. The Bell System technical journal . ue, THE TRANSISTOR AS A NI<7rWlement is e(|ually well known. Consider the sectionshown in Fig. 4 operating between teiminations R and ha\ing seriesarms, A,i and a shunt arm, Rn . Normalize by letting a = Ra/R and 6 =Rn/R- Ins(>rtion loss is plotted vs. I> with a as the third parameter. Forb positive the usual loss pattern results; for 6 negative, a more complexsituation de\elops. When b is very large and negative, the section is stillproducing a small loss, but as b l)ecomes smaller in magnitude the lossdrops to zero and finally becomes a gain. Th
. The Bell System technical journal . ue, THE TRANSISTOR AS A NI<7rWlement is e(|ually well known. Consider the sectionshown in Fig. 4 operating between teiminations R and ha\ing seriesarms, A,i and a shunt arm, Rn . Normalize by letting a = Ra/R and 6 =Rn/R- Ins(>rtion loss is plotted vs. I> with a as the third parameter. Forb positive the usual loss pattern results; for 6 negative, a more complexsituation de\elops. When b is very large and negative, the section is stillproducing a small loss, but as b l)ecomes smaller in magnitude the lossdrops to zero and finally becomes a gain. There is a lower limit on themagnitude of 6 beyond which oscillations will occur. This limit is reachedwhen 26 = -(a + 1).. IN KILOCYCLES PER SECOND Pig. 3 — Transmission of confluent band filters. 336 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 Singularities of Confluent Band Filter Recent work on insertion loss design and potential analog methods byS. Darlington and others has fostered the practice of characterizing anetwork by plotting its natural modes and infinite loss points in thecomplex frequency plane. In the present case it is instructive to study theeffect that reducing dissipation will have on the singularities. A fullsection confluent band filter has five infinite loss points and eight naturalmodes. In Fig. 5 the singularities of the passive, confluent band filterdiscussed earlier are plotted in the complex freciuency plane and identi-fied by the digit one. A single infinite loss point or zero lies on the nega-tive sigma axis, a pair falls at the origin, and a conjugate pair is locatednear the midband frequency. The natural modes or poles c
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