OPEN-WIRE CROSSTALK 



225 



as follows: 



N = limit of 



F = limit of 



la ' Kdx 

 if 10« 



la Kdx 



as dx approaches zero. 



as dx approaches zero. 



where K is the frequency in kilocycles. For circuits of different 

 characteristic impedances Za and Zj, the above current ratios should 

 be multiplied by the square root of the ratio of the real parts of Zb 

 and Za. This correction is not included in the expressions for A^ and 

 F derived below. 



Figure 31 indicates the equivalent electromotive forces which, if 

 impressed on the disturbed circuit h, would cause the same direct 

 crosstalk currents as the electric and magnetic fields of the disturbing 

 circuit. The series and shunt electromotive forces Vm and Ve corre- 



n) )^e Zb— * 



Fig. 31 — Equivalent e.m.f.'s in a disturbed circuit. 



spond to the magnetic and electric components of the field and cause 

 crosstalk current im and ie. These currents are about equal in magni- 

 tude and they add almost directly at the near end of the length dx 

 and subtract almost directly at the far end. The near-end coefficient 

 is, therefore, inherently much greater than the far-end coefficient. 



To calculate i^ the crosstalk current due to the electric field of 

 circuit a, it is necessary to know the shunt voltage Ve- This depends 

 on the charges on the wires of circuit a in the length dx. These 

 charges are due to a voltage V impressed on the left-hand end of 

 circuit a which may be remote from the length dx. Since it is desired 

 to transmit on the metallic circuit a and not on the circuit composed 

 of its wires with ground return, care is taken to "balance" the im- 

 pressed voltage, i.e., this sending circuit has equal and opposite 

 voltages between its two sides and ground with circuit a disconnected. 



