NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 396

The calibrated S -parameters are obtained by converting the ABCD matrix of the
DUT calculated with (9-56) using Table 9-3.

AB
CD

S 11

S 22
DUT

S 12

DUT ⇒

(9-57)

S 21

Basic deembedding principles utilize the same concepts to remove unwanted
parts of the measurement. For example, Figure 9-32c shows a case where a via is
cascaded with a transmission line. If it is desired to obtain only the measurements
of the transmission line, the effects of the via must be deembedded. If the test
board contains suitable structures to measure the S -parameters of the via in
isolation, it can be effectively deembedded from the measurements using the
same procedure shown in (9-56):

AB
CD

AB
CD

− 1 AB

CD

T-line =

(9-58)

via measured

Using the concept of cascaded matrices, any number of structures can be deem-
bedded from the measured data as long as the S -parameters for the structures are
known.

9.2.6 Changing the Reference Impedance

S -parameters are dependent on the reference impedance of the VNA. If the port
impedance values change, the S -parameters change. It is generally standard to
measure S -parameters assuming a reference impedance of 50 at each port.
However, sometimes the port impedance values need to be adjusted after the
measurements are performed. For example, perhaps the port impedance of the
VNA was determined to be something other than 50 , or the engineer wished
to examine the performance of the circuit referenced to an impedance consistent
with the transmission lines used in a specific board design. When an S -parameter
is measured with a reference impedance at the ports of Z n , it is said to be
normalized to that impedance.
To renormalize the S -matrix from Z n 1 to Z n 2 , the definition of the

Z -parameters from equation (9-35) is used:

S ) − 1 Z = Z n ( U + S )( U − (9-35)

Since the impedance matrix is not dependent on the port impedance, it can be
used to renormalize the S -matrix.

S 1 ) − 1 S 2 ) − 1 Z n 1 ( U + S 1 )( U − = Z n 2 ( U + S 2 )( U −