Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02456.X
K. Kurokawa
This paper discusses the dynamics of high-field propagating domains in bulk semiconductors such as gallium arsenide. First, the origin of a high-field domain and its nucleation mechanism are discussed. Next, important properties of a steady-state high-field domain are briefly reviewed. Then, the “unequal” areas rule is derived to explain transient domain behavior. Domain buildup or decay speeds are discussed in detail, and conditions are presented under which two or more domains can exist simultaneously. Finally, the above discussions are applied to explain the high-field domain behavior in pulse circuits, variable frequency oscillators, waveform generators, and domain bypassing schemes. Numerical examples are also given to illustrate how fast these operations can be performed.
{"title":"The dynamics of high-field propagating domains in bulk semiconductors","authors":"K. Kurokawa","doi":"10.1002/J.1538-7305.1967.TB02456.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02456.X","url":null,"abstract":"This paper discusses the dynamics of high-field propagating domains in bulk semiconductors such as gallium arsenide. First, the origin of a high-field domain and its nucleation mechanism are discussed. Next, important properties of a steady-state high-field domain are briefly reviewed. Then, the “unequal” areas rule is derived to explain transient domain behavior. Domain buildup or decay speeds are discussed in detail, and conditions are presented under which two or more domains can exist simultaneously. Finally, the above discussions are applied to explain the high-field domain behavior in pulse circuits, variable frequency oscillators, waveform generators, and domain bypassing schemes. Numerical examples are also given to illustrate how fast these operations can be performed.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"17 1","pages":"2235-2259"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87926318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02458.X
M. A. Logan
Voltage-current ratios, measured using probes on the surface of a homogeneous conducting sheet, are converted to resistance per square by “conversion factors”. For rectangles, a closed form solution for these factors is obtained by using the complex Jacobian sine-amplitude function $x + iy = {rm sn}[(u+iv),k]$ as a transformation. After transformation, an insulated edge rectangle becomes a semi-infinite sheet. Two conjugate current point images establish the boundary condition. A double-sided rectangle becomes an infinite sheet directly, needing no images. New tables have been prepared for a pattern of probe center locations uniformly distributed over the surface. The probe chosen for these tables is a common arrangement having four equally spaced points on a line parallel to the longer edge of the rectangle.
{"title":"Sheet resistivity measurements on rectangular surfaces–general solution for four point probe conversion factors","authors":"M. A. Logan","doi":"10.1002/J.1538-7305.1967.TB02458.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02458.X","url":null,"abstract":"Voltage-current ratios, measured using probes on the surface of a homogeneous conducting sheet, are converted to resistance per square by “conversion factors”. For rectangles, a closed form solution for these factors is obtained by using the complex Jacobian sine-amplitude function $x + iy = {rm sn}[(u+iv),k]$ as a transformation. After transformation, an insulated edge rectangle becomes a semi-infinite sheet. Two conjugate current point images establish the boundary condition. A double-sided rectangle becomes an infinite sheet directly, needing no images. New tables have been prepared for a pattern of probe center locations uniformly distributed over the surface. The probe chosen for these tables is a common arrangement having four equally spaced points on a line parallel to the longer edge of the rectangle.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"11 1","pages":"2277-2322"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90628601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02464.X
J. Holtzman
This study is primarily concerned with the question: If the method of equivalent linearization indicates the existence of a periodic solution, is there actually a periodic solution near the approximation of equivalent linearization? To answer this question, we use a modification of the contraction mapping fixed point theorem. We discuss applications to differential equations and difference-differential equations (with forcing functions). Also, we show that our use of contraction maps is not applicable (without modification) to autonomous systems because the mapping evaluated in the neighborhood of a periodic solution to an autonomous system is not a contraction in a space of periodic functions.
{"title":"Contraction maps and equivalent linearization","authors":"J. Holtzman","doi":"10.1002/J.1538-7305.1967.TB02464.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02464.X","url":null,"abstract":"This study is primarily concerned with the question: If the method of equivalent linearization indicates the existence of a periodic solution, is there actually a periodic solution near the approximation of equivalent linearization? To answer this question, we use a modification of the contraction mapping fixed point theorem. We discuss applications to differential equations and difference-differential equations (with forcing functions). Also, we show that our use of contraction maps is not applicable (without modification) to autonomous systems because the mapping evaluated in the neighborhood of a periodic solution to an autonomous system is not a contraction in a space of periodic functions.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"1 1","pages":"2405-2435"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91174308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02465.X
T. Cross
In the recent literature, two noise contributors in FM systems have been analyzed: (i) intermodulation noise due to transmission deviations, and (ii) AM/PM intermodulation noise. Even though different, these two contributors have the same property of being functions of the baseband signal. Hence, one would expect them to be correlated to some degree. In this paper, we derive the expression for the power density spectrum for the sum of these two noise contributors. The resulting expression has been programmed on a digital computer. It has been found that, under certain conditions, the correlation can be quite significant. In fact, an example using a representative FM radio relay system shows that the correlation can result in greater than 4 dB error if the two contributors are assumed to be uncorrelated.
{"title":"Power density spectrum of the sum of two correlated intermodulation noise contributors in FM systems","authors":"T. Cross","doi":"10.1002/J.1538-7305.1967.TB02465.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02465.X","url":null,"abstract":"In the recent literature, two noise contributors in FM systems have been analyzed: (i) intermodulation noise due to transmission deviations, and (ii) AM/PM intermodulation noise. Even though different, these two contributors have the same property of being functions of the baseband signal. Hence, one would expect them to be correlated to some degree. In this paper, we derive the expression for the power density spectrum for the sum of these two noise contributors. The resulting expression has been programmed on a digital computer. It has been found that, under certain conditions, the correlation can be quite significant. In fact, an example using a representative FM radio relay system shows that the correlation can result in greater than 4 dB error if the two contributors are assumed to be uncorrelated.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"50 1","pages":"2437-2452"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91156199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02462.X
D. Maurer
A method of cathode activity measurement which yields fundamental cathode parameters has been developed. Basically, it is a modified dip test and consists of plotting cathode current vs cathode temperature. A simple geometric analysis of the data plot yields data that can be related from one tube to another and to the cathode work function. Thus, experience gained by this simple and rapid technique may be translated from one tube type to another. This technique can be used to obtain the work function as a function of cathode temperature and a method is suggested for obtaining work function as a function of current density.
{"title":"Cathode activity measurement: A modification of the dip test","authors":"D. Maurer","doi":"10.1002/J.1538-7305.1967.TB02462.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02462.X","url":null,"abstract":"A method of cathode activity measurement which yields fundamental cathode parameters has been developed. Basically, it is a modified dip test and consists of plotting cathode current vs cathode temperature. A simple geometric analysis of the data plot yields data that can be related from one tube to another and to the cathode work function. Thus, experience gained by this simple and rapid technique may be translated from one tube type to another. This technique can be used to obtain the work function as a function of cathode temperature and a method is suggested for obtaining work function as a function of current density.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"30 1","pages":"2363-2374"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73969515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02457.X
R. Standley
Interest in circular-electric mode channel-dropping filters has been stimulated by recent advances in the repeater art. This paper presents the theory and establishes design procedures for filters having two-pole maximally flat response functions. The basic structure uses mode-conversion resonators, i.e., the resonating mode is the TE 02 circular electric mode, for three of the resonators. The rejection filter portion of the structure is conventional in that two resonators separated by an odd multiple of π/2 radians realize the desired characteristic. The branching filter is novel in that a rectangular waveguide is wrapped around a mode-conversion resonator and coupled to the TE 02 resonating mode via a multiplicity of apertures. The rectangular guide is then resonated to permit realization of the two-pole branching filter. The theory developed is an extension of Marcatili's original work on mode-conversion resonators. The mode-conversion resonator parameters are related to the elements of a lumped constant prototype network thus extending the utility of mode-conversion resonators. Experimental results are presented on several filter models. The agreement between theory and experiment is generally good. Four filters were developed for use in an all solid-state repeater experiment with successful results.
{"title":"A millimeter wave, two-pole, circular-electric mode, channel-dropping filter structure","authors":"R. Standley","doi":"10.1002/J.1538-7305.1967.TB02457.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02457.X","url":null,"abstract":"Interest in circular-electric mode channel-dropping filters has been stimulated by recent advances in the repeater art. This paper presents the theory and establishes design procedures for filters having two-pole maximally flat response functions. The basic structure uses mode-conversion resonators, i.e., the resonating mode is the TE 02 circular electric mode, for three of the resonators. The rejection filter portion of the structure is conventional in that two resonators separated by an odd multiple of π/2 radians realize the desired characteristic. The branching filter is novel in that a rectangular waveguide is wrapped around a mode-conversion resonator and coupled to the TE 02 resonating mode via a multiplicity of apertures. The rectangular guide is then resonated to permit realization of the two-pole branching filter. The theory developed is an extension of Marcatili's original work on mode-conversion resonators. The mode-conversion resonator parameters are related to the elements of a lumped constant prototype network thus extending the utility of mode-conversion resonators. Experimental results are presented on several filter models. The agreement between theory and experiment is generally good. Four filters were developed for use in an all solid-state repeater experiment with successful results.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"49 1","pages":"2261-2276"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87175187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02466.X
E. Nagelberg
We studied the phase progression properties of normal modes in a conical waveguide in order to develop techniques for analysis of multimode microwave antennas. We found that the large-order asymptotic expansions of Bessel functions developed by F. W. J. Olver are most appropriate for such calculations by virtue of their simplicity and uniformity with respect to argument. These expansions are applied to analysis of the conical TE 11 and conical TM 11 modes and, in addition, to an examination of the “quasi-cylindrical approximation” in which the conical waveguide is regarded as a cylindrical waveguide with gradually changing cross section.
为了发展多模微波天线的分析技术，我们研究了锥形波导中正模的相进特性。我们发现由F. W. J. Olver提出的贝塞尔函数的大阶渐近展开式由于其在参数上的简单性和一致性是最适合于这种计算的。这些展开式应用于锥形t11和锥形t11模式的分析，此外，还应用于“准圆柱形近似”的检验，其中锥形波导被视为具有逐渐变化的截面的圆柱形波导。
{"title":"Phase progression in conical waveguides","authors":"E. Nagelberg","doi":"10.1002/J.1538-7305.1967.TB02466.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02466.X","url":null,"abstract":"We studied the phase progression properties of normal modes in a conical waveguide in order to develop techniques for analysis of multimode microwave antennas. We found that the large-order asymptotic expansions of Bessel functions developed by F. W. J. Olver are most appropriate for such calculations by virtue of their simplicity and uniformity with respect to argument. These expansions are applied to analysis of the conical TE 11 and conical TM 11 modes and, in addition, to an examination of the “quasi-cylindrical approximation” in which the conical waveguide is regarded as a cylindrical waveguide with gradually changing cross section.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"8 1","pages":"2453-2466"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80808065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02460.X
V. Benes
A telephone connecting network is given, and with full information at all times about its state, routing policies are sought which minimize the expected number of attempted calls denied service in some finite interval. In this paper, the search is pursued as a mathematical problem in the context of a standard traffic model in terms of optimal control theory and dynamic programming. Certain combinatorial properties of the network, earlier found to be the key to minimizing the loss, also turn out to be relevant here: they lead to policies which differ from optimal policies only in accepting all unblocked call attempts, and provide a “practical” solution of the problem posed. In many cases, the policies found vindicate heuristic policies earlier conjectured to be optimal.
{"title":"Optimal routing in connecting networks over finite time intervals","authors":"V. Benes","doi":"10.1002/J.1538-7305.1967.TB02460.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02460.X","url":null,"abstract":"A telephone connecting network is given, and with full information at all times about its state, routing policies are sought which minimize the expected number of attempted calls denied service in some finite interval. In this paper, the search is pursued as a mathematical problem in the context of a standard traffic model in terms of optimal control theory and dynamic programming. Certain combinatorial properties of the network, earlier found to be the key to minimizing the loss, also turn out to be relevant here: they lead to policies which differ from optimal policies only in accepting all unblocked call attempts, and provide a “practical” solution of the problem posed. In many cases, the policies found vindicate heuristic policies earlier conjectured to be optimal.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"36 1","pages":"2341-2352"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76139534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-12-01DOI: 10.1002/J.1538-7305.1967.TB02463.X
D. Maurer, C. M. Pleass
The coated powder cathode is an inexpensive, reproducible emitter which combines the virtues of various conventional cathode types, and is suited to use in modern high-power, high-reliability electron tubes. It is best considered as a modification of the classic oxide cathode in which each particle of the emissive coating is covered with a thin layer of nickel. Inherent advantages of this cathode over the oxide cathode include the ability to sustain current densities up to 1 amp/cm2 over long, calculable lifetimes, increased flexibility in time and temperature during processing, and improved coating adhesion. This paper describes the concept, fabrication and mechanism of the cathode and presents data obtained from a diode evaluation program.
{"title":"The CPC: A00000000 medium current density, high reliability cathode","authors":"D. Maurer, C. M. Pleass","doi":"10.1002/J.1538-7305.1967.TB02463.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB02463.X","url":null,"abstract":"The coated powder cathode is an inexpensive, reproducible emitter which combines the virtues of various conventional cathode types, and is suited to use in modern high-power, high-reliability electron tubes. It is best considered as a modification of the classic oxide cathode in which each particle of the emissive coating is covered with a thin layer of nickel. Inherent advantages of this cathode over the oxide cathode include the ability to sustain current densities up to 1 amp/cm2 over long, calculable lifetimes, increased flexibility in time and temperature during processing, and improved coating adhesion. This paper describes the concept, fabrication and mechanism of the cathode and presents data obtained from a diode evaluation program.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"8 1","pages":"2375-2404"},"PeriodicalIF":0.0,"publicationDate":"1967-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90381543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1967-11-01DOI: 10.1002/J.1538-7305.1967.TB04242.X
V. Prabhu
A general analysis of stability conditions of pumped nonlinear systems is presented in this paper. The type of instability investigated for these systems is that which causes spurious tones to appear at any point in the system in the vicinity of an appropriate harmonic carrier. A set of stability criteria that assure stability for the system has been given in terms of scattering parameters of the system. These criteria have then been applied to investigate the stability of lossless varactor harmonic generators that have been shown in this paper to be potentially unstable systems. It is then investigated for these multipliers how instability arises, and how it can be avoided by proper terminations. For some simple terminations, which are usually used in practice, sufficient conditions, that assure total stability of the multipliers, are explicitly given.
{"title":"Stability considerations in lossless varactor frequency multipliers","authors":"V. Prabhu","doi":"10.1002/J.1538-7305.1967.TB04242.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1967.TB04242.X","url":null,"abstract":"A general analysis of stability conditions of pumped nonlinear systems is presented in this paper. The type of instability investigated for these systems is that which causes spurious tones to appear at any point in the system in the vicinity of an appropriate harmonic carrier. A set of stability criteria that assure stability for the system has been given in terms of scattering parameters of the system. These criteria have then been applied to investigate the stability of lossless varactor harmonic generators that have been shown in this paper to be potentially unstable systems. It is then investigated for these multipliers how instability arises, and how it can be avoided by proper terminations. For some simple terminations, which are usually used in practice, sufficient conditions, that assure total stability of the multipliers, are explicitly given.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"3 1","pages":"2035-2060"},"PeriodicalIF":0.0,"publicationDate":"1967-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78434316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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