Radiation from a Dipole Questions and Answers

Q: Why is the current zero at the ends of a dipole?

Continuity requires that current vanish where the conductor ends, because there is nowhere for the charge to go. Charge accumulates instead, so the voltage is indeed a maximum there, but that is a consequence rather than the cause. Radiation resistance is a terminal quantity for the whole antenna and not a function of position, and the taper of the wire is irrelevant. The boundary condition at the ends is what forces the standing wave pattern along the whole element.

Q: What is the directivity of a half wave dipole?

The half wave dipole's directivity is 1.64, which is 2.15 decibels above isotropic. The figure 1.5 belongs to the ideal short dipole and 2.15 is the decibel value being offered as a ratio, which is the standard trap in this question. Doubling to 3.28 would correspond to a monopole over a perfect ground plane, which radiates the same pattern into half the space. Knowing these few numbers exactly saves a good deal of arithmetic elsewhere.

Q: What is the input impedance of an ideal thin half wave dipole?

An exactly half wavelength thin dipole presents about 73 ohms of resistance with some 42.5 ohms of inductive reactance, and shortening it by a few per cent removes the reactance to leave a resonant 70 ohms or so. That trimming is why practical dipoles are cut a little short of a half wavelength. The 36.5 ohm figure belongs to the quarter wave monopole and 300 ohms to the folded dipole, both derived from this same base value.

Q: What does the image of a vertical monopole in a perfect ground plane look like?

A vertical element's image is the same length below the surface with its current in the same direction, so the two together form a full dipole. A horizontal element's image carries opposite current, which is why a low horizontal antenna nearly cancels itself at low angles. The image is a mathematical device that satisfies the boundary condition of zero tangential electric field at a perfect conductor, and it applies to any source above such a plane.

Q: Why does a horizontal dipole close to the ground radiate poorly at low angles?

The out of phase image means the direct and reflected fields nearly cancel along the surface, leaving radiation directed steeply upward. Raising the antenna towards a half wavelength brings the reflection back into phase at useful angles. Ground absorbs partially rather than completely, radiation resistance changes but does not vanish, and lobe splitting occurs at greater heights rather than at low ones. It is the phase of the image, not any absorption, that governs the effect.

Q: What is the effect on directivity of placing a dipole above a perfect reflecting plane?

With the reflection reinforcing the direct wave, power that would have gone downward is redirected upward and the directivity can approach double the free space figure, giving up to six decibels of field enhancement in the favoured direction. The height above the plane determines the angles at which reinforcement occurs, so the result is certainly not height independent. This is the operating principle of the corner reflector and of every ground plane antenna.

Q: What is a folded dipole?

The folded dipole is a loop of two closely spaced parallel wires, one broken at its centre for the feed, and it behaves as a dipole with four times the input impedance. The extra conductor also widens the bandwidth appreciably. Bending an element changes the pattern, turning the ends back is a shortening technique, and stacking is an array arrangement. The folded form is the standard driven element in Yagi arrays for exactly the impedance reason.

11.

Why is the current zero at the ends of a dipole?

A.Charge cannot flow beyond the end of the conductor
B.The radiation resistance falls right down to zero there
C.The voltage is a maximum at the ends
D.The conductor is thinnest at the ends

Answer: A

Continuity requires that current vanish where the conductor ends, because there is nowhere for the charge to go. Charge accumulates instead, so the voltage is indeed a maximum there, but that is a consequence rather than the cause. Radiation resistance is a terminal quantity for the whole antenna and not a function of position, and the taper of the wire is irrelevant. The boundary condition at the ends is what forces the standing wave pattern along the whole element.

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12.

The far field pattern of a half wave dipole is \( \cos(\tfrac{\pi}{2}\cos\theta)/\sin\theta \). What is its value along the wire axis?

A.0.707, the half power value
B.Zero
C.One
D.Infinite

Answer: B

Setting theta to zero makes the cosine argument pi over two, whose cosine is zero, and although the denominator also vanishes the limit is zero:

\[ \lim_{\theta \to 0} F(\theta) = 0 \]

so there is a null along the wire. The pattern is maximum broadside at ninety degrees, where the function equals one. Every linear current distribution shares this axial null, which is why a vertical dipole radiates nothing straight up.

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13.

What is the directivity of a half wave dipole?

A.2.15
B.3.28, twice the isolated value
C.1.64
D.1.50

Answer: C

The half wave dipole's directivity is 1.64, which is 2.15 decibels above isotropic. The figure 1.5 belongs to the ideal short dipole and 2.15 is the decibel value being offered as a ratio, which is the standard trap in this question. Doubling to 3.28 would correspond to a monopole over a perfect ground plane, which radiates the same pattern into half the space. Knowing these few numbers exactly saves a good deal of arithmetic elsewhere.

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14.

What is the input impedance of an ideal thin half wave dipole?

A.73 ohms with no reactive part
B.36.5 plus j21 ohms
C.300 ohms resistive, as for a folded dipole
D.73 plus j42.5 ohms

Answer: D

An exactly half wavelength thin dipole presents about 73 ohms of resistance with some 42.5 ohms of inductive reactance, and shortening it by a few per cent removes the reactance to leave a resonant 70 ohms or so. That trimming is why practical dipoles are cut a little short of a half wavelength. The 36.5 ohm figure belongs to the quarter wave monopole and 300 ohms to the folded dipole, both derived from this same base value.

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15.

Why is a practical half wave dipole cut slightly shorter than half a wavelength?

A.To remove the inductive reactance and reach resonance
B.To reduce the radiation resistance to fifty ohms
C.To narrow the beamwidth in the horizontal plane
D.To raise the efficiency by reducing the conductor loss

Answer: A

At exactly half a wavelength the impedance is inductive, so shortening by around five per cent, more for a thick element, cancels the reactance and leaves a purely resistive feed. The resistance falls only slightly and certainly not to fifty ohms, the pattern is essentially unchanged over such a small adjustment, and conductor loss is negligible in either case. The shortening factor depends on the length to diameter ratio, which is why thick elements need more of it.

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16.

What is the radiation resistance of a quarter wave monopole over a perfect ground plane?

A.18.25 ohms, a quarter of the dipole value
B.36.5 ohms
C.73 ohms
D.50 ohms

Answer: B

The monopole radiates the dipole's pattern into a hemisphere with the same terminal current, so it radiates half the power and its radiation resistance is half that of the dipole, about 36.5 ohms. Its directivity is correspondingly doubled to 3.28. Fifty ohms is a cable convention and the quarter value corresponds to nothing. The image principle gives both results at once and is much quicker than any direct integration.

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17.

What does the image of a vertical monopole in a perfect ground plane look like?

A.A horizontal element lying in the plane itself
B.No image forms for a vertical element
C.An identical element below the plane carrying current in the same sense
D.An identical element below the plane carrying opposite current

Answer: C

A vertical element's image is the same length below the surface with its current in the same direction, so the two together form a full dipole. A horizontal element's image carries opposite current, which is why a low horizontal antenna nearly cancels itself at low angles. The image is a mathematical device that satisfies the boundary condition of zero tangential electric field at a perfect conductor, and it applies to any source above such a plane.

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18.

Why does a horizontal dipole close to the ground radiate poorly at low angles?

A.The ground absorbs horizontally polarised waves almost completely
B.The radiation resistance falls to zero near the ground
C.The pattern splits into many lobes at low height
D.Its image carries opposite current and cancels the direct wave

Answer: D

The out of phase image means the direct and reflected fields nearly cancel along the surface, leaving radiation directed steeply upward. Raising the antenna towards a half wavelength brings the reflection back into phase at useful angles. Ground absorbs partially rather than completely, radiation resistance changes but does not vanish, and lobe splitting occurs at greater heights rather than at low ones. It is the phase of the image, not any absorption, that governs the effect.

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19.

What is the effect on directivity of placing a dipole above a perfect reflecting plane?

A.It can approach twice the free space value
B.It is unchanged by the presence of the plane
C.It falls to half the free space value
D.It becomes independent of the height above the plane

Answer: A

With the reflection reinforcing the direct wave, power that would have gone downward is redirected upward and the directivity can approach double the free space figure, giving up to six decibels of field enhancement in the favoured direction. The height above the plane determines the angles at which reinforcement occurs, so the result is certainly not height independent. This is the operating principle of the corner reflector and of every ground plane antenna.

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20.

What is a folded dipole?

A.Two dipoles stacked one above the other and fed in phase
B.Two parallel conductors joined at the ends and fed at one centre
C.A dipole bent through ninety degrees at its centre
D.A dipole whose ends are turned back to shorten it

Answer: B

The folded dipole is a loop of two closely spaced parallel wires, one broken at its centre for the feed, and it behaves as a dipole with four times the input impedance. The extra conductor also widens the bandwidth appreciably. Bending an element changes the pattern, turning the ends back is a shortening technique, and stacking is an array arrangement. The folded form is the standard driven element in Yagi arrays for exactly the impedance reason.

Discuss in Forum

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