7. TDR Measurement Theory
7.4. Velocity of Propagation (VoP, Vp)
As mentioned in previous sections, a transmission line, such as a coaxial cable, has uniform
geometry with a characteristic signal propagation velocity. This velocity of propagation (Vp, VoP,
or VP), sometimes also called the velocity factor (VF) or wave propagation speed, is the measure
of the velocity of an electrical signal within a cable expressed as a fraction of the speed of light in a
vacuum. With the CT100B, Vp can be set between 0.250000 and 1.000000.
Nominal Vp values for most types of cable can be found in the manufacturer’s datasheet, and
Appendix D: V
p
of Common Cables contains nominal values for a variety of commonly used cable
types. These values can be a good start for basic cable Distance-to-Fault measurements. However,
it is important to be aware that Vp values for a given cable type may vary from manufacturer to
manufacturer and from one manufacturing lot to the next even from the same manufacturer. In
addition, cable aging due to temperature, radiation, or other environmental parameters may alter
the original characteristic velocity of propagation for a given cable. For this reason, if accuracy is
particularly important for a particular cable Distance-to-Fault measurement, it is generally a good
idea to establish a known Vp for a sample of the specific cable under test.
The velocity of propagation (V p) is related to the dielectric constant (relative permittivity, ε
r
) of
the dielectric medium according to:
V p ≈
1
√
ε
r
Velocity of propagation is also related to the distributed inductance (L) and shunt capacitance (C)
of a lossless transmission line according to:
V p =
1
c
√
LC
7.5. Distance-to-Fault (DTF) and Cable Length
Once the operator identifies an impedance discontinuity such as a cable fault or open or short cable
termination, the distance to the fault (D) is related to the velocity of propagation (V p), the speed
of light (c), and the measured round-trip time (t) to the fault, according to:
D =
V p · c ·t
2
The product is divided by 2 because the CT100B measures the time for the pulse to travel to and
from the point of interest.
7.6. Impedance
As mentioned previously, TDR instruments measure reflection coefficient directly but must
calculate impedance according to:
Z(t) = −Z
S
Γ(t) + 1
Γ(t) − 1
CT100B TDR Cable Analyzers Operator’s Manual 99
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