(3.23)
(3.24)
Even Mode.
Even-mode propagation mode occurs when two coupled transmission lines are driven with
equal magnitude and are in phase with one another. The effective capacitance of the
transmission line will decrease by the mutual capacitance and the equivalent inductance will
increase by the mutual inductance. To examine the effect that even-mode propagation on
two adjacent traces will have on the characteristic impedance and on the velocity, consider
Figure 3.7
.
In even-mode propagation, the currents on the lines, I
1
and I
2
, will always be driven with
equal magnitude and in the same direction. First, let's consider the effect of mutual
inductance. Again, refer to
Figure 3.8
. The analysis that was done for odd-mode switching
can be done to determine the effective even-mode capacitance and inductance. For even-
mode propagation, I
1
= I
2
and V
1
= V
2
; therefore,
equations (3.13)
and
(3.14)
yield
(3.25)
(3.26)
Therefore, the equivalent inductance seen by line 1 in a pair of coupled transmission line
propagating in even mode is
(3.27)
Similarly, the effect of the mutual capacitance can be derived. Again, refer to
Figure 3.9
.
Substituting I
1
= I
2
and V
1
= V
2
for even-mode propagation, therefore,
equations (3.18)
and
(3.19)
yield
(3.28)
(3.29)
Therefore, the equivalent capacitance seen by trace 1 in a pair of coupled transmission line
propagating in even mode is
(3.30)
Subsequently, the even-mode transmission characteristics for a coupled two-line system are
(3.31)
(3.32)
Summary :
Substituting I 1 = I 2 and V 1 = V 2 for even-mode propagation, therefore, equations (3.18) and (3.19) yield (3.28) (3.29) Therefore, the equivalent capacitance seen by trace 1 in a pair of coupled transmission line propagating in even mode is (3.30) Subsequently, the even-mode transmission characteristics for a coupled two-line system are (3.31) (3.32)
Tags :
eenmode,transmission,inductance,capacitance,mode,propagation,mutual,therefore,coupled,een,line,effect,figure