DIFFERENTIAL SIGNALING - Advanced Signal Integrity for High-Speed Digital Design - page 305

the phase difference reaches 180 ◦ ( π ), the differential signal launched at the driver
is converted completely to a common-mode signal at the receiver, and equation
(7-9) is unity.

Example 7-1 For the differential pair shown in Figure 7-10, calculate the fre-
quency where the differential signal injected at the driver is 100% converted to
a common-mode signal at the receiver.

SOLUTION
Step 1: Calculate the propagation constant of the transmission lines. Equation
(2-46) defines the propagation constant in terms of the wavelength:

2 π
λ

β = rad / m

equation (2-45) defines wavelength in the terms of the frequency where the speed
of light in a vacuum has been replaced with the speed of light in the media ( ν p ):

ν p
λ

f = Hz

and equation (2-52) calculates the speed of light in the media (assuming that
µ r = 1):

c
√ ε r

ν p = m / s

Therefore, the propagation constant is calculated as a function of frequency:

2 πf √ ε r
c

10 − 9 )f β = = ( 41 . 866 × rad / s

Step 2: Use equation (7-9) to plot the differential-to-common mode conversion.
Since V(z = 1, the terms v 1 1 and v 2 0 ) = 1 and V(z = 0 ) =− = =− 1. The

plot is shown in Figure 7-11. When ACCM = 1, the phase error due to the length

mismatch equals 180 ◦ and the differential signal launched at the driver shows

Receiver

Driver

l 1 = 0.254 meters

V ( z = 0) = 1 V ( z = l 1 )

ε r = 4.0

V ( z = 0) = − 1 V ( z = l 2 )

l 2 = 0.260 meters

Figure 7-10 Figure for Example 7.1.