CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 159

0.005 in 0.005 in 0.005 in

0.002 in

ε r = 4.0

0.005 in

Figure 4-10 Cross section of the PCB-based coupled transmission-line pair for

Example 4-2.

LC product will be mode dependent in a nonhomogeneous system. The LC prod-
uct, however, will remain constant for a given mode. Therefore, a microstrip will
exhibit both a velocity and an impedance change, due to different switching pat-
terns. It should be noted that the description above holds for a single frequency.
The product of LC varies with frequency but remains constant at each frequency
point for a given mode.

Example 4-2 The PCB transmission lines depicted in Figure 4-10 have the
following inductances and capacitances:

3 . 592

10 − 7

10 − 7 10 − 8

× ×

3 . 218

L = H / m

10 − 8

3 . 218 × 3 . 592 ×

10 − 11

10 − 11 10 − 12 8 . 501 × − 2 . 173 ×

C = F / m

10 − 12 − 2 . 173 × 8 . 501 ×

Assume that the waveform is driven into the line at t = 1 ns.

We have designed the PCB traces to have a typical (isolated) characteristic
impedance of approximately 65 with a length of 0.2794 m (11 in.). They are
driven by a 1-V 65- source, and are terminated to ground in 65 at the far
end. The rise and fall times are 0.1 ns. Compare the analytical results with those
from a fully coupled simulation for even- and odd-mode propagation.

SOLUTION
Step 1: Calculate the impedances and velocities for all of the switching pat-
terns.

3 . 592

× 10 − 7 + 3 . 218 × 10 − 8 H / m

Z 0 , even =

10 − 12 F / m =

68 . 7

8 . 501 × 10 − 11 − 2 . 173 ×

3 . 592

10 − 7 10 − 8 H / m × − 3 . 218 ×

Z 0 , odd =

10 − 12 ) F / m =

61 . 2

8 . 501 × 10 − 11 + 2 . 173 ×