Abstract:
Active transmission lines, a generalization of classical transmission
lines, are useful electrical devices. They can be utilized to
realize distributed amplifiers and to obtain other electrical characteristics unattainable with passive lines. Active lines have historical
significance and model many physical processes including heat
conduction in an internally heated material, a vibrating string, pressure
waves in gas, neutron diffusion and fission, and semiconductor
photodetection. This paper fully develops the analysis and synthesis
of active transmission lines using a network theory approach.
An active line is characterized by distributed series voltage and
shunt current sources in addition to the passive line parameters.
These sources may be of independent and/or dependent type.
It is shown that independent sources may be removed from the line
if appropriate modifications' in port conditions are made. Extraction
integrals are formulated for this purpose. Examples of independent
sources include initial condition generators; they also occur in
devices exhibiting active coupling such as the traveling-wave transistor.
Dependent sources however change the two-port parameters of the active line. These sources have their outputs controlled by either
line voltage or current (a source at position x has an output which
depends on either voltage or current at position x). Two basic types
of lines are therefore possible.
The uniform active line having dependent distributed sources is
completely analyzed. Its traveling-wave characteristics including
characteristic impedances and propagation functions are presented.
Laplace transformation techniques are used to analyze the driving-point
and transfer admittances, gain, bandwidth, step response, rise
and delay time, and sensitivity of uniform rcg active lines.
The general nature of the pole-zero patterns of nonuniform active
lines having distributed dependent sources are investigated using
several results from differential equation theory. Their two-port
parameters are readily expressed using the basic set notation and self-adjoint
properties of the active line equations. Lack of pole-zero
cancellation is noted utilizing the Wronskian of the basic set solutions.
Sturm-Liouville theory establishes the general pole-zero
locations. many of the powerful theorems concerning lumped passive
networks are seen to parallel those of active lines.
Active transmission lines are readily synthesized directly in the
time or frequency domain using variational calculus techniques. The
parameter distributions required to produce specified port response for
arbitrary excitations and loadings (consistent with parameter bounds,
etc.) are generated by expressions involving voltage and current along
the original line and a so-called adjoint line. The method is readily
implemented by digital and hybrid computers. At the present time, active transmission lines cannot be realized
because of the inability to distribute dependent sources along a
passive line. Therefore artificial active lines are presently utilized
The topology and two-port parameter requirements of the iterative two port
are discussed.
Future advances in solid-state electronics and thin-film technology should overcome this difficulty. Several current research studies
involving semiconductor bulk effects and solid-state traveling-wave
amplifiers are cited.
Although this thesis is concerned with the class of active distributed
network having an active transmission line equivalent, the
various considerations are readily extendable to networks having other
differential models. more generally then, this investigation is
concerned with developing methods for analyzing and synthesizing
active distributed networks.