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Coupled Mode Synthesis
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Traditional Modal Synthesis
A Reformulation
For reasons to be discussed in the next section, Van Duyne reformulates the second-order filter of Eq.
1
with
as
(
2
)
where
is a first order allpass filter of the form
(
3
)
and
.
With
, the resonator does not decay but rather behaves like an oscillator with frequency
.
Eq.
2
has an additional zero at
that is not present in Eq.
1
, though this has little affect on the resonating behavior of the filter.
A block diagram of the resulting filter structure is shown in Fig.
13
.
Figure 13:
The CMS resonator filter structure.
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.