2.1. Transmission Lines

A transmission line is a connector designed to transmit energy efficiently from one point to another. Its behavior is defined by four main parameters:

• Resistance (R): The opposition to current flow, influenced by material resistivity, temperature, and frequency. At high frequencies, the Skin Effect causes current to concentrate near the conductor’s surface, increasing resistance.
• Inductance (L): The property that opposes a change in current, arising from the magnetic field induced by AC current flow.
• Conductance (G): Represents the leakage current flowing between conductors or to the ground, typically through the insulator surface.
• Capacitance (C): Arises from the electric field between conductors separated by a dielectric medium.

Together, resistance and inductance form the transmission line impedance, while capacitance and conductance form the admittance.

Key Transmission Line Concepts

• Characteristic Impedance (): The ratio of voltage to current amplitudes for a wave traveling in one direction on a uniform, lossless line with no reflections.
  • General formula: Z_0 = \sqrt{\frac{R + jwL}{G + jwC}}
  • For a lossless line: Z_0 = \sqrt{\frac{L}{C}}
• Impedance Matching: To achieve maximum power transfer, the load impedance must be the complex conjugate of the source impedance (R_L = R_S and X_L = -X_S).
• Reflection Coefficient (): The ratio of the reflected voltage to the incident voltage at the load terminals, quantifying the mismatch. A perfect match results in \rho=0.
• Voltage Standing Wave Ratio (VSWR): The ratio of the maximum to minimum voltage along the line, resulting from the interference of incident and reflected waves. It is a measure of impedance mismatch.
  • S = \frac{\left |V_{max} \right |}{\left |V_{min} \right |}
  • S = \frac{1 + \rho }{1 – \rho }
  • A perfect match yields a VSWR of 1.
• Losses from Mismatch: Mismatched impedances lead to various power losses, including Attenuation, Reflection, Transmission, Return, and Insertion Loss.
• Stub Matching: A technique using short-circuited or open-circuited line sections (stubs) connected in shunt with the main line to achieve impedance matching. Single Stub Matching is used for a fixed frequency, while Double Stub Matching allows for adjustments as the load changes.

2.2. Waveguides

A waveguide is a hollow metallic tube of uniform cross-section that transmits electromagnetic waves via successive reflections from its inner walls. They are a special form of transmission line but have no center conductor.

Characteristics and Advantages

• The tube wall provides distributed inductance, and the empty space provides distributed capacitance.
• They are easy to manufacture and can handle very large power (kilowatts).
• They offer very low attenuation loss, making them more efficient for high-frequency energy transfer than coaxial cables.

Comparison: Transmission Lines vs. Waveguides

2.3. Modes of Propagation

The orientation of electric (E) and magnetic (H) fields relative to the direction of propagation (z-axis) defines the mode of propagation.

• TEM (Transverse Electromagnetic): Both E and H fields are purely transverse to the direction of propagation (E_z = 0, H_z = 0). Supported by multi-conductor lines.
• TE (Transverse Electric): The E-field is purely transverse, but the H-field has a component in the direction of propagation (E_z = 0, H_z \ne 0). Supported by waveguides.
• TM (Transverse Magnetic): The H-field is purely transverse, but the E-field has a component in the direction of propagation (E_z \ne 0, H_z = 0). Supported by waveguides.
• HE (Hybrid): Neither the E-field nor the H-field is purely transverse (E_z \ne 0, H_z \ne 0). Supported by open conductor guides.

2.4. Types of Transmission Lines and Waveguides

• Multi-conductor Lines: Include Coaxial lines, Strip lines, Micro strip lines, Slot lines, and Coplanar lines. These are widely used in microwave integrated circuits.
• Single-conductor Lines (Waveguides): Include Rectangular, Circular, Elliptical, Single-ridged, and Double-ridged waveguides.
• Open Boundary Structures: Waveguides not entirely enclosed in a metal shield, such as dielectric rods and optical fibers.