MEASUREMENT OF PRESSURES 203 



In measurements of explosion pressures, the area under the pressure- 

 time curve, or impulse, is of considerable importance and it is evident 

 that the low-frequency response will modify measured areas consider- 

 ably. One can, in fact, show very easily that the integrated response 

 to infinite time of a pulse of finite area is zero for any a-c amplifier or 

 other circuit with no d-c response, a conclusion made plausible by the 

 negative values of response at long times indicated in the example of 

 Fig. 5.25. (It is interesting to note that, if the circuit considered does 

 have a non-zero response to a fixed voltage, it is quite generally true 

 that the integrated response is independent of the high frequency re- 

 sponse characteristics, being determined primarily by the low-frequency 

 response.) If the integration of the response curve is carried out to a 

 finite time t' , the fractional error AA in the area A (^') for an exponen- 

 tial pulse is readily shown from Eq. (5.15) to be approximately given by 



AA ^ t' - e 



A ~ X 



if the time t' is less than lOX. Thus, if the error is to be less than 5 per 

 cent, the amplifier low-frequency time constant must be at least 20 

 times that of the pulse. 



The low-frequency demands of pulses encountered in explosion 

 measurements are so severe that, except in a very few cases, commercial 

 standards of response (flat to say 20 cycles/sec.) are grossly inadequate. 

 Frequently the simplest solution, as far as amplifier characteristics are 

 concerned, is to eliminate the problem entirely by the use of d-c ampli- 

 fiers. This solution cannot be applied to the input circuit for a piezo- 

 electric gauge which has inherently no static or d-c response because of 

 the equivalent capacitative internal impedance of the gauge. Although 

 low-frequency compensation could be applied to improve the charac- 

 teristics of such input circuits, it has been found adequate, and simpler 

 in practice, to use uncompensated circuits with input impedances as 

 high as 100 megohms. (Higher values than this are usually difficult to 

 obtain in field work with cables in salt water, and the value quoted is 

 sometimes inconveniently large.) 



The requirements on amplifiers, in addition to those of frequency 

 response, are conventional except that the linearity and gain stability 

 need to be rather better than ordinarily found in commercial amphfiers. 

 The more important elaborations for this purpose are regulated supply 

 voltages and liberal use of feedback. In addition, instruments which 

 are to perform reliably in the field under frequently trying conditions 

 need to be developed with attention to such things as ruggedness, ac- 

 cessibility and ease of repair; only the existence of these factors in design 

 and use can be indicated here. 



