. The thermionic vacuum tube and its applications . the receiver shunt makes it possible to express theaudibiUty in a shnple wa3^ If id be the detecting current and /o the least audible current in the receiver the audibiHty — can be Hexpressed in miles of standard cable by making use of the equa-tions developed in Sections 104 and 105. Thus, taking the casein which the detecting current is proportional to the square of theinput voltage, we obtain cl = 2K log Cg-i-K (log a-log io), (39) which thus gives a linear relation between the logarithm of theinput voltage and the audibility when expresse
. The thermionic vacuum tube and its applications . the receiver shunt makes it possible to express theaudibiUty in a shnple wa3^ If id be the detecting current and /o the least audible current in the receiver the audibiHty — can be Hexpressed in miles of standard cable by making use of the equa-tions developed in Sections 104 and 105. Thus, taking the casein which the detecting current is proportional to the square of theinput voltage, we obtain cl = 2K log Cg-i-K (log a-log io), (39) which thus gives a linear relation between the logarithm of theinput voltage and the audibility when expressed in tenns of miles 352 THERMIONIC VACUUM TUBE d instead of current ratio, the relation between d and the cur-rent ratio being given by equation (28). The intercept of thisHne, obtained by putting Cg^Q, is A(log a-log/()), (40) and gives a measin-e of the audibility officiciicy of the tube ex-pressed in miles/(volt)^. The simple linear relation (39) makes it possible to obtain theaudible efficiency as an average of a large number of observa- 70. \.Z LogClnpuf Voltage) Fig. 209. tions. A number of such observations plotted against the logar-ithm of the corresponding input voltages are shown in Fig. individual points vaiy considerably compared with the obser-vations shown in Fig. 205, which were obtained with the othermethod discussed above, but these points are evenly groupedabout a straight line the slope of which is about 41. The theo-retical value of the slope is The slope of the line dependsupon the attenuation constant of the shunt and the simple quad-ratic relation (17) between the detecting current and the inputvoltage. The intercept of this line, on the other hand, is infiu- DETECTION OF CURRENTS WITH THE VACUUM TUBE 353 enced also by the detection coefficient a of the tube and by whatconstitutes the least audible signal ?o for the particular telephonereceiver used and for the obsei-vcr at the particular time of makingthe measurements. The
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