Radar System Engineering

SEC. 10.7] PULSER CIRCUITS 359
tude of the first reflection would be only 7 per cent of that of the main
pulse, and the power involved in that reflection is only 0.5 per cent of that
of the main pulse. Forall practical designs, a mismatch of 20t030 per
cent is acceptable from the standpoint of energy loss. Design considerations
for the best use of available components usually make it preferable
to keep the impedance 20 small, generally about 50 ohms. The load
resistances encountered in practice are approximately 500 ohms or higher.
In such a case, the load and the line are matched through a pulse transformer.
The voltage step-up ratio of the pulse transformer, n, is chosen
to make n2 = RL/Zo.
If R. = Zo, it can be shown easily that all the energy stored in the
transmission line is dissipated in the load. Again, from elementary
theory,
Z, = ~L/C = -;
6=lm=m0,
where 1 is the length of the line, L and C its inductance and capacity per
unit length, Lo = lL the total inductance of the line, and Co = lC its total
capacity. The energy stored is given by
but
w
= + Cov:,
On the other hand, the energy dissipated in the load is given by
or, since
v;
‘0 = FL ‘0’
v.=: and R= = 20,
w, = ~go to = w;
therefore all the energy stored in the line is dissipated in the load.
This method thus provides a very efficient way of obtaining a rectangular
pulse of energy in a resistance load. It is usually impractical to use
actual transmission lines or cables in actual pulsers; a cable to supply a
l-psec pulse would be approximately 500 ft long. This difficulty can be
easily circumvented by the use of artificial transmission lines or of a pulsefdrming
network.