274 BELL SYSTEM TECHNICAL JOURNAL 



one resonant frequency may be located. As many of these resonant 

 frequencies may be located in this way as there are adjustable elements 

 in the mesh. Since the condensers are not adjustable, all of the 

 frequencies of series and parallel resonance in a complex mesh, will not, 

 in general, be capable of adjustment. If the mesh is composed of 

 n condensers and m coils, and the difference between m and w is not 

 more than 1 (if this condition is violated the mesh can be reduced to 

 an electrically equivalent one containing a smaller number of elements) , 

 the number of resonant and anti-resonant frequencies is clearly 

 (w + « — 1). However, since the number of adjustments possible is 

 equal only to the number of coils, w, the number of frequencies which 

 cannot be exactly located is {n — 1), or one less than the number of 

 condensers. This condition is not very objectionable in practice as 

 the mesh configuration is usually chosen to be of a form which permits 

 the more important critical frequencies to be adjusted. In a four- 

 element mesh, the largest usually encountered in an ordinary filter 

 structure, two of the three resonant frequencies may be adjusted, and 

 furthermore, the adjusted frequencies may be any two of the three; 

 in most cases the adjustment of two frequencies is sufficient. 



The frequency adjustment is actually made on a bridge circuit, 

 the schematic of which is shown in Fig. 8. Two of the bridge arms 

 are, of course, ratio arms; the mesh to be adjusted is connected in 

 circuit as a third arm, and the fourth arm is a variable resistance. 

 For series resonance adjustment, the desired frequency is impressed 

 on the bridge, and the inductance of the adjustable coils varied so 

 that the impedance of the mesh becomes a pure resistance, which is 

 balanced by an adjustment of the resistance in the opposite bridge arm. 

 For a parallel resonance measurement, a resistance of 10,000 ohms is 

 shunted across the mesh being adjusted, and the coil varied until the 

 reactance component of the mesh impedance vanishes, when the 

 resistance of the 10,000 ohms in parallel with the resistance of the mesh 

 can be balanced in the fourth bridge arm. 



This frequency adjustment of filter arms involved a change in 

 filter manufacturing procedure. Ordinarily the coils and condensers 

 for the filter are individually adjusted, then mounted, wired, and the 

 filter finally tested as a whole, but an additional step is required in 

 the construction of filters employing adjustable coils. It is necessary 

 to adjust the resonant frequencies of meshes after the elements are 

 mounted, but before the filter is finally wired and tested, and further- 

 more, it is necessary to adjust these elements under exactly the same 

 conditions that obtain during filter operation if the full benefit of the 

 adjustable feature is to be realized. This requirement presented a 



