The principles underlying radio communication by United States. Army. Signal Corps & United States. National Bureau of Standards

Author:United States. Army. Signal Corps & United States. National Bureau of Standards
Language: eng
Format: epub
Tags: Telegraph, Wireless
Publisher: Washington : Govt. print. off.
Published: 1919-03-25T05:00:00+00:00

Variation of reactance with the Frequency L-So ©microhenries C-o ocS^mfd.

Corves -fo Series Ci'rcuit with Different Resistances

Resis>"fence on the of Reaondnee Curve

frequency for resonance. To do so, the condition must be fulfilled, that

(70)

which shows that the frequency at resonance must be

1

Applying this relation to the example under discussion, and substituting therein L =0.0005 henry, C=5/10 9 farad, the resonance frequency is found to about 100,700 cycles per second. The reactances of both the coil and the condenser at this frequency are the same and have the value 316.2 ohms. This value may, of course, be calculated by using for/ the value of the resonance frequency in

either of the expressions 2-n-fL or 0 fn - It is of interest to note

^jTTy O

that each of these expressions for reactance reduces simply to -• /—»

when the frequency has the resonance value.

There exists, then, for any series circuit containing inductance and capacitance, a definite value of the frequency, for which the total reactance in the circuit is zero, and the impedance is simply equal to the resistance of the circuit. This frequency is called the resonance frequency, and the circuit is said to be in a condition of resonance. The impedance has its smallest value, and the current which flows in the circuit when the applied emf. has any value whatever has the largest value possible with that value of frequency.

These facts may be readily verified experimentally by inserting in a simple radio circuit a suitable ammeter for measuring the current. If now the frequency of the applied emf. is gradually raised, the current will at first be small and will increase very slowly as the frequency is increased. In the immediate neighborhood of the resonance frequency, the current will suddenly begin to increase rapidly, for small changes of frequency, and after passing through a maximum, will rapidly decrease again as the frequency is raised to still higher values. The results of such an experiment may be shown by a curve in which frequencies are measured in the horizontal direction, while the values of the current corresponding are

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