# Performance of a complimentary antenna?

Suppose the performance of an antenna is calculated.

tech99

tech99
Gold Member
An antenna and its complement are related by Babinet's Principle, which was originally devised for simple problems with light.
The input impedance, for instance, of the two antennas is related by 2 x SQRT(Z1 x Z2) = Zo, where Zo is 377 Ohms, the intrinsic impedance of free space. For instance, a strip dipole might have an input impedance of 70 Ohms. Its complement will be a slot having the same dimensions and cut in a large sheet of metal. The input impedance across the centre of the slot will be 507 Ohms.
The radiation pattern of one antenna in its E-plane should be the same as the other in its H-plane. However, there is a little uncertainty about this because a half wave slot does not seem to replicate a dipole pattern exactly.
In his book "Antennas", J D Kraus introduces the term "Magnetic Dipole" for antennas which are complementary to a dipole. By this he meant that the E plane pattern of a dipole resembles the H plane pattern of a slot or loop. Unfortunately, this has led to some confusion over the radiation mechanism of the two. For both classes of antenna, radiation is caused by the acceleration of electrons.

Klystron and berkeman
An antenna and its complement are related by Babinet's Principle, which was originally devised for simple problems with light.
The input impedance, for instance, of the two antennas is related by 2 x SQRT(Z1 x Z2) = Zo, where Zo is 377 Ohms, the intrinsic impedance of free space. For instance, a strip dipole might have an input impedance of 70 Ohms. Its complement will be a slot having the same dimensions and cut in a large sheet of metal. The input impedance across the centre of the slot will be 507 Ohms.
The radiation pattern of one antenna in its E-plane should be the same as the other in its H-plane. However, there is a little uncertainty about this because a half wave slot does not seem to replicate a dipole pattern exactly.
In his book "Antennas", J D Kraus introduces the term "Magnetic Dipole" for antennas which are complementary to a dipole. By this he meant that the E plane pattern of a dipole resembles the H plane pattern of a slot or loop. Unfortunately, this has led to some confusion over the radiation mechanism of the two. For both classes of antenna, radiation is caused by the acceleration of electrons.

You mentioned impedance and the radiation pattern of such antenna. How about other properties?

Baluncore
2019 Award
Suppose the performance of an antenna is calculated.
By performance, do you mean the drive impedance or the radiation pattern?

The radiation pattern of an array of elements is important. This becomes very important with arrays of slots in a waveguide, such as often used for marine radar antennas. Are you only interested in single elements and their complement?

There is an elegant design, halfway between the electric-dipole and it's complement, the magnetic-slot.
That special case is the self-complementary antenna, where the conductor and space are symmetric in pattern.
The self-complementary antenna has an input impedance of 376.73 / 2 = 188.365 ohm.
http://bbs.hwrf.com.cn/downrf/self-complementary Antenna.pdf

By performance, do you mean the drive impedance or the radiation pattern?

The radiation pattern of an array of elements is important. This becomes very important with arrays of slots in a waveguide, such as often used for marine radar antennas. Are you only interested in single elements and their complement?

There is an elegant design, halfway between the electric-dipole and it's complement, the magnetic-slot.
That special case is the self-complementary antenna, where the conductor and space are symmetric in pattern.
The self-complementary antenna has an input impedance of 376.73 / 2 = 188.365 ohm.
http://bbs.hwrf.com.cn/downrf/self-complementary Antenna.pdf

There are many self-complementary antenna on the web.
However, I am not talking about self-complementary antenna.

Baluncore
2019 Award
You mentioned impedance and the radiation pattern of such antenna. How about other properties?
What other properties are there that you are interested in?

What other properties are there that you are interested in?

Everything we can calculated from an antenna.

tech99
Gold Member
Everything we can calculated from an antenna.
The near fields also seem to be complementary. For instance, if we approach a dipole along the equatorial plane, when we get closer than about lambda/6, the power flux density no longer grows with 1/D^2 but flattens off until we reach the antenna. The E-field remains uniform from lambda/6 until we almost touch the antenna, whilst the B field continues upward with 1/D. But for a slot antenna, the opposite happens; the E field grows with 1/D whilst the B field remains constant as the antenna is approached.
If we bring two dipoles towards each other, the loss between them is reaches 3dB approx. at a spacing of lambda/6 and then flattens off and is still 3dB when they touch. But I am sad to say, with a slot and a dipole, once they touch the same thing does not happen.

sophiecentaur
Gold Member
A bit of a necropost but I have to wonder what fundamental laws are being used to lead one to expect that a 'similarity' is several respects (Kraus) should demand that there would be total equivalence. I know that this complementary idea is always taught in EM courses but that doesn't mean there should be any significant principle involved.
The principle of Reciprocity tells us that transmit and receive antennae could be interchanged and the loss over any path would be the same but reciprocity has to run out of steam once the antennae are near enough together. We also tend to analyse antennae as either Transmit or Receive, depending on which suits us and we assume the patterns will come out right.

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tech99
Gold Member
A bit of a nectar post but I have to wonder what fundamental laws are being used to lead one to expect that a 'similarity' is several respects (Kraus) should demand that there would be total equivalence. I know that this complementary idea is always taught in EM courses but that doesn't mean there should be any significant principle involved.
The principle of Reciprocity tells us that transmit and receive antennae could be interchanged and the loss over any path would be the same but reciprocity has to run out of steam once the antennae are near enough together. We also tend to analyse antennae as either Transmit or Receive, depending on which suits us and we assume the patterns will come out right.
The reciprocity idea seems hard to disprove. For instance, if I have two dipoles very close to one another, the loss between them is fixed at approx 3dB. As the antennas are identical, I measure 3dB whichever way round I do the test.
Regarding complementary antennas, it is based on Babinet's Principle with additional work by Booker. However, I have a nagging doubt about it as a slot does not seem to have exactly the same pattern as an equivalent dipole.

sophiecentaur
Baluncore