Antennas and Microwave Components

What to remember

• An antenna is a transducer: it changes guided waves in a line into free-space waves and back. It obeys reciprocity, so its gain and pattern are the same for sending and receiving.
• Key numbers: half-wave dipole = 73 Ω and 2.15 dBi; folded dipole = 292 Ω; rectangular waveguide dominant mode = TE10; cutoff frequency fc = c / 2a.
• Microwave devices are matched to a line: reflection coefficient Γ = (ZL − Z0)/(ZL + Z0) and VSWR = (1 + |Γ|)/(1 − |Γ|). A perfect match gives VSWR = 1.

Basic antenna parameters

An antenna sends power into space in a radiation pattern. An isotropic radiator sends equally in all directions and is only a reference. It has directivity 1 (0 dBi).

• Directivity (D): maximum radiation intensity divided by the average radiation intensity.
• Gain (G): G = η × D, where η is the radiation efficiency (power radiated / power fed).
• Radiation resistance: the resistance that would dissipate the same power as is radiated.
• Half-power beamwidth (HPBW): the angle between the two directions where power falls to half (−3 dB) of the peak.
• Front-to-back ratio (FBR): power in the forward direction compared to the backward direction.
• Bandwidth: the range of frequencies over which the antenna works to specification.
• Polarization: the direction of the electric field. It may be linear (vertical or horizontal), circular or elliptical.
• Effective aperture: Ae = λ²G / 4π.
• Far field: distances greater than about 2D²/λ, where D is the largest antenna size. In the far field the pattern does not change with distance.
• Gain in dB: G(dB) = 10 log10 G. Gain of 100 = 20 dB. A gain over a half-wave dipole is in dBd; over an isotropic source it is in dBi. dBi = dBd + 2.15.

Friis free-space formula: Pr = Pt × Gt × Gr × (λ / 4πR)².

Common antenna types

Arrays: several elements fed together to shape the beam. Broadside arrays radiate at right angles to the array line (elements in phase). End-fire arrays radiate along the line (phase shift between elements equals the spacing in phase). The total pattern = element pattern × array factor. Uniform spacing and amplitude give the narrowest beam. Binomial arrays have no side lobes. Dolph-Chebyshev arrays give the narrowest beam for a chosen side-lobe level.

Wave propagation

• Ground wave: follows the earth surface; used below about 2 MHz (MF and lower); vertical polarization.
• Sky wave: bent back by the ionosphere; used for HF (3 to 30 MHz) for long distance.
• Space wave: line of sight; used for VHF, UHF and microwave; TV, FM, mobile.
• Radio horizon: d = 4.12 (√h1 + √h2) km, with heights in metres (this includes normal atmospheric bending).
• Critical frequency: the highest frequency reflected from a layer at vertical incidence.
• MUF (maximum usable frequency): MUF = fc × sec θ, where θ is the angle of incidence.
• Skip distance: shortest ground distance reached by the sky wave at a given frequency.
• Ionosphere layers: D (day only, absorbs), E, F1 and F2 (F2 is the highest and strongest reflector).

Microwave transmission and waveguides

Microwaves lie roughly between 300 MHz and 300 GHz. Waveguides carry them with low loss and high power; they have a cutoff frequency below which waves do not propagate.

• Rectangular guide of broad side a: fc = c / 2a for the dominant TE10 mode.
• Guide wavelength: λg = λ0 / √(1 − (fc/f)²). It is always greater than free-space λ0.
• Waveguides carry TE (no electric field along the guide) and TM modes; they cannot carry TEM. Circular guides have TE11 as dominant mode.
• Phase velocity is greater than c; group velocity is less than c; vp × vg = c².

Microwave components

Microwave sources: the klystron uses velocity modulation (reflex klystron is a low-power oscillator); the magnetron is a crossed-field oscillator used in radar and ovens; the travelling wave tube (TWT) gives wide-band amplification. Solid-state: Gunn diode (transferred-electron effect), IMPATT diode (high power, noisy), varactor diode, and Schottky diode (detector and mixer).

S-parameters: S11 is the input reflection and S21 the forward transmission. For a reciprocal network S12 = S21. For a lossless network the S-matrix is unitary.

Antenna selection and practical points

• Feeding: a coaxial cable is unbalanced and a dipole is balanced, so a balun is used between them. A quarter-wave stub or transformer also matches impedances.
• Beamwidth and gain: a narrow beam means high gain. A rough rule for a dish is HPBW ≈ 70 λ / D degrees; for D = 1 m at λ = 0.1 m the beam is about 7°.
• Side lobes waste power and pick up interference, so designers try to keep them low.
• Polarization match: a receiving antenna must have the same polarization as the incoming wave. A mismatch of 90° (vertical to horizontal) gives a very large loss.
• Antenna height: taller towers give a longer radio horizon for VHF, UHF and microwave links. Microwave links use dishes on towers about 40 to 50 km apart.
• Radar and satellite use: dishes and horns are common; phased arrays steer the beam electronically by changing the phase at each element, with no moving parts.
• Mobile base stations use sector antennas (arrays with a wide horizontal beam and a narrow vertical beam).

Worked examples

• 1. Dipole length: at 300 MHz, λ = c/f = 3×10⁸ / 3×10⁸ = 1 m. A half-wave dipole is about 0.5 m long.
• 2. Cutoff frequency: a = 2.286 cm gives fc = 3×10⁸ / (2 × 0.02286) ≈ 6.56 GHz.
• 3. Dish gain: D = 2 m, f = 3 GHz (λ = 0.1 m), η = 0.6. G = 0.6 × (π × 20)² ≈ 0.6 × 3948 ≈ 2369, about 33.7 dB.
• 4. VSWR: ZL = 100 Ω, Z0 = 50 Ω. Γ = 50/150 = 1/3. VSWR = (4/3)/(2/3) = 2.
• 5. MUF: fc = 6 MHz, θ = 60°. MUF = 6 × sec 60° = 6 × 2 = 12 MHz.
• 6. Radio horizon: transmitter height 100 m and receiver at ground: d = 4.12 × 10 = 41.2 km.
• 7. Far field: D = 1 m, λ = 0.1 m gives 2D²/λ = 20 m.

Exam traps

• Half-wave dipole is 73 Ω; folded dipole is 292 Ω; quarter-wave monopole is 36.5 Ω.
• Directivity is a pattern property; gain includes efficiency. They are equal only for a lossless antenna.
• In a Yagi, the reflector is longer than the driven element and the directors are shorter.
• Broadside means elements in phase; end-fire means progressive phase shift.
• Guide wavelength is longer than free-space wavelength; phase velocity is above c.
• Waveguides cannot support TEM mode; coaxial lines can.
• E-plane tee is series; H-plane tee is shunt.
• An isolator is two-port and passes one way; a circulator has three or more ports.
• Ground wave is for low frequencies; sky wave is for HF; space wave is for VHF and above.
• dBi is relative to isotropic; dBd is relative to a half-wave dipole.

One-liners

• 1. Antennas are reciprocal.
• 2. Isotropic radiator has directivity 1.
• 3. Effective aperture Ae = λ²G / 4π.
• 4. Far field begins beyond 2D²/λ.
• 5. Helical antenna in axial mode gives circular polarization.
• 6. Log-periodic antenna is a wide-band design.
• 7. A horn is a flared waveguide.
• 8. Dominant mode in a rectangular guide is TE10.
• 9. A magic tee is a four-port hybrid junction.
• 10. A klystron works by velocity modulation.
• 11. A magnetron is a crossed-field oscillator used in radar.
• 12. VSWR = 1 means a perfect match.

Practice questions

1. What is the approximate radiation resistance of a half-wave dipole in free space?

   1. 292 Ω
   2. 377 Ω
   3. 36.5 Ω
   4. 73 Ω
   Answer

   D. 73 Ω

   A half-wave dipole has a radiation resistance of about 73 Ω.

2. What is the directivity of an isotropic radiator?

   1. 1.5
   2. 1.64
   3. 1 (0 dBi)
   4. 2
   Answer

   C. 1 (0 dBi)

   An isotropic source radiates equally in all directions, so its directivity is 1.

3. The input impedance of a folded dipole is about

   1. 73 Ω
   2. 292 Ω
   3. 36.5 Ω
   4. 600 Ω
   Answer

   B. 292 Ω

   A folded dipole steps up the 73 Ω dipole impedance by a factor of 4, to about 292 Ω.

4. The dominant mode in a rectangular waveguide is

   1. TM11
   2. TE10
   3. TE11
   4. TEM
   Answer

   B. TE10

   TE10 has the lowest cutoff frequency in a rectangular guide.

5. In a Yagi-Uda antenna the element that is slightly longer than the driven element is the

   1. folded element
   2. feed horn
   3. director
   4. reflector
   Answer

   D. reflector

   The reflector is longer than the driven element; directors are shorter.

6. Which wave propagation is mainly used for long-distance HF communication?

   1. Ground wave
   2. Sky wave
   3. Space wave
   4. Surface wave at VLF only
   Answer

   B. Sky wave

   HF waves (3 to 30 MHz) are reflected by the ionosphere, giving sky-wave links over long distances.

7. Which device passes microwave power in one direction only and absorbs the reverse wave?

   1. H-plane tee
   2. Magic tee
   3. Directional coupler
   4. Isolator
   Answer

   D. Isolator

   An isolator is a two-port ferrite device that is non-reciprocal and absorbs reverse power.

8. A microwave tube that works on velocity modulation is the

   1. magnetron
   2. varactor
   3. Gunn diode
   4. klystron
   Answer

   D. klystron

   The klystron bunches electrons by velocity modulation.

9. The effective aperture of an antenna of gain G at wavelength λ is

   1. λ²G / 4π
   2. λG / 4π
   3. λ² / 4πG
   4. 4πG / λ²
   Answer

   A. λ²G / 4π

   Ae = λ²G/4π is the standard relation.

10. The VSWR on a line with a perfect match is

    1. 0
    2. 2
    3. 1
    4. infinity
    Answer

    C. 1

    With Γ = 0, VSWR = (1+0)/(1−0) = 1.

11. A magnetron is mainly used in

    1. optical fibres
    2. radar and microwave ovens
    3. audio amplifiers
    4. FM broadcasting receivers
    Answer

    B. radar and microwave ovens

    The magnetron is a high-power crossed-field oscillator used in radar and ovens.

12. Gain of an antenna is equal to its directivity multiplied by

    1. bandwidth
    2. beamwidth
    3. VSWR
    4. radiation efficiency
    Answer

    D. radiation efficiency

    G = η × D, where η is radiation efficiency.

13. A quarter-wave monopole above a perfect ground plane has an impedance of about

    1. 50 Ω
    2. 73 Ω
    3. 36.5 Ω
    4. 292 Ω
    Answer

    C. 36.5 Ω

    It is half of the half-wave dipole value, about 36.5 Ω.

14. The usual far-field distance for an antenna of largest dimension D at wavelength λ is

    1. 2D²/λ
    2. D²/4λ
    3. D/2λ
    4. λ²/2D
    Answer

    A. 2D²/λ

    The Rayleigh distance 2D²/λ marks the start of the far field.

15. Waveguides cannot support which mode?

    1. TE10
    2. TEM
    3. TE20
    4. TM11
    Answer

    B. TEM

    A hollow single-conductor guide cannot carry TEM waves.

16. What is the length of a half-wave dipole (ideal) at 150 MHz?

    1. 2 m
    2. 0.5 m
    3. 0.25 m
    4. 1 m
    Answer

    D. 1 m

    λ = 3×10⁸/150×10⁶ = 2 m; half is 1 m.

17. The cutoff frequency of a rectangular guide with broad side a = 3 cm (TE10) is

    1. 5 GHz
    2. 2.5 GHz
    3. 10 GHz
    4. 6.6 GHz
    Answer

    A. 5 GHz

    fc = c/2a = 3×10⁸/(2×0.03) = 5×10⁹ Hz.

18. A transmission line of Z0 = 50 Ω is ended with a 150 Ω load. The VSWR is

    1. 2
    2. 1.5
    3. 3
    4. 4
    Answer

    C. 3

    Γ = 100/200 = 0.5; VSWR = 1.5/0.5 = 3.

19. An antenna has gain 100. Its gain in dB is

    1. 100 dB
    2. 20 dB
    3. 40 dB
    4. 10 dB
    Answer

    B. 20 dB

    10 log10 100 = 20 dB.

20. The MUF for a layer with critical frequency 5 MHz and angle of incidence 60° is

    1. 2.5 MHz
    2. 8.66 MHz
    3. 5 MHz
    4. 10 MHz
    Answer

    D. 10 MHz

    MUF = fc sec θ = 5 × 2 = 10 MHz.

21. The radio horizon for a transmitting antenna 100 m high and a receiver at ground level, using d = 4.12√h km, is about

    1. 41.2 km
    2. 4.12 km
    3. 20.6 km
    4. 412 km
    Answer

    A. 41.2 km

    4.12 × √100 = 41.2 km.

22. A dish of diameter 2 m at 3 GHz with efficiency 0.6 has a gain closest to

    1. 20 dB
    2. 33.7 dB
    3. 43 dB
    4. 26 dB
    Answer

    B. 33.7 dB

    λ = 0.1 m; G = 0.6(π×20)² ≈ 2369, which is 33.7 dB.

23. A lossless antenna has gain 20 dBi. Convert to dBd.

    1. 20 dBd
    2. 10 dBd
    3. 17.85 dBd
    4. 22.15 dBd
    Answer

    C. 17.85 dBd

    dBd = dBi − 2.15 = 17.85.

24. A dipole antenna (gain 100) at wavelength 0.3 m has effective aperture closest to

    1. 0.0072 m²
    2. 7.2 m²
    3. 0.72 m²
    4. 0.09 m²
    Answer

    C. 0.72 m²

    Ae = 0.09 × 100 / 12.57 ≈ 0.716 m².

25. For a guide with fc = 6 GHz operating at 10 GHz, the guide wavelength relative to free-space wavelength λ0 is

    1. 1.25 λ0
    2. 1.67 λ0
    3. 0.8 λ0
    4. 0.6 λ0
    Answer

    A. 1.25 λ0

    λg = λ0/√(1−0.36) = λ0/0.8 = 1.25 λ0.

26. For a dish of D = 1 m at λ = 0.1 m, the far-field distance 2D²/λ is

    1. 200 m
    2. 20 m
    3. 2 m
    4. 0.2 m
    Answer

    B. 20 m

    2 × 1 / 0.1 = 20 m.

27. For a rectangular guide, the product of phase velocity and group velocity is

    1. 1/c²
    2. c
    3. c/2
    4. c²
    Answer

    D. c²

    vp × vg = c² for waveguide propagation.

28. Which microwave junction has all four ports isolated in pairs, with the E-arm and H-arm isolated from each other?

    1. E-plane tee
    2. H-plane tee
    3. Rat-race ring only
    4. Magic tee
    Answer

    D. Magic tee

    The magic tee is a hybrid junction with E and H arms mutually isolated.

29. Which antenna is preferred for a very wide bandwidth with a repeating pattern against the logarithm of frequency?

    1. Log-periodic antenna
    2. Microstrip patch
    3. Small loop
    4. Half-wave dipole
    Answer

    A. Log-periodic antenna

    The log-periodic antenna has impedance and pattern repeating in log-frequency steps.

30. A helical antenna operating in the axial mode radiates

    1. vertically polarized waves only
    2. circularly polarized waves
    3. horizontally polarized waves only
    4. no waves in the forward direction
    Answer

    B. circularly polarized waves

    Axial-mode helices give circular polarization and a wide band.

31. Which diode works on the transferred-electron effect?

    1. Varactor diode
    2. Zener diode
    3. Gunn diode
    4. IMPATT diode
    Answer

    C. Gunn diode

    The Gunn diode uses the transferred-electron effect.

32. In an array, the pattern of the whole array equals

    1. element pattern × array factor
    2. element pattern + array factor
    3. element pattern ÷ array factor
    4. array factor only
    Answer

    A. element pattern × array factor

    Pattern multiplication principle.

33. Which array gives the narrowest beam for a given side-lobe level?

    1. Uniform array
    2. Single dipole
    3. Dolph-Chebyshev array
    4. Binomial array
    Answer

    C. Dolph-Chebyshev array

    Dolph-Chebyshev gives the optimum trade of beamwidth against side-lobe level.

34. Consider the statements about waveguides: 1. Guide wavelength is longer than free-space wavelength. 2. Phase velocity inside the guide is less than the speed of light.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Guide wavelength exceeds λ0, and phase velocity exceeds c (group velocity is below c). Only 1 is correct.

35. Consider: 1. A half-wave dipole has directivity of about 1.64. 2. An isotropic radiator has directivity of 1.5.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Half-wave dipole is 1.64 (2.15 dBi); isotropic is 1.

36. Consider: 1. A circulator is a non-reciprocal device. 2. An isolator is a ferrite device with two ports.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct; both use ferrite and are non-reciprocal.

37. Consider: 1. In a Yagi-Uda antenna the directors are shorter than the driven element. 2. A Yagi is a broadband antenna.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Directors are shorter; a Yagi is a narrow-band antenna.

38. Consider: 1. Ground waves are used mainly for low frequencies. 2. Space waves are used for VHF and above.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both statements are standard propagation facts.

39. Consider: 1. The E-plane tee is a shunt junction. 2. The H-plane tee is a series junction.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    D. Neither 1 nor 2

    The E-plane tee is series and the H-plane tee is shunt, so both are wrong.

40. Consider: 1. A broadside array has elements fed in phase. 2. An end-fire array radiates along the line of the array.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both describe the two standard array types.

41. Match the device (first) to its use (second): 1. Directional coupler 2. Cavity resonator 3. TWT. Which pairing is correct?

    1. Directional coupler – isolation of reverse wave; cavity resonator – wide-band amplification; TWT – power sampling
    2. Directional coupler – power sampling; cavity resonator – frequency selection; TWT – wide-band amplification
    3. Directional coupler – wide-band amplification; cavity resonator – power sampling; TWT – frequency selection
    4. Directional coupler – frequency selection; cavity resonator – wide-band amplification; TWT – power sampling
    Answer

    B. Directional coupler – power sampling; cavity resonator – frequency selection; TWT – wide-band amplification

    Couplers sample power, cavities resonate (high Q), TWTs amplify over a wide band.

42. Match the antenna to its impedance: 1. Half-wave dipole 2. Folded dipole 3. Quarter-wave monopole.

    1. 292 Ω, 73 Ω, 36.5 Ω
    2. 73 Ω, 36.5 Ω, 292 Ω
    3. 36.5 Ω, 73 Ω, 292 Ω
    4. 73 Ω, 292 Ω, 36.5 Ω
    Answer

    D. 73 Ω, 292 Ω, 36.5 Ω

    Dipole 73 Ω, folded dipole 292 Ω, monopole 36.5 Ω.

43. Match the propagation mode to the frequency band: 1. Ground wave 2. Sky wave 3. Space wave.

    1. 3 to 30 MHz; below about 2 MHz; above 30 MHz
    2. Below about 2 MHz; 3 to 30 MHz; above 30 MHz
    3. Below 2 MHz; above 30 MHz; 3 to 30 MHz
    4. Above 30 MHz; 3 to 30 MHz; below 2 MHz
    Answer

    B. Below about 2 MHz; 3 to 30 MHz; above 30 MHz

    Ground wave is LF/MF, sky wave is HF, space wave is VHF and above.

44. A parabolic dish feed is placed at the

    1. edge of the dish
    2. centre of the aperture plane behind the dish
    3. vertex
    4. focus
    Answer

    D. focus

    The feed sits at the focal point so the reflected wave is a plane wave.

45. Which statement is true of reflection coefficient magnitude for a short-circuited load?

    1. |Γ| = infinity
    2. |Γ| = 1
    3. |Γ| = 0
    4. |Γ| = 0.5
    Answer

    B. |Γ| = 1

    ZL = 0 gives Γ = −1, so |Γ| = 1 and VSWR is infinite.