Radar System Engineering

SEC.124] I-F AMPLIFIER DESIGN 447
is vaned to give the desired response characteristic, usually that obtained
just before the curve becomes double-humped. The loading R, and R,
may be divided as shown, or placed on one side only. Two cases will be
considered: (1) both sides are loaded so that the Q of the primary is equal
to the Q of the secondary; (2) the loading is on one side only. With
transitional coupling’ the shape of the response curve is the same in either
case, but the gain and bandwidth are
not.
In the case of equal Q’s on both
sides, the gain is given by
G=g~~ ~,
J
‘5) W@
where C= and C, are the circuit capacities
associated with primary and
secondary respectively. The bandwidth is
i)+
FIG. 12. 7.—Double-tuned i-f amplifier.
*
~=~ti
27rRPCP”
(6)
Hence the gain-bandwidth
product is
(7)
If the loading is entirely on one side, either primary or secondary,
above equations become
the
(8)
11
a = % @RPCP’
(9)
Gx@=fi~.
2“ dcpc,
(lo)
If one compares the gain-bandwidth products given above with those
previously quoted for single-tuned circuits, it will be seen that there is an
improvement by a factor of 3.8 db in the equal-Q case and by a factor of
6.8 db in the case of loading on one side only.2 There is the further
1.As the coupling between two circuits of unequal Q is increased from zero, the
response at resonance rises to a maximum at the “critical coupling” point and then
decreases (with a flatter and flatter top to the response curve) until the point of
“transitional” coupling is reached, after which the curve becomes “double-humped.”
If the two circuits hnve equal Q’s, transitional coupling and critictd coupling are
the same.
2Values of C= and C, of 7 and 14ppf, respectively, were used for this calculation.