In a given linear, multistage, cascaded amplifier [1] comprising passive coupling circuits and active two-ports alternatively, the problem is where in the amplifier the stabilizing circuit elements should be placed to eliminate instability, and of what type and value. Our investigations are based on a new recursive formula for the determinant of tridiagonal matrices. Relation of our results to the Stern stability factor has been obtained. A verification in numerical examples has also been provided.
References
[1]
Ladvánszky, J. (1999) On the Stability of Multistage Amplifiers. Proceedings of the European Conference on Circuit Theory and Design, ECCTD’99, Stresa, August 29-September 2 1999, 635-638.
[2]
Llewellyn, F.B. (1952) Some Fundamental Properties of Transmission Systems. Proceedings of the IRE, 271-283.
[3]
FolkeBolinder, E. (1957) Survey of Some Properties of Linear Networks. IRE Transactions on Circuit Theory, 70-78.
[4]
Karp, M.A. (1957) On Gain and Stability. IRE Transactions on Circuit Theory, 339-340.
[5]
Stern, A.P. (1957) Stability and Power Gain of Tuned Transistor Amplifiers. Proceedings of the IRE, 335-343.
[6]
Lim, M. (1960) Power Gain and Stability of Multistage, Narrow-Band Amplifiers Employing Nonunilateral Electron Devices. IRE Transactions on Circuit Theory, 158-166.
[7]
Youla, D. (1959) A Stability Characterization of the Reciprocal Linear Passive N Port. Proceedings of the IRE, 1150-1151.
[8]
Venkateswaran, S. (1961) An Invariant Stability Factor and Its Physical Significance. IEEE Monograph.
[9]
Rollett, J.M. (1962) Stability and Power Gain Invariants of Linear Twoports. IRE Transactions on Circuit Theory, 29-32.
[10]
Mason, S.J. (1954) Power Gain in Feedback Amplifiers. IRE Transactions on Circuit Theory, CT-1, 20-25. https://doi.org/10.1109/TCT.1954.1083579
[11]
Youla, D. (1960) A Note on the Stability of Linear, Nonreciprocal n-Ports. 121-122.
[12]
Kuo, Y.L. (1968) A Note on the n-Port Passivity Criterion. IEEE Transactions on Circuit Theory, 74-76. https://doi.org/10.1109/TCT.1968.1082767
[13]
Scanlan, J.O. and Singleton, J.S. (1962) The Gain and Stability of Linear Two-Port Amplifiers. IRE Transactions on Circuit Theory, 240-246.
[14]
Scanlan, J.O. and Singleton, J.S. (1962) Two-Ports-Maximum Gain for a Given Stability Factor. IRE Transactions on Circuit Theory, 428-429.
[15]
Singhakowinta, A. and Boothroyd, A.R. (1964) On Linear Two-Port Amplifiers. IRE Transactions on Circuit Theory, 169.
[16]
Ku, W.H. (1966) Unilateral Gain and Stability Criterion of Active Two-Ports in Terms of Scattering Parameters. Proceedings of the IEEE, 54, 1617-1618.
https://doi.org/10.1109/PROC.1966.5229
[17]
Woods, D. (1976) Reappraisal of the Unconditional Stability Criteria for Active 2-Port Networks in Terms of S Parameters. IEEE Transactions on Circuits and Systems, 23, 73-81. https://doi.org/10.1109/TCS.1976.1084179
[18]
Youla, D.C. (1980) A Maximum Modulus Theorem for Spectral Radius and Absolutely Stable Amplifiers. IEEE Transactions on Circuits and Systems, 27, 1274-1276. https://doi.org/10.1109/TCS.1980.1084757
[19]
Zeheb, E. and Walach, E. (1981) Necessary and Sufficient Conditions for Absolute Stability of Linear n-Ports. Circuit Theory and Applications, 9, 311-330.
https://doi.org/10.1002/cta.4490090306
[20]
Bhaya, A. and Desoer, C.A. (1985) Absolute k-Stability of Linear Distributed n-Ports. IEEE Transactions on Circuits and Systems, 32, 625-634.
https://doi.org/10.1109/TCS.1985.1085775
[21]
Bose, N.K. and Shi, Y.Q. (1987) A Simple General Proof of Kharitonov’s Generalized Stability Criterion. IEEE Transactions on Circuits and Systems, 34, 1233-1237. https://doi.org/10.1109/TCS.1987.1086055
[22]
Meys, R.P. (1990) Review and Discussion of Stability Criteria for Linear 2-Ports. IEEE Transactions on Circuits and Systems, 37, 1450-1452.
https://doi.org/10.1109/31.62423
[23]
Edwards, M.L. and Sinsky, J.H. (1992) A Single Stability Parameter for Linear 2-Port Circuits. IEEE MTT-S Digest, 885-888.
[24]
Edwards, M.L. and Sinsky, J.H. (1992) A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter. IEEE Transactions on Microwave Theory and Techniques, 40, 2303-2311. https://doi.org/10.1109/22.179894
[25]
Ohtomo, M. (1993) Stability Analysis and Numerical Simulation of Multidevice Amplifiers. IEEE Transactions on Microwave Theory and Techniques, 41, 983-991.
[26]
Youla, D.C. (1963) On the Stability of Linear Systems. IEEE Transactions on Circuit Theory, 276-279. https://doi.org/10.1109/TCT.1963.1082108
[27]
Kuh, E.S. (1965) Stability of Linear Time-Varying Networks—The State Space Approach. IEEE Transactions on Circuit Theory, 12, 150-157.
https://doi.org/10.1109/TCT.1965.1082427
[28]
Trick, T.N. (1969) Asymptotic Stability of a Class of Networks Containing a Nonlinear Time-Varying Capacitor and Periodic Inputs. IEEE Transactions on Circuit Theory, 16, 217-219. https://doi.org/10.1109/TCT.1969.1082929
[29]
Sandberg, I.W. (1965) Some Results on the Theory of Physical Systems Governed by Nonlinear Functional Equations. Bell System Technical Journal, 44, 871-898.
https://doi.org/10.1002/j.1538-7305.1965.tb04161.x
[30]
Choma, J. (1972) Frequency Domain Stability Criteria for Large-Signal Tuned COmmon-Base Amplifiers. IEEE Transactions on Circuit Theory, 19, 265-270.
https://doi.org/10.1109/TCT.1972.1083460
[31]
Vidkjaer, J. (1976) Instabilities in RF-Power Amplifiers Caused by a Self-Oscillation in the Transistor Bias Network. IEEE Journal of Solid-State Circuits, 11, 703-712.
https://doi.org/10.1109/JSSC.1976.1050801
[32]
Baranyi, A. and Ladvánszky, J. (1984) On the Stability of Non-Linear Two-Port Amplifiers. Circuit Theory and Applications, 12, 123-131.
https://doi.org/10.1002/cta.4490120206
[33]
Belevitch, V. (1959) Théorie des circuits non-linéariesen régime alternatif. Uystpruyst, Louvain.
[34]
Kolumbán, G. and Frigyik, B. (1999) Robust Chaotic Communications without Syncronization. Proceedings of the European Conference on Circuit Theory and Design, Stresa, 29 August-2 September 1999.
[35]
Rózsa, P. (1991) Linear Algebra and Its Applications. In Hungarian, Budapest, Tankönykiadó.
[36]
Gantmacher (1959) Theory of Matrices. Chelsea.
[37]
DesignSoft Inc. (1995) TINA 3.0—Toolkit for Interactive Network Analysis. User’s Guide.