layout symmetrical and wiring lengths identical. If you don’t have a suitable toroidal ferrite core, the antenna can be built without the balun following the layout shown in Fig.5.24 overleaf. However, if you use this arrangement, the results will be less predictable, and you may find that the antenna’s directional properties will be affected by the proximity of the feeder cable. The reference dipole antenna should be connected to the receiver or other equipment using a short length of good-quality coaxial cable fitted with BNC male connectors. A 2m length of RG-58 coaxial cable should be adequate for most applications, but longer cable lengths can also be used where necessary. Fig.5.25 (overleaf) shows the prototype antenna mounted on a camera tripod during testing in the author’s garden. Testing The dipole antenna can be easily tested using a VHF receiver (the SDR described last month is ideal). Set up the antenna in a clear space about 1.52m above the floor and well away from other electronic devices and mains wiring. The antenna should ideally be mounted on a tripod, but a timber stool or table is a viable alternative. Connect the coaxial feeder from the antenna to the receiver, ensuring that the feeder is led away from the Fig.5.23: the arrangement of the toroidal balun. Practical Electronics | March | 2026 29 Fig.5.24: the alternative construction without the balun; this is not recommended but it will work, albeit with reduced performance. antenna at 90° before being dropped vertically to the floor. You should also avoid running the feeder close to the two telescopic elements, as this may impact the antenna’s directional characteristics. With the aid of a tape measure, adjust the telescopic elements so they have an overall length of 1.3m. Tune the receiver to a local broadcast FM signal, rotate the antenna to obtain the strongest signal and then rotate the antenna through a full angle of 360°, observing the effect on the received signal strength. You should find two directions of maximum response and two nulls at right angles to them (see Fig.5.27). Fig.5.26: VSWR variation with frequency for the reference dipole antenna at (a) 70MHz and (b) 144MHz. (a) 70MHz (VSWRmin. = 1.2 at 71MHz) (a) 70MHz (VSWRmin. = 1.2 at 71MHz) Fig.5.25: testing the Hands-On dipole antenna in my garden. (b) 144MHz (VSWRmin. = 1.05 at 144.3MHz) 30 Practical Electronics | March | 2026 0° The prototype antenna performed well over a frequency range extending from 66MHz to 232MHz (see Table 5.3). To extend the frequency coverage above 232MHz, the antenna can be configured as a 1.5-wave dipole where required. Note how the VSWR increases above 300MHz. The reference dipole antenna can be used for low-power (typically less than 10W) operation in the VHF amateur bands. Table 5.4 gives the overall antenna lengths required, but some further adjustment may be required to obtain the lowest VSWR at your desired operating frequency. The variation of antenna VSWR with frequency for the UK 4m and 2m amateur bands is shown in Fig.5.26. This indicates minimum VSWR values of less than 1.2 on both bands, indicating an excellent match. Finally, Fig.5.27 shows the antenna’s polar response measured at 125MHz. The two nulls are down by approximately 14dB on the antenna’s maximum response. 270° 90° Coming up! Next month, Teach-In will cover key RF testing and measurement. Our Hands-On project will be a probe for in-circuit RF voltage measurements viewable on a standard PE multimeter. Join us then! 180° Fig.5.27: a polar response plot of the reference dipole at 125MHz. Table 5.3: overall antenna length, operating frequency and VSWR Half-wave dipole 1.5-wave dipole Overall Telescope length sections Frequency VSWR Frequency VSWR Table 5.4: antenna length for VHF hams Amateur Overall Typical Frequency band length VSWR 1.5m 223MHz 51cm 1.5 2m 145MHz 89cm 1.1 4m 70.2MHz 202cm 1.2 48cm 77cm 104cm 132cm 158cm 186cm 212cm 1 2 3 4 5 6 7 232MHz 165MHz 124MHz 100MHz 85MHz 76MHz 66MHz 1.6 1.3 1.1 1.1 1.1 1.1 1.2 – – 370MHz 300MHz 255MHz 225MHz 197MHz – – 1.3 1.2 1.1 1.1 1.1 Parts List – VHF dipole reference antenna 1 ABS or polycarbonate IP67 sealed enclosure, 115 × 65 × 40mm 2 7-segment 130cm+ telescopic antennas with screw terminals [eg, https://www.aliexpress.com/item/1005010403940280.html] 1 BNC panel-mount socket 1 Amidon Fair-Rite FT50-43 toroidal core, 12.7 × 7 × 4.9mm 2 10cm lengths of medium-duty hookup wire (red & blue) 2 3mm solder lugs 2 M3 × 9mm tapped spacers 4 M3 × 6mm panhead machine screws 1 2m-long RG-58 cable terminated with BNC plugs 1591 ABS flame-retardant enclosures Learn more: hammondmfg.com/1591 uksales<at>hammfg.com • 01256 812812 Practical Electronics | March | 2026 31