OPEN-WIRE CROSSTALK 229 



small compared with their interaxial distances. The "image" wires 

 of Fig. 32 should, theoretically, be located farther below the equivalent 

 ground plane for calculations of mutual inductance. This alters Su, 

 etc. Since the distances between wires are small compared to those 

 between wires and images, the values of 5 are all about equal and have 

 practically no effect on the value of pab- 



Therefore, Mah in c.g.s. elmg. units may be assumed numerically 

 equal to pah or: 



Mah = pah = -TT-, ' 



In c.g.s. elst. units CJ = wn ;r^ which is also the expression 



2(^11 - P12) 



for XjLa' in c.g.s. elmg. units where LJ is the external inductance of 



circuit a, i.e., the inductance due to the magnetic field external to the 



wires of circuit a. Therefore : 



Mah = TabLa , 



where Mah and La may be expressed in any system of units. 



The near-end or far-end direct coeflficient for the magnetic field 

 may, therefore, be written : 



(2) N^ = F„,= - hl^K 109. 



^h 



The above expression is almost equal to Ne, the near-end coefficient 

 for the electric field. 

 It may be written: 



Nm = N. 



jcoLa'jcoCa' 

 ZajwCaZbjcoCb 



Now ZajcoCa is vcry nearly equal to Za(Ga + jo^Ca) which is ja- Like- 

 wise ZbjwCb is very nearly equal to 76. If the circuits had no resistance 

 or leakance the propagation constant would be 70 — jw^LJCa' or 

 joijv where v is the speed of light in miles per second. Therefore: 



AT ^^TO^ 1 



JMm = very nearly. 



7a76 



The total direct crosstalk coefficients are: 



(3) Na = Nr, + N. = nA\-^^\ = 2N, approx. 



\ 7«76 / 



At carrier frequencies the ratio of 70 to 7,, (or 7/,) is about equal to 



