7. TDR Measurement Theory
incident voltage trace is reflected back to the TDR instrument, insertion loss (S
21
) is half of the
corresponding S
11
return loss measurement in dB:
Cable Loss CL =
RL
2
dB
Again, this relationship is valid if the cable is terminated with a short or open. One drawback to
this technique is that the round-trip insertion loss reduces the length of cable that can be tested
over a given bandwidth relative to a 2-port measurement because the attenuation of the test signal
is doubled. However, for many applications it is adequate.
7.12. Normalized TDR Traces
The S-parameter OSL calibration process mathematically models the TDR pulser-sampler system
as a two-port error network and subtracts systemic pulser-sampler errors from the S
11
matrix.
Convolution of the S
11
matrix with an idealized Gaussian step or other idealized excitation signal
allows the CT100B to create and display a normalized TDR trace. The normalized TDR trace has
lower aberration and improved impedance accuracy compared with the original TDR trace.
Although cable fault detection is the most sensitive when using an excitation signal with the
fastest rise time possible, by changing the rise time of the Gaussian step, the importance of a given
cable or connector fault can be estimated at different signal rise times and bandwidths. For
instance if the cable under test is typically used with 1 ns rise time signals, the severity of a cable
fault can be determined by using a 1 ns rise time normalized TDR trace. Localized cable faults will
always appear less severe when examined using slower rise time excitation signals.
7.13. Layer Peeling/Dynamic Deconvolution
Layer peeling (or dynamic deconvolution) is a general method to solve the inverse scattering
problem in partially reflective transmission lines such as cables. When applied to TDR traces, this
method attempts to extract the underlying real reflection coefficients and impedance in the
presence of multiple reflections caused by the presence of impedance discontinuities in the cable
assembly under test.
As implemented in the CT100B (see Section 5.8), the layer-peeling method iteratively examines the
TDR trace at each time step and attempts to correct for forward and backward signal propagation
to extract impedance values at each time step. This is diagrammed in Figure 7.11 showing
measured voltages V (t) taken from the TDR trace and their relationship to actual reflection
coefficients (Γ) at time (t) and impedance values (Z
x
) at different physical distances. The diagram
shows that for each time step forward in the TDR trace, there are increasingly complex
contributions from forward and backward reflections as they interact with each new impedance
boundary.
For instance, the test signal moving forward from the Z
0
/Z
1
impedance boundary is reduced by the
energy reflected by the Z
0
/Z
1
boundary. Likewise the Z
1
/Z
2
impedance boundary is “tested” by
the original TDR test signal at time t
1
but also interacts with reflected signals at every subsequent
time point due to internal reflections in the cable. The layer-peeled TDR trace partially corrects
CT100B TDR Cable Analyzers Operator’s Manual 107
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