778
��Popular Science Monthly
��points (the maxima) of the curves will be farther from the zero line. If the resistance in the circuit is increased, there will be fewer oscillations before the current dies away to a small value; that is, the damping will be increased. These three electrical effects correspond in the mechanical case, to changing the length of the pendulum string, pulling it farther from zero before releasing it, and putting on the fan to increase the wind-resistance.
If an oscillogram made in this way,
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��Fig. 5. Oscillation for various decrements
showing the free oscillatory discharge in such a circuit as indicated by Fig. 4, is measured with a pair of dividers, it is found that the ratio of the maximum amplitudes remains constant. Just as with the pendulum, the logarithm of this ratio may be taken and thus the logarithmic decrement of the circuit determined. If the ratio (or damping factor) is found to be 1.05, the table above shows the decrement to be 0.05 per period. If the ratio is made as large as 1.28 by increasing the resis- tance, the decrement is increased to 0.25 per period. The numerical range of de- crement values for circuits used in radio telegraphy is very much the same as
��that of mechanical vibrating systems; the electrical oscillations in an ordinary spark sender for radio will die away at about the same rate as the mechanical oscillations of a springy steel rod held in a vise. There is a variation of decre- ment values in wireless transmitters from about 0.03 to about 0.5 per period ; the present laws of the United States require that the logarithmic decrement shall be 0.2 or less, since otherwise there are so few oscillations in a wave-train that tuning is not of very great value.
If every time it was desired to measure the damping of a circuit one had to set up a high-frequency oscillograph and make a photograph of the free oscillation, and then measure the amplitudes of the current maxima from that and finally compute the ratio and the logarithm, there would be very few such measure- ments made. It happens that since the damping in any circuit depends upon the effective capacity, inductance and resistance of that circuit, one may compute the decrement directly from known values of those quantities. The rule is not complicated ; it merely states that the logarithmic decrement of any simple circuit may be found by the following four steps: (i) Divide the effective capacity, in farads, by the effective inductance, in henrys; (2) take the square root of this result; (3) multiply this root by the effective resistance in ohms; and (4) multiply this product by 3.14; the answer is the logarithmic decrement, per complete period, of the circuit in question.
This rule for computing decrement may be applied to a simple circuit, for example that of Fig. 4. Let us assume that the effective capacity is o.ooi microfarad, which equals o.ooooooooi farad; the inductance may be 0.0 1 millihenry, which is o.ooooi henry; and the resistance we may assume as 3 ohms total. Following out the rule, the first step gives 0.000 1 as a preliminary result; the square root of this is o.oi; multiplied by 3 this becomes 0.03; and multiplying again by 3.14, the logarith- mic decrement is found to be 0.095 or a trifle under O.i per complete period. It is often difficult to measure the three quantities resistance, capacity and in- ductance in an oscillating circuit in
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