Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500164
V. Belevitch
{"title":"Rational feedback and equalizer circuits or regulators with prescribed properties","authors":"V. Belevitch","doi":"10.1109/TCT.1955.6500164","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500164","url":null,"abstract":"","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116110339","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500152
M. C. Herrero
ASA logical continuation of the studies of systems with fixed parameters, there has been increasing interest in systems whose parameters are functions either of the dependent variable (nonlinear systems) or of the independent variable (time-varying systems). A general approach to the analysis of time-varying systems is so difficult, that at the present stage of development in this field one is restricted to the solution of relatively simple problems arising in practical applications.
{"title":"Resonance phenomena in time-varying circuits","authors":"M. C. Herrero","doi":"10.1109/TCT.1955.6500152","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500152","url":null,"abstract":"ASA logical continuation of the studies of systems with fixed parameters, there has been increasing interest in systems whose parameters are functions either of the dependent variable (nonlinear systems) or of the independent variable (time-varying systems). A general approach to the analysis of time-varying systems is so difficult, that at the present stage of development in this field one is restricted to the solution of relatively simple problems arising in practical applications.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123168396","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500149
A. Gerlach
THE USE OF integral transforms to solve dynamical problems in physics and engineering has received considerable prominence in the last half century. Integral transforms have, since their usefulness was discovered by Heaviside in the late nineteenth century, gone through the cycle of: (1) rigorization of technique;1, 2 (2) tabulation of many specific transform pairs;3, 4 and (3) generalization of transform methods.5–8. In the present paper on extension of this generalization will be made which is applicable only to time series and its use precludes the acceptance of the fundamental postulate of cause and effect. That is, the present response anywhere in a physical system can in no way depend on future values of a stimulus elsewhere in the system.
{"title":"A time-variable transform and its application to spectral analysis","authors":"A. Gerlach","doi":"10.1109/TCT.1955.6500149","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500149","url":null,"abstract":"THE USE OF integral transforms to solve dynamical problems in physics and engineering has received considerable prominence in the last half century. Integral transforms have, since their usefulness was discovered by Heaviside in the late nineteenth century, gone through the cycle of: (1) rigorization of technique;1, 2 (2) tabulation of many specific transform pairs;3, 4 and (3) generalization of transform methods.5–8. In the present paper on extension of this generalization will be made which is applicable only to time series and its use precludes the acceptance of the fundamental postulate of cause and effect. That is, the present response anywhere in a physical system can in no way depend on future values of a stimulus elsewhere in the system.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129935978","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500156
W. A. Edson
THE BASIC idea of frequency memory is conveniently illustrated by Fig. 1 in which it is assumed that the antiresonant circuits are of comparable selectivity and impedance and are tuned to frequencies that are unrelated but of the same order of magnitude. Oscillation at either f1 or f2 can be initiated by supplying to the input a signal of suitable magnitude and the desired frequency. An input of short duration suffices, for once started the oscillation persists without change until the other frequency is injected or the power is turned off. That is, the circuit remembers the frequency of the last input. The output may be taken from other points, but the plate node is particularly convenient.
{"title":"Frequency memory in multi-mode oscillators","authors":"W. A. Edson","doi":"10.1109/TCT.1955.6500156","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500156","url":null,"abstract":"THE BASIC idea of frequency memory is conveniently illustrated by Fig. 1 in which it is assumed that the antiresonant circuits are of comparable selectivity and impedance and are tuned to frequencies that are unrelated but of the same order of magnitude. Oscillation at either f1 or f2 can be initiated by supplying to the input a signal of suitable magnitude and the desired frequency. An input of short duration suffices, for once started the oscillation persists without change until the other frequency is injected or the power is turned off. That is, the circuit remembers the frequency of the last input. The output may be taken from other points, but the plate node is particularly convenient.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121429975","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500151
A. P. Bolle
THE APPLICATION of complex symbolism to linear fixed networks (i.e. networks governed by linear differential equations with constant coefficients) is effective by virtue of the fact that the principle of superposition is applicable to such networks. The same principle is applicable also to linear variable networks (i.e. networks governed by linear differential equations with coefficients that are dependent on time, but not on current or voltage). This suggests that it must also be possible to make use of the complex symbolism in the case of linear variable networks.
{"title":"Application of complex symbolism to linear variable networks","authors":"A. P. Bolle","doi":"10.1109/TCT.1955.6500151","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500151","url":null,"abstract":"THE APPLICATION of complex symbolism to linear fixed networks (i.e. networks governed by linear differential equations with constant coefficients) is effective by virtue of the fact that the principle of superposition is applicable to such networks. The same principle is applicable also to linear variable networks (i.e. networks governed by linear differential equations with coefficients that are dependent on time, but not on current or voltage). This suggests that it must also be possible to make use of the complex symbolism in the case of linear variable networks.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121804255","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500159
R. Sallen, E. Key
IN THE FREQUENCY range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductance-capacitance (LC) or resistance-inductance-capacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut-off filters at very low frequencies. In many cases the active elements can be simple cathode-follower circuits that have stable gain, low output impedance and a large dynamic range.
{"title":"A practical method of designing RC active filters","authors":"R. Sallen, E. Key","doi":"10.1109/TCT.1955.6500159","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500159","url":null,"abstract":"IN THE FREQUENCY range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductance-capacitance (LC) or resistance-inductance-capacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut-off filters at very low frequencies. In many cases the active elements can be simple cathode-follower circuits that have stable gain, low output impedance and a large dynamic range.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121962738","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500148
W. Bennett
THE GENERAL problem of transmitting signals through linear systems in which one or more parameters vary periodically with time has an extensive literature. One widely used method is based on Fourier series representation of the varying parameters. This leads to an infinite number of simultaneous linear equations expressing the relations between the coefficients in the corresponding Fourier series representation of the steady-state response. The solution of the equations can be expressed in terms of determinants of infinite order which in turn can be evaluated by various approximation techniques. In practical cases it is often permissible to neglect all but a few dominant components; the number of equations is thereby made finite and reasonably small.
{"title":"Steady-state transmission through networks containing periodically operated switches","authors":"W. Bennett","doi":"10.1109/TCT.1955.6500148","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500148","url":null,"abstract":"THE GENERAL problem of transmitting signals through linear systems in which one or more parameters vary periodically with time has an extensive literature. One widely used method is based on Fourier series representation of the varying parameters. This leads to an infinite number of simultaneous linear equations expressing the relations between the coefficients in the corresponding Fourier series representation of the steady-state response. The solution of the equations can be expressed in terms of determinants of infinite order which in turn can be evaluated by various approximation techniques. In practical cases it is often permissible to neglect all but a few dominant components; the number of equations is thereby made finite and reasonably small.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125543060","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500157
L. A. Pipes
IN RECENT years a great deal of attention has been given to the general theory and performance of circuits the parameters of which are functions of the time. The mathematical analysis of circuits of this type leads to the solution of linear differential equations with variable coefficients. Examples of linear time-varying circuits of practical importance occur in the theory of electrical communications. Frequency modulation circuits, for example, involve variations of capacitance or, to a lesser extent, inductance. The carbon microphone circuit consists of essentially of a variable resistance the value of which is varied by some source of energy outside the circuit. The condenser microphone circuit contains a variable capacitance. Super-regeneration involves circuits that contain a periodically-varying resistance parameter.
{"title":"A mathematical analysis of a series circuit containing periodically varying resistance","authors":"L. A. Pipes","doi":"10.1109/TCT.1955.6500157","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500157","url":null,"abstract":"IN RECENT years a great deal of attention has been given to the general theory and performance of circuits the parameters of which are functions of the time. The mathematical analysis of circuits of this type leads to the solution of linear differential equations with variable coefficients. Examples of linear time-varying circuits of practical importance occur in the theory of electrical communications. Frequency modulation circuits, for example, involve variations of capacitance or, to a lesser extent, inductance. The carbon microphone circuit consists of essentially of a variable resistance the value of which is varied by some source of energy outside the circuit. The condenser microphone circuit contains a variable capacitance. Super-regeneration involves circuits that contain a periodically-varying resistance parameter.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121599980","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 : 1955-03-01DOI: 10.1109/TCT.1955.6500158
H. Robbins
AT FIRST sight, the application of W.K.B. approximation to a time-dependent circuit seems perfectly straightforward. Unfortunately, there are two different and equally plausible ways to apply it to the circuit treated by Pipes, and the two results will generally not agree. The W.K.B. solution of the homogeneous equation (43) contains two arbitrary constants. These can be chosen so that at some particular time τ, q = 0 and dq/dt = 1. Call this solution q1(t, τ). Alternatively, the constants can be chosen so that q = 1 and dq/dt = 0 at time τ. Call this solution q2(t, τ). The response of the system at time t to a unit voltage impulse applied at some earlier time τ is q1(t, τ)/L, hence, by the superposition principle, we get a general solution of the inhomogeneous equation $q_1 (t) = {1 over L} int_{-infty}^t q_1(t, tau) E(tau) dtau. eqno{hbox{(1)}}$.
{"title":"Comment on the paper “A mathematical analysis of a series circuit containing periodically varying resistance” by L. A. Pipes","authors":"H. Robbins","doi":"10.1109/TCT.1955.6500158","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500158","url":null,"abstract":"AT FIRST sight, the application of W.K.B. approximation to a time-dependent circuit seems perfectly straightforward. Unfortunately, there are two different and equally plausible ways to apply it to the circuit treated by Pipes, and the two results will generally not agree. The W.K.B. solution of the homogeneous equation (43) contains two arbitrary constants. These can be chosen so that at some particular time τ, q = 0 and dq/dt = 1. Call this solution q<inf>1</inf>(t, τ). Alternatively, the constants can be chosen so that q = 1 and dq/dt = 0 at time τ. Call this solution q<inf>2</inf>(t, τ). The response of the system at time t to a unit voltage impulse applied at some earlier time τ is q<inf>1</inf>(t, τ)/L, hence, by the superposition principle, we get a general solution of the inhomogeneous equation <tex>$q_1 (t) = {1 over L} int_{-infty}^t q_1(t, tau) E(tau) dtau. eqno{hbox{(1)}}$</tex>.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131424288","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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