Radar System Engineering

SW. 1618] THE SUPERSONIC DELAY LINE 671
as the diameter of the tube and directly as the square root of frequency.
An experimental value is 0.1 db/in. at 10 Me/see with a ~-in. tube.
The efficiency of the crystals can be stated in terms of the transfer
impedance of the delay line, as follows:
V2 – 2R,R2
~R~’
where 11 is the current driving the transmitting crystal, V2 is the voltage
developed across the receiving crystal, R, is the load resistance shunting
the transmitting crystal and R, that for the receiving crystal, Rk is the
electrical equivalent of the characteristic impedance of the line. The
equation applies to the case of reflecting end cells. Now R1 and Rz
depend on the bandwidth that is required, since the bandwidth at each
crystal is inversely proportional to the product of the loading resistance
and the total capacity, including the electrostatic capacity of the crystal
and the stray capacity of cable connections. This assumes that singletuned
coupling circuits are used.
The characteristic impedance R~ is inversely proportional to the
active area of the crystal and to the square of the frequency. At 10
Me/see the value is 22,000 ohms for an active area of 1 in.2 With this
area the total capacity at each crystal is about 50 ppj, and the bandwidth
is then 3.8 Me/see per end if RI = Rz = 300 ohms. These values give
a transfer impedance of 8.6 ohms. It will be noticed that no account is
taken of the inherent bandwidth of the crystals. This is because the
bandwidth for both crystals in series is more than ~ of the carrier
frequency.
It can be shown that, for a given bandwidth, the transfer impedance
is a maximum when the crystal diameter is chosen so that the active
crystal capacity equals the total stray capacity.
The carrier frequency for mercury lines may range from 5 to 30
Me/see, with the most usual values in the range from 10 to 20 Me/see.
Choice of frequency depends upon the’ delay-line attenuation, and on
the fact that the number of carrier cycles per pulse must be sufficient to
allow accurate demodulation.
It was mentioned earlier that the quartz-mercury combination has
adequate inherent bandwidth. In a reflecting end cell the response is
actually flat over a frequency range equal to 40 per cent of the carrier
frequency. This allows a simple cure for a practical difficulty that is
frequently encountered with this type of cell. Because the reflecting end
cell is loaded on one side only, a slight smudge or spot of scum will unload
a portion of the crystal area without removing the electrical excitation.
When this happens, the pass band exhibits sharp spikes at the resonant
frequency of the quartz. These seriously impair the quality of cancella-