NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 393

a 1 b 2

Port 1 Port 2

b 1 a 2

a 3 b 2

Port 3 4 port network Port 4

a 2

b 3

Figure 9-34 Four-port network.

needed to separate the S -parameters of the DUT from the test fixture, cables,
or probes. In this section we introduce the basic calibration and deembedding
methodologies so that the concept will be understood. Since each measurement
setup requires a specialized calibration and deembedding procedure, the breadth
of the topic is too wide to be covered here.
The terms calibration and deembedding refer to the same concept: remstepov-
ing an unwanted part of the measurement. More specifically, calibration refers
to removing the effect of the VNA cables and probes, and deembedding refers
to removing unwanted portions of the DUT, such as a via, a test fixture, or a
cable connector. A VNA measures S -parameters as ratios of complex voltage
amplitudes. The reference for the measurement is some place within the VNA,
not at the cable ends which are attached to the DUT, so the measurement will
include the losses and phase delays of the cables, connectors, and probes used
to connect the DUT to the analyzer. Calibration refers to the removal of these
unwanted effects from the measured response so that only the measured response
of the DUT remains. Figure 9-35 demonstrates this concept.
For calibration purposes, it is convenient to work with ABCD parameters. For
example, the measurement setup in Figure 9-35 can be represented by cascaded
ABCD matrices:
AB
CD

AB
CD

AB
CD

AB
CD

− 1

measured =

(9-50)

error port1 DUT error port2

Note that the ABCD matrix for port 2 is inverted because the VNA drives into
the port and measures the responses at all other ports. The inversion simply
ensures that it represents current flowing from port 2 into the DUT and not the
other way around. Equation (9-50) suggests that if the ABCD matrices of the
errors are known, the ABCD matrix (and thus the S -parameters) of the DUT can
be calculated. In short, the calibrated measurement is simply the error-corrected
S -parameters.
The most straightforward method to remove the errors and calibrate a VNA
is to use three or more carefully controlled loads, such as a short, open, and