Shortening factor
The shortening factor VKF (also NVP from English Nominal Velocity of Propagation ) is a dimensionless number of lines . It is defined as the ratio of the signal speed on a line to the speed of light . In the limit case of high frequencies, it corresponds to the reciprocal of the refractive index for homogeneous optical propagation media , but depends not only on the material, but also on the geometry of the line cross-section.
Determination and typical values
The VKF can be determined experimentally by time domain reflectometry . For this purpose, the signal propagation time is determined which a very short square pulse needs to run through the cable.
High propagation velocities (and low losses) can u. a. in coaxial cables . An inner conductor is held in place by a foamed dielectric . The low permittivity of the dielectric reduces according to u. G. Formulas determine the capacitance per unit length of the line and thus increase the shortening factor . Some values for high frequency cables:
Cable type | VKF |
---|---|
Open band line | 95-99% |
Belden 9085 (ribbon cable) | 80% |
RG-8X Belden 9258 (coaxial cable) | 82% |
RG-213 CXP213 (coaxial cable) | 66% |
Conversely, highly permittive material is used for delay lines with a particularly low shortening factor.
calculation
The shortening factor is calculated as:
With
- the speed of light
- the phase velocity of the electromagnetic wave . It is the quotient of the vacuum speed of light and the effective refractive index of the medium:
with the two sizes
- Effective permittivity number
- Permeability number of the medium
Both permittivity and permeability depend on the frequency of the signal under consideration.
Insertion into the formula of the shortening factor results in:
To calculate the shortening factor, short square-wave pulses are considered, which correspond to high frequencies at which a limit value is approaching.
For most cables (e.g. copper , aluminum ) the following applies:
The following applies to a lossless line :
With
- the capacity coverage
- the inductance of the line
literature
- Klaus W. Kark: Antennas and radiation fields . Electromagnetic waves on lines in free space and their radiation, Springer-Verlag, Berlin / Heidelberg 2016, ISBN 978-3-658-13965-0 .
- Andres Keller: Broadband cables and access networks. Technical principles and standards. Springer-Verlag, Berlin / Heidelberg 2011, ISBN 978-3-642-17631-9 .
- Frieder Strauss: Basic course in high frequency technology. An introduction. 2nd Edition. Springer Verlag, Berlin / Heidelberg 2016, ISBN 978-3-658-11899-0 .
Individual evidence
- ↑ Chapter 22: Component Data and References . In: H. Ward Silver, N0AX (Ed.): The ARRL Handbook For Radio Communications , 88th. Edition, ARRL , 2011, ISBN 978-0-87259-096-0 , p. 22.48.
- ↑ Television technology without ballast, Otto Limann, Franzis-Verlag 1973, ISBN 3-7723-5270-7 , p. 179 / transit time cable
- ↑ Nominal Propagation Velocity. Retrieved July 23, 2015 .