NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 412

1.0

0.9

S 21

0.8

0.7

0.6

0.5

S 11

0.4

0.3

0.2

0.1

0.0

0 1 2 3 4 5 6 7 8 9 10

Frequency, GHz

Figure 9-48 Figure for Problem 9-3.

Z odd = 50

50 50

∼

v

Z odd = 50 Z 0 = 50

50 50

∼

− v

7 inches

I = 100 mils

Figure 9-49 Figure for Problem 9-9.

9-10 Derive the equations to renormalize the S -matrix measured with 50-
loads at each port to arbitrary and different reference impedances at each
port.
9-11 Derive the two-port S -parameters for a frequency-dependent, causal 10-in.
transmission line from 10 Hz to 100 GHz. Using a tool such as Mathe-
matica or Matlab, plot the S -parameters and prove that they are passive
and causal.
9-12 From the S -parameters calculated from the transmission line in Problem
9-11, calculate the pulse (single-bit) response for a 15-Gbit/s data rate.
9-13 Create the S -matrices for 4- and 10-in. transmission lines using the method
derived in Problem 9-11. Cascade the S -parameters to get the equivalent
S -matrix for a 14-in. transmission line. Compare the cascaded S -matrix
to that of a single 14-in. transmission line.