5. TDR Measurement Theory
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
5.5. 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.
5.6. Impedance
As mentioned previously, TDR instruments measure reflection coefficient essentially but must
calculate impedance according to:
Z
(
t
) =
−
Z
S
Γ(
t
) + 1
Γ(
t
)
−
1
Where
Z
(
t
) is the impedance at time
t
,
Z
S
is the source impedance, and Γ(
t
) is the reflection
coefficient at
t
. This is the basis for the CT100B ohms-at-cursor measurements and ZTrace
impedance traces. It is important to note that impedance is nonlinear with respect to reflection
coefficient, as shown in Figure 5.6.
Because TDRs measure reflection coefficient, noise and uncertainty on a TDR trace is in units of
millirho, not ohms. Given a fixed amount of uncertainty in reflection coefficient, the
corresponding impedance uncertainty will be low at impedances less than the TDR source
impedance (typically 50 ohms) and increasingly larger and nonlinear for impedance values
greater than the TDR source impedance.
The CT100B factory calibration provides typical vertical accuracy of approximately 0.1 ohm
near 50 ohms and approximately 10-20 ohms near 1000 ohms for most cable testing applications.
CT100B TDR Cable Analyzers Operator’s Manual
71
