Radar System Engineering

SEC.11.6] THE MIXER CRYSTAL 413
semiconductor. Atsufficiently high frequencies, thecapacity til shortcircuit
the high back-resistance of r. and reduce the rectification efficiency.
In series with this combination is R, the so-called “spreading resistance,”
representing the bulk resistance of the silicon. Analysis shows that RC
must be small compared with the time of one r-f cycle for efficient rectification.
The effects of R and C can be minimized by small contact
area, and it is possible to make crystals with nearly as good conversion
efficiency as would be obtained from
+20, , r 1
111111.L
a simple diode at much lower fre-
[ quenc~es. The conversion loss, de-
+15
2 fined as ratio of r-f signal power to i-f
c
“; +10 signal power, runs from 5 to 8 db for
& . typical microwave crystals.
~+5
z
‘o
/
-5
-2.0 -1,5 -1.0 -0.5 0 +0.5 +1.0
Appliedvoltagein volts
FIO. 11.20.—Typical characteristiccurve of
a silicon rectifier.
‘c=
FIG,ll 21.-Equivalent circuit
of a crystal rectifier.
Experimentally it is found that in the presence of local-oscillator
power flowing through it, a crystal generates more noise power than would
an equivalent resistor at that temperature. As a measure of this property,
a crystal is assigned a “noise temperature, ” defined as the ratio of
the absolute temperature at which an equivalent resistor would generate
the observed noise to the actual temperature. Noise temperatures
between 1.1 and 3.0 are typical. The noise generated by the crystal
increases with local-oscillator input. There is a rather broad region of
best over-all performance at 0.5 to 1.0 mw input which is a compromise
between increasing noise at high inputs and greater conversion loss at
low inputs. This optimum input corresponds to the widely used standard
operating point of 0.5-ma d-c crystal current.
The contact area between the whisker and the silicon is of the order
of l~b cmz. Relatively low currents, therefore, yield high current
densities, with attendant local heating and danger of burnout. For
continuously applied power the danger line is of the order of a watt; this
would apply to the flat part of the TR-tube leakage. The initial preignition
spike (Fig. 11. 16) is so short (less than 0.01 psec) that the heat
cannot be conducted away from the contact; consequently the total spike
energy rather than the peak power is the important quantity. Experience
has shown that burnout is far more likely to come from the spike
than from the flat. Since TR-tube conditions are difficult to reproduce,