NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 371

S 21 - Insertion loss S 31 - Reverse crosstalk

1.0

0.8

0.6

0.4

0.2

0.0

0 0.2 0.4 0.6 0.8 1

Frequency, GHz

0.147 GHz

Figure 9-21 Insertion loss and reverse crosstalk for Example 9-6.

described by equation (9-3b). Consequently, when S 11 and S 31 are maximum,
S 21 must be minimum and is calculated with equation (9-32a):

100
Z even

100
100

S 21 = =

25 =

0 . 8

+ Z odd +

A simulation of this case is shown in Figure 9-21.

Relationship Between S- and Z-Parameters Perhaps the most intuitive form of
network analysis are the Z -parameters, which were explained in Section 9.2.1.
The disadvantage of using an impedance (or admittance) matrix is simply that
they are impossible to measure directly at high frequencies. Fortunately, it is
relatively easy to convert

Z -parameters into S -parameters and vice versa. The

derivation is shown here.
In matrix form, let's begin with the voltage at port n of an N -port system,
which is composed of an ingoing wave ( v + ) and an outgoing wave ( v − ):

v n = v n + v n

where the current is calculated from the port voltage and the port (reference)
impedance Z n :

v n ) 1
Z n

i n i n (v n i n = − = −