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, 



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 



