TOPICS IN HIGH-SPEED CHANNEL MODELING - Advanced Signal Integrity for High-Speed Digital Design - page 435

~62% of the power is
radiated into the
plane

0.1 0.7

0.9

0.6

S 21

P plane

0.8

0.5

0.7

0.6

0.4

0.5 S 11

0.3

0.4

0.3

0.2

0.2

0.1

0.1

0.0 0.0

0 10 20 30 40 50

Frequency, GHz

Figure 10-21 At resonance, a large percentage of the total power can be radiated into
the layers between reference planes. This example shows the S -parameters and the power
radiated into the plane for a 37.8-mil via stub, as shown in Figure 10-17.

P loss
P incident

− S 11 S 11 − S 21 S 21 1 = (10-11a)

where

P loss
P incident

P plane = (10-11b)

Note that as the frequency nears resonance, the energy transfer into the plane is
most efficient.
Figure 10-22 shows an equivalent circuit and its response. The resistor repre-
sents the losses due to energy being sourced into the parallel-plate mode between
reference layers 2 and 3. The L and C values were extracted from Ansoft Q3D,
and the resistor value was varied until the value of S 21 matched the HFSS result.
Note that this circuit is only a crude approximation of the via behavior. The only
methodology that can model this effect accurately is to use a 3D field simulator
such as Ansoft's HFSS.

10.3.3 Parallel-Plate Waveguide
To promote the understanding of how the energy propagates between reference
layers after it has been sourced from a resonant via structure, it is useful to
derive the equations that govern the parallel-plate waveguide. A parallel-plate
waveguide is formed from two flat plates, as shown in Figure 10-23. For this
analysis it is assumed that the width w is much larger than the vertical separation
between the plates h , so that any fringing fields at the edges can be ignored. Since