HITEQUEST
Apr 2002
How to identify a transmission line

 
 

The boundary between a simple point-to-point interconection and a transmittion line, which has distributed elements, sometimes is difficult to define.
Because the effects of these distributed elements in transmittion lines can crop up in unexpected places, designers often overcompensate by preparing for the wave reflections that cannot possibly occur.
How to identify a transmittion line?

In the real world all wires have finite signal propagation delay. Practical numbers are about 1-2nS per foot , depending on charachteristics of the wire.
When wire delays are on the same order as the transition times of the signals that they carry, the wires must be treated not as zero-delay perfect conductors, but as the "transmittion lines" that they really are.
When wire delays are insignificant in comparisson to "slow" transition times of the signal - then we deal with simple interconnections that permit the use of Kirchhoff's circuit laws.
For transmittion lines the mathematics of the system becomes more complex. You can analyze any interconnection from either a frequency or time domain perspective.

When using frequency domain analysis, if the length of the interconnection is greater than 1/15 of the wavelength of the signal it carries, consider the interconnection to be a transmittion line.
L = v / f ,
where L - Wavelength;
v - velocity of propagation;
f - highest frequency, present in the signal.
Cable manufacturers instead of velocity of propagation sometimes specify the inverse value t- propagation delay.
Propagation delay is proportional to the square root of the dielectric constant. For example the propagation delay of signals travelling in air is 85 ps/inch, for coax cable it is 113 ps/inch, for pc-board traces it is about 180 ps/inch.

When using time domain analysis, if the time required for the signal to travel the length of the interconnection is greater than 1/8 of the signal rise time, consider the interconnection to be a transmittion line.
Time T required for the signal to travel the length of the interconnection can be calculated from the above Wavelength equation, L = v * T.
Rise time information is usually specified between 10% and 90% amplitude points. For example for ECL family rise time is about 1 nS.


References:
1.John F. Wakerly Digital design,principles and practices,Second Edition,Prentice Hall,1994
2.Transmittion lines & interconnections,David Royle,EDN,June23,1988



HITEQUEST
Apr 2002