274 



National Resources Planning Board 



DETERMINANTS 



WVW- 



D = 



z, -z„ -z,3 o -z,5 z„ 



^12 ^2 ^23 ~^24 ^ ~^26 



Z,3 -Z„ Z3 -Z3, Z3, o 



o -z,, -Z3, Z, Z,, z,, 



Z„ O -Z3S -z,, z, -z,, 



z„ -z,. o z.. z.. z. 



-16 



-26 



46 



-56 



k=l 



Driving point impedance in mesh j = Z(jj)= -ry~ 



Transfer impedance between meshj and mesh k= Z{A) = -¥y- 



( Djk = the first minor of the element Zjk in D ) 



Many properties of the complicated networks studied at Bell Telephone laboratories are most 



fwnTeniently eipressed by means of determinants. Above are shown a sii-mesh network; its 



**cir«uit discriminant**, D; and some formulae which illustrate how simply the properties of the 



system can be found from D. Note that, since Zjk = Zkji D is symmetrical. 



Figure 84 



