Gain Bandwidth Limitations of Microwave Transistor

Gain Bandwidth Limitations of Microwave Transistor Filiz Güneş 1 Cemal Tepe 2 1 Department of Electronic and Communication Engineering, Yıldız Technical University, Beşiktaş 80750, Istanbul, Turkey 2 Alcatel, 5501 Reunion Point, #304, Raleigh, North Carolina 27609 Received 14 June 2001; accepted 28 February 2002 ABSTRACT: This work enables one to obtain the potential gain (G T ) characteristics with the associated source (Z S ) and load (Z L ) termination functions, depending upon the input mismatching (V i ), noise (F), and the device operation parameters, which are the configuration type (CT), bias conditions (V DS, I DS ), and operation frequency (f). All these functions can straightforwardly provide the following main properties of the device for use in the design of microwave amplifiers with optimum performance: the extremum gain functions (G T max, G T min ) and their associated Z S, Z L terminations for the V i and F couple and the CT, V DS, I DS, and f operation parameters of the device point by point; all the compatible performance (F, voltage standing wave ratio V i,g T ) triplets within the physical limits of the device, which are F > F min, V i > 1, G T min < G T < G T max, together with their Z S, Z L termination functions; and the potential operation frequency bandwidth for a selected performance (F, V i,g T ) triplet. The selected performance triplet and termination functions can be realized together with their potential operation bandwidth using the novel amplifier design techniques. Many examples are presented for the potential gain characteristics of the chosen low-noise or ordinary types of transistor. 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 483 495, 2002. Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mmce.10049 Keywords: transducer power gain; input voltage standing wave ratio; noise figure; source termination; load termination I. INTRODUCTION The characterization of active microwave devices and design of the wide-band microwave amplifiers are among major interests in communication engineering. Especially in designing microwave amplifiers, many sophisticated numerical methods are utilized to optimize system performance. Generally, the optimization is focused on the transducer power gain (G T ) over the frequency band of operation without controlling the other performance criteria such as the noise (F), the input voltage standing wave ratio (VSWR, V i ), and the output VSWR (V o ). It should also be mentioned Correspondence to: Dr. F. Güneş; e-mail: gunes@yildiz.edu.tr. that the optimization process of the performance is highly nonlinear in terms of the descriptive parameters of the system. Certainly, within the optimization process, one can easily embed the desired performance goals without knowing the physical limits and/or compromise relations among F, V i, and G T appropriately. Unfortunately, this process often fails to attain the desired goals. However, the complete performance characterization of a microwave transistor overcomes all the above-mentioned handicaps. In this work the upper (G T max ) and lower (G T min ) gain bounds are easily obtained for the chosen noise F F min and V i 1 pairs point by point in the operation domain of the transistor. Furthermore, one can have all the interrelations among the performance 2002 Wiley Periodicals, Inc. 483

484 Güneş and Tepe Figure 1. A neural block diagram of the gain bandwidth limitations of a microwave transistor. measure components F, V i, G T for determined bias conditions (V DS, I DS ) and operation frequency ( f ) condition set. These can give all the necessary information to design a microwave amplifier with optimum performance because the F, V i, and G T can be determined only by the active devices in the amplifier circuits with the lossless and reciprocal matching circuits. Two approaches can be followed in the utilization of the (F, V i, G T ) triplet and the Z L, Z S functions in the design of the microwave amplifier circuits: 1. Only the (F, V i, G T ) triplet function can be employed to provide the reference values over the predetermined bandwidth to the optimization process of the element parameters of the front- and back-end matching networks that was recently applied and completed by Aliyev [1]. 2. In the second approach only the Z S, Z L termination functions can be employed in the design of the front- and back-end matching networks, respectively, to obtain the corresponding performance (F, V i, G T ) triplet over the predetermined bandwidth. Yarman and Aksen [2] recently completed an immitance-based tool to model passive one-port devices by means of Darlington equivalents. On the other hand, it is well known that modeling problems of the behaviors of linear and nonlinear elements and circuits in RF and microwave systems are very complicated and large scale. Therefore, in the last few years artificial neural network techniques have been developed and applied to the RF and microwave areas as the solution methods for these types of problems [3 5]. This work can be described in three main stages (Fig. 1): In the first stage the signal and noise behaviors of the small-signal transistor are modeled by a multiple bias and configuration, signal noise neural network so that the scattering (S) and noise (N) parameters can result from the output of this neutral network as the functions of the configuration type (CT), the V DS, I DS, and the f. This part of the work can be considered as the function approximation through the neural network technique, and it includes highly accurate approximations of the eight scattering and four noise functions [6, 7]. The second stage consists of determining the compatible performance (F req, V i req, G T req ) triplets and their associated source (Z S req ) and load (Z L req ) terminations. In this part of the work the performance characterization theory of the transistor is employed, the details of which are given in [8] and [9] using, respectively, the impedance [8] and scattering parameter [9] approaches. The input of the second block is the S and N parameters resulting from the signal noise neural network, and the free variables of F req F min, V i req 1, and G T min G T req G T max. The second block results in the following triplet and termination data in the operation domain of the device: Freq, V i req, G T max N Z S max R S max jx S max ; Z L max R L max jx L max ;

Gain Bandwidth Limitations 485 Figure 2. A two-port model of a small-signal microwave transistor. F req, V i req, G T min N Z S min R S min jx S min ; Z L min R L min jx L min ; F req, V i req, G T req N Z S req R S req jx S req ; Z L req R L req jx L req. The third stage of the work is to obtain the gain bandwidth limitations of a small-signal microwave transistor, depending on the other performance components F, V i in the operation domain (CT, V DS, I DS ). The originality of the work presented in this article is essentially based upon this final stage of the work. The motivation underlying this is mainly to put forward new design methods based upon active device characterization for microwave amplifiers. These methods can employ the resulting (F, V i, G T ) triplet or Z L, Z S termination functions in the design of microwave amplifiers in narrow, medium, or broad bands, so that the optimization processes can be applied in a more deterministic and analytical manner [10]. In the next section the performance characterization of the device is briefly considered as the center of the gain bandwidth limitations. II. COMPATIBLE PERFORMANCE (F, V i, G T ) TRIPLETS AND (Z S, Z L ) TERMINATIONS A. Two-Port Representation of Microwave Transistor and Performance Measure Functions All the performance (F, V i, G T ) triplets and their source Z S R S jx S and load Z L R L jx L terminations can be obtained from simultaneously solving the following three nonlinear performance equations in the operation domain of the active device: F S/N i F R S/N S, X S F min O R N Z opt 2 Z S Z opt 2 R S ; input VSWR V i V i R S, X S, R L, X L 1 i 2 1 i 2, G T P L P AVS G R S, X S, R L, X L (1) i Z S Z* i Z S Z i ; (2) 4R S R L z 11 Z S z 22 Z L z 12 z 21 2. (3) The solution subsets {Z S, Z L /R S 0, R L 0} in which we are interested are the sets that ensure stable working of the transistor within its physical limitations: Re Z i 0, Re Z O 0; (4a) G T min G T G T max, V i 1, F F min. (4b) Figure 2 presents a two-port representation for a transistor with its impedance ( z) and noise parameters. The V I equations of the transistor can be written in the form V 1 V 2 z 11 z 12 z 21 z 22 I 1 I. (5) 2

486 Güneş and Tepe Furthermore, the termination equations and the Z i and Z o impedances of the transistor can be given as V 2 I 2 Z L, V 1 V S I 1 Z S ; (6) All the source Z S R S jx S terminations that satisfy V i (R S, X S, R L, X L ) V i req for a fixed passive load Z L take place on the circle of Z S Z cv r v, Z i V 1 I 1 z 11 z 12z 21 z 22 Z L ; Z o V 2 I 2 z 22 z 12z 21 z 11 Z S. (7a) (7b) where Z cv is the center phasor and r v is the radius of Z cv 1 i 2 i 1 i 2 R i jx i, r v 2 1 i 2 R i. (9) The problem of the physical limitations can be described as a mathematically constrained extremum problem, which is to find the extremum stable values of the function G{R S, X S, R L, X L } subject to 1 F req F(R S, X S ) 0, 2 V i req V i (R S, X S, R L, X L ) 0, and the corresponding values of the source and load terminations Z S R S jx S, Z L R L jx L, where F req F min, V i req 1 are the required noise figure and the input VSWR, respectively. Here an analysis based on a geometrical method [8, 9] is employed to solve this constrained extremum problem. The fundamentals of this geometrical method are given in the following subsection. B. Performance Characterization Here all the possible (F req, V i req, G T ) triplets and their (Z S, Z L ) terminations are determined using z parameters in the Z S and Z i planes. Noise Figure, Input VSWR, and Gain in Z S Plane. The variations of the noise figure, input VSWR, and gain in the Z S plane can be briefly described. All the source Z S R S jx S terminations that satisfy F{R S, X S } F req take place on the circle of Z S Z cn r n, (8a) where Z cn is the center phasor and r n is the radius, which can be given as Z cn R opt N jx opt, r n N N 2R opt, (8b) where N F req F min 2R N Z opt 2. (8c) So all the Z s values satisfying the other required components of performance, V i req and G T req, must be chosen among the Z s values on the F F req noise circle. A V i V i req circle corresponds to a constant gain circle for a fixed load Z L, which can be expressed using eqs. (2) and (3) as G T 1 i 2 R L R i z 21 2 z 22 Z L 2. (10) Therefore, only the required noise and the input VSWR circles are sufficient to be taken into account in the Z S plane. As already shown, while the required noise circle is fixed in the Z S plane the required input VSWR circle can travel, depending on the load impedance Z L, via the input impedance Z i in a manner given by the center and radius relations in eq. (9). Thus, the following situations are possible: these circles may not touch, they become tangential, or they cut each other (Fig. 3). In the following section, each of these positions is controlled from the Z i plane. Solution Regions and Control Parameter Z i. The solution regions in the Z i plane are now briefly summarized (Fig. 4). Because both the external and internal tangential positions are the transition positions between the solution and no-solution positions, these positions must first be controlled from the Z i plane via the following general equation in the Z S plane: Z cn Z cv 2 r n r v 2. (11) Substituting the Z cn, r n, Z cv, r v expressions in eqs. (8a), (8b), and (9) into the above equation, another couple of circle equations that represent the two different tangent positions of the noise and the input VSWR circles in the Z S plane can be obtained in the Z i plane. The center phasors Z ct1, Z ct2 and radii r t1 and r t2 of the circles, which are the mappings of the external and internal tangent positions in the Z S plane, respectively, can be given as follows: Z ct1 R cn U r n V jx opt, r t1 Z ct1 2 Z opt 2 N T 1 circle region 2 ; (12)

Gain Bandwidth Limitations 487 Figure 3. The positions of the input VSWR circles with respect to the noise circle in the Z S plane controlled by the regions in Figure 4. Z ct2 R cn U r n V jx opt, r t2 Z ct2 2 Z opt 2 N T 2 circle region 4 (13) where U and V are given by U 1 i 2 1 i 2, V i 1 i 2. (14) As seen from eqs. (12) and (13), the centers of the T 1 and T 2 circles lie on the same imaginary axis, (X opt ), and it can also be proved that circle T 2 is always situated inside circle T 1 without touching as shown in Figure 4. All the Z i values ensuring intersection positions of both the noise and input VSWR circles in the Z S plane are situated in region 3 between the T 1 and T 2 circles in the Z i plane, which is shown in Figures 3 and 4. The remaining regions numbered 1 and 5, which are the outermost and innermost regions, respectively, are impossible solution regions that include Z i values controlling all the nontouching positions in the Z S plane (Figs. 3, 4). In order to find physically realizable solutions, the unconditionally stable working area (USWA) and the gain circles constrained by the V i req must also be constructed in the Z i plane, so the design configuration will have been formed in the Z i plane. Gain Circles in Z i Plane Constrained by Input VSWR. The constant gain circles constrained by the V i req can be formed using eq. (10), which is different for the two stability cases. In the unconditional stability case, the necessary and sufficient conditions can be given as r 11 0, r 22 0, and 2r 11 r 22 r z ; (15a) where r ii Re z ii, i 1, 2; z z 12 z 21 r jx. (15b) In the absolute stability case, all the passive impedances can be employed as either source or load terminations and the USWA is the area inside the G T 0 circle. The center phasors Z cg R cg jx cg and

488 Güneş and Tepe Figure 4. case. The solution geometry of the constrained maximum gain for the unconditional stability radii r g of the gain circles in this stability case can be expressed in terms of z parameters, G T, and i 2 as follows: Z cg 1 1 Q P j 2x r 22 r 11 r 22 x ; 22 r g 1 r 22 P 2 2QP z 2 ; (16a) (16b) P z 12 2 G T 1 i 2, Q 2r 11 r 22 r. (16c) It can be seen from eqs. (16a) (16c) that R cg decreases with the increase of G T req G T max when X cg remains constant (Fig. 4) and the G T max is only achieved at the point where the r g equals zero. Setting r g to zero in eq. (16b) gives G T max Q Q 2 z 2 1 i 2 z 12 2, (17) which is only achieved when the device is absolutely stable; otherwise the square root in (17) becomes negative because conditions are given by (15a) and (15b). The Z i max input impedance providing G T max can be found by substituting (17) into (16a) as follows: Z i max Z cg max R cg max jx cg, R cg max 1 r 22 Q 2 z 2. (18) The minimum gain limit circle is the G T 0 circle N input stability circle whose center phasor Z cg min R cg min jx cg min and r g min can be given as follows:

Gain Bandwidth Limitations 489 Figure 5. Constant gain circles in the Z i plane for a conditionally stable transistor. R cg min Q 2r 22, X cg min X cg, r g min z 2r 22. (19) Because Q is greater than z for the absolutely stable device, R cg min is greater than r g min, which results in the G T 0 circle being entirely in the right half of the Z i plane with the positive real part and enclosing all the circles for G T 0 (Fig. 4). In the case of the gain circles of the conditionally stable transistor, the USWA is the region between the input and conjugate source stability circles. The constrained gain formula eq. (10) can be rearranged in terms of the radius and center of the source plane stability circle as Z i 2 2 R cs S R i 2X cs X i Z cs 2 r 2 s 0, (20) where S z 12 2 G T 2r 22 1 i 2, (21) where Z cs R cs jx cs and r s are the center and radius of the source plane stability circle, respectively, which can be written as follows: R cs 2r 11r 22 r 2r 22, X cs 2x 11r 22 r 2r 22, r s Z 2r 22. (22) Thus, the center Z cg R cg jx cg and the r g of the gain circle family will be

490 Güneş and Tepe plane (shaded area in Fig. 5), and the center phasors of these circles are always on the line X i X cs.it should be noted that in the case of unconditional stability, all the G T circles are situated entirely in the right half of the Z i plane. In the conditionally stable case, the maximum gain will be obtained on the arc of the conjugate stability circle remaining in the positive real Z i plane. It can be found by substituting R cg R cs in eq. (23). Referring to eq. (22), the maximum gain subject to the V i can be expressed for the conditional stability case as G T 2 1 i 2 z 12 2 2r 11 r 22 r ; (24) and, setting i 0, eq. (24) yields the maximum stable gain (MSG), where is the stability factor, MSG 2 z 21 z 12, (25) 2r 11r 12 r. (26) z For conditionally stable cases, it has values between zero and unity (0 1). Figure 6. The G T max variations for the NE38018 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] R cg R cs S, X cg X cs, r g S 2 2SR cs r 2 s. (23) The features of the G T circles, which can be derived from eqs. (20) (23), can be ordered (Fig. 5). All G T circles cut the imaginary axis at the same points, which are the intersection points of the conjugate of the source plane stability circle with the same axis. The G T 0 circle, whose center is Z cg min R cs jx cs with r g min r s, is symmetrical with the conjugate of the stability circle with respect to the imaginary axis. The G T max G T 0 circles always take place in the area bounded by the G T 0 circle and the arc of the conjugate of the stability circle remaining in the right half of the input impedance C. Design Configuration and Performance (F req, V i req, G T req ) Triplets Using the performance theory given briefly above, for a small-signal transistor with the given operation conditions and the required noise F req and V i req, the basic performance measure function given by eqs. (1) (3) can be represented in a geometrical configuration in the Z i plane. This configuration may be called the design configuration, which consists of the USWR, the T 1 and T 2 circles, and the constrained gain family. In this design configuration all the physically possible (F req, V i req, G T ) triplets of the microwave transistor must take place in the intersection areas of possible solution regions 2, 3, and 4 with the USWA of the transistor. Therefore, no physical solution can exist for the G T constrained by the F req and V i req when the USWA takes place completely in region 1 or 5. The determination processes for the required (F req, V i req, G T ) triplets with G T min G T G T max among the infinite number of possible triplets are again based on the geometrical analyses [8, 9], depending on the type of design configuration.

Gain Bandwidth Limitations 491 Figure 7. The G T max f curves for the NE02135 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] A compact computer program was completed in [11] to obtain all the physically possible (F req, V i req, G T ) triplets and the (Z S, Z L ) terminations as functions of the device operation parameters CT, V DS, I DS, and f. These functions can be employed in the manufacturer s data sheets of the transistor to give full information to the designer of the active microwave circuits. The next section focuses on the constrained gain characteristics. Then the gain bandwidth limitations are determined, depending on the other performance components (F req, V i req ), operation conditions (CT, V DS, I DS, f ), and the magnitude of the gain itself. of I D 10 ma and the same values of the other performance components (V i req, F req ). In the second step the effect of noise on the gain performance is given by the G T max f curves at III. POTENTIAL GAIN CHARACTERISTICS For the potential gain characteristics, three typical microwave transistors are employed. Two of them are low-noise application transistors (NE38018 and NE329S01); the other is an ordinary transistor (NE02135). Thus, the characteristics can be discussed in three steps. In the first step the effect of the bias condition on the gain performance is given by G T max (db) I D (ma) characteristics at F req 0.5 db; V i req 1, 1.5, and 2; f 1 GHz for NE38018 [Fig. 6(a)]. Concerning these curves, for an efficient gain performance the transistor must have a bias current (I D ) that is greater than a certain I DT value, and the effect of change in the input mismatching is around 1 db at most. In Figure 6(b) the G T max (db) f(ghz) characteristic is given for the same transistor at a reasonable value Figure 8. The [F min ( f ), 1.2, G T max ( f )] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

492 Güneş and Tepe Figure 9. The termination functions of the [F min ( f ), 1.2, G T max ( f )] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience. wiley.com.] V i req 1.5, V CE 10 V, and I C 5 ma and various noise levels from 2 to 4.5 db for the NE02135 transistor (Fig. 7). From these curves it can be concluded that the noise acts essentially as a band-limiting factor on the gain performance of the transistor. In the third step the characteristics in Figures 8 13 are basically gain frequency characteristics belonging to the various (F, V i, G T ) triplets for the low-noise, high quality NE329S01 transistor biased at V CE 2V and I C 10 ma and with an operation bandwidth of 2 18 GHz. Figure 8(a,b) gives variations of the minimum noise figure and the maximum gain with respect to the frequency, and Figure 9(a,b) gives the corresponding source and load terminations. The constraints for the gain are that F req is equal to the minimum noise figure F min at each f and V i req is 1.2. It should be noted that there are no stable gain solutions at the first three frequencies of 2, 3, and 4 GHz; the stable gain performance starts at the operating frequency of 5 GHz. The source Z S ( ) and load Z L ( ) terminations for the constant gain level of 10 db for the same constraints are given in Figure 10(a,b). Again in this case, unstable gain performances are met at the frequencies of 2, 3, 4, and 18 GHz, so the operation band is between 6 and 17 GHz. Figures 11 and 23 provide graphics of the triplets [0.46 db, 1, G T max ( f )] and Z S ( ) and Z L ( ) termination functions, respectively. In this case the input port is completely matched and F req is taken as a constant 0.46 db; various bands of operation can be considered as the design applications of the narrow-, medium-, and broad-band circuits. The final curves in Figure 13(a,b) give the Z S ( ) and Z L ( ) functions for the (0.46 db, 1, 12 db) triplets. As seen from Figure 13(a,b), the Z S ( ) and Z L ( ) functions provide an operation with the parameters of G T 12 db, V i 1, F 0.46 db over the band of 2 11 GHz and cannot go further because of the unstable operation. IV. CONCLUSIONS The contributions of the theory for the performance characterization of an active device to circuit theory are given in detail in [8] and [9]. The importance of this work is particularly focused on the design aspects of active microwave circuits. In fact, the core of the work can essentially be briefly given as the neural block diagram in Figure 1. As seen from this diagram, the output is the possible performance (F req, V i req, G T ) triplets with G T min G T G T max and their

Gain Bandwidth Limitations 493 Figure 10. The termination functions of the [F min ( f ), 1.2, 10 db] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] associated source (Z S req ) and load (Z L req ) terminations as the functions of the device operation conditions, which are sufficient to completely characterize the potential performance features of the active device Figure 11. The [0.46 db, 1, G T max ( f )] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] for linear amplification. These output functions can provide the straightforward fundamental information necessary for the design of a microwave amplifier with optimum performance, which can be ordered as follows: the extremum gain functions G T max, G T min and their associated Z S, Z L terminations for the V i and F couple and the CT, V DS, I DS, and f operation parameters of the device point by point; all the compatible performance (F, V i, G T ) triplets within the physical limits of the device, which are F F min, V i 1, G T min G T G T max, together with their Z S, Z L termination functions; and the potential operation frequency bandwidth for a selected performance (F, V i, G T ) triplet. Thus, the designer is able to instantly know: the optimum bias conditions V DS, I DS ; the available stable gain dynamic between G T min and G T max for the required F req, V i req couple, depending on the f; the compromise relations among the F, V i, and G T ; the selection of the performance (F, V i, G T ) triplet using the compromise relations; the operation frequency bandwidth that the device is capable of giving for the selected (F, V i, G T ) triplet;

494 Güneş and Tepe Figure 12. The termination functions of the [0.46 db, 1, G T max ( f )] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience. wiley.com.] Figure 13. The termination functions of the [0.46 db, 1, 12 db] triplets for the NE329S01 transistor. [Color figure can be viewed in the online issue, which is available at www.interscience. wiley.com.]

Gain Bandwidth Limitations 495 and the Z S, Z L termination functions over this potential frequency bandwidth. Finally, this work gives the potential gain performance of a microwave transistor, which depends on the input mismatching, noise, and device operation parameters. In other words, these are the limitations for the gain performance that the designers can reach by realizing the source Z S ( ) and load Z L ( ) terminations. In this respect, by combining the novel optimization processes and termination data modeling with this work, new design techniques can be generated for microwave amplifiers. The most important feature of these new techniques is expected to be that the optimization will be processed on deterministic and analytical bases so that efficient and high speed communication systems can be realized. REFERENCES 1. I. Aliyev, Design of the microwave amplifier using the performance (F, V i, G T ) triplets, M.S. thesis, Yıldız Technical University, Science Research Institute, Istanbul, November 2001. 2. B.S. Yarman and A. Aksen, An immitance based tool for modelling passive one-port devices by means of Darlington equivalents, Int J Electron Commun 55 (2001), 443 451. 3. Q.J. Zhang and K.C. Gupta, Neural networks for RF and microwave design, Artech House, Norwood, MA, 2000. 4. M. Vai, S. Vu, B. Li, and S. Prasad, Creating neural network based microwave circuit models for analysis and synthesis, Proc Asia Pacific Microwave Conf, Hong Kong, December 1997, pp. 853 856. 5. Y. Harkouss, J. Rousset, H. Chehade, E. Ngoya, D. Barataud, and J.P. Teyssier, The use of artificial neural networks in nonlinear microwave devices and circuits modeling: An application to telecommunication system design, Int J RF Microwave CAE 9 (1999), 198 215. 6. F. Güneş, F. Gürgen, and H. Torpi, Signal noise neutral network model for active microwave device, IEE Proc Circuits Devices Syst 143 (1996), 1 8. 7. F. Güneş, H. Torpi, and F. Gürgen, A multidimensional signal noise neural model for microwave transistor, IEE Proc Circuits Devices Syst 145 (1998), 111 117. 8. F. Güneş, M. Güneş, and M. Fidan, Performance characterisation of a microwave transistor, IEE Proc Circuits Devices Syst 141 (1994), 337 344. 9. F. Güneş and B.A. Çetiner, A novel Smith chart formulation of performance characterisation for a microwave transistor, IEE Proc Circuits Devices Syst 145 (1998), 1 10. 10. F. Güneş and B.S. Yarman, Potential broadband characteristics of a microwave transistor and realization conditions, 2000 PIERS Progress in Electromagnetics Research Symposium, Cambridge, MA, July 5 14, 2000, pp. 8 15. 11. C. Tepe, Modelling and performance analysis of a microwave transistor using neural network, Ph.D. Thesis, Yıldız Technical University, Science Institute, Istanbul, 2000. BIOGRAPHIES Filiz Güneş received her M.S. degree in electronic and communication engineering from Istanbul Technical University in 1972. She attained her Ph.D. degree in communication engineering from Bradford University, London, in 1979. She worked as a Research Fellow at the same university between 1979 and 1983 with contracts from the European Space Agency and British Defence Minister in the areas of the propagation and electromagnetic compatibility. Since 1983 Dr. Güneş has been with Yıldız Technical University, where she is currently a full Professor and head of the Electromagnetic Fields and Microwave Technology Group. Her current research interests are in the areas of multivariable network theory, device modeling, computer-aided circuit design, microwave amplifiers, microwave filters, broad-band matching circuits, monolithic microwave integrated circuits, and electromagnetic compatibility. Cemal Tepe received the B.S. and M.S. degrees in electronics and communication engineering from Istanbul Technical University in 1991 and 1994, respectively. He acquired his Ph.D. degree in communication at Yıldız Technical University in 2000 in Istanbul. Dr. Tepe is currently working as a Software Designer for Alcatel, a telecommunication company in Raleigh, NC. His research interests include microwave device and circuit modeling and analysis, neural networks, and computer-aided design of telecommunication networks.