4.0 Wave Propagation and Physical Transmission Media
For microwave energy to travel from a source to a load, it must be guided by a physical medium. The specific geometry and materials of this medium dictate the possible modes in which the electromagnetic waves can propagate. Understanding these modes and the media that support them is essential for selecting the right components for a given application.
Primary Modes of Propagation
The mode of propagation is defined by the orientation of the wave’s electric (E) and magnetic (H) fields relative to its direction of propagation (conventionally the z-axis).
- TEM (Transverse Electromagnetic Wave): In this mode, both the electric and magnetic fields are purely transverse (perpendicular) to the direction of propagation. There are no field components in the direction of travel (Ez = 0 and Hz = 0). Multi-conductor transmission lines typically support this fundamental mode.
- TE (Transverse Electric Wave): In this mode, the electric field is purely transverse to the direction of propagation, but the magnetic field has a component in the direction of travel (Ez = 0 and Hz ≠ 0).
- TM (Transverse Magnetic Wave): In this mode, the magnetic field is purely transverse to the direction of propagation, while the electric field has a component in the direction of travel (Ez ≠ 0 and Hz = 0).
- HE (Hybrid Wave): In this mode, neither the electric nor the magnetic field is purely transverse. Both fields have components in the direction of propagation (Ez ≠ 0 and Hz ≠ 0).
Common Microwave Transmission Media
At microwave frequencies, several types of physical structures are used to guide electromagnetic waves, each supporting different modes of propagation.
- Multi-conductor Lines: These structures, such as Coaxial lines, Strip lines, and Microstrip lines, consist of at least two separate conductors and are capable of supporting the fundamental TEM mode. They are widely used in circuit boards and for connecting various system components.
- Single-conductor Lines (Waveguides): A waveguide is a hollow metallic tube of a specific cross-section (e.g., rectangular or circular) that guides waves by reflecting them off its inner walls. Because a waveguide consists of only a single conductor, it cannot support the TEM mode. Instead, it guides waves propagating in TE and TM modes.
Comparison: Transmission Lines vs. Waveguides
| Feature | Transmission Lines | Waveguides |
| Supported Mode | Supports TEM wave | Cannot support TEM wave; supports TE and TM waves |
| Frequency Response | Can pass all frequencies* | Only frequencies greater than the cut-off frequency can pass |
| Structure | Two-conductor transmission | One-conductor transmission |
| Propagation of waves | According to “Circuit theory” | According to “Field theory” |
| Wave Travel | Propagation along conductors | A wave travels through reflections from the walls |
| Impedance | Characterized by characteristic impedance | Characterized by wave impedance |
| Return Path | Has a return conductor to earth | Return conductor is not required; the body acts as earth |
| Bandwidth | Bandwidth is not limited | Bandwidth is limited |
| Wave Dispersion | Waves do not disperse | Waves get dispersed |
*While the fundamental TEM mode has no cutoff frequency, at higher frequencies, non-TEM modes can propagate, leading to significant attenuation and performance degradation.
Wave Velocity
Within these guiding structures, two distinct velocities are used to describe wave propagation:
- Phase Velocity (Vp): The rate at which the phase of the wave propagates. It is defined by the formula:
- where ω is the angular frequency and β is the phase constant.
- Group Velocity (Vg): The rate at which the overall envelope of the wave—and thus the energy—propagates through the waveguide. It is defined by the formula:
The inherent properties of these physical media, combined with any imperfections or impedance mismatches, lead directly to measurable power losses that must be quantified and managed for effective system design.