FDTD Analysis of Distributed Amplifiers Based on the Fully Distributed Model

Transcription

1 FDTD Analysis of Distribute Amplifiers Base on the Fully Distribute Moel R. Mirzav 1, A. Abipour 1 A. A. Shishear 1 Amirkabir University of Technoloy, E.E. Department, Microwave/mm-wave & Wireless Communication Research Lab. Hafez Avenue, Tehran, 15914, Iran, (+98) Sharif University of Technoloy, Dept. of Electrical En., Azay ave., P.O. Box: , Tehran, IRAN. rmirzav@aut.ac.ir, abipour@aut.ac.ir, shishear@ee.sharif.eu. Abstract - In this paper a wave approach has been introuce to stuy the performance of a istribute amplifier. The time omain response of a FET is obtaine by means of the fully istribute moel. By applyin the proceure to a pi-ate GaAs MESFET, the S matrix is compute from time omain results over a frequency rane of -0 GHz. Scatterin parameters of ate rain lines are extracte from three-imensional FDTD simulation. The result obtaine by this wave approach is compare with evice lumpe moel Quasi static approach of transmission line. Keywors: istribute amplifier, istribute moel, MESFET, Finite-Difference Time-Domain, scatterin parameter 1. Introuction Distribute amplifiers (also known as travelinwave amplifiers) were first presente by Ginzton [1]. The extensive research evelopment efforts have been mae with reat success in broab communication systems various applications that require wieb amplification with oo phase linearity []. In early 80 s, istribute amplifiers were successfully implemente as monolithic microwave interate circuits (MMIC s), which inspire a new wave of exploration, incluin stuy of theory esin uielines [3], noise analysis [4], application of new evices new circuit techniques [5]. Recently, istribute amplifiers have also been implemente in state-of-art silicon technoloies [7]. The strenth of a istribute amplifier resies in its ability to eliver, from a iven evice technoloy, a ain-bwith prouct not easily achievable by other circuit confiurations. The basic principle of istribute amplification overcomes the limitations relate to finite ainbwith prouct by parallelin evices so that their ate rain capacitances are absorbe into artificial transmission lines. The amplifier can be esine to ive a flat, low-pass response up to very hih frequencies. Althouh the combination of time-omain fullwave solution, throuh FDTD metho, eneral lumpe-system simulator woul enable reat flexibility in complex system esin analysis [8], accurate perfect analysis of a transistor is the main step in overall analysis of the microwave circuits containin them. Recent evelopments in mm-wave applications of FETs em more attention on moelin problem for their future application. The performance of a three couple active line structure actin as a typical transistor can be investiate by usin ifferent methos. Several moels capable of escribin the operation of a transistor such as the lumpe semi-istribute moels have appeare in the literature [9], [10] [11]. It is obvious that each moel applies to a certain rane of frequency. At hih frequencies, where the imension of the transistor becomes comparable to the wavelenth, avance methos accountin for wave propaation alon the ate-with irection are neee. The most eneralize accurate approach is the Full-wave metho. Unfortunately this metho is time-consumin causes an aitional complexity in the solvin process. The analysis of the transistor at hih frequencies leas us to evelop the semi-istribute moel. The istribute moel is a moifie version of the slice moel (semi-istribute moel) obtaine by increasin the number of sements to infinite. In the semiistribute moel, a eneral response is achieve by cascain the limite sements that consist of elements in which scalin metho is use [1]. On the other h, in the istribute moel obtaine from quasi TEM assumption, the KVL KCL are applie to the equivalent circuit. The selection of the best moel is a traeoff between proceure complexity response accuracy. Usin the istribute moel in comparison with slice moel will have an ability to increase frequency rane. Also in this technique loain effects as an external parameter coul be investiate.. AMPLIFIER DESIGN AND ANALYSIS A istribute amplifier is mae up of a series of active evices cell istribute between two

2 transmission lines. A schematic representation of a four section FET istribute amplifier is shown in Fi.1. The resultant transmission lines are referre to as the ate rain lines. The lines are couple by the transconuctances of the FET s. An RF sinal applie at the input en of the ate line travels own the line to the terminate en, where it is absorbe. The equivalent ate rain transmission lines are shown in Fi.. In esinin microwave istribute amplifiers, it is usually esirable to achieve the maximum ainbwith prouct allowe by the selecte transistor. Basic esinin equations are: ln( A / A ) N opt = (1) A A 1/ n n( A + A ) / m ( R01R0 ) sinh[ ( A A )] e () A = ω 1/ ω 1/ 1 [1 + ( ) ] [1 ( ) ] sinh[ ( A A )] ω ωc N opt where is the optimal number of sections A is the manitue of the voltae ain of sinle amplifier stae. R 01 R 0 are the characteristic resistances of the ate rain lines, A A are the attenuations ω per section on the ate rain lines, finally c ω are the raian cutoff frequency of lines, respectively [3]. The example amplifier has been optimize to obtain: 4-18 GHz frequency b S1 > 10 B S11 < -10 B S < -10 B Usin FETs with lumpe element values as: C s =0.1pF, C =0.033pF, C s =0.005pF, m =0.08s, R s =1.77Ω, R s =31Ω GateWith=80μm 3. FDTD Analysis.1 Three-Dimensional FDTD Analysis To have an accurate simulation for a istribute amplifier, transmission lines must be simulate scholastic, so three-imensional FDTD is selecte for this part of simulation. The FDTD metho is formulate by iscreitin Maxwell's curl equations. Scatterin parameters of ate rain lines are extracte from three-imensional FDTD simulation usin follow equation. i F. T. { E z } Sij = (3) F. T. E j { } z Fiure 1: Schematic of FET istribute amplifier Fiure : Gate transmission line. Drain transmission line.. The FDTD Formulation for FETs A typical layout of millimeter-wave FET is shown in Fi. 3. The propose evice consists of three couple electroes fabricate on a thin layer of GaAs, supporte by a semi insulatin GaAs substrate. In the propose moel each unit sement is ivie into two parts, active passive, whose elements are per unit lenth. The passive part escribes the behavior of the transistor as a three passive couple line the interaction between them. The active part relates to the star performance of a FET, which in this paper is moele by a linear circuit. Fi. 4 shows the two parts of one sement of the three couple microstrip line. The current-voltae ifferential equations that escribe the moel of Fi. 4 coul be written as follows:

3 Fiure 3: 3D structure of FET use in millimeter wave frequency. Fiure 5: The schematic of a pi-ate FET incluin parasitic elements. The transistor has a μm ate which is V V biase at s = 3 I ma s = 10. The inuctances capacitances shown in Fi. 5 inicate the effects of bounin. The element values use in the istribute moel are shown in Table. I. Fiure 4: The ifferent parts of a sement in the istribute moel (with linear moel for the active part) I V + ( C + Cp + Cs + Cp) ( C t I V + ( C + Cp + Cp) ( C + C t V I I + R I + L + Lm t t V I I + R I + L + Lm t t V + Cp) + mv + GsV t V V ) + Cs t t p (4) (5) (6) (7) The above equations are obtaine with rear to the effect of parasitic elements. Now a proper technique shoul be selecte to solve the ifferential equations. One of the best numerical methos which can be chosen is FDTD technique. The FDTD technique seeks to approximate the erivatives in obtaine equations with rear to iscrete solution points efine by the spatial temporal cells. By incorporatin the terminal conitions we can reach to the recursive equation system of whose solvin ives time omain response of ifferent iscretize noes. Extenin the problem to nonlinear istribute moelin in the future research raisin the accuracy of response are the main reasons for this selection. The primary iea of usin FDTD technique is taken from [14]. Table 1: Numerical values of istribute moel elements V s = 3 V I, s = 10 ma The istribute moel elements Numerical Values (per unit lenth) C s.771 nf/m C s.0178 nf/m C.1178 nf/m m S/m R i.00 ohm/m L 780 nh/m. L 161 nh/m L m 360 nh/m C p 9.6 ph/m C p 148 ph/m C p 9 ph/m R 900 ohm/m R ohm/m C pk.036 pf/m C pk.096 pf/m l pk.766 nh/m.868 nh/m L pk The Pi-ate structure can be known as a two-port network as shown in Fi. 6. The S parameters of the transistor are compute over a frequency rane of -0 GHz (fi. 7). 4. Result In this work we consier a Pi-ate MESFET transistor suitable for low-noise applications. The schematic of the propose transistor incluin parasitic elements is shown in Fi. 5. The en of each electroe is suppose to be open. This confiuration can be specifie by an S matrix (with the source is roune at all points). Fiure 6: The equivalent network for obtinin the scaterin parameter.

4 -3 Fiure 8: Gate Drain lines topoloy Equivalent wave moel -4-5 Transmissions -6 B Reflection Coefficients Fiure 7: Scatterin parameters of FET S11 S, S1 10 S1 Topoloy of the Gate Drain lines for transmission line moelin with FDTD is shown in fi. 8. As we can see couplin between lines can be consiere much accurate results are achieve. The S parameters of this six-port evice (fi. 8) are compute for frequency rane of -0 GHz usin (5) as shown in fi. 9. Finally a istribute amplifier with four FET has been esine, simulate optimize. In first simulation the lumpe moel for FETs Quasi static approach for transmission lines is consiere (see Fi. 10). The secon simulation uses S parameters of the transistor Quasi static approach for transmission lines as shown in Fi.11. A comparison between ifferent approaches is shown in Fi. 1. The results show that ifference between ifferent approaches will be important at hiher frequencies. B Fiure 9: Scatterin parameters of transmission line structure Transmission Reflection coefficients Isolation between ports Fiure 10: Schematic of istribute amplifier consierin lumpe moel of FETs Quasi static approach for transmission lines

5 Fi.14. Schematic of istribute amplifiers, consierin FDTD approach applie to Transmission Lines FETs (B) S Fi.15. Result of optimize istribute amplifier for ifferent approach Consierin lumpe moel for FETs Quasi static approach for transmission lines Consierin wave approach base on FDTD concept for FETs Full wave approach for transmission lines 5. Summary In the present paper a FDTD approach has been introuce to stuy the performance of a istribute amplifier. Comparison of the results obtaine by wave approach those of evice lumpe moel quasi static approach of transmission line, show that at hiher frequencies, we shoul employ wave approach. References [1] E.L. Ginzton, W.R. Hewlett, J.H. Jasber, J.D. Noe, "Distribute amplification.", Proc. IRE, VOL. 36, pp , Au [] T. Won, Funamentals of Distribute Amplification., Artech House, [3] J.B. Beyer, S.N. Prasa, R.C. Becker, J.E. Norman, G.K. Hohenwarter, "MESFET istribute amplifier esin uielines.", IEEE Trans. Microwave Theory Tech., VOL. 3, NO. 3, pp 68 75, Mar [4] C.S. Aitchison, "The intrinsic noise fiure of the MESFET istribute amplifier.", IEEE Trans. Microwave Theory Tech., VOL. 33, NO. 6, pp , June [5] W. Kennan, T. Anrae, C.C. Huan, "A 1-18 GHz monolithic istribute amplifier usin ual-ate GaAs FET s.", IEEE Trans Electron Devices, VOL. 31, NO. 1, pp ,, Dec [6] R.Khosravi, A.Abipour, "A new wave approach for sinal noise moelin of microwave/mmwave FET base on Green's function concept,",int. J.Electronics, Taylor & Francis Lt, VOL. 90, NO. 5, pp , 003 [7] B.M. Ballweber, R. Gupta, D.J. Allstot, "A fully interate GHz CMOS istribute amplifier.", IEEE J. Soli-State Circuits, VOL. 35, NO., pp 31 39, Feb [8] Wenquan Sui, Time-omain computer analysis of nonlinear hybri systems, CRC press, 00. [9] A.Abipour, A.Pacau, "Complete slice moel of microwave FET's Comparison with lumpe moel experimental results", IEEE Trans. Microwave Theory Tech., Vol. 44,NO. 1, pp. 4-9, Jan [10] M.Waliullah, S.M.El-Ghazaly, S.Goonick, "Lare-sinal circuit-base time omain analysis of hih frequency evices incluin istribute effects", IEEE MTT-S Di., pp , 00. [11] S.J.Nash, A.Plazker, W.Struble, "Distribute small sinal moel for multi-finere GaAs PHEMET/MESFET evices", IEEE Symp. Microwave Millimeter-Wave Monolithic Circuit, pp. 19-, [1] G.Morai, A.Abipour, A.Ghorbani, F.Farzaneh, "Sinal noise analysis in slice moel of a FET mixer", n Int. Conf. Microwave & Millimeter-Wave Tech., pp. 5-8, 00 [13] K.S. Yee, "Numerical Solution of Initial Bounary Value Problems Iinvolvin Maxwell s Equations in Isotropic Meia", IEEE Trans. Ant. Prop., Vol. AP-14, pp , [14] J.A.Roen, C.R.Paul, W.T.Smith, S.D.Geney, "Finite-ifference-time-omain analysis of lossy transmission lines", IEEE Electroma. Compat., vol. 38, NO. 1, pp. 15-4, Feb [15] A.Taeb, A.Abipour A.Mohammai, "FDTD analysis of lossy couple transmission lines loae by nonlinear evices", Asia Pacific Microwave Conference, (APMC 05), China, Vol. 5, pp , Dec [16] E.Onareau, R.G.Bosisio, M.Aubour J.Obreon M.Gayral A non-linear istribute moelin proceure of FETs, Int. Journal Numerical Moelin, Vol. 6,pp , [17] N.O.Saiku, Numerical techniques in electromanetics, CRC Press LLC, Secon Eition, 001.