Bandwidth Limitations in Equalizers and Transistor Output Circuits

The attenuation-integral theorem shows that a limit exists to the power gain times bandwidth product when an ideal current generator drives a network having a finite capacitance in shunt with the input. This paper derives a comparable theorem which includes both capacitance and device behavior like the
\alpha
-cutoff effect in transistors. The result of the theorem is the familiar
\pi/(2RC)
when
\alpha
cutoff can be ignored. The result depends upon both capacitance and
\alpha
cutoff in general. The analysis is somewhat different from the classical method and hence can be considered to provide an alternate derivation of the attenuation-integral theorem. The results can also be interpreted to indicate the limitations of general amplitude equalization by means of a single network driven from a current source. Specific nonminimum-phase networks suitable for equalizing output networks when the (transistor) current source behaves as
\delta/(p + \delta)
are the subject of the second half of this paper. Both networks and convenient design relations are given, as well as a specific example which increases
\delta
-cutoff bandwidth by a factor of 10.