POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 



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formations which leave the stream function (or phase) unaltered. These 

 invariant transformations are easy to understand if we consider the com- 

 ponents of the field intensity. As shown in Fig. 10a the field of any given 

 charge along the co-axis equals the field of an equal charge at the mirror 

 image of the given charge in the real frequency axis. By (27d) these two 

 charges thus give the same rate of change of a with frequency. Similarly 

 two opposite charges, Fig. 10b, at mirror image points have the same 



REAL p 



Fig. 9 — A disjoint contour. 



transverse field intensity across the co-axis. Thus these charges produce 

 the same rate of change of /3 with frequency. 



To sunmiarize in terms of the transmission functions: 1) the zeros and 

 poles of F{p) may be moved from the right half of the />-plane to the left 

 haK, and vice versa, without changing the gain; 2) a singularity of F{p) 

 may be moved from one half of the />-plane to the other without changing 

 the phase, provided the type of singularity is reversed (that is, a zero be- 

 comes a pole and vice versa). 



