334 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1934: 



where 



ao = /?i(l + g) 



a, = Rr\l\{\ + (/) + 7'o + 1\,] + R2r, 



a. = i^i[.-li(l + (/) + Ti(ro + Tn) + .4.] + R/r,7\2 



a3 = /^,[.li(r2 + 7^23) + -42^,] 



ai = R1A1A2 



61 = /?2T] 



Sa = RiTiT^i 

 ^1 = Tx(l + g) 



/33 = TiAs 



This expression with the compensating negative resistance R^ = ^c 

 prockices the characteristic labeled "Practical Passive". 



The dotted curves show the effect of adding various amounts of 

 negative resistance to the shunt branch by letting R? assume negative 

 values. The number on each dotted curve is the ratio of the resistive 

 component of the shunt arm at anti-resonance to the magnitude of the 

 compensating negative resistance. For example, for the curve labeled 

 p = 1, the resistance in the shunt arm is entirely compensated so that 

 the loss is only that due to the resistance in the series arms. By increasing 

 the amount of compensation in the shunt arm so that p > 1, called 

 overcompensation it is possible effectively to nullify the losses in the 

 series arm as well. Comparison of the active curve labeled p = 1.21 

 with the "ideal passive" curve shows that this technique of resistance 

 compensation can produce a practical filter ha\'ing a characteristic equal 

 to that of a filter having ideal elements. Filters of this type have already 

 been successfully used in field test ecjuipment. 



When the degree of compensation is increased still further, the filter 

 begins to provide gain in the band as shown by the p = 1.36 curve. It 

 is clear that continued increases in the compensation will eventually 

 absorb the terminations causing the structure to become unstable. 



Although the curves given in Fig. 3 are all calculated, tests on experi- 

 mental models show excellent agreement. To a reader having long ex- 

 perience with passive filters the development of negative insertion loss 

 may seem a little surprising. In order to lend an air of authenticity to 

 this midband gain it is instructive to consider the behavior of a resistive 

 tee section having a negative element. This is a reasonable analogue, 



