Antenna Fundamentals and Parameters Questions and Answers

Q: An antenna has a beam solid angle of \( 0.04 \) steradians. What is its directivity?

Directivity is four pi divided by the beam solid angle:\[ D = \tfrac{4\pi}{0.04} \approx 314 \]so about 314, or roughly 25 decibels. The relation shows directly that concentrating radiation into a smaller solid angle raises directivity in exact proportion, and it is the cleanest statement of what an antenna does: it redistributes a fixed radiated power over a smaller range of directions rather than creating power.

Q: What is the relationship between gain and directivity?

Gain accounts for the power lost in the structure, so it is the directivity reduced by the radiation efficiency, and the two are equal only for a lossless antenna. A well made reflector may be ninety-nine per cent efficient so the distinction hardly matters, while a small electrically short antenna may be a few per cent efficient and the difference is enormous. Mismatch is usually accounted separately as realised gain, and aperture area enters the formula for directivity rather than this relation.

Q: What is the radiation efficiency of an antenna?

Radiation efficiency is the fraction of the accepted power that leaves as radiation rather than being dissipated in conductor and dielectric loss, and in circuit terms it is the radiation resistance divided by the sum of radiation and loss resistances. Referring to available rather than accepted power folds in the mismatch, which is a separate factor. Aperture illumination uniformity is aperture efficiency, a distinct quantity affecting directivity rather than loss.

Q: What is radiation resistance?

Radiation resistance is a fictitious resistance which, carrying the same current, would dissipate the power the antenna actually radiates. For a half wave dipole it is about seventy-three ohms and for a short dipole only a few ohms, which is why short antennas are inefficient. Conductor loss is a separate resistance in series with it, the feed point resistance is the sum of the two, and ground loss is one particular contribution to the loss term in a monopole.

Q: What is the input impedance of a resonant half wave dipole in free space?

A thin half wave dipole at resonance presents approximately 73 ohms with a small reactive part that vanishes when it is trimmed slightly short of a half wavelength. Fifty ohms is the cable standard rather than the dipole value, three hundred ohms is the folded dipole figure used with twin feeder, and 377 ohms is the intrinsic impedance of free space, which is a property of the medium and not of any antenna. The mismatch between 73 and 50 ohms is small enough to be tolerated in most installations.

Q: What does a voltage standing wave ratio of 1 indicate?

A standing wave ratio of unity means no reflected wave, so all the power delivered to the feed enters the antenna. Total reflection gives an infinite ratio, as an open or short circuit termination does. A perfect match says nothing about efficiency, since a resistor terminating the cable would match perfectly and radiate nothing, and a purely reactive load reflects everything. Confusing a good match with a good antenna is one of the commonest errors in practice.

Q: What is return loss?

Return loss states how far below the incident power the reflected power lies, so a large number in decibels means a good match; ten decibels corresponds to a standing wave ratio near two and twenty decibels to about 1.2. It is the same information as the standing wave ratio in a more convenient form for wideband plotting. Feeder loss, gain asymmetry and balun loss are all separate quantities, though each can disguise a poor match by absorbing the reflected power.

11.

An antenna has a beam solid angle of \( 0.04 \) steradians. What is its directivity?

A.About 12.6, which is the value in decibels
B.About 314
C.About 100
D.About 25

Answer: B

Directivity is four pi divided by the beam solid angle:

\[ D = \tfrac{4\pi}{0.04} \approx 314 \]

so about 314, or roughly 25 decibels. The relation shows directly that concentrating radiation into a smaller solid angle raises directivity in exact proportion, and it is the cleanest statement of what an antenna does: it redistributes a fixed radiated power over a smaller range of directions rather than creating power.

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12.

What is the relationship between gain and directivity?

A.Gain equals directivity for every practical antenna
B.Gain is directivity multiplied by the aperture area
C.Gain is directivity multiplied by radiation efficiency
D.Gain is directivity divided by the standing wave ratio

Answer: C

Gain accounts for the power lost in the structure, so it is the directivity reduced by the radiation efficiency, and the two are equal only for a lossless antenna. A well made reflector may be ninety-nine per cent efficient so the distinction hardly matters, while a small electrically short antenna may be a few per cent efficient and the difference is enormous. Mismatch is usually accounted separately as realised gain, and aperture area enters the formula for directivity rather than this relation.

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13.

What is the radiation efficiency of an antenna?

A.Radiated power divided by the power available from the source
B.Gain divided by directivity multiplied by the mismatch factor
C.The proportion of the aperture that is uniformly illuminated
D.Radiated power divided by power accepted at the terminals

Answer: D

Radiation efficiency is the fraction of the accepted power that leaves as radiation rather than being dissipated in conductor and dielectric loss, and in circuit terms it is the radiation resistance divided by the sum of radiation and loss resistances. Referring to available rather than accepted power folds in the mismatch, which is a separate factor. Aperture illumination uniformity is aperture efficiency, a distinct quantity affecting directivity rather than loss.

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14.

What is radiation resistance?

A.The equivalent resistance accounting for radiated power
B.The ohmic resistance of the conductor at radio frequency
C.The real part of the impedance seen at the feed point
D.The resistance of the ground system beneath a monopole

Answer: A

Radiation resistance is a fictitious resistance which, carrying the same current, would dissipate the power the antenna actually radiates. For a half wave dipole it is about seventy-three ohms and for a short dipole only a few ohms, which is why short antennas are inefficient. Conductor loss is a separate resistance in series with it, the feed point resistance is the sum of the two, and ground loss is one particular contribution to the loss term in a monopole.

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15.

Why is a very short dipole an inefficient radiator?

A.It radiates only in the direction of its own axis
B.Its radiation resistance is small compared with its loss resistance
C.Its radiation pattern has too many side lobes
D.It presents a purely resistive impedance to the feed

Answer: B

Radiation resistance falls as the square of the length in wavelengths, so for a very short element it becomes comparable with or smaller than the conductor and matching losses, and most of the input power is dissipated as heat. Its pattern is in fact very simple, close to that of an ideal dipole with a broad doughnut shape and no radiation along the axis at all, and its impedance is strongly capacitive rather than resistive. Efficiency, not pattern, is the limitation of an electrically small antenna.

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16.

What is the input impedance of a resonant half wave dipole in free space?

A.About 300 ohms resistive
B.About 377 ohms resistive, matching free space
C.About 73 ohms resistive
D.About 50 ohms resistive

Answer: C

A thin half wave dipole at resonance presents approximately 73 ohms with a small reactive part that vanishes when it is trimmed slightly short of a half wavelength. Fifty ohms is the cable standard rather than the dipole value, three hundred ohms is the folded dipole figure used with twin feeder, and 377 ohms is the intrinsic impedance of free space, which is a property of the medium and not of any antenna. The mismatch between 73 and 50 ohms is small enough to be tolerated in most installations.

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17.

What does a voltage standing wave ratio of 1 indicate?

A.Total reflection at the antenna terminals
B.An antenna radiating at its maximum efficiency
C.An antenna whose impedance is purely reactive
D.A perfect match with no reflected power

Answer: D

A standing wave ratio of unity means no reflected wave, so all the power delivered to the feed enters the antenna. Total reflection gives an infinite ratio, as an open or short circuit termination does. A perfect match says nothing about efficiency, since a resistor terminating the cable would match perfectly and radiate nothing, and a purely reactive load reflects everything. Confusing a good match with a good antenna is one of the commonest errors in practice.

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18.

An antenna presents 75 ohms to a 50 ohm feeder. What is the standing wave ratio?

A.1.5
B.1.25
C.2.0
D.0.67, taking the reciprocal

Answer: A

For a purely resistive load the ratio is simply the larger resistance over the smaller:

\[ S = \tfrac{75}{50} = 1.5 \]

giving 1.5, which corresponds to about four per cent of the incident power reflected and is entirely acceptable. By convention the ratio is always quoted as one or greater, so a value below one is a sign that the calculation has been inverted. This simple case is worth remembering because a dipole on a fifty ohm cable is exactly it.

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19.

What is return loss?

A.The loss in the balun at the feed point of the antenna
B.The reflected power expressed in decibels below the incident
C.The power lost in the feeder on the return journey
D.The difference between forward and reverse gain

Answer: B

Return loss states how far below the incident power the reflected power lies, so a large number in decibels means a good match; ten decibels corresponds to a standing wave ratio near two and twenty decibels to about 1.2. It is the same information as the standing wave ratio in a more convenient form for wideband plotting. Feeder loss, gain asymmetry and balun loss are all separate quantities, though each can disguise a poor match by absorbing the reflected power.

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20.

Why can a lossy feeder make an antenna appear better matched than it is?

A.Loss reduces the power delivered so reflection is smaller
B.The measurement instrument compensates for cable loss
C.The reflected wave is attenuated twice on its way back
D.The feeder transforms the impedance to fifty ohms

Answer: C

A reflected wave travels the length of the cable a second time, so it is attenuated twice over and the standing wave ratio measured at the transmitter is closer to unity than the one at the antenna. A very lossy cable can make a completely faulty antenna look acceptable. The cure is to measure at the antenna end or to correct for the known cable loss. Impedance transformation depends on length rather than loss, and instruments do not correct unless told the cable characteristics.

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