The synthesis of lossy lumped-distributed networks is important for many applications; for example, in the analysis of large systems such as the interconnections of the circuits on an LSI or VLSI silicon chip, such networks have been used as models, and a solution of the synthesis problem will thus aid in the design of these chips. In this paper singlevariable realizability conditions and synthesis procedures are established for the class of lossy and/or lossless lumped-distributed cascade networks described by an input-impedance expression of the form Z_0 = \frac{\sum_{i=0}^{6n}a_i(s)e^{sT(2i-n)}}{\sum_{i=0}^{n}b_i(s)e^{sT(2i-n)}} with a_i(s), b_i(s) real polynomials in s . The cascade networks consist of commensurate, uniform, lossless transmission lines interconnected by passive, lumped (lossless and/or lossy) two-ports and terminated in a passive load which can be prescribed as part of the specifications. Moreover, the results of this paper are also applicable to lumpeddistributed cascade networks which contain noncommensurate, tapered and/or lossy transmission lines (e.g., RC lines, distortionless lines) and to nonelectrical systems which can be modeled as distributed or lumpeddistributed cascades of types similar to the ones described above (e.g., acoustic filters).
In this paper we present solutions to a number of problems that arise in microelectronics, printed circuits, and process automation. These problems are broadly concerned with wiring and interconnection of modules, circuit layout design, and the graphic display, manipulation, and alteration of circuits. The solutions are based on a number of results obtained by the author on the characterization, coding, symmetries, and generation of planar graphs. These results are constructive in that they can be given in the form of algorithms and are thus suitable for direct computer implementation.
A procedure for the synthesis of general RC transfer functions by means of unbalanced networks is described. The transfer function need not be minimum phase but may have zeros anywhere in the complex plane except on the positive real axis. Use is made of the technique of zero shifting as in the Guillemin procedure; but the additional use of a network theorem divides the desired network into two parts, with a consequent reduction of the problem to two simpler problems. Zero shifting can now be performed in two directions from within the total network. The theorem plus a method of using fewer paralleled ladders yield a final network with fewer ladders and fewer elements than that given by the Guillemin procedure. In the illustrative example given, twenty‐six elements are used, whereas the Guillemin procedure would use sixty‐six.
A new approach to the realization of n th-order conductance matrices by (n +p) -terminal, n -port networks is described. Results due to Cederbaum and Foster are employed. Cederbaum has given an example of a paramount matrix that is not realizable as either a resistance matrix conductance matrix. Foster has shown that any dominant conductance matrix is realizable. A conductance matrix with any fixed set of off-diagonal elements can be made dominant, by suitably increasing the diagonal elements. Thus we conclude that some sets of diagonal elements will permit a paramount conductance matrix to be realized, while others will not. Therefore, given a conductance matrix with a fixed set of off-diagonal elements, there exists a continuum of n -tuples of diagonal elements which are on the border line of realizability. We define this continuum as the realizability boundary. Networks which realize conductance matrices on the realizability boundary are called minimal networks and are characterized by not having shunt conductances at the ports. Next we apply these principles to the solution of the (n+2) -terminal 4-port case. Using a procedure derived from Guillemin, we find and catalog all possible minimal networks. For any given situation, a maximum of 22 networks is required to be tested. Synthesis procedures and examples are given. In addition, we show that certain ports of some minimal networks have constant driving-point conductances. We illustrate how to predict this effect, and suggest a practical application of this result.
The Zettawatt Equivalent Ultrashort pulse laser System (ZEUS) at the University of Michigan will be a 3-Petawatt laser system that has been funded by the National Science Foundation. It will operate as a user facility, offering access through an independent review process, to explore high-field science and applications. The first experiments expected in late 2023. The system has been designed to be flexible, with 3 independent target areas offering different configurations. When characterized, the laser generated ultrashort secondary sources - electron beams, betatron x-rays, ion or neutron sources - may also be offered to users for applications beyond laser-plasma interaction physics. Target Area 1 offers the possibility to split the 3-PW pulse into 2.5-PW and 500-TW, allowing a colliding beam geometry, with one large f-number focusing optic designed for laser wakefield acceleration (LWFA) experiments. Target Area 2 will offer double plasma mirror and short focusing to achieve high-contrast and high-intensity. Target Area 3 is limited to 500-TW pulses, but can operate with 5-Hz bursts. Additionally, a modest long-pulse capability will be available to drive pump-probe experiments.
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