High frequency. Microwave Transistor Modeling for Time Domain Simulation TRANSISTOR MODELING. Creating a specific model. for a microwave transistor

Transcription

1 From September 2007 High Frequency Electronics Copyright 2007 Summit echnical Media, LLC Microwave ransistor Modeling or ime Domain Simulation By Firas Mohammed Ali he Polytechnic Higher Institute o Yeren High requency Creating a speciic model models o transistors are o inter- or a microwave transistor can help achieve accurate est because they have circuit simulation in the applications to computeraided design o high re- desired requency range or the user s application quency circuits. When these models are derived, a problem encountered is that measured transistor S-parameters do not agree with the hybrid- model. In this article, a simpliied method is described to obtain an optimized classical hybrid- model that predicts the measured S-parameters o the device across the desired requency band. he modeling capabilities o the CAD program ouchstone (now is incorporated with ADS) were utilized to create such a transistor model. he optimization goal is to minimize the error unction between the measured S-parameters and those o the RF transistor equivalent circuit. his technique has been implemented to obtain a high requency circuit model or the RF transistor BFY 90 across the band rom 100 MHz to 500 MHz. Such a model can be used in time-domain circuit analysis programs to predict the transistor behavior. Introduction he characterization o RF transistors is o signiicant importance at high requencies. here are, in general, two methods used to model high requency transistors: he irst one is achieved using S-parameters. In this approach, the transistor is considered as a linear two-port network and is treated as a black box regardless o the internal device elements. he S-parameters are based on the incident and relected waves at the Figure 1 A simple high requency transistor model. transistor input and output ports and can be measured easily using the network analyzer [1]. Microwave transistor manuacturers usually measure and do provide S-parameter sets at dierent requencies and DC bias points. he second technique, on the other hand, is based on the high requency equivalent circuit o the transistor. he hybrid- model is usually used to characterize the RF behavior o the BJ at high requencies. However, the model parameters are very diicult to measure and obtain accurately at such requencies. On the other hand, device data sheets rarely provide ull set o transistor internal parameters at microwave requencies. Package parasitic inductances and capacitances should also be considered because their eects may degrade the AC perormance o high requency transistors. High requency equivalent circuits are, however, very important in circuit analysis programs such as PSpice to simulate the transistor s perormance both in time and requency domains. 52 High Frequency Electronics

2 RF ransistor Models A simple linear high requency transistor model is shown in Figure 1. Basically, this is an extension o the hybrid- model with package lead inductances and resistances at the base and emitter. he requency dependence o the short circuit current gain o the transistor is given by [2]: Figure 2 Frequency characteristics o 2 and h e 2. Figure 3 ypical packaged microwave transistor model. h e he ( ) = 1 + j / β (1) Where h e is the low requency short circuit current gain and β is the cut-o requency. β can be estimated rom the model parameters: β 1 2. rc. (2) he gain-bandwidth requency can also be estimated by: β and are related by: (3) (4) he diusion capacitance o the emitter-base junction C can be approximated by: C g m. τ F (5) where τ F is the total orward transit time, which represents the mean time or the minority carriers to cross (diuse) the base region rom the emitter to the collector and is dependent on the collector current. Replacing equation (5) in (3) yields: he Computer Procedure Prior to computer optimization, an initial circuit model should be created based on the approximate equations stated previously. A good initial circuit model is necessary to ensure quick convergence within a reasonable time and at a reasonable cost. he computer procedure is shown schematically in Figure 5. he Microwave computer pro gm 2. C β = h e 1 2τ. F (6) Figure 4 he modiied hybrid- transistor model used or optimization. which means that the gain-bandwidth requency o the transistor is inversely proportional to the orward transit time. Figure 2 illustrates a comparison between the orward transducer gain 2 and h e 2 or the RF transistor. For packaged microwave transistors, parasitic inductances and capacitances play a signiicant role at microwave requencies and should be modeled accurately. Also, pieces o transmission lines should be included to model the delay in time required or signals to travel rom the terminals o the transistor package to the transistor chip as shown in Figure 3. he Simulated Model In this article, a modiied hybrid- model was adopted or computer simulation and is presented in Figure 4. his model was proposed in a previous work [3] and gave satisactory results. he model diers rom the simpliied hybrid- model o Figure 1 in two things. he irst one is the modeling o the emitter-base junction with additional RC section, while the second one is the addition o two transmission lines at the input and output to model the time delay in the signal that propagates rom the terminals o the package into the transistor chip. 54 High Frequency Electronics

3 ƒ(mhz) S 11 S 11 S 21 S 12 S 12 S 22 S able 1 he S-parameters o the transistor BFY V CE = 10V, I C = 8 ma. Figure 5 he computer procedure or model optimization. gram will irst evaluate the S-matrix o the circuit model and compare it with the measured S-parameters o the microwave transistor at each sample requency within the required band. For this purpose an error unction, which is proportional to the dierence between the measured S- parameters o the transistor and those o the circuit model, should be ormulated and minimized by the microwave circuit optimization and simulation program. his error unction may look like: o model parameters. Several trials are attempted until a satisactory value o the error unction is reached. Procedure Application he computer program ouchstone was used to create a circuit model or the RF transistor BFY 90 in the requency band rom 100 to 500 MHz. his device operates as a small signal ampliier in the VHF/UHF bands. It has a gain-bandwidth product requency o 1.3 GHz. he manuacturer s S-parameters measured at a bias point o V CE = 10 V, and I C = 8 ma are shown in able 1. Initial model parameters should be estimated prior to computer optimization. hese parameters can be calculated as ollows: g m = I C /V = 8 ma/26 mv = mho β = 100 or this device. r = β/g m = Ω. = 1.3 GHz. τ F = 1/2 = 122 ps. C = g m.τ F = 37 pf. wo pieces o transmission lines were added at input and output with Z o = 50 Ω and implemented as coaxial cables. We know that the characteristic impedance o the coaxial cable is: Z o 138 D o = ε log D r i (8) Selecting Z o = 50 Ω, D o = 8 mm, and D i = 2 mm results in a value or ε r o Other model parameters Model 2 ij ( ij ij ) Device E = w S S ij (7) Where S ij Device are the S-parameters o the actual transistor, S ij Model are the calculated S-parameters o the model, and w ij are some weighting actors. he optimization program then systematically attempts to minimize this perormance unction by varying the values o model parameters according to certain optimization technique. Upper and lower constraints can be imposed on the values Figure 6 Graph o S 21 versus requency prior to computer optimization. 56 High Frequency Electronics

4 Parameter Value Unit Parameter Value Unit Z o1 50 Ω r B 10 Ω Z o2 50 Ω r B1 20 Ω l 1 1 mm C B 2 pf l mm r E 1.78 Ω g m 1 mho C pk1 0 pf τ F 200 ps C pk2 2.2 pf C 5 pf L E 1 nh r 27 Ω L B 0.04 nh r o 9.3 kω C o 0.06 pf able 2 he inal optimized model parameters. ƒ(mhz) S 11 S 11 S 21 S 12 S 12 S 22 S able 3 he simulated S-parameters o the optimized model. were chosen arbitrarily. Ater substituting the estimated parameters or the equivalent circuit model, a rough circuit simulation was made to compare its response with the actual device perormance. Figure 6 shows a comparison between S 21 or the circuit model and that o the actual device beore computer optimization. Figure 7 Graph o S 21 versus requency ater computer optimization. he ouchstone circuit ile used in the simulation o the transistor model is presented in the appendix. Actually, ouchstone has a built-in simple hybrid- model or the BJ. his model was modiied by adding urther elements and neglecting some elements such as R µ, C µ,and r c in order to match the equivalent circuit o Figure 4. Choosing the least square error unction and the gradient optimization technique, a total o 50 iterations were required to reduce the error unction rom 10.3 to he resulting optimized values o the model elements are shown in able 2. Figure 7 shows a comparison between the orward transmission coeicient S 21 o the device and that o the optimized model across the requency band o interest. he optimized S-parameters o the circuit model are shown in able 3 and can be compared with those o the device presented in able 1. Conclusion A simple method or creating an equivalent circuit model o high requency transistors has been described and applied to build a model or the RF transistor BFY 90 across the requency band rom 100 to 500 MHz. Such a model can be used in circuit analysis programs to simulate the behavior o the RF device in the time domain as well as in requency domain. It was shown that the accuracy o the resulting model depends on the equivalent circuit chosen and on the type o the perormance error unction to be minimized. Limitations o the technique stem rom the act that the method adopted is based on the linear assumption o the RF device. I the input signal amplitude increases, some o the internal parameters may vary with signal level. his condition occurs in RF power ampliiers where the signal power level is signiicantly high. On the other hand, the high requency 58 High Frequency Electronics

5 model is derived rom one set o S- parameters at a certain operating DC bias point. his means that i the DC bias point is changed then the model will become invalid. Reerences 1. R.W. Anderson, S-Parameter echniques or Faster, More Accurate Network Design, HP Application Note 95-1, February G. Gonzalez, Microwave ransistor Ampliiers Analysis and Design, Prentice-Hall, Inc., 1984, Chapter R.G. Gough, High-Frequency ransistor Modeling or Circuit Simulation, IEEE J. Solid-State Circuits, Vol. SC-17, No. 4, August 1982, pp Author Inormation Firas Mohammed Ali is head o the Department o Electronic Engineering at he Polytechnic Higher Institute o Yeren, Libya. He has worked as a consultant engineer in commercial engineering contracts in telecommunications at Ameen Al- Immary Company or echnical Instruments, and as an external lecturer at the department o Electrical & Electronic Engineering in the College o Engineering, University o Al-Jabal Al-Gharbi, Jado, Libya. He has a BSc Degree in Electrical Engineering and an MSc Degree in Electrical Engineering/Electronics and Communication rom the University o Baghdad. He may be contacted by at irasreng@ yahoo.com. Appendix he ouchstone s circuit ile written or circuit optimization is shown below: DIM RES OH CAP pf IND nh COND /OH FREQ MHz IME ps LNG mm CK HYBPI G# # CPI# & RPI# CMU=0 RMU=1E8 RB# RC=0 RE=0 CAP 4 6 C#.1 2 5! CB RES 3 4 R# ! rb1 RES 6 7 R# ! re IND 7 0 L#0 1 2! LE IND 2 3 L# ! LB CAP 5 0 C#0.06 5! Co RES 5 0 R# ! ro CAP 2 5 C#0 0 4! Cpk1 CAP 4 5 C# ! Cpk2 COAX DI=2 DO=8 L# ER=2.76 AND=0 RHO=1 COAX DI=2 DO=8 L# ER=2.76 AND=0 RHO=1 DEF2P 1 8 RMODEL S2PA BFY90 DEF2P 1 2 DEVICE OU RMODEL DB[S21] GR1 DEVICE DB[S21] GR1 RMODEL SPAR FREQ SWEEP OP RMODEL MODEL DEVICE GRID RANGE GR High Frequency Electronics