The following relation between the relative dielectric constant of a dieletric in a transmission line and the phase velocity of an electromagnetic wave propagating in a dielectric is well known.
Vp = c / sqrt(es) (1) here, Vp = phase velocity of electromagnetic wave (m/s) c = 2.99792458e8 = definition of the speed of light in a vacuum (m/s) es = relative dielectric constant of a dieletric (es >= 1) sqrt(x) = the square root of x (description often used in C language and other programming languages)For example, in polyethylene-insulated coaxial cables with relative dielectric constant 2.3,
Vp = 2.99792458e8 / sqrt(2.3) = 1.97677293e8 (m/s) ,or about 66% of the speed of light.
Looking at specifications of coaxial cables, we often see descriptions such as a "shortening coefficient of wavelength 66%". For waves in general, the relation
v = f * l here, v = speed of wave (m/s) f = frequency (Hz) l = wavelength (m)exists.
If the speed decreases, the wavelength decreases in proportion. The frequency does not change in transmission lines.
As a modern description of transmission speed,
velocity_ratio = phase_velocity / speed_of_light_in_a_vacuumwould be better than the shortening coefficient of a wavelength because the theory of special relativity is well known.
In the old days, measuring the wavelength was much easier than measuring velocity, and therefore the concept of a shortening coefficient of a wavelength was more familiar to specialists.
By looking at equation (1), we can interpret that in dielectrics the velocity of electromagnetic waves decrease by a factor of 1/sqrt(es), but can we really interpret that the propagation velocity (phase velocity) of a electromagnetic waves decrease in dielectrics ?
This is the problem.
Kouichi Hirabayashi, (C) 2004