# Guide wavelength and their relationship with Wavelength in waveguide is different from wavelength in free space. Relation between cutoff frequency and guide wavelength: The. corresponding wavelength, called the guide wavelength, is denoted by λg. =2π/β . The precise relationship between ω and β depends on the type of waveguide. The frequency may then the read from the dial of the meter. For dominated mode TE 10 mode rectangular wave guide the following relation is in use:1/ λ 0 2= 1/.

If we combine Eqs. I that phase velocities greater than light are possible, because it is just the nodes of the wave which are moving and not energy or information. The group velocity of the waves is also the speed at which energy is transported along the guide. If we want to find the energy flow down the guide, we can get it from the energy density times the group velocity. There is also some energy associated with the magnetic field. The driving stub can be connected to a signal generator via a coaxial cable, and the pickup probe can be connected by a similar cable to a detector.

It is usually convenient to insert the pickup probe via a long thin slot in the guide, as shown in Fig. Then the probe can be moved back and forth along the guide to sample the fields at various positions. A waveguide with a driving stub and a pickup probe. These will be the only waves present if the guide is infinitely long, which can effectively be arranged by terminating the guide with a carefully designed absorber in such a way that there are no reflections from the far end. Then, since the detector measures the time average of the fields near the probe, it will pick up a signal which is independent of the position along the guide; its output will be proportional to the power being transmitted.

If now the far end of the guide is finished off in some way that produces a reflected wave—as an extreme example, if we closed it off with a metal plate—there will be a reflected wave in addition to the original forward wave. Then, as the pickup probe is moved along the line, the detector reading will rise and fall periodically, showing a maximum in the fields at each loop of the standing wave and a minimum at each node. This gives a convenient way of measuring the guide wavelength.

Then the detector output will decrease gradually as the pickup probe is moved down the guide. If the frequency is set somewhat lower, the field strength will fall rapidly, following the curve of Fig. Although high frequencies can be transmitted along a coaxial cable, a waveguide is better for transmitting large amounts of power.

First, the maximum power that can be transmitted along a line is limited by the breakdown of the insulation solid or gas between the conductors. For a given amount of power, the field strengths in a guide are usually less than they are in a coaxial cable, so higher powers can be transmitted before breakdown occurs.

Second, the power losses in the coaxial cable are usually greater than in a waveguide. In a coaxial cable there must be insulating material to support the central conductor, and there is an energy loss in this material—particularly at high frequencies.

13E41A0442 Guide Wavelength Phase Velocity and Group Velocity

Also, the current densities on the central conductor are quite high, and since the losses go as the square of the current density, the lower currents that appear on the walls of the guide result in lower energy losses.

To keep these losses to a minimum, the inner surfaces of the guide are often plated with a material of high conductivity, such as silver. Sections of waveguide connected with flanges. For instance, two sections of waveguide are usually connected together by means of flanges, as can be seen in Fig.

Such connections can, however, cause serious energy losses, because the surface currents must flow across the joint, which may have a relatively high resistance. One way to avoid such losses is to make the flanges as shown in the cross section drawn in Fig.

A small space is left between the adjacent sections of the guide, and a groove is cut in the face of one of the flanges to make a small cavity of the type shown in Fig. The dimensions are chosen so that this cavity is resonant at the frequency being used. A low-loss connection between two sections of waveguide. Then you must put something at the end that imitates an infinite length of guide.

Then the guide will act as though it went on forever. Such terminations are made by putting inside the guide some wedges of resistance material carefully designed to absorb the wave energy while generating almost no reflected waves.

### Waveguide Mathematics

You can see qualitatively from the sketches in Fig. Suppose you want to know which way the waves are going in a particular section of guide—you might be wondering, for instance, whether or not there is a strong reflected wave. The unidirectional coupler takes out a small fraction of the power of a guide if there is a wave going one way, but none if the wave is going the other way. Each of the holes acts like a little antenna that produces a wave in the secondary guide. If there were only one hole, waves would be sent in both directions and would be the same no matter which way the wave was going in the primary guide. We found that the waves subtract in one direction and add in the opposite direction. The same thing will happen here. This end is equipped with a termination, so that this wave is absorbed and there is no wave at the output of the coupler.

There are many more. So such fields are called transverse magnetic TM modes. For a rectangular guide, all the other modes have a higher cutoff frequency than the simple TE mode we have described.

It is, therefore, possible—and usual—to use a guide with a frequency just above the cutoff for this lowest mode but below the cutoff frequency for all the others, so that just the one mode is propagated.

Otherwise, the behavior gets complicated and difficult to control. We can do this for the rectangular guide by analyzing the fields in terms of reflections—or images—in the walls of the guide. In the absence of the guide walls such a wire would radiate cylindrical waves. Now we consider that the guide walls are perfect conductors. Then, just as in electrostatics, the conditions at the surface will be correct if we add to the field of the wire the field of one or more suitable image wires. The image idea works just as well for electrodynamics as it does for electrostatics, provided, of course, that we also include the retardations.

We know that is true because we have often seen a mirror producing an image of a light source. The walls can be replaced by the infinite sequence of image sources. We call the direction of the current in the wire positive. It is, in fact just what you would see if you looked at a wire placed halfway between two parallel mirrors. For the fields to be zero at the walls, the polarity of the currents in the images must alternate from one image to the next. The waveguide field is, then, just the superposition of the fields of such an infinite set of line sources.

We know that if we are close to the sources, the field is very much like the static fields. Here the average source strength is zero, because the sign alternates from one source to the next.

Any fields which exist should fall off exponentially with distance. Close to the source, we see the field mainly of the nearest source; at large distances, many sources contribute and their average effect is zero. So now we see why the waveguide below cutoff frequency gives an exponentially decreasing field. At low frequencies, in particular, the static approximation is good, and it predicts a rapid attenuation of the fields with distance. Now we are faced with the opposite question: Why are waves propagated at all?

That is the mysterious part! The reason is that at high frequencies the retardation of the fields can introduce additional changes in phase which can cause the fields of the out-of-phase sources to add instead of cancelling. We'll let you do the math on this multiply lower cutoff frequency by two Thus for WR, the cutoff is 6.

Remember, at the lower cutoff the guide simply stops working. See our page on waveguide loss for more information. Guide wavelength Guide wavelength is defined as the distance between two equal phase planes along the waveguide. The guide wavelength is a function of operating wavelength or frequency and the lower cutoff wavelength, and is always longer than the wavelength would be in free-space.

Here's the equation for guide wavelength: Guide wavelength is used when you design distributed structures in waveguide. The guide wavelength in waveguide is longer than wavelength in free space. This isn't intuitive, it seems like the dielectric constant in waveguide must be less than unity for this to happen Here is a way to imagine why this is The waves are coming in at an angle to the beach New for December !

We now have a video of waves breaking sideways that illustrates phase velocity.

## Waveguide Mathematics

Hopefully soon we will figure out how to embed it on this page for your enjoyment and education, stay tuned! The content on this page requires a newer version of Adobe Flash Player. Phase velocity and group velocity Phase velocity is an almost useless piece of information you'll find in waveguide mathematics; here you multiply frequency times guide wavelength, and come up with a number that exceeds the speed of light! Be assured that the energy in your wave is not exceeding the speed of light, because it travels at what is called the group velocity of the waveguide: The group velocity is always less than the speed of light, we like to think of that this is because the EM wave is ping-ponging back and forth as it travels down the guide.

Group velocity in a waveguide is speed at which EM energy travels in the guide.