<s>
A	O
waffle-iron	B-Algorithm
filter	I-Algorithm
is	O
a	O
type	O
of	O
waveguide	B-Algorithm
filter	I-Algorithm
used	O
at	O
microwave	O
frequencies	O
for	O
signal	O
filtering	O
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
are	O
particularly	O
suitable	O
where	O
both	O
a	O
wide	O
passband	B-Algorithm
,	O
and	O
a	O
wide	O
stopband	O
free	O
of	O
spurious	O
transmission	O
modes	O
,	O
are	O
required	O
.	O
</s>
<s>
Design	O
techniques	O
for	O
waffle-iron	B-Algorithm
filters	I-Algorithm
include	O
image-parameter	O
methods	O
,	O
network	O
synthesis	O
methods	O
and	O
numerical	B-General_Concept
analysis	I-General_Concept
methods	O
.	O
</s>
<s>
Numerical	B-Algorithm
methods	I-Algorithm
can	O
be	O
used	O
to	O
analyse	O
either	O
design	O
.	O
</s>
<s>
The	O
waffle-iron	B-Algorithm
filter	I-Algorithm
was	O
invented	O
by	O
Seymour	O
B	O
.	O
Cohn	O
at	O
Stanford	O
Research	O
Institute	O
in	O
1957	O
.	O
</s>
<s>
In	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
there	O
are	O
,	O
in	O
addition	O
,	O
slots	O
cut	O
through	O
the	O
ridges	O
down	O
the	O
length	O
of	O
the	O
waveguide	O
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
are	O
,	O
in	O
essence	O
,	O
low-pass	B-Algorithm
filters	I-Algorithm
but	O
like	O
all	O
waveguide	O
devices	O
will	O
not	O
transmit	O
anything	O
below	O
the	O
waveguide	O
cutoff	O
frequency	O
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
are	O
used	O
where	O
both	O
a	O
wide	O
passband	B-Algorithm
with	O
low	O
insertion	O
loss	O
,	O
and	O
a	O
wide	O
(	O
sometimes	O
very	O
wide	O
)	O
stopband	O
are	O
needed	O
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
have	O
been	O
built	O
with	O
a	O
wide	O
stopband	O
and	O
attenuation	O
.	O
</s>
<s>
One	O
of	O
the	O
performance	O
issues	O
addressed	O
by	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
is	O
that	O
in	O
many	O
waveguide	B-Algorithm
filters	I-Algorithm
the	O
attenuation	O
is	O
dependent	O
on	O
the	O
transmission	O
modes	O
of	O
the	O
incident	O
signal	O
and	O
some	O
filters	O
can	O
be	O
quite	O
bad	O
at	O
suppressing	O
spurious	O
modes	O
which	O
may	O
be	O
contained	O
in	O
this	O
signal	O
.	O
</s>
<s>
For	O
instance	O
,	O
with	O
the	O
corrugated	O
waveguide	B-Algorithm
filter	I-Algorithm
,	O
on	O
which	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
is	O
based	O
,	O
attenuation	O
of	O
TEn0	O
modes	O
in	O
the	O
stopband	O
is	O
strongly	O
dependent	O
on	O
the	O
mode	O
number	O
.	O
</s>
<s>
This	O
is	O
not	O
the	O
case	O
with	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
which	O
attenuates	O
all	O
TEn0	O
modes	O
nearly	O
equally	O
up	O
to	O
a	O
certain	O
frequency	O
.	O
</s>
<s>
A	O
common	O
application	O
of	O
waffle-iron	B-Algorithm
filters	I-Algorithm
is	O
to	O
remove	O
the	O
harmonics	O
of	O
transmitters	O
,	O
such	O
as	O
high	O
power	O
radar	O
,	O
before	O
applying	O
to	O
the	O
antenna	O
.	O
</s>
<s>
This	O
is	O
an	O
application	O
that	O
usually	O
requires	O
a	O
very	O
wide	O
stopband	O
,	O
a	O
characteristic	O
of	O
waffle-iron	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
For	O
instance	O
,	O
to	O
remove	O
all	O
harmonics	O
up	O
to	O
the	O
fifth	O
it	O
is	O
necessary	O
for	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
to	O
have	O
a	O
stopband	O
greater	O
than	O
three	O
times	O
the	O
passband	B-Algorithm
.	O
</s>
<s>
The	O
wide-band	O
nature	O
of	O
waffle-iron	B-Algorithm
filters	I-Algorithm
finds	O
applications	O
in	O
satellite	O
communications	O
.	O
</s>
<s>
The	O
diplexer	O
must	O
therefore	O
have	O
a	O
stopband	O
that	O
is	O
even	O
wider	O
than	O
the	O
passband	B-Algorithm
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
are	O
used	O
in	O
industrial	O
microwave	O
processes	O
.	O
</s>
<s>
Waffle-iron	B-Algorithm
filters	I-Algorithm
are	O
a	O
useful	O
alternative	O
because	O
the	O
product	O
can	O
be	O
passed	O
between	O
the	O
filter	O
's	O
teeth	O
.	O
</s>
<s>
The	O
earliest	O
waffle-iron	B-Algorithm
filters	I-Algorithm
were	O
designed	O
with	O
the	O
image	O
parameter	O
method	O
of	O
filter	O
design	O
.	O
</s>
<s>
With	O
this	O
approach	O
,	O
the	O
original	O
specification	O
for	O
passband	B-Algorithm
and	O
stopband	O
can	O
be	O
kept	O
while	O
simultaneously	O
improving	O
the	O
impedance	O
matching	O
.	O
</s>
<s>
A	O
common	O
response	O
function	O
used	O
by	O
filter	O
designers	O
is	O
the	O
Chebyshev	O
filter	O
which	O
trades	O
steepness	O
of	O
the	O
transition	B-Algorithm
band	I-Algorithm
for	O
passband	B-Algorithm
ripple	O
.	O
</s>
<s>
However	O
the	O
Chebyshev	O
response	O
is	O
not	O
always	O
the	O
best	O
choice	O
for	O
waffle-iron	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
Low-pass	B-Algorithm
waveguide	B-Algorithm
filters	I-Algorithm
do	O
not	O
pass	O
frequencies	O
all	O
the	O
way	O
down	O
to	O
zero	O
because	O
of	O
the	O
waveguide	O
cutoff	O
effect	O
.	O
</s>
<s>
The	O
Zolotarev	O
response	O
has	O
a	O
stopband	O
at	O
low	O
frequency	O
,	O
the	O
cutoff	O
of	O
which	O
can	O
be	O
controlled	O
by	O
the	O
designer	O
so	O
it	O
is	O
not	O
detrimental	O
in	O
a	O
waveguide	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Another	O
design	O
approach	O
,	O
particularly	O
suitable	O
for	O
CAD	B-Application
because	O
it	O
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
,	O
is	O
to	O
decompose	O
the	O
filter	O
into	O
a	O
number	O
of	O
finite	B-Application
elements	I-Application
.	O
</s>
<s>
The	O
mode	O
matching	O
technique	O
expands	O
the	O
field	O
equations	O
of	O
the	O
element	O
into	O
a	O
series	O
of	O
eigenfunctions	B-Algorithm
and	O
then	O
for	O
each	O
mode	O
matches	O
the	O
field	O
at	O
the	O
interface	O
between	O
elements	O
.	O
</s>
<s>
The	O
Galerkin	B-Algorithm
method	I-Algorithm
expands	O
the	O
field	O
equations	O
into	O
polynomial	O
functions	O
such	O
as	O
Gegenbauer	O
polynomials	O
or	O
Chebyshev	O
polynomials	O
.	O
</s>
<s>
TE0n	O
modes	O
should	O
not	O
,	O
in	O
theory	O
,	O
be	O
excited	O
in	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
because	O
of	O
its	O
vertical	O
symmetry	O
about	O
the	O
centre-line	O
.	O
</s>
<s>
However	O
,	O
in	O
practice	O
they	O
can	O
be	O
caused	O
by	O
poorly	O
mating	O
waveguide	B-Algorithm
flanges	I-Algorithm
or	O
misaligned	O
teeth	O
.	O
</s>
<s>
Very	O
wide	O
stopbands	O
can	O
be	O
achieved	O
by	O
cascading	O
several	O
waffle-iron	B-Algorithm
filter	I-Algorithm
units	O
together	O
.	O
</s>
<s>
Matthaei	O
gives	O
an	O
example	O
of	O
a	O
three	O
unit	O
waffle-iron	B-Algorithm
filter	I-Algorithm
designed	O
to	O
stop	O
all	O
harmonics	O
of	O
the	O
passband	B-Algorithm
from	O
the	O
second	O
to	O
the	O
tenth	O
–	O
a	O
combined	O
stopband	O
of	O
to	O
with	O
a	O
rejection	O
of	O
.	O
</s>
<s>
For	O
instance	O
Matthaei	O
describes	O
a	O
passband	B-Algorithm
filter	O
with	O
rounded	O
teeth	O
and	O
a	O
wide	O
stopband	O
with	O
a	O
power-handling	O
capability	O
of	O
.	O
</s>
<s>
Filter	O
structures	O
that	O
are	O
analogous	O
to	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
are	O
used	O
in	O
photonics	O
but	O
operate	O
at	O
a	O
much	O
higher	O
frequency	O
and	O
are	O
much	O
smaller	O
than	O
those	O
used	O
in	O
electronics	O
.	O
</s>
<s>
These	O
filters	O
can	O
be	O
made	O
using	O
the	O
standard	O
semiconductor	O
industry	O
photolithography	B-Algorithm
manufacturing	O
techniques	O
.	O
</s>
