Basic Microwave Theory

An introduction to basic microwave theory

The basic microwave theory to be considered in this section includes dielectrics, loss mechanisms, power deposited, and interaction of microwaves with dielectrics and metals. The nature of fields in cavities that contain some dielectric load will be examined as well as differences between single and multimode resonant systems.

Wave Propagation in Space

There is an interdependence between the electric and magnetic fields when microwaves propagate through space. In these waves the time-changing magnetic field(H) generates a time varying electric field(E), which in turn generates a magnetic field, and as the process repeats, energy is propagated through empty space at the velocity of light. The directions of E & H are everywhere perpendicular and are both transverse to the direction of wave propagation. Waves of this type are called Transverse Electromagnetic (TEM).

The wave impedance can be found from the ratio of E/H, in free space the ratio is known as the “intrinsic impedance” it has a value of 377 Ohms.

At any instant and any point, the energy stored in the electric field per unit volume is equal to the energy stored in the magnetic field. However if the wave is a standing wave then the electric energy density is a maximum when the magnetic is zero, and vice versa, these points of maximum are 1/4 wavelength apart.

Wave Propagation in Lossy Materials

The affect of losses on the propagating wave is due to the materials response to either the electric or magnetic field. In most cases it is usually the electric field that produces a response. This response can be attributed to two main dielectric mechanisms: ionic polarisation and dipole rotation. There are other mechanisms which can dominate in certain situations, however we are mainly concerned with ionic polarisation and dipole rotation since industrial microwave systems usually involves heating of liquids and non magnetic solids.

As the wave progresses into a lossy material, its amplitude decreases due to the transfer of energy as heat into the material. The field and power flux density falls exponentially with distance from the surface. The rate of decay is proportional to the materials dielectric properties and the wave frequency. The depth of penetration is defined as the distance into the material at which the power flux has fallen to 1/e(=0.368) of its surface value. The wave still penetrates beyond this point however the power flux density is a value less than 0.368 of that on the surface.

Loss Mechanisms

When we think of the heating side of basic microwave theory, we start looking at different loss mechanisms. Ionic Polarisation occurs when ions move in response to an electric field. The ions are electrically charged and receive kinetic energy from the field, this kinetic energy is converted to heat when the ions collide with each other. At high frequencies the rate of collision is increased and is detectable as a temperature rise within the material. The rate of dissipation of energy increases as the frequency is raised, however as the frequency continues to increase a point is reached where the ability of the ions to follow the field oscillations is diminished due to ion inertia.

Dipole Rotation is dependant on the existence of polar molecules. Normally, polar molecules are randomly oriented, however in the presence of an electric field the molecules align themselves with the field. As the field oscillates and the electric field polarity varies at a rate dictated by the frequency, the molecules attempt to follow the changing field, causing friction between the molecules thus heating up the material. This effect is frequency sensitive because the amount of energy dissipated is constant per cycle of applied alternating field, however in practice there are mechanical resonances within molecules which result in peaks of power absorption at specific frequencies.

Waveguides

A waveguide is a structure that causes a wave to propagate in a chosen direction. It is accomplished by an intimate connection between the fields of the wave and the currents and charges on the boundaries, or by some condition of reflection at the boundary.

Various higher order modes can propagate in either rectangular or circular guiding structures. The TE10 mode is the dominant mode in a rectangular waveguide and represents the lowest order mode the waveguide is capable of supporting.

In waveguides the electric and magnetic fields are confined to the space within the guides. Thus no power is lost to radiation. Since the guides are normally filled with air, dielectric losses are negligible. However, there is some power lost to heat in the walls of the guides, but this loss is usually very small.

It is possible to propagate several modes of electromagnetic waves within a waveguide. The physical dimensions of a waveguide determine the cutoff frequency for each mode. If the frequency of the impressed signal is above the cutoff frequency for a given mode, the electromagnetic energy can be transmitted through the guide for that particular mode with minimal attenuation. Otherwise the electromagnetic energy with a frequency below cutoff for that particular mode will be attenuated to a negligible value in a relatively short distance. This grammatical use of cutoff frequency is opposite that used for coaxial cable, where cutoff frequency is for the highest useable frequency. The dominant mode in a particular waveguide is the mode having the lowest cutoff frequency. For rectangular waveguide this is the TE10 mode. The TE (transverse electric) signifies that all electric fields are transverse to the direction of propagation and that no longitudinal electric field is present. There is a longitudinal component of magnetic field and for this reason the TEmn waves are also called Hmn waves. The TE designation is usually preferred.

As can be seen, the first index indicates the number of half wave loops across the width of the guide and the second index, the number of loops across the height of the guide – which in this case is zero. It is advisable to choose the dimensions of a guide in such a way that, for a given input signal, only the energy of the dominant mode can be transmitted through the guide. For example, if for a particular frequency, the width of a rectangular guide is too large, then the TE20 mode can propagate causing a myriad of problems. For rectangular guides of low aspect ratio the TE20 mode is the next higher order mode and is harmonically related to the cutoff frequency of the TE10 mode. It is this relationship together with attenuation and propagation considerations that determine the normal operating range of rectangular waveguide.

Resonant Cavities

A resonant cavity consists of a volume enclosed by metal walls. At specific frequencies there exist resonances where energy is exchanged between the electric and magnetic fields. The situation is analogous to a pendulum where there is an energy balance between the kinetic and potential energy and the oscillation frequency is dependant upon the pendulum specifications.

In a cavity the lowest frequency for which resonance occurs is defined to be the fundamental. Higher order resonances can occur and each has a specific field structure within the cavity. There are an infinite number of discrete resonant frequencies, however only those excited by the frequency generating source will be present for heating purposes.

The cavity fields are closely linked with the currents on the inside surface of the cavity walls and the presence of any material enclosed within the volume. A particular resonant frequency will have its bandwidth broadened depending on the extent to which losses are present in the walls and filling material.

This has been an overview of basic microwave theory. Contact AMT for more specific information or visit microwaves101