Radar System Engineering

446 THE RECEIVING SYSTEM—RADAR RECEIVERS [SEC.124
and the bandwidth
by the equation
11
‘= %R~C’
(3)
where Cis the total capacity resonated byL. Hence the gain-bandwidth
product is
~xa=~~
2r c“
(4)
From Eq. (4) wecansee thenecessity ofusing tubes with as higha
ratio of transconductance to input-plus-output capacitance as possible.
The 6AK5 is slightly better than the 6AC7 in this respect, average tubes
giving gain-bandwidth products of approximately 55 Me/see and 50
Me/see, respectively,, when allowance is made for socket and wiring
capacity. Onecanalso see from Eq. (4) the necessity of keeping extraneous
capacities to a minimum. It is for this reason that the inductance
L is either fixed-tuned or slug-tuned, instead of being used with a tuning
condenser. By the same token, the use of point-to-point wiring and the
mounting of components on the tube sockets are clearly indicated.
Amplifiers with a gain of 120 db and an over-all i-f bandwidth of about
2 Me/see will require a stage bandwidth of over 6 Me/see, which permits
a gain of approximately 7, or 17 db. Thus seven stages will be required.
Assuming a g~ of 7000, a reasonable figure for a 6AC7, the load resistance
R. would be 1000 ohms [Eq. (2)].
Many more stages would be required to increase this bandwidth
greatly, since the gain per stage must be lowered. The over-all bandwidth
of an amplifier consisting of cascaded single-tuned stages is given
approximately by the formula
single-stage bandwidth
Over-all bandwidth = (4)
1.2 {n “
When n, the number of cascaded stages, is larger than 3, this formula is
quite accurate.
Thus the number of single-tuned stages needed in an amplifier of
given gain, even for moderately wide bandwidths, becomes prohibitively
large. Lacking better tubes, the only alternative lies in the use of more
effective circuits. Two things are needed: (1) a coupling circuit that
will give a greater gain-bandwidth product for a given tube, and (2) a
response-vs.-frequency curve that, when cascaded, does not narrow as
rapidly as that given in Eq. (4). The double-tuned (transformercoupled)
circuit does very well in these respects. The elements of the
usual double-tuned circuit are shown in Fig. 12.7.
The primary is tuned to resonate with the capacity in the plate circuit,
the secondary with the capacity in the grid circuit. The coupling