. The thermionic vacuum tube and its applications . .S. values ip .nd eg, equation (8) reducesto equation (22) given in Chapter VII. The second term of equation (8) represents the property ofthe tube that enables it to act as a modulator and value of the coefficient given by the second term in equation(8) will be helpful in the interpretation of the equations thatfollow. For the present we shall use equation (8) in the simpleform J = aie-{-a2e^, (9) 318 THERMIONIC VACUUM TUBE to explain how the second term is instrumental in producing mod-ulation and detection. 98. Modulation. Sup
. The thermionic vacuum tube and its applications . .S. values ip .nd eg, equation (8) reducesto equation (22) given in Chapter VII. The second term of equation (8) represents the property ofthe tube that enables it to act as a modulator and value of the coefficient given by the second term in equation(8) will be helpful in the interpretation of the equations thatfollow. For the present we shall use equation (8) in the simpleform J = aie-{-a2e^, (9) 318 THERMIONIC VACUUM TUBE to explain how the second term is instrumental in producing mod-ulation and detection. 98. Modulation. Suppose that a tube be inserted in a cir-cuit such as that shown in Fig. 187. Let high frequency currentsbe impressed at H. F. and low frequency currents, lying withinthe audible range, at L. F. The total input voltage on the tubeis then, e = ei sin p^+e2 sin gi, (10) where — and ^ represent the high and the low frequencies respectively. In order to obtam the output current, we haveto substitute this expression for e in equation (9). When using the. Fig. 187. tube as a modulator, we are interested only in currents having P-i-Q frequencies lying within the range ^tt— . Hence, substituting Ztt (10) into (9), evaluating and dropping all terms having frequencies lying outside of tliis range, we obtain, J = aiei sin pt-\-2a2eie2 sin pt sin qt. (11) This expression represents a wave of varying ampHtude as shownin Fig. 188, the amplitude of the high frequency carrier^ wave ^ The word carrier is here used as a general term to indicate the highfrequency wave, which is modulated by the signaling wave. It has also amore specific meaning in which it refers to the transmission of high fre-quency currents over wires. DETECTION OF CURRENTS WITH THE VACUUM TUBE 319 varying in accordance with the audio frequency wave impressedon the input of the tube. We can, for purposes of explanation, write equation (11) in the form, J = A sin pt(l-\-B sin qt) (12)
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