Manufacturers of instrumentation are striving to satisfy the demands of modern electronics which continuously require greater bandwidth. There has been a growing tendency to incorporate waveguides, ranging from extremely small units soldered into printed circuits, to larger devices mounted in enclosures.
The natural question that arises is how waveguides differ from ordinary wiring, and why it’s possible to send electrical power down waveguides that are hollow. The explanation begins with how electrical current travels through ordinary conductors.
Electrical current actually is made up of a flow of negative electrons, positive holes or positive or negative ions. For current to flow, a charged particle enters the conductor, collides with another particle, which in turn collides with a third particle, and so on. There is a greater than 50% probability that the overall motion is through the conductors and load toward the opposite pole at the power source. The exact percentage depends upon the applied voltage. What is conducted is the momentum of mobile charge carriers.
A point to note is that ac electrical current in conductors is subject to the skin effect. The density of ac current is greatest near the surface of the conductor and diminishes as the distance from the surface increases. Because of this unequal distribution, the effective cross-sectional area of the conductor is less at higher frequencies, manifesting as greater resistance. The cause of this strange phenomenon is opposing eddy currents greatest at the center of the conductor, induced by the oscillating magnetic field.
If most of the ac current flows near the conductor outer diameter, it is not difficult to envision a scenario where the current-carrying conductor could be hollow with no degradation of the current it carries. This is precisely the situation that explains the rationale for hollow waveguides — the skin effect allows them to carry current on their surface.
It is relatively straightforward to measure electrical parameters in ordinary conductors. Measurements in waveguides are more complicated. For example, there are several ways to define the waveguide characteristic impedance (which usually ranges from about 190 to 750 Ω). One way is by measuring the potential difference between the top and bottom walls in the middle of the waveguide, then taking the value of current to be the integrated value across the top wall. The waveguide impedance can also be determined by taking the ratio of the electric field to the magnetic field at the waveguide center.
As with conventional conductors, the optimum power transfer between a waveguide and its source or load happens when their impedances match. Standing waves result when the impedance of the waveguide differs from that of the source or load. But where conventional circuits may use capacitors and inductors to do the matching, waveguide impedance matching generally involves gradually changing the waveguide dimensions, using a waveguide iris, or using a waveguide post or screw.
Abrupt changes in a waveguide will cause a discontinuity that creates standing waves. Gradual changes in dimensions do not cause this problem. The ability of gradual changes in waveguide dimensions to create impedance matching is what makes horn antennas practical. These are funnel-shaped antennas that provide the waveguide impedance match between the waveguide itself and free space by gradually expanding the waveguide dimensions.
The waveguide iris is basically just an obstruction sitting within the waveguide. But it is an obstruction that provides a capacitive or inductive element. A waveguide iris places a shunt capacitance or inductance across the waveguide. The magnitude of the reactance is directly proportional to the size of the opening.The edges of an inductive iris are perpendicular to the magnetic plane. In a shunt capacitive reactance, the edges of the iris are perpendicular to the electric plane. An iris that has portions across both the magnetic and electric planes forms an equivalent parallel-LC circuit across the waveguide. At the resonant frequency, the iris acts as a high shunt resistance. Above or below resonance, the iris acts as a capacitive or inductive reactance.
The waveguide impedance matching iris may either sit on only one side of the waveguide, or there may be a waveguide iris on both sides to balance the system (known as a symmetrical waveguide iris). A single waveguide iris is often referred to as an asymmetric waveguide iris or diaphragm.
An inductive waveguide iris is positioned within the magnetic field, and a capacitive waveguide iris goes within the electric field. One problem is that irises can be susceptible to breakdown under high power conditions, particularly electric plane irises because they concentrate the electric field. Thus the use of a waveguide iris or screw/post can limit the waveguide power handling capacity.
A combination of both E and H plane waveguide irises can be used to provide both inductive and capacitive reactance. This forms a tuned circuit. At resonance, the iris acts as a high-impedance shunt. Above or below resonance, the iris acts as a capacitive or inductive reactance.
All waveguides have a cut-off frequency below which the waveguide is unable to support power transfer along its length. Of course, the cut-off frequency depends upon waveguide dimensions. Mechanical constraints pretty much limit waveguides to microwave frequencies — waveguides built for lower frequencies would be huge.
In addition to using a waveguide iris, post or screw can also be used to give a similar effect. The waveguide post or screw is literally a post or screw made from a conductive material. A post or screw that is inductive will extend through the waveguide completely and touch both top and bottom walls. A capacitive reactance post or screw will extend only part of the way through the waveguide.
As a rough guide, the width of a waveguide must be the same order of magnitude as the wavelength of the signal it carries. The exact mechanics for the cut-off frequency of a waveguide vary according to its shape.
Signals can progress along a waveguide via a number of modes. The dominant mode is the one having the lowest cut-off frequency. For a rectangular waveguide, this is the TE10 mode. The TE means transverse electric and indicates that the electric field is transverse to the direction of propagation.
It is possible for a number of modes to be active, and this can cause problems. So designers typically select waveguide dimensions such that only the energy of the dominant mode propagates.
If one assumes the TE10 mode is the one propagating, the calculation for the lower cut-off point becomes simple:
fc = 2ca
Where fc = rectangular waveguide cut-off frequency, Hz; c = speed of light within the waveguide, m/sec; a = the largest internal dimension of the waveguide, m. The cut-off frequency is independent of the other waveguide dimensions.
A different formula applies for the cut-off frequency of a circular waveguide.
fc = 1.8412 c 2 π a
Where fc = circular waveguide cut-off frequency, Hz; c = speed of light within the waveguide, m/sec; a = the internal radius for the circular waveguide, m.
This is a very clear explanation!
The basic flaw of the above explanation is that the phenomenon is to be named the ELECTROMAGNETIC WAVE. The DC current is only a special case of it, and needs a pair of conductors. A twisted pair of conductors, a coaxial line and some similar structures can transmit DC current and AC current up to some frequency limit due to propagation loss.
Electromagnetic wave can propagate by reflections from conducting plates (also by dispersion in a dielectric structure) which is the case of waveguides. Due to the above, only electromagnetic wave with a higher than limiting frequency can propagate by reflections from conductors. There are many modes of how such waves can propagate in conducting structures, form resonators and antennas.
fc = 1.8412 c 2 π a … should it be fc = 1.8412 c / 2 π a ?
and for the other fc = 2ca => fc = c/2a ?