Analysis and synthesis of active transmission lines Public Deposited


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  • 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.
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