2.5 Wave Velocity
The velocity of a wave traveling on a transmission line is given by
where L and C refer to the inductance and capacitance per unit length of line, respectively.
This is equal to the velocity of light divided by the square root of the relative dielectric constant or
For circuit boards where the relative dielectric constant is ∼ 4.0, the wave velocity is 0.015 cm/ps. This means a wave travels in a board dielectric about 1/16 inch in 10 ps.
The dielectric constant and the losses along a transmission line will vary as a function of frequency. This means that the sine wave voltages that make up the initial wave do not travel at the same velocity. As the wave travels, the wave front will lose its sharp character. The amount of wave front distortion will depend on the type of dielectric, on line losses, on radiation, and on line length. Board material that is rated to operate at a higher frequency will distort the wave less over a given length of trace.
In microstrip transmission lines (outer traces), a part of the E field is external to the dielectric, which means that some of the field travels at a higher velocity. This distorts the leading edge for short rise time transmissions. This has the effect of increasing cross talk between traces on an outer layer. Traces that are buried in a dielectric or that are routed between conducting planes (stripline) do not have as large a difference in wave velocity (see the discussion on cross talk in Chapter 3).
If the characteristic impedance of a transmission line is known, the inductance per unit length can be determined by dividing Equation 2.2 by Equation 2.3 or Equation 2.4.
The capacitance per unit length can be determined by multiplying Equation 2.2 by Equation 2.3 or Equation 2.4.