Nonlinear Simulation Methods for Active Microwave Circuits

International Journal of Nano Devices, Sensors and Systems (IJ-Nano) Volume 1, No. 2, November 2012, pp. 77-101

Nonlinear Simulation Methods for Active Microwave Circuits: A Review of the Art and Novel Trends Invited Paper El-Sayed M. El-Rabaie ARTICLE INFO Article history: Received October 9, 2012 Revised October 12, 2012 Accepted October 21, 2012 Keyword: CAD of Nonlinear Microwave Circuits, Large Signal Amplifiers, Microwave Multipliers

ABSTRACT This paper discusses in detail, two techniques for the analysis of non-linear electronic circuit. The first technique is an automated version of the traditional time domain solution method (Transient Analysis). For a given circuit topology the state equations are generated by computer and solved numerically. The second technique involves the use of a hybrid timefrequency domain approach and is known as harmonic balance (Steady State Analysis). The formulation and solution methods adopted for both methods are outlined in detail. Emphasis is placed throughout an application to microwave circuits. In order to illustrate the properties of each method, sample analyses for two main circuits are given. The first circuit is that of a linear amplifier operating at 12 GHz and driven into saturation. The second circuit is that of a nonlinear frequency doubler, doubling from 7-14 GHz. Some advanced applications are discussed in order to further highlight the relative advantages and disadvantages of each technique. Finally it is shown how a non-linear CAD package can be produced which allows circuit optimization in a similar way to that allowed by linear CAD programs. Some remaining problems which need more investigations and possible future work are highlighted. © 2012 – Insitute of Advanced Engineeering and Science. All rights reserved.

Affiliation Electronic and Communication Engineering Dept., Faculty of Electronic Engineering, Minoufiya University, 32952 Menouf, EGYPT *Corresponding author, email address: [email protected]

1.

INTRODUCTION

The requirement for computer tools that are sufficiently accurate to allow the design of active microwave circuits to obey given specifications is increasingly important. In the past the design of microwave circuits has been the subject of empiricist post-manufacture tuning. However the ever increasing use of microwave monolithic circuits, highly accurate circuits simulators are essential. A large class of active monolithic microwave circuits operate in the nonlinear regime. These circuits, which include amplifiers, oscillators, frequency multipliers and mixers may be efficiently designed using nonlinear tools. This paper addresses two of the most frequently used simulation techniques for active microwave circuits. The first technique uses traditional time domain method based on the solution of state-space variables. The second technique, based on hybrid frequency-time domain analysis, is known as the harmonic balance method. The formulation of the time domain approach encompasses many advanced features including the automatic generation of the state variables for any given circuit topology including these with distributed transmission line elements. Included also is a self-tuning integration routine used to obtain rapid and stable convergence. Fourier analysis is employed to give the harmonic information necessary for many Journal homepage: http://iaesjournal.com/online/index.php/IJ-Nano

ISSN: 2089-4848

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microwave applications. The harmonic balance method depends on partitioning the linear and nonlinear circuit elements. Numerical optimization is then used to match the linear boundary conditions. The formulation and solution technique used are discussed. The nonlinear elements are accommodated in the analysis program by time domain simulation, while the linear elements are processed in frequency domain. By analyzing the linear elements in the frequency domain, the evaluation of highly complex distributed circuits including non-homogenous, lossy and disperse transmission lines becomes possible. Further, it will be shown that the harmonic balance technique can be made the kernel of an optimizing nonlinear CAE program capable of refining a circuit design in order to achieve a given specification. Throughout this paper the relative advantages and disadvantages of the time-domain and harmonic balance technique are described. Advanced applications are discussed which in themselves illustrate the advantages of having access to both methods. The design of a large signal microwave amplifier operating in K-band and driven in saturation is used to compare the application of the two methods. The amplifier is based on the NE71000 MESFET chip for which a new lumped equivalent model that accurately describes the large-signal device behavior is presented. Examples for optimum analysis and design of frequency multipliers (doublers and triplers) using the same chip are illustrated. Included also are the simulation results for an HBT power device using a novel developed large signal model. This paper therefore will act as a review paper and guide for those wishing to achieve the two principal methods for large signal electronic circuit simulation that are accurately in use. The main application emphasis of this paper is to GaAs MESFET and HBT circuits working in the microwave frequency regime. This, however, is not prohibitive and the techniques described are applicable to a very wide range of nonlinear problems in many fields within electronics. Having said that, I feel it incumbent on me to advert the reader to the fact that while the opening pages of the paper might sound familiar to experts. It is the remaining material of the paper that constitutes a real contribution to scholarly work to date. 2.

TIME DOMAIN METHOD

In this approach the circuit including active nonlinear devices are described by state equations, which are a set of coupled first order ordinary differential equations of normal form:







X  f(x, u, t, u)

(1)

Y  f ( x, u, t , u ) where:x:- represents the column vector of selected state variables-normally these are capacitor voltage and inductor currents. u:- represents external driving terms such as microwave drive voltages and D.C. bias voltages. y:- represents the output voltages and/or currents of interest. Both x and y are time dependent. For the resulting set of coupled equations, the non-linear coefficients are solved using numerical integration in to time domain. Consider now the creation of the state-space equations necessary for microwave nonlinear networks. 2.1 Computer Formulation of State-Space Equations For Microwave Nonlinear Circuits The state equation set is generated automatically, following the work of Shoby et al [1-3] and Chua et al [4-6] which is based on the hybrid matrix approach. More details are included in [7-8]. For the case of microwave circuits incorporating transmission lines [9], input voltage and current variables may be expressed as:V(t )  (Z0 )0.5[b2 (t  )  b1 (t )] (2)

I(t )  (Y0 )0.5[b2 (t  )  b1 (t )]

Where Z0, Y0 = line characteristic impedance; admittance,  = line delay, b1,2 = reflected voltage wave variables at input and output ports. Equation (1) becomes therefore:



X( t )  A1X(t)  B1b(t)  C1U(t)  D1 U(t)

b(t)  A2 X(t - )  b(t  )  C2 U(t  ) 

Y( t )  f [X( t ), U( t ), U( t )]  0 where in general the coefficients are nonlinear.

(2)

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2.2 Solution of State-Space Equations The initial conditions for the numerical integration are usually found by solving (3) under D.C. i.e (d/dt =0). The resulting static equations are solved for X using a modified Powell routine [10]. This routine is ideal because of its fast rate of convergence . As the state equations are usually stiff, an implicit Gear’s algorithm with variable order and time step [11-12] is used to perform the same time dependent integration. It has been found that for a circuit consisting mainly of transmission lines with a range of time delays an Adams-Moulton integration algorithm offers an improvement in integration speed [13]. 2.3 Time Domain Program Description The computer program that carries out the state-space formulation and solution for microwave non-linear circuits containing lossless delay lines is called QUMICS [13], and described in Figure (1) in the from of a flowchart. A discrete Fourier transform has been included in the program in order to allow the harmonic content of the non-linear circuit waveform to be evaluated. Having completed an analysis for a single drive level, the drive is increases if required, and the new initial conditions obtained from the previous steady-state values.

Fig. 1. Flowchart of QUMIC program

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Another form of the time domain simulator is the The Modified SPICE Time Domain Simulator [14]. SPICE is a general-purpose simulation program for use in the analysis of electronic circuits. Version 2G.3, enables DC, small signal and large signal time domain simulation to be carried out on circuits containing linear elements, controlled sources, transmission lines, as well as diodes, bipolar transistors and MOSFETs. The approach is to replace the level (1) MOSFET model in this version of SPICE with analytical representations of MESFET characteristics available in the literature. The level(1) MOSFET subroutine (MOSEQ1) effectively defines a nonlinear dual-voltage-controlled current source. The full MESFET model is built up using SPICE circuit elements and grouped together as a sub-circuit. 3.

FORMULATION AND SOLUTION OF HARMONIC BALANCE TECHNIQUE

Figure(2) shows the general analysis problem in which a nonlinear device is embedded in an external circuit which is usually linear [15-16]. The circuit has been partitioned into linear and non-linear parts [17] as shown in Fig.(3) .

Fig. 2. A General Nonlinear Analysis Problem

Fig. 3. The harmonic Balance Approach Assuming that the circuit is driven by a sinusoidal voltage (Vg , fo), voltages and currents will be in general non-sinusoidal and will contain harmonic components at nfo. If Kirchoff’s laws are applied to the circuit, the following equation results [18]:IL1  AVG  BVD  I NL1 (VG , VD ) IL 2  AVG  BVD  I NL2 (VG , VD ) where A, B, C, D are linear circuit admittance’s. These combine with VG current terms IL1 and IL2 .

(4) and

VD to produce linear

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Non-linear current terms INL1 , INL2 are produced by the active device. Once the partition has been completed, the linear circuit is analyzed in the frequency domain, while non-linear circuit elements require time domain analysis. The solution proceeds as follows:a. Assume that the Discrete Fourier coefficients (VG (nfo),VD(nfo)) of the frequency domain representation of VG and VD are known, up to some arbitrarily selected harmonic, K. Usually the properties of the circuit allow an initial estimate to be made. b. Apply the Discrete Fourier Transform to VG(t),VD(t). c. Knowing the approximate values of VG(t), VD(t) at N sampled times over a drive cycle, the nonlinear circuit currents INL1 , INL2 may now be evaluated at each of the N sample time. d. Discrete Fourier Transform allow the Fourier coefficients of I NL1 and INL2 to be determined, up to harmonic K. e. By analyzing the linear circuit in frequency domain to obtain A(nf o), B(nfo), C(nfo) and D(nfo), an equation of the form given below results:A(nfo ) VG(nfo) + B(nfo) VD(nfo) – INL1 = R1(n) C(nfo ) VG(nfo) + D(nfo) VD(nfo) – INL2 = R2(n) n = 0, 1, 2,..........., K For each selected harmonic, four real simultaneous equations results. If the initial assumed values of the Fourier coefficients of VG and VD were correct then the residuals R1 and R2 would be zero. In order to complete the solution, the Fourier coefficients of VG and VD are systematically valid by a numerical optimization routine until the sum of the squares of the residuals over the K selected harmonic is less then some pre-set value. This value is normally chosen to be (1E-12) for weakly nonlinear circuits, four harmonic used, and (1E-4) for strongly non-linear circuits, ten harmonics used. The frequency and time variation of all circuit variables can then be found. Figure(4), shows the flowchart of the non-linear harmonic balance analysis program. For the harmonic balance program kernel a modified Newton Raphson [19-20] algorithm is used. This was selected after consideration of a number of different algorithms giving the best overall performance in terms of convergence and computational speed for both weakly non-linear and strongly non-linear circuits. The harmonic balance technique bypasses the transient solution and yields only steady-state information. More details about the harmonic balance as a tutorial approach are explained in [21-22].

Fig. 4. Flow chart of the Harmonic Balance Program

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3.1 Harmonic-Balance Analysis Convergence Newton’s method is not guaranteed to converge for some cases. Methods to improve convergence have been developed:1- Norm-reduction method [23] (Yeager & Dutton,1992). * Form V(n+1)

= V(n) –  J-1  F(V)(n) V

Where  30 GHz. Design of mesfet harmonic mixers to 40 GHz. Low noise wideband amplifier design 100 MHz - 40 GHz. Harmonic balance evaluation of the large-signal behavior of active filters. Analysis and design of microwave gaas mesfet switches. Optimum design of microwave gaas mesfet attenuators. Large signal modeling of hbt power devices using the multi-layered neural network [57-58]. Intermodulation and distortion analysis of hemt amplifiers using the modified harmonic balance techniques. Optical modulation of gaas mesfet oscillator at very high modulation frequencies. Development of advanced optimizing programs for nonlinear microwave circuit design. Design and Modeling of a Dielectric Resonator-Controlled FET (HEMT) Oscillator.

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12. CONCLUSION This paper has described nonlinear programs that are computationally efficient and which can be used for the demanding application of microwave nonlinear CAD. The normal nonlinear analysis difficulties are increased in microwave applications by the inclusion of distributed elements. It has been shown that the traditional time domain method while very powerful does have shortcomings that can be supplemented by using the harmonic balance approach. The harmonic balance method has been shown to be useful for problems including disperse transmission lines and for problems where nonlinear circuit optimization is necessary. Outlines of the remaining problems, novel trends and suggestions for possible future research projects are included. REFERENCES [1]

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

[18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

M. Sobhy and A. Jastrzebski, "Computer Aided Analysis and Design of Non-linear and Large Signal Microwave Circuits", IEE Colloquium on "Microwave circuit CAD Techniques", Digest No. 1983/38, pp. 611-616, April 1983. M. Sobhy and A. Jastrzebski, "Analysis of Non-linear Microwave Circuits Using State-space Approach", ISCAS 84, pp. 1119-1122, May 1984. M. Sobhy and A. Jastrzebsik, "Direct Integration Methods of Non-linear Microwave Circuits", 15th European Microwave Conf., pp. 110-118, Sept. 1985. L. Chua, "State Variable Formulation of Non-linear LC Network in Explicit Normal Form", Proc. IEEE, Vol. 53, No. 2, pp. 206-207, Feb. 1965. L. Chua and R. Rohren, "On the Dynamic Equations of a Class of Non-linear RLC Networks", IEEE Trans. Circuit Theory, Vol. CT-12, No. 4, pp. 475-489, Dec. 1965. L. Chua and P. Lin, "Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques", Eaglewood Cliffs, N. J., Prentice Hall, 1975. P. Adby, "Applied Circuit Theory, Matrix and Computer Methods", Ellis Harwood, 1980. J. Staudhammer, "Circuit Analysis by Digital Computers", Prentice Hall. L. Kittel, "New General Approach to Commensurate Line Networks Using State Space Techniques", Int. J. Circuit Theory& Appl., pp 339-361, 1973. M. Powell, "A hybrid Method for Non-linear Algebraic Equations", in Numerical Methods for Non-linear Algebraic Equations, Ed. Robinnowits P., Gordon and Breach, 1970. "Gear’s Method for Integration of a Stiff System of First Order Ordinary Differential Equations”, Nag. Fortran Library DO2EBF. G. Hall and J. Watt, "Modern Numerical Methods for Ordinary Differential Equations". E. Choo, "Optimum Design of GaAs MESFET Oscillators", Internal Report, QUB, 1986. T. Brazil, S. EL-Rabaie, et al, "Large-Signal FET Simulation Using Time Domain and Harmonic Balance Methods", Proc. IEE. Part H, 133, No. 5, pp. 363-367, Oct. 1986. F. Filicori, "A Non-linear Microwave Circuit Analysis by Harmonic Balance Techniques", Proc. of 15th European Microwave Conf., Paris, pp. 1104-1109, Sept. 1985. M. Nakhla and J. Blach, "A Piecewise Harmonic Balance Techniques for Determination of the Periodic Response of Non-linear Systems", IEEE Trans., Vol. CAS-23, No. 2, pp. 85-91, Feb. 1976. S. El-Rabaie and J. Seeger,"An Automatic Way for linear and Nonlinear Circuit Partitioning Applicable to FET Devices", IEEE-35th Midwest Symposium on Circuits and Systems, The George Washington University, August 9-12, 1992. J. Curtice, "Nonlinear Analysis of GaAs MESFET Amplifiers, Mixers and Distributed Amplifiers Using the Harmonic Balance Techniques", IEEE Trans. on MTT., Vol. MTT-35, No. 4, April 1980. S. El-Rabaie, C. Stewart, et al., "A Novel Approach for the Large Signal Analysis and Optimization of Frequency Doublers", IEEE MTT, International Microwave Symposium, 25-27 May, pp. 119-1122, 1988, New York. B. Dixon, "Nonlinear Optimization", Wiley International, 1985. S. El-Rabaie, J. Mckeown, et al., "Optimized Microwave MESFET Nonlinear Circuits Using Harmonic Balance", IEE Colloquium on Microwave Devices, Fundamentals and Applications, Surrey Place, March 1988. S. El-Rabaie, V. Fusco, et al., "Harmonic Balance Evaluation of Nonlinear Microwave Circuits a Tutorial Approach", IEEE Trans. on Education, Vol. 31, No. 3, pp. 181-192, August 1988, H. Yeager and R. Dutton, ”Improvements in Norm-Reducing Newton Methods for Circuit Simulation”, IEEE Trans. on CAD, Vol. 8, pp. 538-546, 1989. V. Rizzoli et al, “Sate-of-the-Art Harmonic Simulation of Forced Nonlinear Microwave Circuits by the Piecewise Technique”, IEEE Trans. on MTT., Vol. 40, No. 1, pp. 12-48, Jan. 1992. R. Hicks et al, “Numerical Analysis of Nonlinear Solid State Device Excitation in Microwave Circuits”, IEEE Trans. on MTT., Vol. 30, pp. 251-259, 1982. J. Bandler et al, “Efficient Optimization With Integrated Gradient Approximations”, IEEE Trans. on MTT., Vol. 36, No. 2, pp. 444-455, 1988. S. El-Rabaie, "A CAD Package for Microwave Integrated Circuit Design", Microwave Journal, Vol. 33, pp. 275282, April 1990.

SM. El-Rabaie, “Nonlinear Simulation Methods for Active Microwave Circuits”

99

[28] S. El-Rabaie and I. Saad, "Modeling DC Characteristics of GaAs MESFET Devices Using a Simple Accurate and Analytic Tool", Electronic Letters (Vol. 26, No. 22; 25th October 1990), pp. 1992-1993. [29] S. El-Rabaie, "Limitations of Using Compact DC Models of GaAs MESFET For Large Signal Computer Calculations", IEEE Antennas and Propagation Society, International Symposium, June 19-24, 1994, University of Washington, Seattle, Washington USA. Electron Engineering Bulletin, Faculty of Electronic Engineering, Menoufia University, No. 12, pp. 25-36, July 1996. [30] I. Saad, S. El-Rabaie and N. El-Rabaie, "A Novel and Accurate Compact DC Model for Large Signal Computer Calculations", Electronic Letters, Vol. 27, No. 7, pp. 609-611, March 1991. [31] S. El-Rabaie, "An Exact Small Signal Model for HEMT Devices up to 40 GHz Applicable for the Harmonic Balance Techniques", NRSC90, Seventh National Radio Conference, Feb. 20-22, 1990, EGYPT. [32] S. El-Rabaie, C. Stewart, et al., "Computer Aided Study of the Broad Band Small-Signal Equivalent Circuit of GaAs MESFET", Int. J. Electronics, Vol. 70, pp. 863-874, 1991. [33] S. El-Rabaie, "Mixed Lumped and Distributed Models For HEMT Devices Up to 100 GHz", Electronic Eng. Bulletin, Faculty of Electronic Engineering, Menoufia University, No. 8, pp. 58-63, July 1994. [34] H. Fukui, "Determination of the Basic Device Parameters of GaAs MESFET", Bell System Tech. Journal, pp. 771779, March 1979. [35] A. Materka and T. Kacprzak, "Computer Calculation of Large-Signal GaAs FET Amplifier Characteristics", IEEE Trans. On MTT., Vol. 33, No 2, pp. 276-281, Feb. 1985. [36] Y. Tajima, B. Wrona and K. Mishima, "GaAs FET Large Signal Model and its Application to Circuit Designs", IEEE Trans. Ed. 28, No. 2, pp. 171-175, Feb. 1981. [37] S. El-Rabaie and F. Ghannouchi, "A Universal Large Signal Model for GaAs MESFET and HBT Power Devices", Proc. of the Twelfth National Radio Science Conference (NRSC’95), Alexandria, EGYPT, March 21-23, pp. (D2. 1-7), 1995. [38] R. Hajji, S. El-Rabaie, A. Kouki and F. Ghannouchi, "Large Signal Temperature Dependent DC Model for Hetrojunction Bipolar Transistors", IEE Proc.-Microwave Antennas Propagation, Vol. 142, No.5, pp. 417- 419, October 1995. [39] R. Hajji, A. Kouki, S. El-Rabaie and F. Ghannouchi, “Systematic DC/Small-Signal/Large-Signal of Heterojunction Bipolar Transistors Using a New Consistent Nonlinear Model”, IEEE Transactions on Microwave Theory and Techniques, Vol. 44, No. 2, pp. 233-241, February 1996. [40] S. El-Rabaie, “Prediction of Intermodulation Distortion in HBT Power Devices Using a Novel DC Nonlinear Model”, Electron Engineering Bulletin, Faculty of Electronic Engineering, Menoufia University, No. 11, pp. 10-24, January 1996. [41] T. Brazil, S. El-Rabaie, V. Fusco, et al., "Comparison of Computer Methods for MESFET Intermodulation Characteristics", 1988 IEEE International Symposium on Circuits and Systems, Helsinki University, 7-9 June 1988. [42] R. Gilmore, "Nonlinear Circuit Design Using the Modified Harmonic Balance Algorithm", IEEE Trans. on MTT., Vol. MTT-34, No. 12, pp. 1294-1306, Decem. 1986. [43] A. Ushida and L. Chau, "Frequency Domain Analysis of Non-linear Circuits Driven by Multi-tone Signal", IEEE Trans. CAS-31, No. 9, Sept. 1984. [44] S. El-Rabaie, "Simulation of Nonlinear Circuits Using the Modified Harmonic Balance Techniques", Microwave and Optical Technology Letters, Vol. 3, No. 1, pp. 13-17, January 1990. [45] S. El-Rabaie, S. Ibrahim and N. El-Rabaie, "Applying the Controlled Aliasing for Fast Prediction of the Output Response of Nonlinear Circuits Driven by Composite Signals", IEE Proc.-Circuits, Devices Systems, Vol. 141, No. 2, pp. 65-68, April 1994. [46] J. Dreifuss, A. Madjer, B. Engel and D. Ber-Lev, "Application of the Harmonic Balance Method for Analysis of MESFET Oscillators and Dual Gate MESFET Mixers", Proc. of 15th Equropean Microwave Conf., Paris, pp. 521561, Sept. 1985. [47] V. Rizzoli, A. Lipperini and E. Menazzi, "A General Purpose Program for Non-linear Microwave Circuit Design", IEEE Trans. on MTT-31, Vol. 9, pp. 762-770, 1983. [48] S. El-Rabaie, “An Accurate Approach For Analysis and Design of Microwave GaAs MESFET Oscillators”, Electronic Engineering Bulletin, Faculty of Electronic Engineering, Menoufia University, No. 13, pp. 62-75, January 1997. [49] M. Sohby et al, “ Direct Integration Methods of Nonlinear Microwave Circuits”, 15 th European Microwave Conf., Paris, Sept. 1985, pp. 1110-1118. [50] G. Zhao, S. El-Rabaie and F. Ghannouchi, “The Effects of Biasing and Harmonic Loading on MESFET Tripler Performance”, Microwave and Optical Technology Letters, Vol. 9, No. 4, pp. 189-194, July 1995. [51] S. El-Rabaie, "Solving Nonlinear Microwave Circuits Using F77 and C Languages on Different Computer Platforms", Electronic Eng. Bulletin, Menoufia University, No. 7, pp. 96-107, January 1994. [52] M. Stephen, Nonlinear Microwave Circuits, Artech House, 1988. [53] P. Bowron et al, “ Harmonic Balance Evaluation of the Large Signal Behavior of Active Filters”, IEE Colloquium, Dece., 1987. [54] C. Snowden et al, “ Two-Dimensional Hot-Electron Models for Short-Gate-Length GaAs MESFETs”, IEEE Trans. ED., Feb. 1987, pp. 212-223. [55] A. Aghami et al, “Power Optimization of GaAs MESFET Amplifier Using Nonlinear Modeling”, IEE Colloquium, Decem. 1987.

100

IJ-NANO Vol. 1, No.2, November 2012, pp. 77-101

[56] D. Pavlidis et al, “Analysis of the Large-Signal Characteristics of Power Hetrojunction Bipolar Transistors Exhibiting Self-heating Effects”, IEEE Trans. on MTT., Vol. 45, No. 4, April 1997. [57] F. Wang et al, “Knowledge Based Neural Models For Microwave Design”, IEEE Trans. on MTT., Vol. 45, No. 12, pp. 2333-2343, 1997. [58] K. Shirakawa et al, “A Large Signal Characterization of an HEMT Using a Multilayered Neural Network”, IEEE Trans. on MTT., Vol. 45, pp. 1630-1633, July 1997. [59] P. Rodrigues, Computer Aided Analysis of Nonlinear Microwave Circuits, Artech House, 1998, Chapter 3. [60] C. Snowden , “Large-Signal Microwave Characterization of AlGaAs/GaAs HBT’s Based on Physics-Based Electro-thermal Model”, IEEE Trans. on MTT., Vol. 45, pp. 58-71, January 1997. [61] V. Kasemsuwan et al, “A Microwave Model for High Electron Mobility Transistors”, IEEE Trans. on MTT., Vol. 45, pp. 420-427, March 1997. [62] C. Chang et al, “Very High Frequency Small Signal Equivalent Circuit for Short Gate Length Inp HEMT’s”, IEEE Trans. on MTT., Vol. 45, pp. 1014-1017, July 1997. [63] A. Parker et al, “A Realistic Large Signal MESFET Model For SPICE”, IEEE Trans. on MTT., Vol. 45, pp. 16301633, Sept. 1997. [64] H. Ghadab, F. Ghannouchi et al, “Small Signal Modeling of HBT’s Using a Hybrid Optimization/Statistical Technique”, IEEE Trans. on MTT., Vol. 48, No. 3, March 1998. [65] S. El-Rabaie, "CAD Tools For Simulation and Optimization of Linear and Nonlinear Microwave FET Circuits Up to 1995", Electronic Eng. Bulletin, Faculty of Electronic Engineering, Menoufia University, No. 13, pp. 1-22, January 1997. [66] S. El-Rabaie, “A Proposal for A Microwave Measurement Center, on the Dept. of Communication Engineering, Faculty of Electronic Engineering, Menoufia University”, August 1997. [67] B. Numo, C. Pedro, J. Wonhoon and M. Steer, "Nonlinear RF Circuits and Systems Simulation When Driven by Several Modulated Signals", IEEE Transaction on Microwave Theory and Techniques, Vol. 54, No. 2, February 2006. [68] P. Sen, H. Woods, J. Rana, et al, "Neural-Network-Based Parasitic Modeling and Extraction Verification for RF Millimeter-Wave Integrated Circuit Design", IEEE Transaction on Microwave Theory and Techniques, Vol. 54, No. 6, June 2006. [69] J. Paulo and N. Borges, "Multitone Phase and Amplitude Measurement for Nonlinear Device Characterization", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 2, June 2005. [70] Y. Hui and J. Joe, "Large-Signal Diode Modeling- An Alternative Parameter-Extraction", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 8, February 2005. [71] Ohta, A. Inoue et al, "Intermediation Distortion Analysis of Class-F and Inverse Class-F HBT Amplifiers", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 6, June 2005. [72] E. Dautbegovic, M. Condon, et al, "An Efficient Nonlinear Circuit Simulation Technique", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 2, February 2005. [73] D. Seron, C. Collado, et al, "Analysis and Simulation of Distributed Nonlinearities in Ferroelectrics and Superconductors for Microwave Applications", IEEE Transaction on Microwave Theory and Techniques, Vol. 54, No. 3, March 2006. [74] C. Pedro and N. Borges, "Designing Multisine Excitations for Nonlinear Model Testing", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 1, January 2005. [75] Raffo, A. Santarelli, et al, "Accurate pHEMT Nonlinear Modeling in the Presence of Low-frequency Dispersive Effects", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 11, November 2005. [76] G. Crupi, M. Dominique, et al, "Accurate Multibias Equivalent-Circuit Extraction for GaN HEMTs", IEEE Transaction on Microwave Theory and Techniques, Vol. 54, No. 10, October 2006. [77] Santarelli, V. Giacomo, et al, " A Nonquisi-Static Empirical Model of Electron Devices", IEEE Transaction on Microwave Theory and Techniques, Vol. 54, No. 12, December 2006. [78] A. Jarndal and K. Gunter, " A new Small-Signal Modeling Approach Applied to GaN Devices", IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 11, November 2005. [79] S. EL-Rabaie and S. Tamer, "A Graphical Approach for Evaluation of the Output Response of Severe Nonlinear System Excited by Composite Signals”, (AL AZHAR University Engineering Journal (JAUES10), Vol. 5, pp. 154162, 2010. [80] S. EL-Rabaie and S. Tamer, "Extraction Coefficients of Nonlinear Systems Excited by Composite Signals" , 2nd International Conference on Signal Processing Systems (ICSPS), Vol. 3, PP. 263-267, 2010. [81] S. EL-Rabaie and S. Tamer, “Harmonic Distortion Analysis for Nonlinear Circuits by Using Volterra Series and SPICE Software”, First International Conference on Electrical and Computer Engineering (ECSE2010), Cairo, November 1-3, 2010. [82] Rania R. Elsharkawy, Sayed El-Rabaie, Moataza Hindy, Reda S. Ghoname, and Moawad I. Dessouky, “Neural FET Small-Signal Modeling Based on Mel-Frequency Cepstral Coefficients”, 2009 International Conference on Computer Engineering and Systems(ICCE’09), Cairo, Egypt, December 14-16, 2009. [83] R. R. Elsharkawy, M. Hindy, S. EL-Rabaie and M. I. Dessouky, “FET Small-signal Modeling Using MELFrequency Cepstral Coefficients and the Discrete Cosine Transform”, Journal of Circuits, Systems, and Computers, Vol. 19, No. 8 (2010) pp. 1835-1846. [84] R. R. Elsharkawy, S. El-Rabaie, M. Hindy and R. S. Ghoname and M. I. Dessouky, “FET Small- Signal Modeling Based on the DST and MEL Frequency Cepstral Coefficients”, Progress In Electromagnetic Research B, Vol. 18, 185-204, 2009.

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[85] R. R. Elsharkawy, S. El-Rabaie, M. Hindy and and M. I. Dessouky “A New Approach For FET Small Signal Modelling Based on Cepstral Coefficients and Discrete Transforms”, International Journal of Electronics , Volume 98, Issue 3, March 2011, pp. 379-391.

BIOGRAPHY OF AUTHORS Prof. S. El-Rabaie (SM’92) was born in Sires Elian, Egypt, in 1953. He received the B.Sc. degree (with honors) in radio communications from Tanta Uni-versity, Tanta, Egypt, in 1976, the M.Sc. degree in communication systems from Menoufia Univer-sity, Menouf, Egypt, in 1981, and the Ph.D. degree in microwave Device engineering from Queen’s University of Belfast, Belfast, U.K., in 1986. In his doctoral research, he constructed a computer-aided design (CAD) package used in nonlinear circuit simulations based on the harmonic balance techniques. Up to February 1989, he was a Postdoctoral Fellow with the Department of Electronic Engineering, Queen’s University of Belfast. He was invited as a Re-search Fellow in the College of Engineering and Technology, Northern Arizona University, Flagstaff, in 1992 and as a Visiting Professor at Ecole Polytechnique de Montreal, Montreal, QC, Canada, in 1994. He is currently a Professor of electronics and communications engineering with the Faculty of Electronic Engineering, Menoufia University. He has authored and coauthored more than 120 papers and technical reports and 15 books under the titles Computer Aided Simulation and Optimization of Nonlinear Active Microwave Circuits, The Whole Dictionary for the Computer and the Internet Terminologies, Basics and Technologies of Data Communications in Computer Networks, Technologies and Internet Programming, The Distance Learning and Its Technologies on the Third Millennium, Computer Principles and Their Applications in Education, Software Engineering (Volume 1), Management of Computer Networks (Volumes 1 and 2), Advanced Internet Programming, Data-Base Principles , Building of Compilers, Software Engineering (Volume 2), and Ethics of Profession. He has participated in translating the first part of the Arabic Encyclopedia. He has been involved in different research areas, including CAD of nonlinear microwave circuits, nanotechnology, communication systems, and digital image processing. Dr. El-Rabaie was a recipient of the Egyptian Academic Scientific Research Award (Salah Amer Award of Electronics) in 1993 and the Best Researcher Award on CAD from Menoufia University in 1995. He can be contacted though e-mail: [email protected] or Mobile: (+20)0128498170