THE THANSISTOR AS A NMO'inN'OKK ELEMENT 349 



is unity regardless of the size of A', and the plmsc and resultant delay are 

 frequency dependent, because X is a function of fretjuency. It is theo- 

 retically possible to produce the most complicated delay equali/.er 

 characteristic by this method proN'ided the negative resistance remains 

 constant over the d(;sired freciuency band. As examples only a single 180° 

 section and a single 3()0° section will be considered. 



A 300° section results when the reactance is a single antiresonance 

 gi\'en by 



,.7" 



X = 



1 - co^LC 

 the transmission is 



-e ^ ip — k)' + (^l ^ 1 — QT^coZ^p + uZV 

 ^ (p + ky + c,^ 1 + Q-'co-ip + <o-Y 



where 



k =^ -o)m and Q = (co„/?oC)"^ 



In this case there are two degrees of freedom, namely, the width of 

 the delay characteristic and the location of the peak freciuency. 



The circuit is shown on Fig. 14, where the transistor supplies the 

 negative resistance, the magnitude of which is controlled by the ad- 

 justable resistance. A typical delay characteristic is also shown on 

 Fig. 14. 



A single 180° section can be obtained by simply omitting the coil in 

 the above circuit. This is equivalent to letting X = — (ojC)"" so that 



-$ ^ p — Up 

 p + ooq 



where uo = {RoC)~^ 



IV. IMPEDANCE INVERSION 



Two networks are said to be inverse if the product of their impedance 

 functions is a constant. Given a network of passive elements, there are 

 standard topological methods for finding its structural inverse if it exists. 

 Another method is to use an active circuit in conjunction with the given 

 impedance so that the combination offers an impedance inverse to that 

 of the original impedance. This is a special case of modifying an im- 

 pedance by feedback. By means of such methods passive circuit ele- 

 ments can be made to a])peai' electrically much lai'ger or much smaller 



