DIFFERENTIAL SIGNALING - Advanced Signal Integrity for High-Speed Digital Design - page 309

l = 5 inches l = 10 inches

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

5 10 15 20 5 10 15 20

Frequency, GHz Frequency, GHz

(a) (b)

Figure 7-15 Waveforms for Example 7-2: (a) length = 5 in. (b) length = 10 in.

and the propagation constant ( β ) changes:

v 1 e − jβ 1 l + v 2 e − jβ 2 l V(z = l) + V(z = l)

V(z =

ACCM =

0 ) =

(7-10)

v 1 − v 2

0 ) − V(z =

2 πf √ ε r, eff2 /c , l the differential pair length, and
v 1 and v 1 are the driving voltages.

2 πf √ ε r, eff1 /c , β 2 where β 1 = =

Example 7-2 Determine the frequency where the differential-to-common mode
conversion is 100% for a 10-in. (0.254-m) and a 5-in. (0.178-m) differential pair
routed where one leg is over a bundle and one leg is between glass bundles. Use
the measured data shown in Figure 6-15.

SOLUTION
Step 1: Determine the maximum spread in the effective dielectric permittivity.
From Figure 6-15 the spread is 0.23:

ε eff ≈ 3 . 73 − 3 . 5 = 0 . 23

Step 2: Calculate β 1 and β 2 :

2 πf √ 3 . 73
3

2 πf √ ε r, eff1
c

10 − 9 β 1 = = = f · 40 . 429 × rad/s

× 10 8

2 πf √ 3 . 5
3

2 πf √ ε r, eff2
c

10 − 9 β 2 = = = f · 39 . 163 × rad/s

× 10 8

Step 3: Plot the differential-to-common mode conversion using (7-10).
The plots are shown in Figure 7-15a and b. When the length is 10 in., the
differential-to-common mode conversion is 100% at about 10 and 20 GHz for
5 in.

Mitigation of the fiber-weave effect was discussed briefly in Section 6.5.2.