E9F: Transmission Lines

A transmission line carries RF energy between a transmitter and an antenna, and its electrical characteristics — velocity factor, length relative to wavelength, and termination — determine what impedance it presents to the transmitter.

This lesson covers velocity factor and what determines it, why electrical length differs from physical length, the impedance of shorted and open lines at various fractions of a wavelength, microstrip, foam vs solid dielectric coaxial cable, parallel conductor line loss, and a physical length calculation.

Velocity Factor

The velocity factor (VF) of a transmission line is the ratio of the speed of the electromagnetic wave in the line to the speed of light in free space:

VF = v_line / c

Velocity factor is always less than 1 because electromagnetic waves travel more slowly through insulating dielectric material than through a vacuum. The insulating dielectric material has the biggest effect on velocity factor — the higher the dielectric constant of the insulator, the slower the wave travels and the lower the velocity factor. Air-insulated lines have a VF near 1.0; solid polyethylene dielectric drops it to about 0.66; foam dielectric is typically 0.78–0.88.

Electrical vs Physical Length

Because waves travel more slowly in a coaxial cable than in free space, the electrical length of a coaxial cable is longer than its physical length. A piece of cable that is physically 1 meter long acts like more than 1 meter of free-space transmission line electrically, because the wave takes longer to travel the same distance through the dielectric. This is why antenna matching networks built from coaxial stubs must use the electrical length (corrected by velocity factor) to calculate the required physical length.

Shorted and Open Stub Impedances

The impedance presented by a transmission line stub depends on its electrical length and whether its far end is shorted or open:

Microstrip

Microstrip is a type of transmission line made from precision printed circuit conductors above a ground plane that provide constant characteristic impedance interconnects at microwave frequencies. By controlling the width of the conductor and the thickness and dielectric constant of the PCB substrate, the designer achieves a precise impedance (typically 50 Ω) on a printed circuit board. Microstrip is the standard interconnect technology for microwave circuits and amplifiers.

Coax vs Parallel Conductor Line

Compared to coaxial cable with a plastic dielectric, parallel conductor (open wire) transmission line has significantly lower loss. The air dielectric between the conductors contributes almost no dielectric loss, whereas the solid plastic in coaxial cable absorbs some energy. The trade-off is that open wire line is more susceptible to interference and must be kept away from metal objects, but its loss advantage is decisive for high-power HF operation on long feed lines.

Foam dielectric coaxial cable compared to solid dielectric coax of the same dimensions has: lower loss per unit length, higher velocity factor, and lower maximum safe operating voltage — all three statements are true.

Physical Length Calculation

E9F Practice Questions