<s>
A	O
waveguide	B-Algorithm
filter	I-Algorithm
is	O
an	O
electronic	B-Architecture
filter	I-Architecture
constructed	O
with	O
waveguide	O
technology	O
.	O
</s>
<s>
Filters	O
are	O
devices	O
used	O
to	O
allow	O
signals	O
at	O
some	O
frequencies	O
to	O
pass	O
(	O
the	O
passband	B-Algorithm
)	O
,	O
while	O
others	O
are	O
rejected	O
(	O
the	O
stopband	O
)	O
.	O
</s>
<s>
Waveguide	B-Algorithm
filters	I-Algorithm
are	O
most	O
useful	O
in	O
the	O
microwave	O
band	O
of	O
frequencies	O
,	O
where	O
they	O
are	O
a	O
convenient	O
size	O
and	O
have	O
low	O
loss	O
.	O
</s>
<s>
Waveguide	B-Algorithm
filters	I-Algorithm
were	O
developed	O
during	O
World	O
War	O
II	O
to	O
meet	O
the	O
needs	O
of	O
radar	B-Application
and	O
electronic	O
countermeasures	O
,	O
but	O
afterwards	O
soon	O
found	O
civilian	O
applications	O
such	O
as	O
use	O
in	O
microwave	B-Application
links	I-Application
.	O
</s>
<s>
A	O
particular	O
feature	O
of	O
waveguide	B-Algorithm
filter	I-Algorithm
design	O
concerns	O
the	O
mode	O
of	O
transmission	O
.	O
</s>
<s>
The	O
chief	O
advantages	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
over	O
other	O
technologies	O
are	O
their	O
ability	O
to	O
handle	O
high	O
power	O
and	O
their	O
low	O
loss	O
.	O
</s>
<s>
There	O
is	O
a	O
wide	O
array	O
of	O
different	O
types	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
One	O
of	O
the	O
most	O
common	O
types	O
consists	O
of	O
a	O
number	O
of	O
coupled	O
resonant	B-Algorithm
cavities	I-Algorithm
.	O
</s>
<s>
Other	O
waveguide	B-Algorithm
filter	I-Algorithm
types	O
include	O
dielectric	O
resonator	O
filters	O
,	O
insert	O
filters	O
,	O
finline	O
filters	O
,	O
corrugated-waveguide	O
filters	O
,	O
and	O
stub	O
filters	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
construct	O
waveguides	O
out	O
of	O
dielectric	O
rods	O
,	O
the	O
most	O
well	O
known	O
example	O
being	O
optical	B-Architecture
fibres	I-Architecture
.	O
</s>
<s>
Amongst	O
the	O
uses	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
are	O
the	O
construction	O
of	O
duplexers	O
,	O
diplexers	O
,	O
and	O
multiplexers	B-Protocol
;	O
selectivity	O
and	O
noise	O
limitation	O
in	O
receivers	O
;	O
and	O
harmonic	O
distortion	O
suppression	O
in	O
transmitters	O
.	O
</s>
<s>
A	O
waveguide	B-Algorithm
filter	I-Algorithm
is	O
a	O
filter	O
composed	O
of	O
waveguide	O
components	O
.	O
</s>
<s>
Somewhere	O
in	O
the	O
very	B-Algorithm
high	I-Algorithm
frequency	I-Algorithm
band	O
,	O
designers	O
switch	O
to	O
using	O
components	O
made	O
of	O
pieces	O
of	O
transmission	O
line	O
.	O
</s>
<s>
These	O
kinds	O
of	O
designs	O
are	O
called	O
distributed	B-Algorithm
element	I-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
At	O
still	O
higher	O
frequencies	O
,	O
the	O
microwave	O
bands	O
,	O
the	O
design	O
switches	O
to	O
waveguide	B-Algorithm
filters	I-Algorithm
,	O
or	O
sometimes	O
a	O
combination	O
of	O
waveguides	O
and	O
transmission	O
lines	O
.	O
</s>
<s>
Waveguide	B-Algorithm
filters	I-Algorithm
have	O
much	O
more	O
in	O
common	O
with	O
transmission	O
line	O
filters	O
than	O
lumped	O
element	O
filters	O
;	O
they	O
do	O
not	O
contain	O
any	O
discrete	O
capacitors	O
or	O
inductors	O
.	O
</s>
<s>
Indeed	O
,	O
the	O
design	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
frequently	O
starts	O
from	O
a	O
lumped	O
element	O
design	O
and	O
then	O
converts	O
the	O
elements	O
of	O
that	O
design	O
into	O
waveguide	O
components	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
important	O
differences	O
in	O
the	O
operation	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
compared	O
to	O
transmission	O
line	O
designs	O
concerns	O
the	O
mode	O
of	O
transmission	O
of	O
the	O
electromagnetic	O
wave	O
carrying	O
the	O
signal	O
.	O
</s>
<s>
This	O
multiplicity	O
of	O
modes	O
can	O
cause	O
problems	O
in	O
waveguide	B-Algorithm
filters	I-Algorithm
when	O
spurious	O
modes	O
are	O
generated	O
.	O
</s>
<s>
Another	O
feature	O
peculiar	O
to	O
waveguide	B-Algorithm
filters	I-Algorithm
is	O
that	O
there	O
is	O
a	O
definite	O
frequency	O
,	O
the	O
cutoff	O
frequency	O
,	O
below	O
which	O
no	O
transmission	O
can	O
take	O
place	O
.	O
</s>
<s>
This	O
means	O
that	O
in	O
theory	O
low-pass	B-Algorithm
filters	I-Algorithm
cannot	O
be	O
made	O
in	O
waveguides	O
.	O
</s>
<s>
However	O
,	O
designers	O
frequently	O
take	O
a	O
lumped	O
element	O
low-pass	B-Algorithm
filter	I-Algorithm
design	O
and	O
convert	O
it	O
to	O
a	O
waveguide	O
implementation	O
.	O
</s>
<s>
The	O
filter	O
is	O
consequently	O
low-pass	B-Algorithm
by	O
design	O
and	O
may	O
be	O
considered	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
for	O
all	O
practical	O
purposes	O
if	O
the	O
cutoff	O
frequency	O
is	O
below	O
any	O
frequency	O
of	O
interest	O
to	O
the	O
application	O
.	O
</s>
<s>
The	O
next	O
highest	O
cutoff	O
modes	O
are	O
TE20	O
,	O
at	O
exactly	O
twice	O
the	O
TE10	O
mode	O
,	O
and	O
TE01	O
which	O
is	O
also	O
twice	O
TE10	O
if	O
the	O
waveguide	O
used	O
has	O
the	O
commonly	O
used	O
aspect	B-Device
ratio	I-Device
of	O
2:1	O
.	O
</s>
<s>
Thus	O
,	O
there	O
is	O
an	O
octave	B-Language
over	O
which	O
the	O
dominant	O
mode	O
is	O
free	O
of	O
spurious	O
modes	O
,	O
although	O
operating	O
too	O
close	O
to	O
cutoff	O
is	O
usually	O
avoided	O
because	O
of	O
phase	O
distortion	O
.	O
</s>
<s>
Like	O
transmission	O
line	O
filters	O
,	O
waveguide	B-Algorithm
filters	I-Algorithm
always	O
have	O
multiple	O
passbands	B-Algorithm
,	O
replicas	O
of	O
the	O
lumped	O
element	O
prototype	O
.	O
</s>
<s>
In	O
most	O
designs	O
,	O
only	O
the	O
lowest	O
frequency	O
passband	B-Algorithm
is	O
useful	O
(	O
or	O
lowest	O
two	O
in	O
the	O
case	O
of	O
band-stop	O
filters	O
)	O
and	O
the	O
rest	O
are	O
considered	O
unwanted	O
spurious	O
artefacts	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
true	O
low-pass	B-Algorithm
and	O
high-pass	O
filters	O
cannot	O
exist	O
in	O
waveguide	O
.	O
</s>
<s>
At	O
some	O
high	O
frequency	O
there	O
will	O
be	O
a	O
spurious	O
passband	B-Algorithm
or	O
stopband	O
interrupting	O
the	O
intended	O
function	O
of	O
the	O
filter	O
.	O
</s>
<s>
The	O
range	O
of	O
frequencies	O
over	O
which	O
waveguide	B-Algorithm
filters	I-Algorithm
are	O
useful	O
is	O
largely	O
determined	O
by	O
the	O
waveguide	O
size	O
needed	O
.	O
</s>
<s>
At	O
frequencies	O
this	O
high	O
,	O
fibre-optic	B-Architecture
technology	O
starts	O
to	O
become	O
an	O
option	O
.	O
</s>
<s>
One	O
of	O
the	O
main	O
advantages	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
over	O
TEM	O
mode	O
technologies	O
is	O
the	O
quality	O
of	O
their	O
resonators	O
.	O
</s>
<s>
Waveguides	O
have	O
good	O
power	O
handling	O
capability	O
,	O
which	O
leads	O
to	O
filter	O
applications	O
in	O
radar	B-Application
.	O
</s>
<s>
Despite	O
the	O
performance	O
advantages	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
,	O
microstrip	O
is	O
often	O
the	O
preferred	O
technology	O
due	O
to	O
its	O
low	O
cost	O
.	O
</s>
<s>
Development	O
of	O
distributed	B-Algorithm
element	I-Algorithm
filters	I-Algorithm
began	O
in	O
the	O
years	O
before	O
World	O
War	O
II	O
.	O
</s>
<s>
Much	O
development	O
on	O
waveguide	B-Algorithm
filters	I-Algorithm
was	O
carried	O
out	O
during	O
World	O
War	O
II	O
driven	O
by	O
the	O
filtering	O
needs	O
of	O
radar	B-Application
and	O
electronic	O
countermeasures	O
.	O
</s>
<s>
While	O
Cauer	O
's	O
work	O
concerns	O
lumped	O
elements	O
,	O
it	O
is	O
of	O
some	O
importance	O
to	O
waveguide	B-Algorithm
filters	I-Algorithm
;	O
the	O
Chebyshev	O
filter	O
,	O
a	O
special	O
case	O
of	O
Cauer	O
's	O
synthesis	O
,	O
is	O
widely	O
used	O
as	O
a	O
prototype	O
filter	O
for	O
waveguide	O
designs	O
.	O
</s>
<s>
This	O
filter	O
was	O
based	O
on	O
quarter-wave	O
impedance	O
transformers	O
of	O
various	O
widths	O
and	O
was	O
able	O
to	O
produce	O
designs	O
with	O
bandwidths	O
up	O
to	O
an	O
octave	B-Language
(	O
a	O
fractional	O
bandwidth	O
of	O
)	O
.	O
</s>
<s>
This	O
principle	O
was	O
not	O
at	O
first	O
much	O
used	O
by	O
waveguide	B-Algorithm
filter	I-Algorithm
designers	O
,	O
but	O
it	O
was	O
used	O
extensively	O
by	O
mechanical	O
filter	O
designers	O
in	O
the	O
1960s	O
,	O
particularly	O
R	O
.	O
A	O
.	O
Johnson	O
at	O
Collins	O
Radio	O
Company	O
.	O
</s>
<s>
The	O
initial	O
non-military	O
application	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
was	O
in	O
the	O
microwave	B-Application
links	I-Application
used	O
by	O
telecommunications	O
companies	O
to	O
provide	O
the	O
backbone	B-General_Concept
of	O
their	O
networks	O
.	O
</s>
<s>
Previously	O
,	O
satellite	O
communications	O
systems	O
used	O
a	O
separate	O
component	O
for	O
delay	B-Algorithm
equalisation	I-Algorithm
.	O
</s>
<s>
An	O
alternative	O
approach	O
to	O
designing	O
smaller	O
waveguide	B-Algorithm
filters	I-Algorithm
was	O
provided	O
by	O
the	O
use	O
of	O
non-propagating	O
evanescent	O
modes	O
.	O
</s>
<s>
Jaynes	O
and	O
Edson	O
proposed	O
evanescent	O
mode	O
waveguide	B-Algorithm
filters	I-Algorithm
in	O
the	O
late	O
1950s	O
.	O
</s>
<s>
Since	O
then	O
,	O
evanescent	O
mode	O
waveguide	B-Algorithm
filters	I-Algorithm
have	O
seen	O
successful	O
use	O
where	O
waveguide	O
size	O
or	O
weight	O
are	O
important	O
considerations	O
.	O
</s>
<s>
Multiplexers	B-Protocol
were	O
first	O
described	O
by	O
Fano	O
and	O
Lawson	O
in	O
1948	O
.	O
</s>
<s>
Pierce	O
was	O
the	O
first	O
to	O
describe	O
multiplexers	B-Protocol
with	O
contiguous	O
passbands	B-Algorithm
.	O
</s>
<s>
Multiplexers	B-Protocol
with	O
compensating	O
immittance	O
resonators	O
at	O
each	O
junction	O
are	O
largely	O
the	O
work	O
of	O
E	O
.	O
G	O
.	O
Cristal	O
and	O
G	O
.	O
L	O
.	O
Matthaei	O
in	O
the	O
1960s	O
.	O
</s>
<s>
Multi-channel	O
,	O
multi-octave	O
multiplexers	B-Protocol
were	O
investigated	O
by	O
Harold	O
Schumacher	O
at	O
Microphase	O
Corporation	O
,	O
and	O
his	O
results	O
were	O
published	O
in	O
1976	O
.	O
</s>
<s>
The	O
principle	O
that	O
multiplexer	B-Protocol
filters	O
may	O
be	O
matched	O
when	O
joined	O
together	O
by	O
modifying	O
the	O
first	O
few	O
elements	O
,	O
thus	O
doing	O
away	O
with	O
the	O
compensating	O
resonators	O
,	O
was	O
discovered	O
accidentally	O
by	O
E	O
.	O
J	O
.	O
Curly	O
around	O
1968	O
when	O
he	O
mistuned	O
a	O
diplexer	O
.	O
</s>
<s>
A	O
formal	O
theory	O
for	O
this	O
was	O
provided	O
by	O
J	O
.	O
D	O
.	O
Rhodes	O
in	O
1976	O
and	O
generalised	O
to	O
multiplexers	B-Protocol
by	O
Rhodes	O
and	O
Ralph	O
Levy	O
in	O
1979	O
.	O
</s>
<s>
From	O
the	O
1980s	O
,	O
planar	O
technologies	O
,	O
especially	O
microstrip	O
,	O
have	O
tended	O
to	O
replace	O
other	O
technologies	O
used	O
for	O
constructing	O
filters	O
and	O
multiplexers	B-Protocol
,	O
especially	O
in	O
products	O
aimed	O
at	O
the	O
consumer	O
market	O
.	O
</s>
<s>
Waveguide	B-Algorithm
filter	I-Algorithm
designs	O
frequently	O
consist	O
of	O
two	O
different	O
components	O
repeated	O
a	O
number	O
of	O
times	O
.	O
</s>
<s>
Lumped	O
element	O
filters	O
are	O
commonly	O
ladder	O
topology	O
,	O
and	O
such	O
a	O
circuit	O
is	O
a	O
typical	O
starting	O
point	O
for	O
waveguide	B-Algorithm
filter	I-Algorithm
designs	O
.	O
</s>
<s>
Filter	O
performance	O
parameters	O
,	O
such	O
as	O
stopband	O
rejection	O
and	O
rate	O
of	O
transition	O
between	O
passband	B-Algorithm
and	O
stopband	O
,	O
are	O
improved	O
by	O
adding	O
more	O
components	O
and	O
thus	O
increasing	O
the	O
length	O
of	O
the	O
filter	O
.	O
</s>
<s>
This	O
approach	O
is	O
typically	O
used	O
in	O
filter	O
designs	O
which	O
use	O
a	O
large	O
number	O
of	O
closely	O
spaced	O
elements	O
such	O
as	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Chebyshev	O
waveguide	B-Algorithm
filters	I-Algorithm
are	O
used	O
where	O
the	O
filtering	O
requirements	O
are	O
rigorous	O
,	O
such	O
as	O
satellite	O
applications	O
.	O
</s>
<s>
Many	O
waveguide	B-Algorithm
filter	I-Algorithm
components	O
work	O
by	O
introducing	O
a	O
sudden	O
change	O
,	O
a	O
discontinuity	O
,	O
to	O
the	O
transmission	O
properties	O
of	O
the	O
waveguide	O
.	O
</s>
<s>
A	O
basic	O
component	O
of	O
waveguide	B-Algorithm
filters	I-Algorithm
is	O
the	O
cavity	B-Algorithm
resonator	I-Algorithm
.	O
</s>
<s>
A	O
given	O
geometry	O
of	O
cavity	O
will	O
resonate	B-Application
at	O
a	O
characteristic	O
frequency	O
.	O
</s>
<s>
The	O
resonance	B-Application
effect	O
can	O
be	O
used	O
to	O
selectively	O
pass	O
certain	O
frequencies	O
.	O
</s>
<s>
Tuning	O
screws	O
are	O
screws	O
inserted	O
into	O
resonant	B-Algorithm
cavities	I-Algorithm
which	O
can	O
be	O
adjusted	O
externally	O
to	O
the	O
waveguide	O
.	O
</s>
<s>
An	O
iris-coupled	O
filter	O
consists	O
of	O
a	O
cascade	O
of	O
impedance	O
transformers	O
in	O
the	O
form	O
of	O
waveguide	O
resonant	B-Algorithm
cavities	I-Algorithm
coupled	O
together	O
by	O
irises	O
.	O
</s>
<s>
A	O
post	O
filter	O
consists	O
of	O
several	O
rows	O
of	O
posts	O
across	O
the	O
width	O
of	O
the	O
waveguide	O
which	O
separate	O
the	O
waveguide	O
into	O
resonant	B-Algorithm
cavities	I-Algorithm
as	O
shown	O
in	O
figure	O
7	O
.	O
</s>
<s>
The	O
existing	O
manufacturing	O
techniques	O
of	O
printed	O
circuit	O
board	O
or	O
low	B-Algorithm
temperature	I-Algorithm
co-fired	I-Algorithm
ceramic	I-Algorithm
can	O
be	O
used	O
to	O
make	O
post-wall	O
waveguide	O
circuits	O
.	O
</s>
<s>
These	O
capacitors	O
resonate	B-Application
with	O
the	O
preceding	O
length	O
of	O
evanescent	O
mode	O
waveguide	O
which	O
has	O
the	O
equivalent	O
circuit	O
of	O
an	O
inductor	O
,	O
thus	O
producing	O
a	O
filtering	O
action	O
.	O
</s>
<s>
They	O
are	O
used	O
in	O
applications	O
which	O
simultaneously	O
require	O
a	O
wide	O
passband	B-Algorithm
,	O
good	O
passband	B-Algorithm
matching	O
,	O
and	O
a	O
wide	O
stopband	O
.	O
</s>
<s>
They	O
are	O
essentially	O
low-pass	B-Algorithm
designs	O
(	O
above	O
the	O
usual	O
limitation	O
of	O
the	O
cutoff	O
frequency	O
)	O
,	O
unlike	O
most	O
other	O
forms	O
which	O
are	O
usually	O
band-pass	O
.	O
</s>
<s>
The	O
waffle-iron	B-Algorithm
filter	I-Algorithm
is	O
a	O
variant	O
of	O
the	O
corrugated-waveguide	O
filter	O
.	O
</s>
<s>
In	O
the	O
waffle-iron	B-Algorithm
filter	I-Algorithm
,	O
channels	O
are	O
cut	O
through	O
the	O
ridges	O
longitudinally	O
down	O
the	O
filter	O
.	O
</s>
<s>
However	O
,	O
a	O
broadband	B-General_Concept
design	O
for	O
the	O
same	O
item	O
requires	O
many	O
more	O
elements	O
and	O
the	O
design	O
takes	O
on	O
the	O
nature	O
of	O
a	O
filter	O
.	O
</s>
<s>
Other	O
possible	O
applications	O
include	O
multiplexers	B-Protocol
,	O
demultiplexers	O
,	O
negative-resistance	O
amplifiers	O
,	O
and	O
time-delay	O
networks	O
.	O
</s>
<s>
In	O
a	O
frequency	B-Architecture
filter	I-Architecture
typically	O
the	O
parameter	O
optimised	O
is	O
stopband	O
rejection	O
,	O
passband	B-Algorithm
attenuation	O
,	O
steepness	O
of	O
transition	O
,	O
or	O
some	O
compromise	O
between	O
these	O
.	O
</s>
<s>
For	O
instance	O
the	O
rat-race	B-Algorithm
coupler	I-Algorithm
(	O
which	O
can	O
be	O
implemented	O
directly	O
in	O
waveguide	O
)	O
works	O
on	O
a	O
completely	O
different	O
principle	O
but	O
still	O
relies	O
on	O
certain	O
lengths	O
being	O
exact	O
in	O
terms	O
of	O
λ	O
.	O
</s>
<s>
Steps	O
need	O
to	O
be	O
taken	O
to	O
prevent	O
the	O
filters	O
from	O
coupling	O
to	O
each	O
other	O
when	O
they	O
are	O
at	O
resonance	B-Application
which	O
would	O
cause	O
degradation	O
of	O
their	O
performance	O
.	O
</s>
<s>
For	O
instance	O
,	O
if	O
the	O
filters	O
are	O
of	O
the	O
iris-coupled	O
type	O
then	O
the	O
iris	O
nearest	O
to	O
the	O
filter	O
junction	O
of	O
filter	O
A	O
is	O
placed	O
λgb/4	O
from	O
the	O
junction	O
where	O
λgb	O
is	O
the	O
guide	O
wavelength	O
in	O
the	O
passband	B-Algorithm
of	O
filter	O
B	O
.	O
</s>
<s>
This	O
works	O
because	O
when	O
filter	O
A	O
is	O
at	O
resonance	B-Application
,	O
filter	O
B	O
is	O
in	O
its	O
stopband	O
and	O
only	O
loosely	O
coupled	O
and	O
vice	O
versa	O
.	O
</s>
<s>
This	O
arrangement	O
can	O
be	O
extended	O
to	O
multiplexers	B-Protocol
with	O
any	O
number	O
of	O
bands	O
.	O
</s>
<s>
For	O
diplexers	O
dealing	O
with	O
contiguous	O
passbands	B-Algorithm
proper	O
account	O
of	O
the	O
crossover	B-Algorithm
characteristics	O
of	O
filters	O
needs	O
to	O
be	O
considered	O
in	O
the	O
design	O
.	O
</s>
<s>
Here	O
a	O
low-pass	B-Algorithm
and	O
a	O
high-pass	O
filter	O
are	O
used	O
instead	O
of	O
band-pass	O
filters	O
.	O
</s>
<s>
The	O
synthesis	O
techniques	O
used	O
here	O
can	O
equally	O
be	O
applied	O
to	O
narrowband	O
multiplexers	B-Protocol
and	O
largely	O
remove	O
the	O
need	O
for	O
decoupling	O
resonators	O
.	O
</s>
