Antenna Classification

A rhombic antenna is a non-resonant (travelling-wave) HF wire antenna made of four long wires arranged as a horizontal rhombus (diamond), fed at one acute corner and terminated in a resistor at the opposite corner. It gives a unidirectional, high-gain beam for long-distance sky-wave links.

Construction

                  pole
                 /    \
         leg 1  /      \  leg 3
               /   φ    \
 feeder ==> A <    ->    > B --[ R ≈ 600-800 Ω ]--
(balanced)     \   main /        termination
         leg 2  \ beam /  leg 4
                 \    /
                  pole
  each leg length l = 2λ to 8λ, height H above ground

• Four straight wires, each several wavelengths long, supported on four poles at height H (≈ 0.25λ to 1λ).
• φ = tilt angle (half of the acute angle at the feed corner).
• Fed at corner A by a balanced 600 Ω open-wire line.
• Corner B is terminated in a non-inductive resistor equal to the characteristic impedance (≈ 600–800 Ω).

Working principle

1. Because the far end is matched, the current travels from A to B as a travelling wave; there is no reflected wave, so no standing waves.
2. A long travelling-wave wire radiates a conical main lobe at an angle θₘ to the wire, given by cosθₘ ≈ 1 − 0.371λ/l.
3. The tilt angle φ is chosen so that one main lobe of each of the four legs points in the same forward direction (along A → B). These four lobes add in phase.
4. Lobes pointing in other directions largely cancel; the backward wave is absorbed by the termination, so the pattern is unidirectional.
5. The ground acts as a reflector; height H sets the elevation angle Δ of the beam.

Alignment design for maximum field at elevation Δ:

H = λ / (4 sinΔ)
φ = 90° − Δ
l = λ / (2 sin²Δ)

Characteristics

Advantages and disadvantages

• Simple, cheap, wide bandwidth, high gain, easy matching to an open-wire line.
• Needs large land area; much power wasted in the termination; significant side lobes; beam direction fixed.

Applications: long-distance HF point-to-point sky-wave communication and broadcast reception.

A Marconi antenna is a vertical quarter-wave (λ/4) monopole whose lower end is connected to ground through the transmitter. The conducting earth produces an image of the antenna, so a λ/4 monopole behaves like a λ/2 dipole (Hertz antenna) in the upper half-space.

      ^  I = 0 (top)
      |  current
 λ/4  |  distribution        Pattern (vertical plane)
      |  max at base               _ _
      |                         .'  |  '.
  ~ TX|________ ground       __/____|____\__ ground
 ////////////////////////     max along ground,
   image (λ/4) below          null overhead

Major characteristics

1. Length: λ/4 physical height; the image supplies the other λ/4.
2. Current distribution: maximum at the base (feed), zero at the top; voltage maximum at the top.
3. Radiation pattern: same as the upper half of a half-wave dipole; omnidirectional in the horizontal plane, maximum along the ground, null overhead.
4. Polarization: vertical, ideal for ground-wave propagation at LF/MF.
5. Input (radiation) resistance: ≈ 36.5 Ω, half of a dipole's 73 Ω, because it radiates into a half space only.
6. Directivity: 3.28 (5.15 dBi), double that of a half-wave dipole, since power goes into half space.
7. Ground system: needs good earth; buried radial wires, or a counterpoise (wire mesh above ground) where soil is poor. Ground loss reduces efficiency.
8. Height reduction: at MF, λ/4 is tall (e.g. 75 m at 1 MHz), so top loading (capacitance hat, T or inverted-L) or base loading coil is used.

Marconi vs Hertz

Applications: AM (MF) broadcasting towers, car whip antennas, mobile and handheld radios.

A V-antenna is a travelling/standing-wave wire antenna made of two long straight wires (legs) arranged in the shape of a "V", fed at the apex by a balanced line. It is a simple directive HF antenna for point-to-point links.

Construction

 Structure (top view)           Non-resonant type
                                    R/2
         leg 1 (l = several λ) ____/\/\_
        /                         |
 feeder<  apex angle 2θₘ  ===> beam  (bisector)
        \                         |
         leg 2 ________________/\/\_
                                    R/2

• Two straight wires of length l (2λ to 8λ), horizontal, on poles above ground.
• Apex angle = 2θₘ, where θₘ is the angle of the main lobe of one long wire: cosθₘ ≈ 1 − 0.371λ/l.
• Fed at the apex by a 600 Ω open-wire balanced line, 180° out of phase.
• Far ends left open (resonant V) or terminated with resistors (non-resonant V).

Working principle

1. Each long wire radiates a conical main lobe at angle θₘ to the wire.
2. Since the legs are fed in antiphase and are mirror images, choosing the apex angle equal to 2θₘ makes one main lobe of each leg lie along the bisector; there they add in phase.
3. Lobes in other directions are out of phase and partly cancel, giving a directive beam.
4. In the resonant (unterminated) V, the wave reflects from the open ends, forming standing waves; radiation goes both ways along the bisector (bidirectional).
5. In the non-resonant (terminated) V, matched resistors absorb the forward wave, so only a travelling wave exists and the beam is unidirectional.

Radiation pattern

 Resonant V (bidirectional)   Terminated V (unidirectional)
    <===  ◁V▷  ===>              ◁V  ====>
   back lobe = front lobe        weak back lobe

Characteristics

Advantages: simple, cheap, needs only 3 poles, wide band. Disadvantages: large area, side lobes, fixed beam, power loss in terminating resistors. Applications: HF point-to-point communication, amateur radio.

Parasitic elements of a Yagi-Uda array

The Yagi-Uda array has one driven element (fed λ/2 or folded dipole) and two kinds of parasitic elements (not fed; excited by mutual coupling):

1. Reflector – one element, slightly longer than λ/2, placed behind the driven element.
2. Directors – one or more elements, slightly shorter than λ/2, placed in front.

  R      DE     D1     D2     D3
  |      |      |      |      |
  |      |      |      |      |  ====> beam
  |     -o-     |      |      |
  |      |      |      |      |
 longest  fed   shorter ->

Significance

• Reflector: being longer than resonant length, it is inductive; its induced current lags so that its field cancels radiation in the backward direction and reinforces the forward direction. It sets the front-to-back ratio. Usually one reflector is enough; more add little.
• Directors: shorter, so capacitive; their currents lead and give a progressive phase towards the front, guiding the wave like an end-fire array. Each extra director increases gain (about 1 dB per director for the first few) and narrows the beam.
• Parasitic coupling lowers the input impedance of the driven element, so a folded dipole (≈ 300 Ω alone) is often used to restore a convenient impedance.

Yagi-Uda vs log periodic dipole array (LPDA)

A log-periodic antenna is a frequency-independent antenna whose geometry repeats in a logarithmic manner, so its impedance and pattern repeat periodically with the logarithm of frequency. The most common form is the log-periodic dipole array (LPDA).

Construction

         apex angle 2α
   <----- direction of beam ------
      Ln ...  L3    L2     L1 (longest)
       |  |   |     |      |
       |  |   |     |      |
  feed>X--X---X-----X------X     ← crossed (transposed)
       |  |   |     |      |       feed line
       |  |   |     |      |
       <-dn-> R3    R2     R1   distances from apex

• A series of dipoles of different lengths placed side by side; lengths, spacings and distances from the apex all scale by a constant ratio τ (< 1):

τ = Lₙ₊₁/Lₙ = Rₙ₊₁/Rₙ = dₙ₊₁/dₙ

• Ends of the dipoles lie on two straight lines meeting at the apex with half-angle α.
• All elements are fed by a transposed (crisscrossed) two-wire line, energised at the short (front) end; adjacent elements are 180° apart in feed.

Working principle

1. At any frequency, only the few elements near λ/2 long (the active region) radiate strongly.
2. Elements just behind the active region (longer, inductive) act as reflectors; shorter ones in front act as directors, as in a Yagi. Crossed feeding gives the progressive phase for end-fire radiation towards the apex (shorter elements).
3. Elements much longer than λ/2 receive little energy because the active region radiates it first; shorter ones are off-resonance and carry little current.
4. As frequency changes, the active region simply moves along the structure. Properties repeat when f changes by τ: f₂/f₁ = 1/τ, i.e. periodic in ln f.
5. Bandwidth limits: lowest frequency when L₁ ≈ λ_max/2, highest when Lₙ ≈ λ_min/2.

Design (Carrel method)

1. Choose directivity D -> optimum τ and σ (Carrel chart)
   σ = dₙ/(2Lₙ)   spacing factor
2. Apex half angle: α = tan⁻¹[(1 - τ)/(4σ)]
3. Active-region bandwidth:
   Bar = 1.1 + 7.7(1 - τ)² cot α
4. Structure bandwidth: Bs = B × Bar, B = f_max/f_min
5. Number of elements: N = 1 + ln(Bs)/ln(1/τ)
6. Longest element: L₁ = λ_max/2;  then Lₙ₊₁ = τLₙ
7. Spacing: d₁ = 2σL₁;  dₙ₊₁ = τdₙ
8. Boom length: L = (λ_max/4)(1 - 1/Bs) cot α

Example: τ = 0.9, σ = 0.16 → α = tan⁻¹(0.1/0.64) ≈ 8.9°.

Characteristics

• Bandwidth up to 10:1 or more; nearly constant gain (≈ 6–10 dBi), pattern and input impedance over band.
• Unidirectional end-fire beam towards the apex; linear polarization in the plane of the elements.
• Lower gain than a Yagi of the same length.

Applications: all-channel VHF/UHF TV reception, HF communication, EMC and spectrum measurements, wideband radar.

A reflector antenna uses a large conducting surface (plane, corner or curved) to reflect and focus the radiation of a small primary feed, producing a highly directive beam. The most important is the parabolic reflector (dish).

Parabolic reflector: principle

A paraboloid has the property that every ray leaving the focus F and reflected by the surface travels the same total distance to the aperture plane (FP + PQ = constant). So a spherical wave from a feed at F becomes a plane wave across the aperture, giving a narrow pencil beam. In reception, a plane wave is focused onto F.

          reflector
           )|
          ) |----------->
         )  |----------->  plane wavefront
  F  o  )   |----------->  (parallel rays)
  feed  )   |----------->
         )  |----------->
          ) |
           )|  aperture diameter D
  f = focal length, f/D ≈ 0.25 to 0.5

Characteristics

Gain:       G = η(πD/λ)²     η ≈ 0.55-0.7
HPBW:       θ ≈ 70 λ/D  degrees
FNBW:       ≈ 140 λ/D  degrees

• Very high gain (30–60 dBi), very narrow beam; used at microwave frequencies (above ~1 GHz).
• Efficiency is reduced by spillover, aperture blocking, non-uniform illumination and surface errors.
• Polarization follows the feed.

Radiation pattern

            main lobe (pencil)
   side  ___ /‾‾‾‾\ ___  side
   lobes     |    |       lobes
 ---<|dish>--+----+-------> axis
   small back lobe

A narrow main lobe along the axis, low side lobes (−20 to −30 dB with tapered illumination) and a small back lobe from spillover.

Feed systems

1. Dipole with reflector (front feed): a λ/2 dipole at F with a small parabolic/plane reflector behind it to send energy only towards the dish. Simple, for lower microwave.
2. Horn feed (front feed): a waveguide horn at F pointing at the dish; good illumination control; the waveguide run is long and blocks part of the aperture.
3. Offset feed: only part of the paraboloid is used, with the feed outside the beam path; no aperture blocking (DTH dishes).
4. Cassegrain feed: a hyperboloid subreflector near F reflects the wave from a horn located at the dish vertex. Short waveguide, low noise; used in satellite earth stations.
5. Gregorian feed: like Cassegrain but with an ellipsoidal subreflector placed beyond the focus.

 Front feed          Cassegrain
   )                    )
  )  <--[horn]         ) ( <- subreflector
  )   at F             )  
   )                 [horn] at vertex

A helical antenna is a conducting wire wound in the form of a helix (screw), usually fed by a coaxial line against a ground plane. It is the standard antenna for circular polarization at VHF/UHF.

        ____
       /    \   <- turn, circumference C = πD
       \____/
       /    \   spacing S between turns
       \____/   pitch angle α = tan⁻¹(S/C)
       /    \   N turns, axial length L = NS
  =====\____/=====  ground plane (≥ λ/2)
          |
        coax feed

Parameters: diameter D, circumference C = πD, spacing S, pitch angle α, number of turns N.

Modes of operation

• Normal (broadside) mode: helix dimensions ≪ λ (NL ≪ λ). Maximum radiation is normal to the axis, like a short dipole plus a small loop; polarization is elliptical, circular when C = √(2Sλ). Low efficiency, narrow band. Used for small whips in handsets.
• Axial (end-fire) mode: C ≈ λ (0.75λ < C < 1.33λ), S ≈ λ/4, α ≈ 12°–14°. A single main beam along the axis, circularly polarized, wide band.

Axial-mode formulas (Kraus)

HPBW ≈ 52 λ^(3/2) / (C √(NS))  degrees
D    ≈ 15 N C² S / λ³
Zin  ≈ 140 (C/λ)  Ω

Advantages: circular polarization, wide bandwidth (about 1.7:1), moderate gain (10–15 dBi), simple. Applications: satellite and space telemetry, GPS, radio astronomy, feeds for reflectors.

A microstrip (patch or printed) antenna is a thin metallic patch etched on one side of a dielectric substrate whose other side is a ground plane. It is made by printed-circuit techniques.

        patch (L x W)
     _______________
    |_______________|___ feed line
 ///////////////////////////  substrate εr, h
 ===========================  ground plane
  fringing fields at the two radiating edges

Construction and working

• Patch shapes: rectangular, square, circular, triangular. Substrate εr ≈ 2.2–12, height h ≈ 0.003λ–0.05λ.
• The patch behaves as a cavity; for the dominant mode its length is about half a guided wavelength:

L ≈ λ₀ / (2√εr)   (slightly less, due to fringing)

• Radiation comes from the fringing fields at the two open edges, which act like two slots in phase; the beam is broadside (normal to the patch).

Feeding methods: microstrip line (inset), coaxial probe, aperture coupling, proximity coupling.

Advantages: low profile, light, cheap, conformal to curved surfaces, easy to integrate with circuits and to form arrays, linear or circular polarization possible.

Disadvantages: narrow bandwidth (≈ 1–5 %), low efficiency and gain (≈ 6–8 dBi), low power handling, surface-wave losses.

Applications: mobile phones, GPS, Wi-Fi, RFID, aircraft and missile antennas, satellite terminals.

The Cassegrain feed is a dual-reflector method of feeding a parabolic reflector in which the primary feed (horn) is placed at the vertex of the main paraboloid and radiates towards a small hyperboloidal subreflector placed in front, which reflects the energy back onto the main dish.

          main paraboloid
            )
           )      sub-reflector
          )        (hyperboloid)
         )   F'        (
  [horn]=o vertex ---> (  F = focus of paraboloid
  at F'  )   <-------- (    = one focus of hyperbola
          )             (
           )
            )
 horn feed at F' (other focus of hyperbola)

Geometry and working

1. The hyperboloid has two foci. One focus coincides with the focus F of the paraboloid; the horn's phase centre is placed at the other focus F′, near the vertex of the main dish.
2. Waves from the horn diverge as if coming from F′; after reflection from the hyperboloid they appear to come from F.
3. Since they appear to come from the focus of the paraboloid, the main reflector converts them into a plane wave, forming a narrow pencil beam.
4. The system is equivalent to a single paraboloid of much longer focal length: f_eq = M·f, with magnification M = (e + 1)/(e − 1), e = eccentricity of the hyperboloid.

Advantages

• Feed and receiver/transmitter can be placed behind the main dish; very short waveguide, so low loss and low noise temperature.
• Long effective focal length with a compact structure; better control of aperture illumination.
• Feed spillover points to the cold sky instead of the warm ground, lowering noise; useful for satellite earth stations.
• Easier maintenance of the feed and receiver.

Disadvantages

• The subreflector and its supports block part of the aperture, so it suits only large dishes (D > ~50λ).
• More complex, costlier and needs accurate alignment.

Applications: satellite earth stations, radio telescopes, deep-space communication, tracking radars.

A horn antenna is a hollow waveguide whose end is flared out into a larger opening. The flare gives a gradual transition from the waveguide impedance to free-space impedance (≈ 377 Ω), reducing reflection and producing a directive beam. It is the commonest aperture antenna at microwave frequencies.

 waveguide       flare        aperture
  ______      .-'‾‾‾‾‾‾‾‾‾‾|
 |______|===<     flare    |  ---> beam
             '-.__________|
               length L, aperture a x b

Types

• Sectoral horn: flared in one plane only — E-plane sectoral (flare in E direction) or H-plane sectoral.
• Pyramidal horn: flared in both planes; most common, used as gain standard.
• Conical horn: flared circular waveguide, used with circular polarization.

Design points

• If the flare angle is too large, the path from throat to the aperture edge differs from the axial path by δ, giving phase error. Optimum horn: δ ≈ 0.25λ (E-plane) and ≈ 0.4λ (H-plane).
• Gain: G ≈ 4πA_e/λ² ≈ 7.5 A/λ² (aperture efficiency ≈ 0.6).
• HPBW (optimum horn): E-plane ≈ 56λ/a_E deg, H-plane ≈ 67λ/a_H deg.

Advantages: wide bandwidth, simple, moderate gain (10–25 dBi), low VSWR, easy to make. Applications: feed for parabolic reflectors, standard gain antenna for measurement, radar, microwave links.

A 5-element Yagi-Uda antenna has 1 reflector + 1 driven dipole + 3 directors. Design rules used (standard empirical rules):

• Driven element (DE) = 0.48λc (given effective length).
• Reflector ≈ 5 % longer than DE; each director ≈ 5 % shorter than the element before it.
• Spacing between adjacent elements = 0.15λc (given).

Step 1: Wavelength

λc = c / f = (3 × 10⁸) / (100 × 10⁶) = 3 m

Step 2: Driven element

L_DE = 0.48 λc = 0.48 × 3 = 1.44 m

Step 3: Reflector

L_R = 1.05 × L_DE = 1.05 × 1.44 = 1.512 m  (≈ 0.504λ)

Step 4: Directors

L_D1 = 0.95 × 1.44   = 1.368 m  (0.456λ)
L_D2 = 0.95 × 1.368  = 1.300 m  (0.433λ)
L_D3 = 0.95 × 1.2996 = 1.235 m  (0.412λ)

Step 5: Spacing and boom length

S = 0.15 λc = 0.15 × 3 = 0.45 m
Boom (R to D3) = 4 gaps × 0.45 = 1.80 m

Design summary

  R      DE      D1      D2      D3
  |      |       |       |       |
 1.512  1.44   1.368   1.300   1.235 m
  |     -o-      |       |       |    ====> to
  |   feed       |       |       |   transmitter
  |<0.45>|<0.45->|<0.45->|<0.45->|
  <------------ boom 1.80 m ----->

Practical notes: elements are aluminium tubes of diameter about 0.005λ–0.01λ (≈ 1.5–3 cm here), mounted on a metal boom at their centres (voltage nulls). The driven element is usually a folded dipole fed with 300 Ω line or a balun to 75 Ω coax. The array points towards the directors, i.e. D3 faces the FM transmitter.

Answer: λc = 3 m; reflector 1.512 m, driven 1.44 m, directors 1.368 m, 1.300 m, 1.235 m; spacing 0.45 m; boom length 1.80 m.

A Yagi-Uda antenna is an end-fire array of one driven half-wave (usually folded) dipole and several parasitic elements — one reflector behind and one or more directors in front — mounted parallel to each other on a common boom. It gives a moderate-gain unidirectional beam with a single feed point.

Construction

   R      DE      D1     D2     D3
   |      |       |      |      |
   |      |       |      |      |
 --+-----(o)------+------+------+--> boom & beam
   |    feed      |      |      |
   |      |       |      |      |
 ≈0.5λ  0.46-   0.45λ  shorter ->
       0.48λ
   <SR=0.15-0.25λ><SD=0.1-0.35λ>

• Driven element: resonant λ/2 dipole or folded dipole connected to the feeder.
• Reflector: one element ≈ 5 % longer than the driven element (≈ 0.5λ), spaced 0.15–0.25λ behind.
• Directors: elements ≈ 5 % shorter than the preceding one (≈ 0.45λ downwards), spaced 0.1–0.35λ.
• Elements are metal tubes/rods fixed at their centres (voltage zero) to a metal boom, so no insulation is needed.

Working principle

1. RF current in the driven element radiates; this field induces currents in the parasitic elements by mutual coupling, and they re-radiate.
2. The reflector, longer than resonant length, has an inductive impedance; its current lags. With spacing ≈ 0.15–0.25λ, its re-radiated field cancels the driven element's field in the backward direction and adds in the forward direction.
3. Each director, shorter than resonant length, is capacitive; its current leads. The directors form a chain with progressive phase, so the wave is guided forward like an end-fire array.
4. Result: a unidirectional beam along the boom towards the directors. More directors → higher gain and narrower beam (with diminishing returns).
5. Parasitic coupling lowers the driven element's impedance (to ≈ 20–30 Ω for a simple dipole), so a folded dipole (≈ 4 × 73 ≈ 292 Ω alone) is used to give a convenient ≈ 50–75 Ω or 300 Ω input.

 Radiation pattern (top view)
            .--.
  back    .'    '.
   ==o===(R DE D D)======>  main lobe
          '.    .'
            '--'
  small back lobe; front-to-back ≈ 10-20 dB

Design procedure

Design rules (standard empirical rules):

1. λc = c / fc   (fc = centre frequency of band)
2. Driven element  L_DE = 0.46λ to 0.48λ
3. Reflector       L_R  = 1.05 L_DE  (≈ 0.5λ)
4. Directors       L_D1 = 0.95 L_DE,  L_Dk+1 = 0.95 L_Dk
5. Spacing R-DE    S_R  = 0.25λ (0.15-0.25λ)
   Spacing DE-D, D-D   S_D = 0.15λ (0.1-0.35λ)
6. Element diameter d ≈ 0.0025λ to 0.01λ

Example: 5-element Yagi at fc = 200 MHz, L_DE = 0.48λ.

λc   = 3×10⁸ / 200×10⁶ = 1.5 m
L_DE = 0.48 × 1.5      = 0.720 m
L_R  = 1.05 × 0.720    = 0.756 m
L_D1 = 0.95 × 0.720    = 0.684 m
L_D2 = 0.95 × 0.684    = 0.650 m
L_D3 = 0.95 × 0.650    = 0.617 m
S_R  = 0.25 × 1.5      = 0.375 m
S_D  = 0.15 × 1.5      = 0.225 m
Boom = 0.375 + 3(0.225) = 1.05 m

Characteristics

Advantages: light, cheap, simple single feed, good gain and directivity. Disadvantages: narrow bandwidth, gain limited (~ 15–17 dBi), sensitive to element lengths. Applications: TV and FM reception, VHF/UHF point-to-point links, amateur radio, radar.

The EIRP of a transmitting system is the transmitter power minus feeder (waveguide) loss plus antenna gain (all in dB). From EIRP we find the gain, then the diameter from the parabolic gain formula G = η(πD/λ)².

Given: η = 0.85, f = 3 GHz, waveguide loss L = 2.5 dB, EIRP = 46 dBW, Pₜ = 500 W.

Step 1: Wavelength

λ = c/f = (3 × 10⁸)/(3 × 10⁹) = 0.1 m

Step 2: Transmit power in dBW

Pₜ(dBW) = 10 log₁₀(500) = 26.99 dBW

Step 3: Antenna gain from EIRP

EIRP = Pₜ − L + G
G    = EIRP − Pₜ + L
     = 46 − 26.99 + 2.5
     = 21.51 dB
G    = 10^(21.51/10) = 141.59  (ratio)

Step 4: Diameter

G = η (πD/λ)²
D = (λ/π) √(G/η)
  = (0.1/π) √(141.59/0.85)
  = 0.03183 × √166.58
  = 0.03183 × 12.906
  = 0.4108 m

Check: 0.85 × (π × 0.4108/0.1)² = 0.85 × 166.58 ≈ 141.6 → 21.51 dB. ✓

Beamwidth for interest: HPBW ≈ 70λ/D = 70 × 0.1/0.4108 ≈ 17°.

Answer: Antenna gain = 21.51 dB (141.6); required dish diameter D ≈ 0.411 m (41.1 cm).

Travelling wave antenna

A travelling wave (non-resonant) antenna is one in which the current travels along the conductor in one direction only, because the far end is terminated in a matched load (equal to the characteristic impedance). There is no reflected wave, so no standing wave; the current amplitude is nearly uniform and the phase changes progressively along the wire. Such antennas are unidirectional, wideband and have nearly constant resistive input impedance. Examples: terminated long wire (Beverage), terminated V, rhombic.

 feed            travelling wave  →            R = Z₀
 ~ o==========================================/\/\/--⏚
   max radiation tilted forward, towards the load end

V-antenna: construction

              leg 1 (l = 2λ to 8λ)
           /‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ (R/2)
  600 Ω  <    apex angle = 2θₘ      ===> beam
  feeder   \___________________________ (R/2)
              leg 2

• Two long horizontal wires forming a "V", fed at the apex in antiphase by a balanced open-wire line.
• Apex angle chosen as 2θₘ, where θₘ is the main-lobe angle of a single long wire: cosθₘ ≈ 1 − 0.371λ/l (e.g. l = 4λ → θₘ ≈ 25°, apex ≈ 50°).
• Far ends open (resonant) or terminated by resistors to ground (non-resonant).

Working principle

Each leg radiates a cone of radiation at angle θₘ to its wire. When the apex angle equals 2θₘ, one major lobe of each leg lies along the bisector of the V, and because the legs are fed in antiphase and are mirror images, these lobes add in phase there. Lobes in other directions are partly cancelled. Ground reflection sets the elevation angle of the beam.

Characteristics

• Directive, with gain about twice (3 dB more than) a single long wire of the same leg length; ≈ 10–15 dBi for long legs.
• Horizontal polarization, HF band (3–30 MHz).
• Input impedance high (≈ 500–800 Ω); wide bandwidth, especially when terminated.
• Requires large space but only three supports.

Types of V-antenna

 Resonant:    <=== V ===>      Terminated:   V ====>

Applications: HF point-to-point communication and reception.

Characteristics of UHF band

The Ultra High Frequency (UHF) band covers 300 MHz to 3 GHz (wavelength 1 m to 10 cm).

1. Propagation by space (line-of-sight) wave: direct plus ground-reflected wave; range limited to the radio horizon, d ≈ 4.12(√hₜ + √hᵣ) km (h in m).
2. No ionospheric reflection: waves pass through the ionosphere, so no sky-wave long-distance links; useful for satellites.
3. Ground wave negligible: surface wave attenuates very fast.
4. Affected by terrain, buildings and trees (shadowing, diffraction, multipath fading); some penetration into buildings.
5. Tropospheric effects: refraction, ducting and troposcatter can extend range occasionally.
6. Small antennas with high gain (Yagi, corner reflector, patch, helix) because λ is short.
7. Wide bandwidth available, suiting TV and data.
8. Low atmospheric noise; rain attenuation still small below 3 GHz.

Uses: UHF TV, GSM/4G mobile, GPS (1.575 GHz), Wi-Fi/Bluetooth (2.4 GHz), microwave ovens, radar, walkie-talkies.

Log-periodic antenna

A log-periodic dipole array (LPDA) is a frequency-independent antenna whose impedance and pattern repeat periodically with the logarithm of frequency.

Construction

  beam <---- apex (short end)    long end
         Ln ..  L3    L2      L1
         |  |   |     |       |
  feed ->X--X---X-----X-------X   crossed
         |  |   |     |       |   feeder
         |  |   |     |       |
   τ = Lₙ₊₁/Lₙ = Rₙ₊₁/Rₙ = dₙ₊₁/dₙ   (< 1)
   σ = dₙ/(2Lₙ),  tan α = (1 − τ)/(4σ)

• Dipoles of gradually increasing length and spacing, scaled by the design ratio τ; their ends lie on two lines meeting at the apex (half-angle α).
• Fed by a transposed (crisscrossed) two-wire line from the short end, so neighbouring dipoles are 180° out of phase.

Working principle

1. At a given frequency only the elements about λ/2 long (the active region) carry large current and radiate.
2. Longer elements behind act as reflectors; shorter ones in front act as directors. The crossed feed gives end-fire radiation towards the apex (short end).
3. As frequency changes, the active region moves along the array; properties repeat whenever f is multiplied by 1/τ.
4. Band limits: L₁ ≈ λ_max/2 (lowest frequency) and Lₙ ≈ λ_min/2 (highest).

Characteristics

• Very wide bandwidth (up to 10:1), nearly constant input impedance (≈ 50–75 Ω with balun) and pattern over the band.
• Unidirectional, linearly polarized, gain ≈ 6–10 dBi (less than a Yagi of equal size).
• Uses: all-channel TV reception, HF/VHF communication, EMC testing.

Folded dipole: current distribution and pattern

A folded dipole is two parallel λ/2 conductors joined at both ends, with one of them split at the centre for feeding. The currents in both conductors are in the same direction and phase, each following a half-sine distribution, so it radiates like a dipole carrying double current.

 Current distribution (both arms in phase)
  _________________________
 |  -->  -->  I  -->  -->  |
 |                         |
 |__-->  -->  ~  -->  -->__|
     max at centre, zero at ends

 Pattern (plane containing the dipole)
          90°
        .-""-.
        \    /
  0° ----[==]---- 180°  nulls along
        /    \          dipole axis
        '-..-'
          270°  figure-8

• Input impedance: Z = N² × 73 Ω = 4 × 73 ≈ 292 Ω for 2 equal conductors.
• Pattern: same figure-8 as a λ/2 dipole in the plane containing it; omnidirectional in the plane perpendicular; directivity 1.64.
• Wider bandwidth than a simple dipole; ideal driven element of a Yagi.

Design of 5-element Yagi for 785–895 MHz

5 elements = 1 reflector + 1 driven folded dipole + 3 directors.

Design rules used (standard empirical Yagi rules):

λc   = c / fc
L_DE = 0.48 λc               (driven, given)
L_R  = 1.05 L_DE  (≈ 0.5λc)  (reflector 5 % longer)
L_D1 = 0.95 L_DE, L_Dk+1 = 0.95 L_Dk  (5 % shorter each)
S_R  = 0.25 λc   (reflector to driven)
S_D  = 0.15 λc   (driven to D1 and between directors)

Step 1: Centre frequency and wavelength

fc = (f₁ + f₂)/2 = (785 + 895)/2 = 840 MHz
λc = 3×10⁸ / 840×10⁶ = 0.3571 m = 35.71 cm

Step 2: Element lengths

L_DE = 0.48 × 35.71    = 17.14 cm
L_R  = 1.05 × 17.14    = 18.00 cm
L_D1 = 0.95 × 17.14    = 16.29 cm
L_D2 = 0.95 × 16.29    = 15.47 cm
L_D3 = 0.95 × 15.47    = 14.70 cm

Step 3: Spacings and boom

S_R  = 0.25 × 35.71 = 8.93 cm
S_D  = 0.15 × 35.71 = 5.36 cm
Boom = 8.93 + 3 × 5.36 = 25.00 cm

  R     DE    D1    D2    D3
  |     |     |     |     |
 18.0 17.14 16.29 15.47 14.70 cm
  |    (o)    |     |     | ===> beam
  |<8.93>|<5.36>|<5.36>|<5.36>|
  <------- boom 25.0 cm ------>

The band is 110 MHz wide (≈ 13 % of fc), which is large for a Yagi; the folded dipole driven element helps by its wider bandwidth. Element diameter ≈ 0.005λ ≈ 2 mm.

Answer: fc = 840 MHz, λc = 35.71 cm; R = 18.00 cm, DE = 17.14 cm, D1 = 16.29 cm, D2 = 15.47 cm, D3 = 14.70 cm; spacings 8.93 cm and 5.36 cm; boom 25.0 cm.

Role of the driven element

The driven element is the only element of a Yagi-Uda antenna connected to the feed line; usually a resonant λ/2 dipole or folded dipole.

• It receives RF power from the transmitter (or delivers received power to the receiver) — the single feed point of the array.
• Its radiated field induces currents in the reflector and directors by mutual coupling; without it the parasitic elements would carry no current.
• It fixes the operating (resonant) frequency and the input impedance; a folded dipole (≈ 292 Ω alone) compensates for the impedance drop caused by the close parasitic elements and matches the feeder.
• Its position between reflector and directors sets the phase relationships that produce the forward beam.

Design of 5-element Yagi at 760 MHz

Design rules used (standard empirical Yagi rules):

λc   = c / fc
L_DE = 0.48 λc               (driven, given)
L_R  = 1.05 L_DE  (≈ 0.5λc)  (reflector 5 % longer)
L_D1 = 0.95 L_DE, L_Dk+1 = 0.95 L_Dk  (5 % shorter each)
S_R  = 0.25 λc   (reflector to driven)
S_D  = 0.15 λc   (driven to D1 and between directors)

Step 1: Wavelength

λc = 3×10⁸ / 760×10⁶ = 0.3947 m = 39.47 cm

Step 2: Element lengths

L_DE = 0.48 × 39.47 = 18.95 cm
L_R  = 1.05 × 18.95 = 19.89 cm
L_D1 = 0.95 × 18.95 = 18.00 cm
L_D2 = 0.95 × 18.00 = 17.10 cm
L_D3 = 0.95 × 17.10 = 16.25 cm

Step 3: Spacings and boom

S_R  = 0.25 × 39.47 = 9.87 cm
S_D  = 0.15 × 39.47 = 5.92 cm
Boom = 9.87 + 3 × 5.92 = 27.63 cm

  R     DE    D1    D2    D3
  |     |     |     |     |
 19.89 18.95 18.00 17.10 16.25 cm
  |    (o)    |     |     | ===> beam
  |<9.87>|<5.92>|<5.92>|<5.92>|
  <------ boom 27.63 cm ------>

Answer: λc = 39.47 cm; R = 19.89 cm, DE = 18.95 cm, D1 = 18.00 cm, D2 = 17.10 cm, D3 = 16.25 cm; S_R = 9.87 cm, S_D = 5.92 cm; boom ≈ 27.6 cm.

A monopole antenna is a single straight vertical conductor mounted over a conducting ground plane and fed between its base and the ground. The most common is the quarter-wave (λ/4) monopole (Marconi antenna).

      |  λ/4 monopole
      |
      |
  ====o==== ground plane / radials
     feed
      :   image λ/4 (formed by ground)

Principle: by image theory, the ground plane creates an image of the monopole, so above ground it behaves like a λ/2 dipole fed at the centre.

Characteristics

• Radiation pattern: upper half of a dipole pattern; omnidirectional in the horizontal plane, max along the ground, null overhead.
• Polarization: vertical.
• Radiation resistance ≈ 36.5 Ω (half of 73 Ω); directivity ≈ 3.28 (5.15 dBi), twice a dipole's.
• Needs a good ground: earth with buried radials, metal car body, or 3–4 radial wires (ground-plane antenna).
• Can be shortened by top loading or loading coils.

Applications: MF AM broadcasting towers, car whip antennas, walkie-talkies, mobile base stations, Wi-Fi routers.

A rhombic antenna is a non-resonant (travelling-wave) antenna formed by four long wires arranged as a horizontal rhombus, fed at one acute corner and terminated at the opposite corner by a resistor equal to its characteristic impedance (≈ 600–800 Ω).

            pole
           /    \
     l    /      \   l
         /   φ    \
 TX ==> <          > --/\/\/-- R (≈ 800 Ω)
         \        /     ===> beam
     l    \      /   l
           \    /
            pole       height H above ground

Working principle

1. The matched termination absorbs the wave arriving at the far end, so a travelling wave flows from feed to load with no reflection.
2. Each long leg (several λ) radiates a main lobe at angle θₘ to the wire, cosθₘ ≈ 1 − 0.371λ/l.
3. The tilt angle φ is chosen so that one main lobe of each of the four legs lies along the long diagonal in the forward direction, where all four add in phase.
4. Other lobes cancel partly; backward radiation is absorbed in the resistor, so the beam is unidirectional.
5. Ground reflection (height H) lifts the beam to the desired elevation angle Δ:

H = λ/(4 sinΔ),  φ = 90° − Δ,  l = λ/(2 sin²Δ)

Characteristics

• HF band (3–30 MHz); horizontal polarization.
• Unidirectional beam along the major axis; gain ≈ 10–17 dBi.
• Non-resonant: almost constant input impedance (≈ 600–800 Ω) over a wide band (2:1 or more).
• Efficiency ≈ 50–75 %, as part of the power is dissipated in the terminating resistor.

Advantages

1. Very wide bandwidth; pattern and impedance change little with frequency.
2. High gain and directivity with a simple structure.
3. Simple, cheap construction with wires and four poles.
4. Easy to match to an open-wire line; insensitive to small dimensional errors.
5. Unidirectional pattern reduces interference from the back.

Disadvantages

• Requires very large land area; significant side lobes; power lost in termination; beam fixed.

Applications

• Long-distance HF sky-wave point-to-point communication (telegraph, telephone links).
• HF broadcast and reception stations, military and diplomatic HF links.

Operation of parabolic reflector

A parabolic reflector antenna is a large conducting surface shaped as a paraboloid of revolution, with a small primary antenna (feed) placed at its focus. It converts the spherical wave of the feed into a plane wave and so produces a very narrow, high-gain pencil beam.

Geometry: a parabola is the locus of points equidistant from the focus F and a fixed line (directrix). The distance from vertex to focus is the focal length f; the opening (aperture) has diameter D; f/D is usually 0.25–0.5.

            )|
           ) |---->
   ray    )  |---->   all paths
  F o-->-)   |---->   F→P→Q equal
   feed   )  |---->   (plane wave)
           ) |---->
            )|
       <-f-> aperture plane, diameter D

Working

1. Equal path (phase) property: for every point P on the surface, FP + PQ = constant, where Q is on the aperture plane. Hence all rays from F arrive at the aperture in phase.
2. Parallel ray property: the tangent at P makes equal angles with FP and the axis, so every reflected ray is parallel to the axis.
3. The aperture therefore has a uniform phase distribution and radiates a plane wave: a narrow beam along the axis.
4. By reciprocity, an incoming plane wave along the axis is focused at F, where the receiving feed is placed.
5. The feed must radiate mostly towards the dish; energy spilling past the rim (spillover) and the shadow of the feed (aperture blocking) reduce efficiency.

Performance

Gain   G = η (πD/λ)²       η ≈ 0.55-0.7
HPBW   ≈ 70 λ/D degrees
FNBW   ≈ 140 λ/D degrees

E.g. D = 3 m at 6 GHz (λ = 5 cm): HPBW ≈ 1.17°, gain ≈ 43 dBi (η = 0.6).

Uses: satellite communication, radar, microwave links, radio astronomy.

Cassegrain feed system

The Cassegrain feed is a dual-reflector feed: a horn located at the vertex of the main paraboloid illuminates a small hyperboloidal subreflector placed near the focus, which reflects the waves back onto the main reflector.

        main paraboloid
          )
         )        hyperboloid
        )          subreflector
       )   <------- (
 [horn]o --------> (  F (focus of paraboloid
 at F' )   <------- (     = near focus of hyperbola)
        )
         )
          )
 horn at F' = far focus of hyperbola, near the vertex

• One focus of the hyperboloid coincides with the focus F of the paraboloid; the feed is at the other focus F′. Waves reflected from the subreflector appear to come from F, so the main dish produces a plane wave.
• Advantages: feed and receiver behind the dish (short waveguide, low loss, low noise), long effective focal length, easy maintenance.
• Disadvantage: subreflector blocks part of the aperture, so it is used with large dishes such as satellite earth stations.

An aperture antenna is one that radiates through an opening (aperture) whose size is several wavelengths, rather than from currents on thin wires. The fields across the aperture act as secondary sources (Huygens' principle), and the radiation pattern is found from the aperture field distribution.

 waveguide   aperture (E-field across opening)
  ______   .‾‾‾‾‾‾‾‾‾|
 |______|=<  horn    |  ===> beam
           '_________|

Examples

• Open-ended waveguide and horn antennas (sectoral, pyramidal, conical).
• Slot antennas cut in a metal sheet or waveguide wall.
• Reflector antennas (parabolic dish) – the dish mouth is the aperture.
• Lens antennas and microstrip patches (radiating edges).

Key relations

Effective aperture  A_e = η A    (η ≈ 0.5-0.8)
Gain                G = 4π A_e / λ²
Beamwidth           ≈ k λ / D   (k ≈ 50-70 degrees)

Features: high gain and narrow beam because the aperture is large compared with λ; wide bandwidth; easily flush-mounted on aircraft and vehicles; used mainly at microwave frequencies (above ~1 GHz). Applications: radar, satellite links, microwave relays, feeds for reflectors and gain standards.

A reflector antenna combines a small primary radiator (feed) with a large conducting reflecting surface that redirects and focuses the feed's energy into a desired direction. Common types: plane reflector, corner reflector, parabolic (dish), and dual-reflector (Cassegrain, Gregorian).

Special features

1. Very high gain and directivity: gain G = η(πD/λ)² for a dish; 30–60 dBi is common.
2. Narrow pencil beam: HPBW ≈ 70λ/D degrees, giving precise pointing and low interference.
3. Equal path property: paraboloid converts a spherical wave from the focus into a plane wave in phase across the aperture.
4. Wide bandwidth: the reflector is frequency independent (if the surface error ≪ λ/16); the bandwidth is set by the feed only.
5. Simple feed: only one small feed is needed; polarization follows the feed (linear, dual or circular).
6. Low side lobes by tapering the feed illumination (edge taper ≈ −10 dB).
7. Reduced efficiency by spillover, aperture blocking, phase errors; typical η = 55–70 %.
8. Mechanically steerable; used at microwave frequencies (above ~1 GHz) where size is practical.

              )|
             ) |--->
 feed at F  o  |---> plane wave
             ) |--->
              )|
        D = aperture diameter, f = focal length

Types of feeds

1. Dipole with parasitic reflector (front feed): a λ/2 dipole at the focus with a small plane or spherical reflector behind it so that energy goes towards the dish instead of forward directly.

      )
     )  <== |(  dipole + small reflector at F
      )

2. Horn feed (front feed): a pyramidal or conical horn at the focus facing the dish; gives good control of illumination and polarization. The waveguide must run to the focus and causes some blocking.

      )
     )  <==<|=== waveguide
      )    horn at F

3. Offset feed: only an off-axis section of a paraboloid is used, and the horn is placed outside the reflected beam; no aperture blocking, lower side lobes. Used in DTH dishes.

     )
    )  ---->
   )   \
        [horn] below the beam

4. Cassegrain feed: horn at the vertex of the main dish illuminates a convex hyperboloid subreflector, whose one focus coincides with the dish focus. Short waveguide, low noise; used in earth stations.

     )        (
    ) [horn]-> ( subreflector
     )        (

5. Gregorian feed: like Cassegrain but with a concave ellipsoidal subreflector placed beyond the focus.

Aperture antennas vs conventional (wire) antennas

Theory of radiation from a rectangular horn

A rectangular horn is a rectangular waveguide (dominant TE₁₀ mode) flared into a larger aperture of size a_H × a_E. The flare matches the guide impedance to free space (377 Ω) and enlarges the aperture to give a directive beam.

          side view (E or H plane)
            .-‾‾‾‾‾|
   ____  .-'   δ   |   L = axial length
  |____|<-----L--->|   a = aperture width
         '-._______|   δ = path difference

1. Aperture field: the TE₁₀ field is carried to the aperture. Across the H-plane width the amplitude is cosine shaped, cos(πx/a_H); across the E-plane it is uniform.
2. Phase error: waves from the throat reach the aperture edge by a longer path than along the axis. The extra path is

δ = √(L² + (a/2)²) − L ≈ a²/(8L)

A large δ gives a non-uniform phase, broadening the beam and lowering gain. 3. Radiation: each element of the aperture acts as a Huygens source; integrating them (a Fourier transform of the aperture field) gives the far field. Uniform E-plane distribution gives a sin(u)/u pattern (narrow beam, higher side lobes ≈ −13 dB); cosine H-plane distribution gives a wider beam with lower side lobes (≈ −23 dB). 4. Optimum horn: δ ≈ 0.25λ in the E-plane and ≈ 0.4λ in the H-plane gives maximum gain for a given length, L = a²/(8δ). 5. Optimum-horn results:

HPBW (E-plane) ≈ 56 λ / a_E   degrees
HPBW (H-plane) ≈ 67 λ / a_H   degrees
Directivity    D ≈ 7.5 a_E a_H / λ²   (η ≈ 0.6)

So a longer horn with a bigger mouth gives more gain, as long as the phase error is kept within the optimum limit.

EIRP = transmitter power − feeder (waveguide) loss + antenna gain (in dB). Find the gain from EIRP, then the diameter from G = η(πD/λ)².

Given: η = 0.75, f = 3 GHz, waveguide loss L = 2.5 dB, EIRP = 46 dBW, Pₜ = 500 W.

Step 1: Wavelength

λ = c/f = (3 × 10⁸)/(3 × 10⁹) = 0.1 m

Step 2: Transmit power in dBW

Pₜ = 10 log₁₀(500) = 26.99 dBW

Step 3: Antenna gain

EIRP = Pₜ − L + G
G    = 46 − 26.99 + 2.5 = 21.51 dB
G    = 10^(2.151) = 141.59

Step 4: Diameter

D = (λ/π) √(G/η)
  = (0.1/π) √(141.59/0.75)
  = 0.03183 × √188.79
  = 0.03183 × 13.740
  = 0.4374 m

Check: 0.75 × (π × 0.4374/0.1)² = 0.75 × 188.8 ≈ 141.6 → 21.51 dB. ✓

With lower efficiency (75 % instead of 85 %), a slightly larger dish is needed for the same gain.

Answer: G = 21.51 dB (141.6); diameter D ≈ 0.437 m (43.7 cm).

A helical antenna is a conductor wound into a helix (like a spring), fed at one end by a coaxial cable whose outer conductor is connected to a ground plane. Depending on its size relative to λ, it works in the normal mode or the axial mode.

Structural design

          _____
         /     \    D  = helix diameter
         \_____/    C  = πD (circumference)
         /     \    S  = spacing (pitch) between turns
         \_____/    α  = pitch angle = tan⁻¹(S/C)
         /     \    N  = number of turns
         \_____/    L  = NS = axial length
  ===============   ground plane ≥ 0.5λ
         |
       coax feed
 one turn unrolled:  L₀ = √(C² + S²)

Special cases: α = 0° → loop; α = 90° → straight wire (monopole).

Normal (broadside) mode

• Condition: helix dimensions ≪ λ (NL₀ ≪ λ, D ≪ λ).
• Working: each turn behaves like a small loop (gives E_φ) plus a short dipole of length S (gives E_θ). Both have the same doughnut pattern, so radiation is maximum normal to the helix axis, null along the axis.
• Polarization: elliptical; axial ratio AR = 2Sλ/C². It becomes circular when C = √(2Sλ).
• Merits: very compact; can replace a long whip (shortened monopole).
• Demerits: narrow bandwidth, low radiation resistance and efficiency; circular polarization only at one frequency.
• Applications: compact "rubber-ducky" antennas in walkie-talkies and handsets.

 Normal mode            Axial mode
   <==  |||  ==>           |||  ====>
   max ⊥ axis              max along axis

Axial (end-fire) mode

• Condition: 3/4 λ < C < 4/3 λ (C ≈ λ), S ≈ λ/4, pitch angle 12°–14°, N > 3.
• Working: the wave travels along the helix as a travelling wave; with one wavelength per turn, the fields of successive turns add along the axis. The current rotates around the axis, so the radiated field is circularly polarized (sense same as winding), giving a single main lobe along the axis away from the ground plane.
• Formulas (Kraus):

HPBW ≈ 52 λ^(3/2) / (C √(NS))   degrees
FNBW ≈ 115 λ^(3/2) / (C √(NS))  degrees
D    ≈ 15 N C² S / λ³
Zin  ≈ 140 (C/λ) Ω    (≈ 100-200 Ω)
AR   ≈ (2N + 1)/(2N)

• Merits: circular polarization, wide bandwidth (≈ 1.7:1), moderate to high gain (10–15 dBi), simple and robust, almost resistive input impedance.
• Demerits: bulky at low frequencies, needs a ground plane and matching from ≈ 140 Ω to 50 Ω.
• Applications: satellite and space-probe telemetry, GPS, radio astronomy, feed for parabolic reflectors.

A V-antenna is a directive HF antenna made of two long wires (legs) arranged as a horizontal "V" and fed at the apex by a balanced transmission line.

Construction

              leg 1 (l = 2λ to 8λ)
         /‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
  600 Ω <   apex angle 2θₘ     ===> beam
 feeder  \___________________________
              leg 2

• Two straight wires of length l (several λ), supported by poles above ground.
• Apex angle = 2θₘ, θₘ being the angle of the main lobe of a single long wire: cosθₘ ≈ 1 − 0.371λ/l.
• Legs fed in antiphase by a 600 Ω open-wire line; far ends open or terminated.

Working principle

Each leg radiates a conical main lobe at θₘ to its axis. When the legs are set at ±θₘ about the bisector, one major lobe of each leg points along the bisector, and these lobes add in phase there (the antiphase feed and mirror geometry make them additive). Lobes in other directions cancel partly, so the radiation concentrates along the bisector. Gain is roughly double (3 dB more than) a single long wire.

Types and patterns

1. Resonant V (unterminated): ends open; standing waves; bidirectional pattern along the bisector (both forward and backward).
2. Non-resonant V (terminated): each end grounded through R ≈ Z₀/2; travelling wave; unidirectional pattern.

 Resonant V                 Terminated V
     _.-.                         _.-.
 <==(    )  <V>  (    )==>   <V>(    )====>
     '-'_            '-'          '-'
 equal front & back lobes    weak back lobe

Advantages

• Simple and cheap; only three supports needed.
• High directivity and gain (≈ 10–15 dBi for long legs).
• Wide bandwidth (especially terminated type).
• Easy matching to an open-wire line.

Disadvantages

• Large space needed; side lobes; fixed beam; power lost in terminations.

Applications

• HF (3–30 MHz) point-to-point sky-wave communication and reception, amateur and military radio links.

A corner reflector antenna consists of a half-wave dipole (driven element) placed on the bisector of two flat conducting sheets that meet at an angle, usually 90°. The corner reflects the dipole's backward radiation forward, giving a directive beam.

     \  sheet / grid
      \
       \   S
  apex  >-----o dipole  ====> beam
       /
      /   corner angle 90°
     /  sheet / grid

Construction

• Corner angle α: 90° most common (also 60°, 45°).
• Dipole spacing from apex S ≈ 0.25λ–0.7λ (≈ 0.5λ typical).
• Each sheet length ≥ 2S (≈ 1–2λ); sheets are often grids of parallel rods spaced < 0.1λ to reduce weight and wind load.

Working (image theory): for a 90° corner, the two sheets create three images of the dipole (two with opposite current, one with the same). The dipole and its images form a 4-element array whose fields add along the bisector. For α = 180°/n, the number of images is 2n − 1.

Characteristics

• Gain ≈ 10–12 dB over a λ/2 dipole (90° corner, S ≈ 0.5λ); higher for smaller angles.
• Front-to-back ratio high; beamwidth ≈ 40°–60°.
• Input impedance depends on S (≈ 70–150 Ω for S ≈ 0.5λ).
• Linear polarization, moderate bandwidth.

Applications: UHF TV reception, point-to-point VHF/UHF links, radar.

Aperture antenna

An aperture antenna radiates through an opening (aperture) that is several wavelengths in size; the field across the opening acts as a set of Huygens sources. Examples: horn, slot, lens and parabolic reflector antennas, used mainly at microwave frequencies.

Parabolic antenna: construction

            )|
           ) |---->
          )  |---->   plane wave
  feed F o   |---->   (pencil beam)
          )  |---->
           ) |---->
            )|
     <- f -> aperture plane, diameter D

• A conducting paraboloid of revolution (solid sheet or wire mesh with gaps < λ/10).
• Aperture diameter D (many λ); focal length f; ratio f/D ≈ 0.25–0.5.
• A small primary antenna (feed) at the focus F, supported by struts; mounted on a steerable pedestal.

Working principle

1. Equal-path property: for any point P on the dish, FP + PQ = constant (Q on the aperture plane), so all waves from F reach the aperture in phase.
2. Parallel-ray property: reflected rays are all parallel to the axis.
3. Thus the spherical wave from the feed becomes a plane wave, giving a narrow high-gain beam. In reception, incoming plane waves are focused at F.
4. Gain G = η(πD/λ)², HPBW ≈ 70λ/D degrees; η ≈ 0.55–0.7, reduced by spillover, blocking and phase errors.

Feeding mechanisms

1. Dipole with reflector: λ/2 dipole at F with a small reflector behind it to direct energy to the dish.
2. Horn feed (front feed): horn at F facing the dish; good illumination control.
3. Offset feed: only part of the paraboloid used, feed outside the beam; no blocking (DTH).
4. Cassegrain feed: horn at the dish vertex illuminates a hyperboloid subreflector, whose one focus coincides with F; short waveguide, low noise.
5. Gregorian feed: ellipsoidal subreflector placed beyond the focus.

 Front feed            Cassegrain
     )                     )      (
    )  <==[horn]          ) [horn]->( sub-
     )   at F              )       ( reflector

Applications: satellite earth stations, DTH, radar, microwave links, radio telescopes.

A Yagi-Uda antenna is an end-fire array of a driven λ/2 dipole (often folded) with one reflector behind and one or more directors in front, all parallel and mounted on a common boom. Only the driven element is fed; the others are parasitic.

Construction

   R      DE      D1     D2     D3
   |      |       |      |      |
 --+-----(o)------+------+------+--> beam
   |     feed     |      |      |
 longest        shorter ->
  <0.15-0.25λ><-- 0.1-0.35λ -->

• Reflector ≈ 0.5λ (5 % longer than driven element).
• Driven element ≈ 0.46–0.48λ, folded dipole for impedance.
• Directors ≈ 0.45λ and shorter, each ≈ 5 % less than the previous.
• Elements fixed at centres to a metal boom.

Working principle

The driven element's field induces currents in the parasitic elements by mutual coupling. The longer reflector is inductive (current lags) and cancels backward radiation; the shorter directors are capacitive (current leads) and guide the wave forward with progressive phase, like an end-fire array. The result is a unidirectional beam towards the directors.

Design (rules of thumb)

λ = c/f
L_DE = 0.48λ,  L_R = 1.05 L_DE,  L_Dk+1 = 0.95 L_Dk
S_R  = 0.25λ,  S_D = 0.15λ

Example, 3 elements at 500 MHz (λ = 0.6 m): L_DE = 28.8 cm, L_R = 30.24 cm, L_D = 27.36 cm, S_R = 15 cm, S_D = 9 cm.

Advantages

• High gain (7–15 dBi) and good front-to-back ratio with a single feed point.
• Light, compact, cheap and easy to build and mount.
• Unidirectional beam reduces interference and ghost images.
• Folded-dipole driven element gives convenient 300 Ω/75 Ω matching.

Disadvantages

• Narrow bandwidth (≈ 2–5 %); gain limited to ~ 17 dBi; sensitive to element dimensions.

Applications

• VHF/UHF TV and FM reception (rooftop antennas).
• Point-to-point VHF/UHF links, amateur radio, radio direction finding, radar and RFID readers.

EIRP = transmitter power − waveguide loss + antenna gain (all in dB). Find the antenna gain first, then the diameter from G = η(πD/λ)².

Given: η = 0.75, f = 5 GHz, waveguide loss L = 3 dB, EIRP = 50 dBW, Pₜ = 600 W.

Step 1: Wavelength

λ = c/f = (3 × 10⁸)/(5 × 10⁹) = 0.06 m

Step 2: Transmit power in dBW

Pₜ = 10 log₁₀(600) = 27.78 dBW

Step 3: Antenna gain

EIRP = Pₜ − L + G
G    = 50 − 27.78 + 3 = 25.22 dB
G    = 10^(2.522) = 332.54

Step 4: Diameter

D = (λ/π) √(G/η)
  = (0.06/π) √(332.54/0.75)
  = 0.019099 × √443.39
  = 0.019099 × 21.057
  = 0.4022 m

Check: 0.75 × (π × 0.4022/0.06)² = 0.75 × 443.4 ≈ 332.5 → 25.22 dB. ✓

HPBW ≈ 70λ/D = 70 × 0.06/0.4022 ≈ 10.4°.

Answer: G = 25.22 dB (332.5); diameter D ≈ 0.402 m (40.2 cm).

A log-periodic (logarithmic) antenna is a frequency-independent antenna whose structure is scaled by a constant ratio, so its impedance and radiation pattern repeat periodically with the logarithm of frequency. The usual form is the log-periodic dipole array (LPDA).

  beam <-- short end              long end
          Ln .. L3   L2     L1
          |  |  |    |      |
  feed -> X--X--X----X------X   crossed feeder
          |  |  |    |      |
   τ = Lₙ₊₁/Lₙ = Rₙ₊₁/Rₙ = dₙ₊₁/dₙ < 1

Design parameters

• Scale factor τ (≈ 0.8–0.95), spacing factor σ = dₙ/(2Lₙ), apex half-angle α with tan α = (1 − τ)/(4σ).
• Frequency period: properties repeat when f changes by 1/τ, i.e. ln f₂ − ln f₁ = ln(1/τ).
• Lowest frequency: L₁ ≈ λ_max/2; highest: Lₙ ≈ λ_min/2.

Working: dipoles are fed by a transposed line from the short end. At each frequency only the elements near λ/2 (the active region) radiate; longer ones behind act as reflectors and shorter ones as directors, so the beam points towards the short end (apex). As frequency changes, the active region slides along the structure.

Characteristics: very wide bandwidth (up to 10:1), nearly constant input impedance and pattern, gain ≈ 6–10 dBi, linear polarization.

Applications: all-channel TV reception, HF/VHF communication, EMC testing and spectrum monitoring.

Antenna

An antenna is a metallic structure (transducer) that converts guided electromagnetic energy from a transmission line into free-space electromagnetic waves, and vice versa during reception (IEEE: "a means for radiating or receiving radio waves"). It also matches the line impedance to free-space impedance (377 Ω).

Types of wire antennas

Patterns below are in the plane containing the antenna (E-plane), with the wire drawn vertical unless noted.

 Dipole / monopole       Small loop          Helix (axial)
      |  .-.                 .-.  .-.            ___
  .-. | (   )             (   )O(   )         |///| ===>
 (   )|  '-'               '-'  '-'            ‾‾‾
  '-' |                 max in loop plane    beam on axis
 max ⊥ wire, null on axis  null ⊥ loop       circular pol.

 Long wire (l = several λ)     V / rhombic
   \ / \ /                      <V   ===>
  ---------- wire               unidirectional
   / \ / \   lobes tilt           (terminated)
            towards far end

• Dipole antennas suit HF–UHF use (broadcast reception, TV, FM).
• Monopole is used for MF broadcast and mobile whips.
• Loop antennas are used for direction finding and AM receivers.
• Long-wire, V and rhombic are HF travelling-wave antennas.
• Helix gives circular polarization for satellite links.

Standing wave vs travelling wave antenna

A standing wave (resonant) antenna has its far end open, so the wave reflects and forms standing waves; a travelling wave (non-resonant) antenna is terminated in its characteristic impedance, so the wave travels only forward.

V antenna: construction

                 leg 1, length l (2λ-8λ)
           /‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ (R)
  open-  <   apex angle 2θₘ      ===> beam
  wire     \___________________________ (R)
  feeder         leg 2      (R only in non-resonant V)

• Two long horizontal wires forming a V, fed at the apex by a 600 Ω balanced line in antiphase.
• Apex angle = 2θₘ, θₘ = main-lobe angle of a long wire, cosθₘ ≈ 1 − 0.371λ/l (e.g. l = 4λ → θₘ ≈ 25°).

Working principle

Each leg is a long wire radiating its main lobe at θₘ to the wire. By placing the legs at ±θₘ to the bisector, one main lobe from each leg points along the bisector, where they add in phase; elsewhere they partly cancel. With open ends the V carries standing waves and is bidirectional; with terminated ends it carries travelling waves and is unidirectional.

Characteristics

• HF band, horizontal polarization, gain ≈ 3 dB more than a single long wire (≈ 10–15 dBi for long legs).
• Wide bandwidth; input impedance ≈ 500–800 Ω.
• Simple (three poles), but needs large area and has side lobes.
• Used for HF point-to-point communication.

Yagi antenna: construction and working

A Yagi-Uda antenna is an end-fire array of one driven λ/2 (folded) dipole, one reflector behind it and several directors in front, mounted parallel on a boom. Only the driven element is fed.

   R      DE      D1     D2     D3
   |      |       |      |      |
 --+-----(o)------+------+------+---> beam
   |     feed     |      |      |
  ≈0.5λ  0.48λ   shorter towards the front

Working: the driven element's field induces currents in the parasitic elements by mutual coupling. The reflector (longer, inductive, current lags) cancels radiation backwards and reinforces it forwards. The directors (shorter, capacitive, current leads) produce a progressive phase that guides energy forward, as in an end-fire array. The beam points towards the directors; gain rises with the number of directors (≈ 7 dBi for 3 elements, ≈ 9–10 dBi for 5).

Design procedure: choose λ from the frequency; take the driven element ≈ 0.46–0.48λ; reflector ≈ 5 % longer; each director ≈ 5 % shorter than the previous; reflector spacing ≈ 0.15–0.25λ and director spacing ≈ 0.1–0.35λ.

Design: 5 elements at 800 MHz

Design rules used (standard empirical Yagi rules):

λc   = c / fc
L_DE = 0.48 λc               (driven, given)
L_R  = 1.05 L_DE  (≈ 0.5λc)  (reflector 5 % longer)
L_D1 = 0.95 L_DE, L_Dk+1 = 0.95 L_Dk  (5 % shorter each)
S_R  = 0.25 λc   (reflector to driven)
S_D  = 0.15 λc   (driven to D1 and between directors)

Interpretation: "effective dipole length of 0.48λ" is taken as the driven element length.

Step 1: Wavelength

λc = 3×10⁸ / 800×10⁶ = 0.375 m = 37.5 cm

Step 2: Element lengths

L_DE = 0.48 × 37.5   = 18.00 cm
L_R  = 1.05 × 18.00  = 18.90 cm
L_D1 = 0.95 × 18.00  = 17.10 cm
L_D2 = 0.95 × 17.10  = 16.25 cm
L_D3 = 0.95 × 16.245 = 15.43 cm

Step 3: Spacings and boom

S_R  = 0.25 × 37.5 = 9.375 cm
S_D  = 0.15 × 37.5 = 5.625 cm
Boom = 9.375 + 3 × 5.625 = 26.25 cm

  R     DE    D1    D2    D3
  |     |     |     |     |
 18.90 18.00 17.10 16.25 15.43 cm
  |    (o)    |     |     | ===> beam
  |<9.375>|<5.625>|<5.625>|<5.625>|
  <-------- boom 26.25 cm -------->

Answer: λ = 37.5 cm; R = 18.90 cm, DE = 18.00 cm, D1 = 17.10 cm, D2 = 16.25 cm, D3 = 15.43 cm; spacings 9.375 cm (R–DE) and 5.625 cm (others); boom 26.25 cm.

A pyramidal horn is a rectangular waveguide flared in both the E-plane and the H-plane, so that its mouth is a larger rectangle (a_H × a_E). It is the most widely used horn antenna and the standard reference for gain measurement at microwave frequencies.

 waveguide a x b        aperture a_H x a_E
   ____         ___________
  |____|=====> |           |  ===> beam
  TE₁₀ mode    |___________|
           flare in both planes, length L

Working: the TE₁₀ wave in the guide spreads gradually through the flare, which matches the waveguide impedance to free space (377 Ω). The aperture field (uniform in E-plane, cosine in H-plane) radiates a directive beam along the axis.

Design

• Path-difference (phase error) limits for an optimum horn: δ ≈ 0.25λ (E-plane), δ ≈ 0.4λ (H-plane), with δ ≈ a²/(8L).
• Both flares must give the same throat point so the horn can be built (physical realizability).

Performance (optimum horn)

Gain       G ≈ 7.5 a_E a_H / λ²   (η ≈ 0.6)
HPBW (E) ≈ 56 λ/a_E deg,  HPBW (H) ≈ 67 λ/a_H deg

Advantages: high gain (15–25 dBi), wide bandwidth, low VSWR, simple, accurately predictable gain. Applications: gain standard, feed for reflectors, radar, microwave test benches.

Advantages of Yagi antenna

1. Good gain (≈ 7 dBi for 3 elements, up to ~15 dBi) and directivity with a single feed point.
2. Unidirectional beam with good front-to-back ratio, reducing interference and ghost images.
3. Light, compact, cheap and easy to build from rods and a metal boom (no insulation needed at element centres).
4. Folded-dipole driven element gives easy matching to 300 Ω/75 Ω lines.
5. Can be stacked for more gain; easy to rotate and point.

Design of 3-element Yagi at 3 GHz

3 elements = 1 reflector + 1 driven dipole + 1 director. Driven element length is not given, so the usual value 0.48λ is assumed.

Design rules used (standard empirical Yagi rules):

λc   = c / fc
L_DE = 0.48 λc               (driven, given)
L_R  = 1.05 L_DE  (≈ 0.5λc)  (reflector 5 % longer)
L_D1 = 0.95 L_DE, L_Dk+1 = 0.95 L_Dk  (5 % shorter each)
S_R  = 0.25 λc   (reflector to driven)
S_D  = 0.15 λc   (driven to D1 and between directors)

Step 1: Wavelength

λ = 3×10⁸ / 3×10⁹ = 0.1 m = 10 cm

Step 2: Element lengths

L_DE = 0.48 × 10   = 4.80 cm
L_R  = 1.05 × 4.80 = 5.04 cm
L_D  = 0.95 × 4.80 = 4.56 cm

Step 3: Spacing and boom

S_R  = 0.25 × 10 = 2.5 cm
S_D  = 0.15 × 10 = 1.5 cm
Boom = 2.5 + 1.5 = 4.0 cm

   R      DE     D
   |      |      |
  5.04   4.80   4.56 cm
   |     (o)     |   ===> beam
   |<2.5->|<1.5->|
   <-- boom 4.0 cm -->

At 3 GHz the elements are small rods (diameter ≈ 0.5–1 mm, ≈ 0.005–0.01λ), often printed on a PCB.

Answer: λ = 10 cm; reflector 5.04 cm, driven 4.80 cm, director 4.56 cm; spacings 2.5 cm and 1.5 cm; boom 4.0 cm.

A parasitic array is an antenna array in which only one element (the driven element) is fed from the transmitter; the other elements, called parasitic elements, are not connected to the feed line. They get current by mutual coupling (induction) from the driven element and re-radiate, so that the total field is strengthened in one direction. The best-known example is the Yagi–Uda antenna.

 Reflector  Driven   D1    D2    D3
    |         |      |     |     |   -> max radiation
    |        =|=     |     |     |
    |         |      |     |     |
 <-0.25λ-> <-0.1 to 0.3λ spacing->

Elements

• Driven element: a half-wave dipole or folded dipole (about 0.46–0.48λ), connected to the feeder.
• Reflector: about 5% longer than the driven element (≈0.5λ). Its reactance is inductive, so its re-radiated field cancels radiation behind it.
• Directors: about 5% shorter (≈0.43–0.45λ). Their reactance is capacitive, so their fields add in the forward direction.
• Spacing: 0.1λ to 0.3λ between elements.

Working: the current induced in a parasitic element depends on its length (its self-reactance) and its spacing (the phase delay). With the right length and spacing, the fields from all elements add in phase toward the directors and nearly cancel toward the reflector, giving an end-fire, unidirectional beam.

Features

• Gain about 7 dB for 3 elements, rising with more directors (but slowly).
• Narrow bandwidth (a few %), since element lengths are resonant.
• Feed impedance of the dipole drops (to about 20–25 Ω), so a folded dipole is used to raise it.
• Simple, light and cheap; used for TV reception, VHF/UHF links and amateur radio.

Standing wave vs travelling wave antenna

A standing wave (resonant) antenna is open at its ends, so the current reflects and forms a standing wave; a travelling wave (non-resonant) antenna is terminated in its characteristic impedance, so the current travels only one way with no reflection.

Rhombic antenna

Construction: four straight wires (legs), each of length L = 2λ to 8λ, are arranged as a rhombus (diamond) and held horizontally on four poles at a height H above ground. One acute-angled end is fed by a balanced line; the other acute end is terminated by a non-inductive resistor of about 600–800 Ω, equal to the characteristic impedance of the antenna.

               B
             /   \
   feed    /       \     R ≈ 800 Ω
  --- A <           > C ---/\/\---
           \       /      (load)
             \   /
               D
   Main beam: along A -> C (major axis)
   φ = tilt angle (half of obtuse angle at B, D)

Working principle

• Because of the matched termination, each leg carries a travelling wave. A long travelling-wave wire radiates a conical main lobe tilted at a small angle to the wire, pointing toward the load.
• The rhombus angles are chosen so that the main lobes of all four legs line up along the major axis (A to C). Lobes of the other directions cancel in pairs.
• The ground reflection (image) adds the direct wave in phase at the wanted elevation angle Δ when H is chosen properly.
• Result: a unidirectional, horizontally polarised beam toward the terminated end. Backward energy is absorbed in the resistor.

Characteristics

• Non-resonant, so input impedance (≈ 700–800 Ω) and pattern stay steady over a wide band (about 2:1 frequency range).
• High gain (roughly 10–15 dB) and directive, used for HF (3–30 MHz) point-to-point sky-wave links.
• Simple to build and adjust.
• Drawbacks: needs a large land area; about half the power is lost in the terminating resistor (low efficiency); many side lobes.
• Design rules (maximum-output design): H = λ/(4 sin Δ), φ = 90° − Δ, L = 0.371λ / sin² Δ.

Advantages of aperture antennas

An aperture antenna radiates through an opening (aperture), such as the mouth of a horn, a slot or a reflector dish. Its advantages:

• High gain and narrow beam: gain G = 4πAₑ/λ² grows with aperture area.
• Wide bandwidth: no sharp resonance (a horn works over most of the waveguide band).
• Easy feeding directly from a waveguide; low loss at microwave frequencies.
• Flush mounting is possible (slots on aircraft and missiles).
• Low VSWR and good matching; simple, robust construction.
• Used as standard gain antennas and as feeds for reflectors.

Types of horn antenna

1. E-plane sectoral horn (flared in the E-plane only)
2. H-plane sectoral horn (flared in the H-plane only)
3. Pyramidal horn (flared in both planes)
4. Conical horn (flared circular waveguide)
5. Exponential (tapered) horn
6. Biconical horn
7. Corrugated horn and dual-mode (Potter) horn
8. Ridged horn (very wide band)

Rectangular horn

A rectangular horn is a rectangular waveguide (TE₁₀ mode) whose walls are flared out to a larger opening. The flare gives a gradual change of impedance from the guide (≈ 500 Ω) to free space (377 Ω), so reflection is small and the wave is launched with a larger aperture, giving more directivity.

 E-plane sectoral   H-plane sectoral   Pyramidal
   (flare in b)       (flare in a)      (both)
      __                 ____            ______
  ___/  |            ___/    |       ___/      |
  ___   |  E         ___     |  H    ___   A×B |
     \__|                \___|          \______|

• E-plane sectoral horn: flare in the direction of E (narrow wall dimension b); the beam narrows in the E-plane.
• H-plane sectoral horn: flare in the direction of H (broad wall a); the beam narrows in the H-plane.
• Pyramidal horn: flare in both planes, giving a pencil beam; most common.

Design points: a long horn with small flare angle has nearly uniform phase over the aperture but is bulky; a short horn with large flare has phase error. The optimum horn keeps the path difference δ ≈ 0.25λ (E-plane) and ≈ 0.4λ (H-plane). For an optimum pyramidal horn of aperture A × B, gain ≈ 7.5AB/λ² (aperture efficiency ≈ 0.6), HPBW ≈ 56λ/B degrees (E-plane) and ≈ 67λ/A degrees (H-plane).

Yagi vs log-periodic antenna

Working principle of log-periodic antenna

An LPDA is a set of dipoles of lengths L₁ < L₂ < … < Lₙ placed along a boom inside a triangle of half apex angle α and fed by a crossed (transposed) two-wire line from the short end.

            apex (feed)
             /|\  α
            / | \
       L1  --+--      shortest (fmax)
          ---+---
         ----+----    active region
        -----+-----
       ------+------  longest (fmin)
     <- beam toward apex (short end)

• Dimensions grow geometrically: τ = Lₙ/Lₙ₊₁ = Rₙ/Rₙ₊₁ = dₙ/dₙ₊₁ < 1, where Rₙ is the distance of dipole n from the apex and dₙ the spacing.
• At any frequency, only the 3–5 dipoles near half-wave length (the active region) carry large current and radiate. Longer dipoles behind act like reflectors; shorter ones in front act like directors, so the beam points toward the apex.
• Changing frequency only moves the active region along the array. Because the structure repeats itself when frequency is multiplied by 1/τ, the impedance and pattern repeat periodically with log f, hence the name. If the variation within one period is small, the antenna is effectively frequency-independent.
• The feeder is transposed between adjacent dipoles to give the 180° phase shift needed for end-fire toward the short end.

Design steps (Carrel method)

1. Choose directivity; from Carrel's chart pick the optimum scale factor τ (0.8–0.98) and spacing factor σ = dₙ/(2Lₙ).
2. Half apex angle: α = tan⁻¹[(1 − τ)/(4σ)].
3. Bandwidth of active region: Bₐᵣ = 1.1 + 7.7(1 − τ)² cot α.
4. Bandwidth of structure: Bₛ = B × Bₐᵣ, where B = f_max/f_min.
5. Number of elements: N = 1 + ln(Bₛ)/ln(1/τ).
6. Longest element: L_max = λ_max/2 (at f_min); then Lₙ₊₁ = τLₙ for the rest.
7. Boom length: L = (λ_max/4)(1 − 1/Bₛ) cot α.
8. Spacings dₙ = 2σLₙ; choose feeder impedance to match the source (typically 50–75 Ω via a balun).

A Marconi antenna is a vertical quarter-wave (λ/4) monopole fed at its base against the ground. The ground acts as a mirror, so the antenna together with its image behaves like a vertical half-wave dipole.

        |  λ/4 radiator
        |
        |
  ~~~~[ ~ ]~~~~~~~ ground (conducting)
        :
        :  λ/4 image
        :

Working principle

• The RF source is connected between the base of the vertical wire and the ground.
• The current is maximum at the base and zero at the top (quarter-wave standing-wave distribution).
• By image theory, a perfectly conducting ground produces an image current in the same direction below the ground. The real wire plus its image form a λ/2 dipole, so the field above ground is the same as that of a half-wave dipole.
• Radiation exists only in the upper half space, so the total radiated power is half that of the dipole for the same current. Hence:
  • Radiation resistance Rᵣ = 73/2 ≈ 36.5 Ω
  • Directivity = 2 × 1.64 = 3.28 (≈ 5.16 dBi)
• Pattern: omnidirectional in the horizontal plane, maximum along the ground, zero overhead; vertically polarised. This suits ground-wave (surface-wave) broadcasting in LF/MF.

Design

1. Physical height: h = λ/4 = 75/f(MHz) m. Allowing about 5% end effect, h ≈ 71/f(MHz) m. Example: at 1 MHz, λ = 300 m, so h ≈ 75 m (≈ 71 m practical).
2. Short heights: at LF/MF, λ/4 is very tall. A shorter mast is used and brought to resonance by:
   • a loading coil (series inductance) at the base to cancel capacitive reactance;
   • top loading (capacity hat, T or inverted-L wire) to make the current more uniform and raise radiation resistance.
3. Ground system: since half of the "antenna" is the ground, a good ground is essential. Usually 60–120 copper radials, each about λ/4 long, are buried a few cm deep around the base; a counterpoise (wire mesh above ground) is used where soil is poor or rocky.
4. Efficiency: η = Rᵣ/(Rᵣ + R_loss); ground loss is the main loss, so a good radial system raises η.
5. Matching: a feeder (50–75 Ω coax) is matched to the base impedance (≈ 36 Ω) through an L-network.

Uses: AM (MW) broadcasting, mobile whips, VLF/LF transmitters.

A rhombic antenna is a non-resonant (travelling-wave) antenna made of four long horizontal wires arranged as a rhombus, fed at one acute corner and terminated in a matched resistor at the other.

               B
             /   \       L = leg length
   feed    /       \
  ===== A <    →    > C --R≈800Ω-- gnd
           \       /
             \   /       height H above ground
               D
  φ = tilt angle = half of the obtuse angle at B, D

Working principle

• The terminating resistor (≈ 600–800 Ω) absorbs the wave, so each leg carries a travelling wave and has a unidirectional conical lobe at an angle θ to the wire, pointing toward the load.
• The tilt angle is chosen so that one lobe of each of the four legs points along the major axis A→C. These four lobes add in phase; the other lobes cancel in pairs.
• The ground image adds to the direct wave at the wanted elevation angle Δ when the height is right.
• The result is a unidirectional, horizontally polarised beam toward the terminated end, tilted up at angle Δ for sky-wave links.

Design (for elevation angle Δ)

The standard design for maximum field intensity at angle Δ:

1. Height above ground (image in phase): H = λ/(4 sin Δ)
2. Tilt angle: φ = 90° − Δ
3. Leg length: L = 0.371λ / sin² Δ

The alignment design keeps H and φ the same but uses L = 0.5λ/sin² Δ, so that the main lobe of each leg points exactly at Δ (gives slightly less field but a cleaner pattern).

Example: f = 15 MHz (λ = 20 m), Δ = 20° (sin Δ = 0.342): H = 20/(4 × 0.342) = 14.6 m, φ = 70°, L = 0.371 × 20 / 0.117 = 63.4 m.

Characteristics

• Wide bandwidth (about 2:1); impedance stays near 700–800 Ω.
• High gain (≈ 10–15 dB), simple construction, easy to build.
• Used for HF (3–30 MHz) long-distance point-to-point and sky-wave communication.
• Drawbacks: very large area; about half the power is wasted in the termination; large side lobes.

A horn is a flared waveguide. Waves from the throat reach the edge of the aperture by a longer path than at the centre, so the aperture field is not in phase. The allowed path difference δ fixes the relation between flare angle θ, axial length L and aperture A.

                 . P (aperture edge)
              .  |
  L + δ    .     | A/2
        .  θ/2   |
  O  .___________| C (aperture centre)
  (apex)    L

Derivation (applies to each plane of the pyramidal horn): From the right triangle OCP, with OC = L, CP = A/2, OP = L + δ:

cos(θ/2) = L / (L + δ)                     ...(1)
tan(θ/2) = (A/2) / L = A / (2L)            ...(2)

(L + δ)² = L² + (A/2)²
L² + 2Lδ + δ² = L² + A²/4
Since δ << L, drop δ²:
2Lδ = A²/4
L = A² / (8δ)                              ...(3)

Flare angle:
θ = 2 tan⁻¹(A / 2L) = 2 cos⁻¹[L / (L + δ)]  ...(4)

Putting (3) into (2):

tan(θ/2) = A / (2 · A²/8δ) = 4δ / A
θ = 2 tan⁻¹(4δ / A)

Optimum horn: for the most directivity with a given length, the path difference is limited to:

• E-plane: δ ≤ 0.25λ (E-field must be nearly in phase)
• H-plane: δ ≤ 0.4λ (field tapers to zero at the edges, so more phase error is allowed)

So for a pyramidal horn with E-plane aperture B and H-plane aperture A:

L_E = B² / (8 × 0.25λ) = B² / (2λ),   θ_E = 2 tan⁻¹(B / 2L)
L_H = A² / (8 × 0.4λ)  = A² / (3.2λ), θ_H = 2 tan⁻¹(A / 2L)

The horn length is the larger of the two; the other flare is then fixed by geometry.

Example: E-plane aperture B = 10λ, δ = 0.25λ: L = 100λ²/(8 × 0.25λ) = 50λ; θ/2 = tan⁻¹(10/100) = 5.71°, so θ ≈ 11.4°.

A vertical monopole (Marconi antenna) is fed between the base of a vertical wire and the earth. The earth is a working part of the antenna, so its quality and the ground system built under the antenna decide the efficiency.

Fundamentals

• Image action: a conducting ground acts as a mirror and produces an image of the monopole. The λ/4 monopole plus its image behaves like a λ/2 dipole: Rᵣ ≈ 36.5 Ω, directivity ≈ 3.28 (5.16 dBi), maximum radiation along the ground, vertically polarised.
• Return current: the antenna current returns to the base through the ground. Displacement current from the wire enters the ground around the antenna (most within λ/2 of the base) and flows radially back to the base.
• Ground loss: the soil has resistance, so this return current produces loss R_g. Efficiency:

η = Rᵣ / (Rᵣ + R_g + R_other)

With Rᵣ only ≈ 36 Ω (much less for short LF/MF masts, sometimes < 5 Ω), even a few ohms of ground loss can waste most of the power.

• Effect of ground constants: good conductivity σ (sea water, wet soil) gives a near-perfect image and low loss; dry, sandy or rocky soil gives large loss and lifts the radiation away from the ground, reducing the ground wave.

Importance of the ground

1. Completes the circuit of the antenna (acts as the second half of the dipole).
2. Decides radiation efficiency and radiation resistance.
3. Shapes the vertical pattern; good ground keeps the beam low along the earth, needed for MF ground-wave service.
4. Gives lightning protection and a stable reference.

Ground system construction

   Top view of radial ground system
          \   |   /
        \  \  |  /  /
     ------  (mast) ------   60-120 radials
        /  /  |  \  \        each ≈ λ/4 to λ/2
          /   |   \          buried 15-30 cm

1. Buried radial wires: 60–120 copper wires (or strips) run out radially from the base, each λ/4 to λ/2 long, buried 15–30 cm deep and joined at the base to a copper ring or plate. 120 radials of λ/4 is the usual broadcast standard; it brings the ground loss down to about 1–2 Ω.
2. Ground screen / mat: a copper mesh close around the base where current density is highest.
3. Counterpoise: where the soil is rocky, sandy or dry, a network of wires is stretched 2–4 m above the ground, insulated from earth, under the antenna. It acts as a capacitor plate and provides a low-loss return path.
4. Earth electrodes: copper rods or plates driven into moist soil, with salt/charcoal treatment, to keep earth resistance low.
5. Over sea water or very wet ground, a simple earth is enough because the soil itself is a good conductor.

A good ground system raises efficiency from 20–30% (poor ground) to over 80–90%, and strengthens the ground-wave field.