Magic Tee
Encyclopedia
A magic tee is a hybrid
or 3dB coupler used in microwave
systems. It is an alternative to the rat-race coupler
. In contrast to the rat-race, the three-dimensional structure of the magic-tee makes is less readily constructed in planar technologies such as microstrip
or stripline
.
The magic tee was originally developed in World-War II, and first published by W. A. Tyrell (of Bell Labs) in a 1947 IRE paper. Robert L. Kyhl and Bob Dicke independently created magic tees around the same time period.
tees. Arm 3 forms an H-plane tee with arms 1 and 2. Arm 4 forms an E-plane tee with arms 1 and 2. Arms 1 and 2 are sometimes called the side or collinear arms. Port 3 is called the H-plane port, and is also called the Σ port, sum port or the P-port (for Parallel). Port 4 is the E-plane port, and is also called the Δ port, difference port, or S-port (for Series). There is no one single established convention regarding the numbering of the ports.
To function correctly the magic tee must incorporate an internal matching structure. This structure typically consists of a post inside the H-plane tee and an inductive iris inside the E-plane limb, though many alternative structures have been proposed. Dependence on the matching structure means that the magic tee will only work over a limited frequency band.
for an ideal magic tee is
(the signs of the elements in the fourth row and fourth column of this matrix may be reversed, depending on the polarity assumed for port 4).
and conservation of energy
it may be shown that the two collinear ports are also matched, and are magically isolated from each other.
The E-field of the dominant mode in each port is perpendicular to the broad wall of the waveguide
. The signals in the E-plane and H-plane ports therefore have orthogonal polarizations, and so (considering the symmetry of the structure) there can be no communication between these two ports.
For a signal entering the H-plane port, a well-designed matching structure will prevent any of the power in the signal being reflected back out of the same port. As there can be no communication with the E-plane port, and again considering the symmetry of the structure, then
the power in this signal must be divided equally between to the two collinear ports.
Similarly for the E-plane port, if the matching structure eliminates any reflection from this port, then the power entering it must be divided equally between the two collinear ports.
Now by reciprocity
, the coupling between any pair of ports is the same in either direction (the scattering matrix is symmetric). So if the H-plane port is matched, then half the power entering either one of the collinear ports will leave by the H-plane port. If the E-plane port is also matched, then half power will leave by the E-plane port. In this circumstance, there is no power 'left over' either to be reflected out of the first collinear port or to be transmitted to the other collinear port. Despite apparently being in direct communication with each other, the two collinear ports are magically isolated.
The isolation between the E-plane and H-plane ports is wide-band and is as perfect as is the symmetry of the device. The isolation between the collinear ports is however limited by the performance of the matching structure.
Hybrid coil
A hybrid coil is a transformer that has three windings, and which is designed to be configured as a circuit having four branches, that are conjugate in pairs....
or 3dB coupler used in microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
systems. It is an alternative to the rat-race coupler
Rat-race coupler
A rat-race coupler is a type of coupler used in RF and Microwave systems. In its simplest form it is a 3dB coupler and is thus an alternative to a magic tee. Compared to the magic tee, it has the advantage of being easy to realize in planar technologies such as microstrip and stripline, although...
. In contrast to the rat-race, the three-dimensional structure of the magic-tee makes is less readily constructed in planar technologies such as microstrip
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
or stripline
Stripline
Stripline is a transverse electromagnetic transmission line medium, that was invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s.- Description :...
.
The magic tee was originally developed in World-War II, and first published by W. A. Tyrell (of Bell Labs) in a 1947 IRE paper. Robert L. Kyhl and Bob Dicke independently created magic tees around the same time period.
Structure
The magic tee is a combination of E and H planeE-plane and H-plane
The E-plane and H-plane are reference planes for linearly polarized waveguides, antennas and other microwave devices.- E-Plane :For a linearly-polarized antenna, this is the plane containing the electric field vector and the direction of maximum radiation. The electric field or "E" plane determines...
tees. Arm 3 forms an H-plane tee with arms 1 and 2. Arm 4 forms an E-plane tee with arms 1 and 2. Arms 1 and 2 are sometimes called the side or collinear arms. Port 3 is called the H-plane port, and is also called the Σ port, sum port or the P-port (for Parallel). Port 4 is the E-plane port, and is also called the Δ port, difference port, or S-port (for Series). There is no one single established convention regarding the numbering of the ports.
To function correctly the magic tee must incorporate an internal matching structure. This structure typically consists of a post inside the H-plane tee and an inductive iris inside the E-plane limb, though many alternative structures have been proposed. Dependence on the matching structure means that the magic tee will only work over a limited frequency band.
Operation
The name magic tee is derived from the way in which power is divided among the various ports. A signal injected into the H-plane port will be divided equally between ports 1 and 2, and will be in phase. A signal injected into the E-plane port will also be divided equally between ports 1 and 2, but will be 180 degrees out of phase. If signals are fed in through ports 1 and 2, they are added at the H-plane port and subtracted at the E-plane port. Thus, with the ports numbered as shown, and to within a phase factor, the full scattering matrixScattering parameters
Scattering parameters or S-parameters describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals....
for an ideal magic tee is
(the signs of the elements in the fourth row and fourth column of this matrix may be reversed, depending on the polarity assumed for port 4).
Magic
If by means of a suitable internal structure, the E-plane (difference) and H-plane (sum) ports are simultaneously matched, then by symmetry, reciprocityReciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints...
and conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
it may be shown that the two collinear ports are also matched, and are magically isolated from each other.
The E-field of the dominant mode in each port is perpendicular to the broad wall of the waveguide
Waveguide (electromagnetism)
In electromagnetics and communications engineering, the term waveguide may refer to any linear structure that conveys electromagnetic waves between its endpoints. However, the original and most common meaning is a hollow metal pipe used to carry radio waves...
. The signals in the E-plane and H-plane ports therefore have orthogonal polarizations, and so (considering the symmetry of the structure) there can be no communication between these two ports.
For a signal entering the H-plane port, a well-designed matching structure will prevent any of the power in the signal being reflected back out of the same port. As there can be no communication with the E-plane port, and again considering the symmetry of the structure, then
the power in this signal must be divided equally between to the two collinear ports.
Similarly for the E-plane port, if the matching structure eliminates any reflection from this port, then the power entering it must be divided equally between the two collinear ports.
Now by reciprocity
Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints...
, the coupling between any pair of ports is the same in either direction (the scattering matrix is symmetric). So if the H-plane port is matched, then half the power entering either one of the collinear ports will leave by the H-plane port. If the E-plane port is also matched, then half power will leave by the E-plane port. In this circumstance, there is no power 'left over' either to be reflected out of the first collinear port or to be transmitted to the other collinear port. Despite apparently being in direct communication with each other, the two collinear ports are magically isolated.
The isolation between the E-plane and H-plane ports is wide-band and is as perfect as is the symmetry of the device. The isolation between the collinear ports is however limited by the performance of the matching structure.