Magic tee

Last updated
A magic T consisting of four rectangular waveguides meeting in a single three-dimensional junction MagicTee.jpg
A magic T consisting of four rectangular waveguides meeting in a single three-dimensional junction

A magic tee (or magic T or hybrid tee) is a hybrid or 3 dB coupler used in microwave systems. [1] It is an alternative to the rat-race coupler. In contrast to the rat-race, the three-dimensional structure of the magic tee makes it less readily constructed in planar technologies such as microstrip or stripline.

Contents

The magic comes from the way it prevents signals from propagating between certain ports under specific conditions. This allows it to be used as a duplexer; for instance, it can be used to isolate the transmitter and receiver in a radar system while sharing the antenna. In practical examples, it is used to both isolate circuits and mix signals, for instance in a COHO radar.

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. [2] Robert L. Kyhl and Bob Dicke independently created magic tees around the same time.

Structure

The magic tee is a combination of E and H plane 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. [3] Thus, with the ports numbered as shown, and to within a phase factor, the full scattering matrix 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, reciprocity 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 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.

Related Research Articles

<span class="mw-page-title-main">Circulator</span> Electronic circuit in which a signal entering any port exits at the next port

In electrical engineering, a circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an external waveguide or transmission line, such as a microstrip line or a coaxial cable, connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1, and so on. An ideal three-port circulator has the following scattering matrix:

<span class="mw-page-title-main">Hybrid transformer</span> Type of electrical transformer

A hybrid transformer is a type of directional coupler which is designed to be configured as a circuit having four ports that are conjugate in pairs, implemented using one or more transformers. It is a particular case of the more general concept of a hybrid coupler.

<span class="mw-page-title-main">Antenna (radio)</span> Electrical device

In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

<span class="mw-page-title-main">Horn antenna</span> Funnel-shaped waveguide radio device

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are widely used as antennas at UHF and microwave frequencies, above 300 MHz. They are used as feed antennas for larger antenna structures such as parabolic antennas, as standard calibration antennas to measure the gain of other antennas, and as directive antennas for such devices as radar guns, automatic door openers, and microwave radiometers. Their advantages are moderate directivity, broad bandwidth, low losses, and simple construction and adjustment.

Scattering parameters or S-parameters describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.

<span class="mw-page-title-main">Orthomode transducer</span> Component for guiding radio waves

An orthomode transducer (OMT) is a waveguide component that is commonly referred to as a polarisation duplexer. Orthomode is a contraction of orthogonal mode. Orthomode transducers serve either to combine or to separate two orthogonally polarized microwave signal paths. One of the paths forms the uplink, which is transmitted over the same waveguide as the received signal path, or downlink path. Such a device may be part of a very small aperture terminal (VSAT) antenna feed or a terrestrial microwave radio feed; for example, OMTs are often used with a feed horn to isolate orthogonal polarizations of a signal and to transfer transmit and receive signals to different ports.

The E-plane and H-plane are reference planes for linearly polarized waveguides, antennas and other microwave devices.

A radio transmitter or receiver is connected to an antenna which emits or receives the radio waves. The antenna feed system or antenna feed is the cable or conductor, and other associated equipment, which connects the transmitter or receiver with the antenna and makes the two devices compatible. In a radio transmitter, the transmitter generates an alternating current of radio frequency, and the feed system feeds the current to the antenna, which converts the power in the current to radio waves. In a radio receiver, the incoming radio waves excite tiny alternating currents in the antenna, and the feed system delivers this current to the receiver, which processes the signal.

<span class="mw-page-title-main">Power dividers and directional couplers</span> Radio technology devices

Power dividers and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. Power entering the output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power equally between two ports is called a hybrid coupler.

Admittance parameters or Y-parameters are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal (linearized) response of non-linear networks. Y parameters are also known as short circuited admittance parameters. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters.

<span class="mw-page-title-main">Rat-race coupler</span> Type of radio-frequency coupler

A rat-race coupler, also known as a hybrid ring coupler, is a type of coupler used in RF and microwave systems. In its simplest form, it is a 3 dB 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 waveguide rat races are also practical. Unlike magic tees, a rat-race needs no matching structure to achieve correct operation.

<span class="mw-page-title-main">Isolator (microwave)</span>

An isolator is a two-port device that transmits microwave or radio frequency power in one direction only. The non-reciprocity observed in these devices usually comes from the interaction between the propagating wave and the material, which can be different with respect to the direction of propagation.

Eigenmode expansion (EME) is a computational electrodynamics modelling technique. It is also referred to as the mode matching technique or the bidirectional eigenmode propagation method. Eigenmode expansion is a linear frequency-domain method.

<span class="mw-page-title-main">Waveguide filter</span> Electronic filter that is constructed with waveguide technology

A waveguide filter is an electronic filter constructed with waveguide technology. Waveguides are hollow metal conduits inside which an electromagnetic wave may be transmitted. Filters are devices used to allow signals at some frequencies to pass, while others are rejected. Filters are a basic component of electronic engineering designs and have numerous applications. These include selection of signals and limitation of noise. Waveguide filters are most useful in the microwave band of frequencies, where they are a convenient size and have low loss. Examples of microwave filter use are found in satellite communications, telephone networks, and television broadcasting.

<span class="mw-page-title-main">Penrose tiling</span> Non-periodic tiling of the plane

A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s.

<span class="mw-page-title-main">Waffle-iron filter</span> Type of waveguide filter

A waffle-iron filter is a type of waveguide filter used at microwave frequencies for signal filtering. It is a variation of the corrugated-waveguide filter but with longitudinal slots cut through the corrugations resulting in an internal structure that has the appearance of a waffle-iron.

<span class="mw-page-title-main">Planar transmission line</span> Transmission lines with flat ribbon-like conducting or dielectric lines

Planar transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines. They are used to interconnect components on printed circuits and integrated circuits working at microwave frequencies because the planar type fits in well with the manufacturing methods for these components. Transmission lines are more than simply interconnections. With simple interconnections, the propagation of the electromagnetic wave along the wire is fast enough to be considered instantaneous, and the voltages at each end of the wire can be considered identical. If the wire is longer than a large fraction of a wavelength, these assumptions are no longer true and transmission line theory must be used instead. With transmission lines, the geometry of the line is precisely controlled so that its electrical behaviour is highly predictable. At lower frequencies, these considerations are only necessary for the cables connecting different pieces of equipment, but at microwave frequencies the distance at which transmission line theory becomes necessary is measured in millimetres. Hence, transmission lines are needed within circuits.

<span class="mw-page-title-main">Coplanar waveguide</span> Type of planar transmission line

Coplanar waveguide is a type of electrical planar transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. On a smaller scale, coplanar waveguide transmission lines are also built into monolithic microwave integrated circuits.

<span class="mw-page-title-main">Port (circuit theory)</span> Point of entry and exit of electrical energy to/from a circuit

In electrical circuit theory, a port is a pair of terminals connecting an electrical network or circuit to an external circuit, as a point of entry or exit for electrical energy. A port consists of two nodes (terminals) connected to an outside circuit which meets the port condition – the currents flowing into the two nodes must be equal and opposite.

<span class="mw-page-title-main">Distributed-element circuit</span> Electrical circuits composed of lengths of transmission lines or other distributed components

Distributed-element circuits are electrical circuits composed of lengths of transmission lines or other distributed components. These circuits perform the same functions as conventional circuits composed of passive components, such as capacitors, inductors, and transformers. They are used mostly at microwave frequencies, where conventional components are difficult to implement.

References

  1. Wolff, Christian (17 November 1998). "Waveguide Junctions". www.radartutorial.eu. Retrieved 31 July 2023.
  2. Tyrrell, W.A. (1947). "Hybrid Circuits for Microwaves". Proceedings of the IRE. Institute of Electrical and Electronics Engineers (IEEE). 35 (11): 1294–1306. doi:10.1109/jrproc.1947.233572. ISSN   0096-8390.
  3. Sisodia, M. L.; Raghuvanshi, G. S. (1987). Basic Microwave Techniques and Laboratory Manual. New Age International. ISBN   978-0-85226-858-2.