The Logarithmic Decrement 



By H. B. Richmond 



SINCE the passage of the radio act 

 of August 13, 1912, the amateur, as 

 well as many commercial, operators have 

 come to realize that the operation of a 

 radio transmitting set is no longer a 

 merely hit or miss affair, but has become 

 an exacting procedure. Resonance, 

 damping, logarithmic decrement and 

 many others are expressions with which 

 they must be familiar. Probably as im- 

 portant as any, and at the same time the 

 least clearly understood, is the logarith- 

 mic decrement. Although this term is 

 by no means limited to radio work, it 

 will here be considered only from that 

 aspect. Let us first consider why the 

 term has such an important place in radio 

 work and then what it really means. 



Suppose there were but four radio sta- 

 tions in the world and each station had 

 identical equipment throughout. Let 

 these stations be located at the corners 

 of a square and A always work with A', 

 and B with B', Fig. i. Let all stations 

 use the same power but operate on slight- 

 ly different wavelengths. If B is receiv- 

 ing from B' and A and A' are working, 

 B will experience interference from A 

 and A'. Interference to the same extent 

 will be experienced by A when A is re- 

 receiving from A' and B and B' are 

 working. The operators of the four sta- 

 tions then get together and agree to re- 

 duce this interference by adjusting their 

 transmitting sets so that A will not hear 

 B or B' and B hear A and A' for a dis- 

 tance of over ten turns on the primary 

 of their loose couplers either side of the 

 point of maximum strength. This is a 

 rather crude agreement, but it serves its 

 purpose by actually limiting the broad- 

 ness of wave which the several stations 

 may use. 



Now let us go one step further and let 

 any one of the four stations work with 

 any of the other three. If A is working 

 with B, B' may say B is all right but A 

 is too broad. The reason for this being 

 that B is farther from B' than A is. The 

 energy received from B is accordingly 

 less than that received from A and it 



will appear to B' that A is broader than 

 B, although in fact they are both the 

 same. Thus it becomes evident that some 

 new method of measuring the broadness 

 must be adopted. And as we increase 

 the number of stations indefinitely using 

 different types of apparatus, different 

 powers, different wave lengths, etc., it 

 at once becomes apparent that any meth- 

 od of measuring the broadness of a wave 

 must take into account wave length, 

 power and all other factors which enter 

 into it. This is exactly what the logarith- 

 mic decrement does. It is a measure of 

 broadness which will apply under all con- 

 ditions of operation. 



Before attempting to conceive of the 

 meaning of the expression as applied to 

 radio work, let us take an example which 

 we can actually see worked out without 

 the aid of any elaborate apparatus. Take 

 a piece of twine or fine wire 39 inches 

 long and fasten a small weight to one 

 end, then suspend the pendulum thus 

 constructed so that it will swing freely. 

 Carry the weight to one side and care- 

 fully release it so that it will start swing- 

 ing straight back and forth and not ac- 

 quire a rotary motion: i.e., its swing will 

 be limited to one plane. It will be ob- 

 served that the time required for the 

 bob to swing from the perpendicular posi- 

 tion at the lowest point of the arc of 

 swing out to the end and back to the 

 center is just one second. To start from 

 the center, swing to the right, swing back 

 past the center to the left, and then 

 swing back to the center again will of 

 course require twice as long as a swing 

 from the center to but one side and 

 back again, and accordingly will require 

 two seconds. This full swing is a com- 

 plete circle of events or cycle, and as 

 frequency is measured in cycles per sec- 

 ond we have a frequency of 0.5. If we 

 had 25 complete swings per second we 

 would have a frequency of 25 cycles. In 

 addition to the fact that the time is re- 

 maining constant for each swing it will 

 be noticed that the distance which the 

 bob swings from the center is constantly 



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