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Equivalent circuit modelling of biopolar transistors

By Monica Dowson


Existing equivalent circuit models of bipolar transistors are reviewed together with techniques for the evaluation of suitable values of the model elements. A method enabling the optimisation of the element values of any particular model in order to match the measured S parameters of a device that is to be modelled is described. This method uses a modified Gauss Newton algorithm to minimise an objective function defined as the sum of the squares of the weighted errors between the required S parameters and those of the model.\ud Details are then given of a new modelling algorithm for the development of accurate equivalent circuit models which was developed from this original optimisation method. The new modelling algorithm requires some S parameter measurements of the device to be modelled' over an appropriate range of frequencies, together with a potentially suitable model. The initial model elements are optimised and then, if necessary, suitable topological changes, involving the addition or deletion of both elements and nodes, are made until a model having the. required accuracy or complexity is obtained.\ud A number of examples are given of small-signal equivalent circuit models of bipolar transistors developed using the algorithm. These particular transistors were operating at frequencies up to lGHz .A further example is given of the use of the modelling algorithm in the development of a bias dependent small-signal model of two similar bipolar transistors operating at frequencies up to 2GHz . Additional S parameter data for the same two transistors is also used to demonstrate that the algoritim can be used successfully for the development of non-linear models

Publisher: University of Leicester
Year: 1982
OAI identifier: oai:lra.le.ac.uk:2381/7641

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  1. 2: S2. S 7.40 -, -'-'7 Ei . E, Cs, :107 E. 'ecl. -15.51 2: 47.4 -24.
  2. 76? I M6.2. c, C1. C10c, -I .
  3. (1975). A Bibliography on Semiconductor Device Modelling", doi
  4. (1965). A Class of Methods for Solving Non-Linear Simultaneous Equations", doi
  5. (1966). A Comparison of Several Current Optimization Methods and the Use of Transformations in Constrained Problems". doi
  6. (1965). A Computer Program for Analysing Networks Containing Three-Terminal Active Devices Characterised by their Two-Port Parameters". Radio and EleCtTon. doi
  7. (1977). A Contrall0#1 Random Search Procedure for Global OPtimL4atavn". COmn-
  8. (1977). A Controlled Random Search Procedure for Global Optimisation", doi
  9. (1978). A Controlled Random Search Procedure for Global Optimisation", in "Towards Gl9bal Optimisation 2",
  10. (1944). A Method for the Solution of Certain Non-Linear Problems in Least Squares",
  11. (1963). A Rapidly Convergent Descent Method for Minimization", doi
  12. (1965). A Simplex Method for Function Minimisation", doi
  13. (1974). A Study of the Evolutionary Approach to Network Synthesis Using Coefficient Matching",
  14. (1972). A Survey of 'Methods for Solving Constrained Minimization Problems via Unconstrained Minimization", in "Numerical Methods for Non-Linear Optimization", edited by Lootsma,
  15. (1981). A Tentative Approach towards the Global Optimization of Electrical Circuits", doi
  16. (1979). A Weighted Simplex Procedure for the Solution of . Simultaneous Non-Linear Equations", doi
  17. (1979). Algorithm 107 -A Weighted Simplex Procedure for the Solution of Simultaneous Nonlinear Equations",
  18. An Algorithm for Least Squares Estimation of Non-Linear Parameters", doi
  19. (1977). An Improved ComplexCurve Fitting Me thod",
  20. (1977). An Investigation into Current Possibilities in Automated Network Design",
  21. (1970). An Investigation into the Uses of Coefficient Matching in Network Synthesis",
  22. (1966). Associated Polynomials and Uniform Methods for the Solution of Linear Problems", doi
  23. (1979). Automated Synthesis of Lumped Linear ThreeTerminal Networks",
  24. (1975). Basic Integrated Circuit Engineering",
  25. C1967), "Simplified Characterisation of H.
  26. Cic j 4S4. 7,16. Z. C *'ý,: E. ý' 16,00. Cicit) -5.51 ' . 4at 1600. Ell-k-i _r -19.2,2 52.3 5. co ý7.1 -9. C-C, 99SI. ý4 9' 196.
  27. (1964). Comparison of Large Signal Models of Junction Transistors"s Proc. doi
  28. Computer Aided Analysis of Electronic Circuits", doi
  29. (1965). Computer Design of Linear Frequency Selective Networks".. doi
  30. (1981). Considerations on Model Modification",
  31. (1963). Department of the Army doi
  32. (1972). Derivative Free Analogues of the Levenberg-Marquardt and Gauss Algorithms for Nonlinear Least Squares Approximation", doi
  33. Design Divisions of the Institution of Electrical Engineers in association with the British Computer Society (BCS)
  34. (1956). Determinants and Matrices",
  35. (1981). Determination of CAD Model Parameters for Bipolar Transistors from Fabrication Data Using the Bipole Numerical Program",
  36. (1970). Device Modelling" in "Computer Aided Desýgn Techniques",
  37. Device Models for Circuit Analysis Programs",
  38. (1975). Electronic Materials and Devices",
  39. (1969). Electronic Principles - Physics, Models and Circuits", doi
  40. (1977). Engineering Applications", course notes for "Interactive Computer Graphics for Engineers",
  41. (1981). Equivalent Circuit Modelling of a Small Signal High Frequency Bipolar Transistor at Different Bias Conditions",
  42. (1979). Experience in Modelling Integrated Circuit Transistors",
  43. (1979). Experience in Modelling Integrated Circuit Transistors".
  44. (1978). Expressions for Optimum Values to Grow Virtual Elements", doi
  45. (1964). Function Minimisation by Conjugate Gradients",
  46. G3 -21%Ct. 7 -1. "-4 3,3 7, cl lrjrdFj. ciclrj -12.: E. r- 241.4 -C.
  47. (1977). I'Modelling Bipolar Transistors", Conf. proc. "Modelling Semiconductor Devices",
  48. (1972). I'Models for the Lateral P-N-P Transistor Including Substrate Interaction",
  49. (1968). IIS-Parameters - Circuit Analysis and Design", Hewlett Packard Application Note 95,
  50. (1981). Interactive Design to TimeDomain Specifications",
  51. (1977). Internal Publication, Philips Research Laboratories.
  52. (1954). Large Signal Behaviour of Junction Transistors", doi
  53. (1970). Linear Active Networks",
  54. (1958). Lumped Models of Transistors and Diodes", doi
  55. (1979). Minimax Optimization Techniques for Electronic Circuits", ibid.,
  56. (1978). Modeling the Bipolar Transistor",
  57. (1977). Modelling Technique for Microwave FETs and Bipolar Transistors",
  58. (1976). Multimodal Univariate Search Techniques and their Application to Optimisation Problems",
  59. (1962). Network Analysis and Synthesis",
  60. (1979). Optimisation and Design of Linear Networks, Including Nested Subnetworks to Some FrequencyDomain Specifications",
  61. (1977). Optimisation of a Small Signal High Frequency Bipolar Transistor Model Using 9 Parameter Measurements at Different Btas Conditions". Conference on Modelling Semiconductor Devices, Ecole Polytechnic do Lausanne,
  62. (1977). Optimisation of a Small Signal High Frequency Bipolar Transistor Using S Parameter Measurements at Different Bias Conditions", Conf. proc., "Modelling Semiconductor Devices! ' Ecole Polytechnique Federale de Lausanne,
  63. (1981). Optimization Procedure for MOS - Transistor Parameter Determination",
  64. (1978). Optimization Techniques and their Application",
  65. (1979). Parameters Identification Method for I. C. Bipolar Transistor Charge Control Model",
  66. (1974). Powerful 2-Part Program for Solution of Nonlinear Simultaneous Equations", doi
  67. (1979). Private communication with
  68. (1977). Private communication with O.
  69. Problem 211, Electronics Circuits and Systems,
  70. (1972). Quasi-Newton Methods for Unconstrained Optimisation", doi
  71. (1966). Scattering Parameters Speed Design of HighFrequency Transistor Circuits"s Electronics,
  72. (1970). Simultaneous Generation of the Coefficients of Network Polynomials and their Partial Derivatives from the Nodal Admittance Matrix", doi
  73. (1971). Simultaneous Generation of the Partial Derivatives of Network Polynomial Coefficients:. Further Details and Results", doi
  74. (1979). SOLUTION VALUES #*A*mAl Cf ktkCTIQN VALUES CURALSeChOlhG 10 1 N. &UkW Of K64.11CLS ANL, VAIlAbLý Th*ComputerJournal Volumt22 Nurnber3 u(g. 6P2). 0 a 20 CONT111.
  75. (1955). Synthesis of Three-Terminal RC Networks", doi
  76. (1966). The Derivation of Equivalent Circuits for Transistors by Optimization Methods, Using a General Purpose Computer Programme", Symposium "The Use of Computers as an Aid to Circuit Design and Analysis",
  77. (1957). The Junction Transistor as a Charge-Controlled Device",
  78. (1979). the Procedure OPCI tes on the data -esoci-ted with a S1161PLEX of N+I Points in N-sp- cc Prior to each iteration the co-ordinates; of dme Points. So (%
  79. (1968). The Transistor: Two Decades of Progress",
  80. (1979). The Use of Second Derivatives in Applied Optimisation",
  81. (1976). Theory and Design of Lumped Linear ThreeTerminal RC Networks".
  82. (1975). Towards a Global Optimisation Technique" in "Towards Global Optimisation",
  83. (1967). Transistor Parameter Measurements", Hewlett Packard Application Note 77-1,
  84. (1959). Variable Metric Method for Minimization", doi
  85. ýS -, ý 25. Z: ,'

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