Digital Circuit Boards: Mach 1 GHz

4.19 Another way to look at Energy Flow in Transmission Lines

Consider a transmission line where the dielectric thickness is 0.01 cm. If the static voltage across the line is 1.0 V then the E field is 10,000 V/m. The energy in the space between the conductors is proportional to the product of the square of the E field and the volume of that space (Section 1.12). Now, consider a part of this line where the conductor separation is increased to 0.1 cm. In this section the E field is only 1000 V/cm. The energy density is reduced by a factor of 100, but the volume is increased by a factor of 10. This means that the static energy stored per unit length in this section is reduced by a factor of 10.

Consider a 0.1-V wave in the two sections of line. When the thickness is 0.1 cm the energy flow in a wave is lowered by a factor of 10. It would take 10 round trips for a wave of equal amplitude to move an equal amount of energy in the section with a thicker dielectric.