1450 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



and to arrive at the value of capacitance to select. First we wish to 

 measure reciprocating motions of the order of 0.050'' and actuating times 

 of the order of 0.005 second. However, the motion takes place in the 

 order of half the actuating time. Hence the average velocity will be of 

 the order of 20 inches per second. An average numerical ratio of velocity 

 to displacement then is 20 divided by 0.05, or 400. Remembering this is 

 average and some part of the velocity will be higher the nearest decimal 

 factor is 1000. 



In this system, as a device being tested is a part of it, the instrument 

 time scale necessarily is identical with real time, that is it cannot be 

 ''slowed down" for more accurate time settings, as can analogue com- 

 puters. 



Now once a convenient gain setting for displacement measurements 

 has been determined, if a capacitor were substituted for the amplifier 

 input resister, related by the equation RC = 1 second, C would be 100 

 mf, a,s R = 10,000 ohms. This would be a substitution where the scale 

 reading for a given number of mil-inches would represent the same num- 

 ber of mil-inches per second. Fortunately, however, we wish rather to 

 represent a much higher velocity of inches per second. This results if the 

 capacitor is reduced by the same factor of 1000. The desired capacitance 

 thus has a value of 0.10 mf. The type used is a stable, low soak poly- 

 styrene dielectric one having }4 per cent accuracy. In this amplifier the 

 feedback and input resistors also must be of 3^^ per cent accuracy as 

 upon these depend the calibration. The 10,000 ohms input resistor neces- 

 sarily is a non-inductive wire wound type with a 10 watt rating, for stable 

 performance with the actual 1.5 watts. The feedback resistors are of the 

 deposited carbon type. 



The remainder of the design now follows. To limit the differentiation 

 action to a 10-kc range, a resistor in series with the 0.1-m/ capacitor of 

 160 ohms is used. A transfer gain of 70 db, which is 10 db less than the 

 internal gain of 80 db, is a voltage ratio of 3,160. Multiplying this by the 

 input resistor value of 160 ohms yields 500,000 ohms as the maximum 

 feedback resistance. Then as an amplifier with an input resistor of 10,000 

 ohms, the gain is 50. Resistances for lesser gains of 20 and 10 are scaled 

 in proportion. 



The linear output voltage range for this amplifier is =b 40 volts. This is 

 much more than needed. For displacement measurements the maximum 

 swing is about 5 volts. In the discussion, we found a maximum capacitor 

 current of about 10 microamperes which also results in an output swing 

 of 5 volts, during velocity measurements. 



Output Amplifier. The schematic of the output amplifier is shown in 

 Fig. 19. This amplifier also has three stages, the first two of which are 



