NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 402

S cd 21

S dd 21

1.0

v

0.8 v

0.6 − v − v

q = 360 °

q = 190 °

q = 270 °

0.4

v

0.2

− v

0.0

0 5 10 15 20 25 30

Frequency, GHz

Figure 9-39 As the frequency increases, small asymmetries in a differential pair will
cause larger phase differences between signals propagating on each leg, causing energy
to be converted from odd to even mode. This shows up as differential insertion loss. In
this case the differential signal is 100% converted to common mode at 18 GHz.

So at 18 GHz, the phase difference at the receiver will be

180 ◦ + θ = 180 ◦ + ( 360 ◦ )( 27 . 77 360 ◦ 10 − 12 )( 18 10 9 ) = × ×

Therefore, at 18 GHz the differential insertion loss is zero because there is no
longer any differential energy being transmitted to the receiver because all the
energy has been converted to the common mode.
Figure 9-39 shows the S -parameters for the loss-free perfectly terminated
asymmetrical transmission line with a interleg delay difference of 27.77 ps. Note
that the differential energy transferred from port 1 to port 2 ( S dd 21 ) decreases
until 18 GHz, after which it begins to increase again. At 1 GHz (where θ =
190 ◦ ), S cd 21

=

0 . 1, which means that 10% of the differential energy is lost to the
common mode. At 18 GHz, S cd 21 1 . 0, so 100% of the energy is lost to the

common mode. It is easy to see that the decrease in S dd 21 corresponds with the
increase in S cd 21 .
Do not falsely conclude that differential signals can be transmitted properly
at frequencies above f 180 (18 GHz in this example). Although S dd 21 increases,
the phase difference between signals on each leg approaches 540 ◦

=

180 ◦ ), not
the ideal value of 180 ◦ . For a digital signal, this means that the bit on line 1 is
180 ◦ out of phase with the next bit in the digital pulse train on line 2. Therefore,
even though the common-mode conversion is small, the data are invalid.
When loss is included in the transmission line, the S cd 21 curve will peak at a
lower frequency that does not correspond to the point where the differential-to-
common mode conversion is 100%, as shown in Figure 9-40. Be careful not
to misinterpret the differential S -parameter data. The mode conversion is 100%
when S dd 21 is zero, not necessarily when S cd 21 is maximum.

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