5. TDR Measurement Theory
5.11. Frequency-Domain Measurements
5.11.1. Scattering Parameters
The scattering parameter or S-parameter approach to describing a device under test (DUT)
assumes that a DUT is a black box network with N ports. The S-parameter matrix contains the
complex reflection and transmission coefficients of the network, describing the amplitude and
phase of reflected and transmitted values from each port in response to excitation of one or
more of the ports.
According to convention, the scattering parameter
S
xy
represents the response of the network in
terms of reflected and/or transmitted voltages at port x in response to excitation of port y.
S
11
and
S
22
are the complex reflection coefficient matrices of port 1 and 2, respectively.
S
21
and
S
12
are the forward and reverse complex voltage gain matrices for port 1 and port 2, respectively.
Considering a 2-port network with incident voltage waves
a
1
=
V
+
1
and
a
2
=
V
+
2
and reflected
waves being
b
1
=
V
−
1
and
b
2
=
V
−
2
, the 2-port S-parameter matrix is described by:
b
1
b
2
!
=
S
11
S
12
S
21
S
22
!
a
1
a
2
!
Solving for
S
11
gives:
S
11
=
b
1
a
1
=
V
−
1
V
+
1
Solving for
S
21
gives:
S
21
=
b
2
a
1
=
V
−
2
V
+
1
Passive networks like cables, splitters, attenuators, and combiners can be considered reciprocal
networks such that
S
11
=
S
22
and
S
21
=
S
12
. One-port measurements can be used to
characterize the return loss (
S
11
/
S
22
) and insertion loss (
S
21
/S
12
) of a variety of 2-port passive
networks such as cables. This will be discussed in the Cable Loss (
S
21
) section on page 77.
You can measure S-parameters directly in the frequency domain using a VNA instrument and
indirectly in the time domain using a TDR instrument. The TDR instrument performs a discrete
Fourier transform (DFT) operation to decompose a TDR trace into the frequency domain.
When calibration is performed at the test plane using open, short, and 50 ohm load (OSL)
terminations, the CT100B is able to mathematically subtract systemic errors in the pulser and
sampler electronics from the measured trace, improving S-parameter accuracy.
S-parameters measured with TDR instruments are accurate with sufficient dynamic range for
most applications. Figure 5.10 shows a comparison of return loss for a 2.4 GHz WiFi patch
antenna measured using a handheld VNA and CT100HF TDR. The TDR-derived return loss
measurements show good accuracy from DC to approximately 8.3 GHz. Both spectra clearly
show the 2.4 GHz bandpass region expected for a 2.4 GHz WiFi antenna.
76
CT100B TDR Cable Analyzers Operator’s Manual
