. The thermionic vacuum tube and its applications . thode the application of a smallvoltage between cathode and anode would almost immediatelygive rise to the saturation current, and the resistance of the tubewould for all values of current less than the saturation current bevery low. This is, however, not the case, since the electrons 162 THERMIONIC VACUUM TUBE in the space exert a mutual repelling force on one another. Thisis the space charge effect explained in Chapters I and IV, andcauses by far the greatest expenditure of energy on the part of theelectrons in moving to the anode. This exp
. The thermionic vacuum tube and its applications . thode the application of a smallvoltage between cathode and anode would almost immediatelygive rise to the saturation current, and the resistance of the tubewould for all values of current less than the saturation current bevery low. This is, however, not the case, since the electrons 162 THERMIONIC VACUUM TUBE in the space exert a mutual repelling force on one another. Thisis the space charge effect explained in Chapters I and IV, andcauses by far the greatest expenditure of energy on the part of theelectrons in moving to the anode. This expenditure of energycauses the heating of the anode. The true d-c. resistance of the tube is, of course, given simplyby the ratio of the total amount of work done to the square of the current, , by y^. The a-c. resistance on the other hand, is given by the slope of the plate current characteristic, and since thecharacteristic is non-linear the a-c. and d-c. resistances are not thesame. Referring to Fig. 80, the d-c. resistance at a voltage Ep is. given by the reciprocal of the slope of the straight line OC, while theimpedance of the tube is given by the ratio of the alternatingvoltage ep between filament and plate to the alternating currentip in the plate circuit. Now, the flow of electrons in the tubeshows no lag, and for frequencies low enough to make the effectof the electrostatic capacity of the tube itself negligibly small,the condensive reactance thus being also practically infinite, the impedance is simply given by -T^=-r (see Fig. 80), and is then of the nature of a pure resistance. For most tubes used at presentthis approximation is satisfactory for frequencies up to the order ofseveral hundred thousand cycles per second. For a tube like thatshown in Fig. 68, for example the filament-plate capacity is of THE THERMIONIC AMPLIFIER 163 the order of a few micro-microfarads. Now we have — = ^~^ when ep and ip are very small. But in practice we generally do notdeal with
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