DIELECTRIC CONSTANTS AND POWER FACTORS 



119 



The above tlieory applies to the quarter wave line. This is a rather 

 difficult practical one; it is best to add anotlier quarter wave to make a half- 

 wave resonator, shorted at both ends, with the dielectric positioned 

 exactly in the center. From conditions of symmetry we then employ the 

 above equations, taking half of our measured quantities. Or, in terms of 

 the actually measured four lengths which constitute an observation on a 

 half -wave line, (d-d'), f, M and X, we have. 



sinli - (d — d') 



P.P. = 



sin ^ (A^* -\- t) 



A 



sin2X 

 2.Y 



— •tan TT 



A 



M + t 



= X tan X 





(15) 



which are the expressions used in this work. 



In practice the dielectric plug is pushed into the half-wave line and the 

 line is tuned. The line center is then calculated and the plug reset to this. 

 Retuning checks the correct location. Two trials are always sufficient if the 

 plug was nearly centered originally. 



There are several shortcomings affecting this theor\'. The Q of the un- 

 loaded line depends partly on' metal power loss along the line. When the 

 line is shortened by the dielectric plug, part of this loss disappears and part 

 is transferred to the dielectric plug. Fortunately these losses are small since 

 they are metal losses at a current node, but for long dielectric plugs or plugs 

 of high dielectric constant the need for correction can arise. The necessary 

 calculations have not yet been reduced to a simple form. 



Again, the calculation of half-wave results by means of a quarter wave 

 theor\' is safe only for a high Q situation. It is easy to show, experimentally, 

 that the maximum line shortening results when the dielectric plug is exactly 

 centered in the line but the calculated power factor is not a maximum here, 

 as might be expected. In the meantime, experience shows that results can 

 be duplicated from day to day and at other frequencies and that over a 

 reasonable range of plug thickness no change in dielectric constant and power 

 factor values, greater than the unavoidable errors of measurement, is ob- 

 tained. 



Description of Apparatus 



The apparatus can be divided into three parts for purposes of description. 

 The high frequency generator consists of a small ''relay rack" assembly. 



