<s>
A	O
double-tuned	B-Algorithm
amplifier	I-Algorithm
is	O
a	O
tuned	B-Algorithm
amplifier	I-Algorithm
with	O
transformer	B-Algorithm
coupling	O
between	O
the	O
amplifier	O
stages	O
in	O
which	O
the	O
inductances	O
of	O
both	O
the	O
primary	O
and	O
secondary	O
windings	O
are	O
tuned	O
separately	O
with	O
a	O
capacitor	O
across	O
each	O
.	O
</s>
<s>
The	O
scheme	O
results	O
in	O
a	O
wider	O
bandwidth	B-Algorithm
and	O
steeper	O
skirts	B-Algorithm
than	O
a	O
single	O
tuned	O
circuit	O
would	O
achieve	O
.	O
</s>
<s>
There	O
is	O
a	O
critical	O
value	O
of	O
transformer	B-Algorithm
coupling	O
coefficient	O
at	O
which	O
the	O
frequency	O
response	O
of	O
the	O
amplifier	O
is	O
maximally	O
flat	O
in	O
the	O
passband	B-Algorithm
and	O
the	O
gain	O
is	O
maximum	O
at	O
the	O
resonant	O
frequency	O
.	O
</s>
<s>
Designs	O
frequently	O
use	O
a	O
coupling	O
greater	O
than	O
this	O
(	O
over-coupling	O
)	O
in	O
order	O
to	O
achieve	O
an	O
even	O
wider	O
bandwidth	B-Algorithm
at	O
the	O
expense	O
of	O
a	O
small	O
loss	O
of	O
gain	O
in	O
the	O
centre	O
of	O
the	O
passband	B-Algorithm
.	O
</s>
<s>
Cascading	O
multiple	O
stages	O
of	O
double-tuned	B-Algorithm
amplifiers	I-Algorithm
results	O
in	O
a	O
reduction	O
of	O
the	O
bandwidth	B-Algorithm
of	O
the	O
overall	O
amplifier	O
.	O
</s>
<s>
Two	O
stages	O
of	O
double-tuned	B-Algorithm
amplifier	I-Algorithm
have	O
80%	O
of	O
the	O
bandwidth	B-Algorithm
of	O
a	O
single	O
stage	O
.	O
</s>
<s>
An	O
alternative	O
to	O
double	O
tuning	O
that	O
avoids	O
this	O
loss	O
of	O
bandwidth	B-Algorithm
is	O
staggered	B-Algorithm
tuning	I-Algorithm
.	O
</s>
<s>
Stagger-tuned	B-Algorithm
amplifiers	I-Algorithm
can	O
be	O
designed	O
to	O
a	O
prescribed	O
bandwidth	B-Algorithm
that	O
is	O
greater	O
than	O
the	O
bandwidth	B-Algorithm
of	O
any	O
single	O
stage	O
.	O
</s>
<s>
However	O
,	O
staggered	B-Algorithm
tuning	I-Algorithm
requires	O
more	O
stages	O
and	O
has	O
lower	O
gain	O
than	O
double	O
tuning	O
.	O
</s>
<s>
However	O
,	O
the	O
collector	O
load	O
consists	O
of	O
a	O
transformer	B-Algorithm
which	O
serves	O
as	O
the	O
inter-stage	O
coupling	O
instead	O
of	O
capacitors	O
.	O
</s>
<s>
The	O
windings	O
of	O
the	O
transformer	B-Algorithm
have	O
inductance	O
.	O
</s>
<s>
Capacitors	O
placed	O
across	O
the	O
transformer	B-Algorithm
windings	O
form	O
resonant	O
circuits	O
which	O
provide	O
the	O
tuning	O
of	O
the	O
amplifier	O
.	O
</s>
<s>
A	O
further	O
detail	O
that	O
may	O
be	O
seen	O
in	O
this	O
kind	O
of	O
amplifier	O
is	O
the	O
presence	O
of	O
taps	O
on	O
the	O
transformer	B-Algorithm
windings	O
.	O
</s>
<s>
These	O
are	O
used	O
for	O
the	O
input	O
and	O
output	O
connections	O
of	O
the	O
transformer	B-Algorithm
rather	O
than	O
the	O
top	O
of	O
the	O
windings	O
.	O
</s>
<s>
This	O
problem	O
can	O
be	O
avoided	O
by	O
using	O
MOSFETs	B-Architecture
which	O
have	O
a	O
very	O
high	O
input	O
impedance	O
.	O
</s>
<s>
The	O
capacitors	O
connected	O
between	O
the	O
bottom	O
of	O
the	O
transformer	B-Algorithm
secondary	O
windings	O
and	O
ground	O
do	O
not	O
form	O
part	O
of	O
the	O
tuning	O
.	O
</s>
<s>
Double	O
tuning	O
,	O
as	O
compared	O
to	O
single	O
tuning	O
,	O
has	O
the	O
effect	O
of	O
widening	O
the	O
bandwidth	B-Algorithm
of	O
the	O
amplifier	O
and	O
steepening	O
the	O
skirt	B-Algorithm
of	O
the	O
response	O
.	O
</s>
<s>
Tuning	O
both	O
sides	O
of	O
the	O
transformer	B-Algorithm
forms	O
a	O
pair	O
of	O
coupled	O
resonators	O
which	O
is	O
the	O
source	O
of	O
the	O
increased	O
bandwidth	B-Algorithm
.	O
</s>
<s>
This	O
response	O
can	O
also	O
be	O
achieved	O
without	O
transformers	B-Algorithm
with	O
two	O
stages	O
of	O
a	O
stagger-tuned	B-Algorithm
amplifier	I-Algorithm
.	O
</s>
<s>
Unlike	O
staggered	B-Algorithm
tuning	I-Algorithm
,	O
double	O
tuning	O
usually	O
tunes	O
both	O
resonators	O
to	O
the	O
same	O
resonant	O
frequency	O
.	O
</s>
<s>
However	O
,	O
a	O
designer	O
might	O
choose	O
to	O
design	O
an	O
overcoupled	O
amplifier	O
in	O
order	O
to	O
achieve	O
a	O
wider	O
bandwidth	B-Algorithm
at	O
the	O
expense	O
of	O
a	O
small	O
dip	O
(	O
typically	O
to	O
maximize	O
the	O
bandwidth	B-Algorithm
)	O
in	O
the	O
centre	O
of	O
the	O
frequency	O
response	O
.	O
</s>
<s>
Like	O
synchronous	B-Algorithm
tuning	I-Algorithm
,	O
adding	O
more	O
stages	O
of	O
double-tuned	B-Algorithm
amplifiers	I-Algorithm
has	O
the	O
effect	O
of	O
reducing	O
the	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
bandwidth	B-Algorithm
of	O
n	O
identical	O
stages	O
,	O
as	O
a	O
fraction	O
of	O
the	O
bandwidth	B-Algorithm
of	O
a	O
single	O
stage	O
,	O
is	O
given	O
approximately	O
by	O
,	O
</s>
<s>
This	O
expression	O
applies	O
only	O
to	O
small	O
fractional	O
bandwidths	B-Algorithm
.	O
</s>
<s>
The	O
circuit	O
can	O
be	O
represented	O
in	O
a	O
more	O
generic	O
way	O
by	O
replacing	O
the	O
amplifiers	O
with	O
a	O
generalised	O
transconductance	B-Algorithm
amplifier	I-Algorithm
as	O
shown	O
.	O
</s>
<s>
where	O
ω0	O
is	O
the	O
resonant	O
frequency	O
expressed	O
in	O
units	O
of	O
angular	O
frequency	O
and	O
the	O
subscripts	O
p	O
and	O
s	O
refer	O
respectively	O
to	O
components	O
on	O
the	O
primary	O
and	O
secondary	O
side	O
of	O
the	O
transformer	B-Algorithm
.	O
</s>
