CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 158

Electric field: Odd mode Electric field: Even mode

Magnetic field: Odd mode Magnetic field: Even mode

Figure 4-9 Odd- and even-mode electric and magnetic field patterns for a simple
two-conductor system.

since the current in the two conductors flows in opposite directions, the currents
induced on each line due to the coupling of the magnetic fields always oppose
each other and cancel the effect of the mutual inductance. Therefore, the mutual
inductance must be subtracted and the mutual capacitance must be added to cal-
culate the odd-mode characteristics. These characteristics of even- and odd-mode
propagation are due to the assumption that the signals are propagating only in
transverse electromagnetic (TEM) mode, so that the electric and magnetic fields
are always orthogonal to each other.
With homogeneous dielectrics, the product of L and C remains constant, since
fields are confined within the uniform dielectric:

1
ν p

=

LC I (4-41)

where I is the identity matrix. Thus, in a multiconductor homogeneous system
such as a stripline array, if L is increased by the mutual inductance, C must
be decreased by the mutual capacitance such that LC remains constant. Subse-
quently, a stripline, or buried microstrip, which is embedded in a homogeneous
dielectric, should not exhibit velocity variations due to different switching modes.
It will, however, exhibit pattern-dependent impedance variation.
In a nonhomogeneous dielectric where the electric fields fringe through more
than one dielectric material, such as an array of microstrip lines, LC is not con-
stant for different propagation modes because the electromagnetic fields travel
partially in air and partially in the board's dielectric material. In a microstrip, the
effective dielectric constant is a weighted average between air and the dielectric
material of the board. Because the field patterns change with different propaga-
tion modes, the effective dielectric constant will change depending on the field
densities contained within the board's dielectric material and the air. Thus, the