837 
PIEZOELECTRIC GAUGES 37 
Comparing the two possibilities, one might expect the 
edge-on gauge to have a much smoother rise in response 
to a step pressure, taking a longer time, but approaching 
the true curve more smoothly. Experimental tests have 
roughly indicated this state of affairs, and practical ex- 
perience has also shown that records obtained with 
gauges in the edge-on orientation give about as much 
usable high frequency resolution as face-on gauges and 
are much cleaner and easier to analyze empirically. 
C. Low Frequency Response 
(1) Internal impedance. Although a piezoelectric 
crystal under ideal conditions develops a potential differ- 
ence between its faces which persists as long as a force is 
applied to it, in practical use unavoidable leakage re- 
sistance and input resistance of recording equipment 
afford conducting paths by which the piezoelectric 
charge is gradually neutralized. As a result, the response 
to applied pressure falls off as the rate of change of 
pressure decreases. The electrical properties of a piezo- 
electric crystal are represented with sufficient accuracy 
for the present discussion by an e.m.f., Vo, proportional 
to applied pressure, in series with the capacitance, Co, of 
the crystal. In actual use the gauge will be shunted by 
lead capacitance C and leakage or other resistance R. 
The,response of such a circuit to a step pressure Po is a 
negative exponential : 
V.=[KA/(C+Cp) ]Poe~*”, (6) 
where V,=terminal voltage ; KA = gauge sensitivity ex- 
pressed as charge developed per unit pressure change; 
and r= R(C+C),). 
From Eq. (6) it is evident that the response in the 
limit of low frequencies or long times approaches zero. 
The useful lower limit is obviously increased by in- 
creasing the time constant 7. Therefore the input 
impedance and other resistances represented by R 
should be made as large as other considerations (for 
example, amplifier stability) permit. Likewise, the time 
constant can also be increased by use of larger values of 
C. (In practically all applications CoC, and increase of 
crystal capacitance would have no appreciable effect 
on 7.) 
Unfortunately, an increase in the value of the padding 
capacity C reduces the output voltage by the same pro- 
portion. If one is limited in allowable gauge sensitivity 
by high frequency considerations or by low pressure 
amplitudes, improvement of low frequency charac- 
teristics in this way requires increased sensitivity of the 
recording system. The best solution in difficult situations 
requires a compromise between gauge size, resistance of 
the circuit, and sensitivity of the recorder. 
(2) Pyroelectric effect. A setond factor that may 
affect the low frequency response of a piezoelectric 
gauge is the development of charge as a result of temper- 
ature changes in the crystal. Such charges can arise 
either directly from increased temperature due to 
adiabatic compression of the crystal, or, indirectly, from 
temperature changes in the surrounding medium or 
from radiation such as sunlight, explosion flashes etc... 
The first effect has been shown to be negligible by 
Keys. The second effect depends upon the amount of 
heat developed external to the crystal and the rate at 
which it can‘raise the crystal temperature by thermal] 
conduction or radiation. 
The pyroelectric sensitivity of tourmaline is such that 
a change in temperature of 1°C produces a charge 
equivalent to that developed by a pressure change of 200 
Ib./in.2. In liquid media, however, the pressure wave 
durations are usually very short, and although the 
adiabatic temperature change of the liquid is appreci- 
able, a gauge can hardly undergo more than a small 
fraction of the ultimately possible temperature change 
during such intervals, particularly in view of the 
thermal insulation afforded by the gauge coating. 
In gaseous media, however, radiation effects, temper- 
ature changes due to adiabatic compression of the 
medium, and effects due to variations of ambient tem- 
perature become very much more pronounced. Special 
care must be taken to provide adequate thermal insula- 
tion by using coatings of sufficient thickness for the 
particular application. Excessive thickness of coating, 
however, has been found to affect the gauge properties 
by introducing spurious oscillations and other unde- 
sirable effects, and a suitable compromise must be found 
in difficult cases. Radiation effects can largely be pro- 
tected against by the use of a bright coating, such as 
silver paint, on the outside of the gauge. 
The longer the duration of the signal being measured, 
the more difficult it becomes to combat interference due 
to pyroelectric effect, and thus the applicability of the 
tourmaline gauge is more severely limited by its 
pyroelectric sensitivity than by the other natural 
limitations of input impedance, time constant, and 
piezoelectric sensitivity. 
VI. REQUIREMENTS OF ASSOCIATED 
RECORDING EQUIPMENT 
Detailed discussions relative to the design and con- 
struction of oscillographic recording equipment and 
cables for use with piezoelectric gauges will be found 
elsewhere.* 7 It is the purpose here to discuss briefly 
only certain requirements of such equipment which are 
intimately associated with the selection and use of the 
piezoelectric gauges themselves. 
From the foregoing considerations, it is obvious that 
the low frequency characteristics of an amplifier should 
be such that its over-all time constant is long relative to 
the duration of the phenomenon being recorded. In ex- 
treme cases this might require a d.c. amplifier. Input 
5D. A. Keys, Phil. Mag. 46, 999 (1923). 
® Cole, Stacey, and Brown, ‘Electrical instruments for study of 
underwater explosions and other transient phenomena,” OSRD 
Report No. 6238; NDRC No. A-360. 
7G, K. Fraenkel, “Apparatus for measurement of air-blast 
pressures by means of piezoelectric gauges,” OSRD Report No. 
6251; NDRC No. A373. 
