An analytic technique

Transcription

1 From June 2010 High Frequency Electronic Copyright 2010 Summit Technical Media, C An Analytic and Graphical Method for NA Deign with Feedback By Alan Victor, Nitronex Corp., and Jayeh Nath, Aviat Network An analytic technique and figure- Thi article explore the trade-off between gain, of-merit (F nm ) for match and noie figure in a the trade-off of noie low noie amplifier, reulting in a new figure-of-merit lo in the deign of low meaure and mimatch for electing the value of noie amplifier i preented. The trade-off ource inductance between variou deign parameter a a function of inductive ource degeneration i evaluated uing the developed deign curve. It i hown that the deign curve are unique to the elected device. Several device demontrated condition whereby the ue of ource degeneration lead to intability and mut be avoided. The technique i traightforward and permit precreening of potential device being conidered for low noie amplifier deign. The reulting deign curve permit accurate election of the range of acceptable feedback value to achieve deired performance. A new figure-ofmerit ha been introduced which allow deigner to chooe the optimum value of ource inductance either analytically or graphically. The new methodology i dicued and wa applied to low noie peudomorphic hetero-junction FET (ph-jfet) amplifier deign at 2.10 GHz and GHz. I. An Overview of Deign Technique Noie figure, available gain, and return lo or the port VSWR are key element in low noie amplifier deign. ow noie figure without adequate gain or poor return lo degrade ytem performance. High gain without adequate noie figure alo compromie ytem performance. Optimizing the input noie figure of an active tage, irrepective of the impedance preented to the ource, preerve the noie figure, however at the expene of other parametric value. For example, high port VSWR can lead to exceive paband inertion lo when filter are ued, a in a preelector deign, or can reult in exceive group delay ditortion. Conequently, although the noie figure may be excellent, the ytem performance can uffer ignificantly. Sytem performance i degraded due to an increae in inter-ymbol interference and lack of decoding enitivity. Noie meaure [2] wa introduced a a figure-of-merit tying together two key component in amplifier deign, noie figure and gain. The noie meaure M i defined a: M = (F 1)/(1 1/G a ) (1) Where F i the noie factor (numeric noie figure) and G a i the numeric amplifier available gain. The goal i to minimize the noie meaure, that i achieve a low a noie figure a poible while maximizing the amplifier available gain. The deired reult i to minimize econnd tage noie contribution in a cacaded ytem. In addition, although not part of noie meaure, thi hould be achieved with a low port VSWR. Mimatch lo and exceive input VSWR for an individual amplifier noie figure i not an iue. A necearily high input VSWR could be required to meet a pecific Editor note Thi article i an extended verion of the paper [1] that received the Bet Student Paper award at the 2010 IEEE Wirele and Microwave Technology Conference (WAMICON). 16 High Frequency Electronic

2 amplifier noie figure target. However, the impact on cacaded ytem performance might be compromied. Mot filter deign are enitive to mimatch lo, which affect both electivity and out of band rejection a well a paband repone. High port VSWR lead to additional noie figure degradation a well a ytem ditortion. Therefore, a technique which lead to NA deign that achieve low input and output VSWR and low noie meaure imultaneouly i highly deirable. The noie figure of a ingle tage amplifier i a function of the output impedance of the ource attached to the input terminal of the tranitor. The value of the ource impedance which correpond to a noie figure near the minimum noie figure, F min, i uually different from the ource impedance required for conjugate match. Therefore, the input matching network can be tuned for either low VSWR or low noie but not both. Available gain contour and noie contour when plotted on the Smith Chart allow aement of the trade-off between a good match and low noie figure [3]. In addition, input and output VSWR circle are overlaid allowing the deigner to evaluate the mimatch lo. Thi proce i tediou. Noie meaure contour, where the noie and gain contour are combined were introduced in [4] to implify the deign proce. One technique for achieving an acceptable tradeoff i by judiciou choice of load impedance. Modification of the load impedance alter the input impedance. If properly choen, the load impedance will permit the ource impedance to lie cloe to the optimum noie impedance. Thi technique, uing an optimization function [5] baed on the noie meaure, permit a modet improvement in performance. However, noiele feedback uing a reactive component in conjunction with load termination adjutment provide further improvement. Graphical technique may be ued in the proce for both adjutment; load termination modification and erie feedback [6]. Thi technique permit the real part of the input impedance to be driven in the direction coincident with the optimum noie impedance through erie feedback while imultaneouly achieving low input VSWR. Thee two degree of freedom ait the deigner by permitting the real part of the input impedance to be modified readily. The relationhip between the input reflection coefficient of the active two-port and the applied load termination i a bilateral tranfer function and i given by equation (2). Reflection feedback for the active device i provided by S21S12Γ S 11 = S S Γ 22 whereby the S-parameter of the two-port are modified by (2) the choice of Γ, the load reflection coefficient. The reflection feedback in conjunction with the two-port ph-jfet erie ource feedback lead to a coherent deign technique for optimizing the noie figure and the input VSWR at a ingle frequency. Serie ource inductive feedback modifie the S-parameter of equation (2). Finding the compoite S-parameter et i traightforward by converion of the active device S-data to Z parameter and adding the matrix et term for term. The compoite et of S-data i ubequently applied in equation (3). Setting the deired input reflection coefficient equal to the optimum noie reflection coefficient yield Γ where the S-parameter of the active two-port and the determinant of the S-matrix, Δ, are function of the erie feedback inductance,. The optimum noie input reflection coefficient i defined a Γ* on [7]. We can achieve the deired input conjugate match point and optimum noie match point through the appropriate load reflection coefficient, Γ provided by equation (3), if it exit. Thi may be achieved a goe to zero. However, thi i achieved provided the magnitude of the required load reflection i within the boundary of the unit Smith chart. The deired input conjugate match point and optimum noie match point, it if exit, can be achieved through the appropriate Γ provided by equation (3). Thi can be accomplihed without the ue of erie inductive feedback if the condition S ( ) = 22 > 1 * Γon S11 * S Γ Δ 22 S12S21 S Γ * on ( ) ( ) ( ) on 11 with i met. If not, then erie inductance feedback i required. The contraint of equation (3) i readily met, and the deign of the load termination and erie feedback i done concurrently to arrive at a uitable Γ ) uing equation (2). Unfortunately, erie feedback may lead to intability. Therefore, additional deign parameter mut be introduced. Multiple amplifier deign parameter uch a tability factor, noie meaure, and return lo may be handled analytically. However, the inight afforded by analytic technique i limited and an intuitive undertanding of the trade-off between port VSWR, available gain, and the noie figure veru actual feedback inductance veru frequency i not evident. A a reult, the deign i typically turned over to a CAD tool for optimization. However, it i poible to recat the noie meaure equation and the mimatch circle a a function of feedback inductance explicitly. Uing Γ ( ) < 1 (3) (4) 18 High Frequency Electronic

3 Figure 1 Simplified ph-jfet input model with erie inductive feedback and load termination. thi technique noie meaure and mimatch lo a function of feedback inductance are plotted for a pecific device. The deign curve readily demontrate whether the feedback i degenerative or regenerative for the choen device. Furthermore, a new figure-of-merit (FOM) i defined and plotted for the given device that clearly highlight an optimum value for feedback. The minimum value in the plot of figure-of-merit i ued to obtain the optimum value of feedback inductance which allow the bet trade-off of noie meaure, mimatch lo, and avoid intability. A review of the feedback technique and equation for variou parameter i preented in the next ection and an explanation of poible regeneration i highlighted. In Section III, comparion of imulation reult uing the new technique with optimized reult decribed in [6] i preented. Finally, in Section IV, experimental reult and comparion of meaured and imulated data i preented. II. Circuit Deign A implified ph-jfet model i hown in Figure 1 and i ued for analyi. Mimatch lo i ued a a metric to gauge the match between the ource impedance and the amplifier port impedance. The lo i derived directly from the two-port tranducer gain for a paive network. For thi cae, S 21 = S 12 = 1, S 11 = S 22 = 0, and the mimatch lo i given by M = 2 2 ( 1 Γx ) 1 Γy 1 ΓΓ ( ) x y 2 The reflection coefficient, Γ x and Γ y provide a meaure of the port relative to the ource and the load. In the context of thi deign work it would be the optimum noie reflection coefficient, either Γ on or Γ om function of noie meaure or noie figure repectively, and the actual input (5) Figure 2 The real input impedance of Figure 1 i either poitive or negative with frequency and i dependent on the active device parameter, the load termination, and the erie feedback reactance. reflection coefficient of the device, Γ in. In thi work the emphai i in applying Γ om. Stability of the network i aeed by oberving the real part of the input impedance, Z 11, between the gate ource terminal with load termination Z. If the gatedrain capacitance i abent or ufficiently mall, the erie inductance feedback will provide degeneration, while erie capacitance provide negative real input impedance. However, adding ufficient gate-drain capacitance and the appropriate load impedance Z, will lead to negative real input impedance for the cae of erie inductance. Figure 2 demontrate the real part of Z 11 for a variety of aigned parameter of Figure 1. A broad frequency range of negative input reitance i upported and i both active device and termination dependent. The variation illutrated in Figure 2 are obtained with the load impedance, Z and the erie feedback alway inductive. In addition C g, C gd and g m are contrained within a typical range for mall low noie FET device. Writing an expreion for the real part of the input impedance, Re(Z 11 ) with an inductive load impedance Z, and feedback C gd preent, we get: Re Z, ( 11 [ ω ]) = ]) = gm C + C g gd ω 2 ( ) g C Z C + C m gd ( g gd ) gmz + Cg ( + Z) The imaginary component i part of the input match and i tuned out, while three ignificant real component remain. The firt poitive real component lead to degeneration and the ability to alter the input impedance in a (6) 20 High Frequency Electronic

4 Figure 3 (a) Noie Meaure, M ), (b) Mimatch o, M ), and (c) Figure-of-Merit (FOM), F nm ) for FHX04X a function of. [1] Figure 4 Available Gain, G a (olid line) and tability factor, k (dahed line) v. for FHX040X, (a) and (c) and NE4210S01, (b) and (d). [1] noiele manner. A econd negative real component lead to regenerative feedback. However, if Z i appropriately modified it i poible to achieve conditional tability, aiting in matching the input and the output, and reducing the port VSWR. The noie meaure, M ), and available gain, G a ), a a function of feedback inductance, can be obtained explicitly. The reflection coefficient, Γ om ) and Γ in ) are the optimum noie meaure and input reflection coefficient repectively with a load termination Γ obtained from Z. The available gain i calculated with ource reflection coefficient et equal to the optimum noie reflection coefficient, Γ )= Γ om ). Converion of device S-parameter to Z-parameter allow the addition of the erie impedance. The modified S-parameter, G a ) and M ) are combined for calculation. The expreion for M developed in [8] i coupled to conjugate-mimatch-lo ratio or input VSWR to create a new figure-of-merit and deign curve inherent to a particular device. Although the minimum value of M i invariant to feedback, M i not. In thi application the input VSWR track the input impedance preented to the device for minimizing the noie meaure, along with the actual input impedance which i a function of the device S-parameter and the load impedance. Uing [8] and [9] noie meaure M ) i derived a function of the ource inductance. The invere mimatch lo a function of i hown in equation (7) [3]: M ( ) = 2 ( 1 Γom ( ) Γin ( )) 1 Γ 1 Γ ( ) 2 2 ( ( om ( ) )) ( in ( )) A new figure-of-merit F nm ) i introduced and defined a the product function of noie meaure, M ) and mimatch lo, M ), both function of. (7) Fnm ( ) = M( ) M( ) For the bet trade-off of noie meaure and mimatch lo, F nm ) mut be minimized. Thi lead to the optimum value of which can be obtained either graphically or analytically. III. Comparative Reult The data for the HEMT device FHX04X optimized in [6] wa ued for comparion with imulation reult obtained uing the propoed technique. Invetigation i conducted at a frequency of 10 GHz. The trade-off of noie meaure and mimatch lo i evident in Figure 3(a) and 3(b). The new figure-of-merit i plotted a a function of ource inductance and a minimum occur for a value of 250 ph; ee Figure 3(c). Thi repreentation of the benefit of feedback i complementary to that on the Smith chart. In addition, it i eaier to interpret than the technique uing tranducer gain and load admittance plane preented in [10]. Next a et of S- parameter baed on a feedback inductance of 250 ph i collected and the matching network deigned and compared to the cae where optimization function are employed, a dicued in [6]. Although the gain i lightly lower at 10.2 db, the NF i identical and noie meaure difference i le than The output match i exact and the input VSWR i le than 1.7:1, a 5 db return lo improvement. Comparative reult are highlighted in Table 1. The available gain a a function of ource inductance i plotted in Figure 4(a) for FHX040X and in Figure 4(b) for NE4210S01 (from NEC Corp.). For the latter device the feedback become regenerative above 200 ph and gain increae exponentially while available gain contin- (8) 22 High Frequency Electronic

5 Table 1 Comparion of imulation data baed on Ref. [4] v. the analytic technique outlined in thi work. ue to decreae monotonically for the former. The tability factor, k, i plotted in Figure 4(c) and 4(d). A een in 4(d) the feedback i initially degenerative but turn regenerative above 200 ph. Separate calculation of tability factor, k, i not neceary if the new figure-of-merit, F nm, i ued for deign. Thi i evident from Figure 3(c) and 5(c), a a ignificant rie and a teep lope in the function i noted. IV. Deign and Experimental Verification The low cot ph-jfet, NE4210S01 dicued in the previou ection wa ued in a common ource configuration. The S-parameter and noie figure data from the device dataheet at 10.0 GHz and 10.5 GHz were interpolated to obtain the data at GHz (ee Table 2) and ubequently utilized in a MathCAD cript to create appropriate network baed on theory preented in ection III. The input and output termination were elected after a review of the plot for noie meaure and conjugate input mimatch lo, ee Figure 5(a) and 5(b). The figure-of-merit for thi device i plotted in Figure 5(c). Thi how that the optimum value of ource inductance i 130 ph, which wa choen for deign for bet trade-off of noie meaure and return lo. If optimum noie match i ued, NF i 0.44 db. While the output match i perfect, the input VSWR under thi condition i 2.8. Uing the technique outlined in thi work, NF i traded off with mimatch lo and i lightly higher at 0.67 db. The input termination force an output termination which, if elected, allow a perfect output match. Intead, thi output termination i ued only to re-calculate a new input reflection coefficient which i ubequently matched. The reult i a minimal hift in the noie meaure M but a ignificant drop in input mimatch lo. The output match i acrificed lightly. The device wa mounted on a 30 mil thick Roger Table 2 S-parameter (MAG/ANGE), noie figure, optimum input reflection coefficient and F min in db at GHz. Figure 5 (a) noie meaure, M ), (b) mimatch lo, M ), and (c) figure-of-merit (FOM) F nm ), for NE4210S01 a function of [1]. Figure 6 Tet Set up for noie figure and gain meaurement at GHz [1]. RO4350B laminate and wa biaed at a V dq of 2 V and I dq of 10 ma with a et of bia tee. External tuner matching wa ued and the device wa degenerated by uing the package lead inductance and a PCB pad with three additional 40 mil via. Meaurement device reference plane wa located at the lead bend in an SO1 package. ead extenion beyond both ource bend added to the deired inductance. The ource lead were oldered to a pad and located within 40 mil of the three ground via. A ground via fence wa located both above and below the device. The tet etup and a cloe-up of the device under tet (DUT) are hown in Figure. 6. Meaured VSWR how an excellent input match and an output VSWR le than 1.5:1, ee Figure 7. In imulation, the reflection coefficient i held contant over a High Frequency Electronic

6 Figure 7 Comparion of meaured (olid) and imulated (dahed) input and output VSWR v. frequency. The minimum value occur at a ource inductance of approximately 130 ph. In imulation, the reflection coefficient i held contant. [1]. Figure 8 Comparion of meaured (olid) and imulated (dah) available gain and noie figure v. frequency. In imulation, the reflection coefficient i held contant. [1] Figure 9 Three tage cacaded amplifier with erie degenerative feedback in each tage. MHz bandwidth around a center frequency of GHz and doe not emulate the tuner repone over the meaured band. Simulation how a NF of 1.37 db acro the bandwidth of interet when corrected for 0.7 db fixture lo. Noie figure (NF) meaurement wa ingle ideband (SSB) uing a down converion mixer-filter centered at GHz. Bia tee, tuner lo, and econd tage contribution lo were accounted for in NF meaurement. Although input reflection coefficient i held contant in imulation, meaured NF how good agreement, ee Figure 8. Gain meaurement doe not account for tuner and bia lo of 3.2 db. Simulation therefore i offet by thi lo for purpoe of comparion. The inertion gain i 10 db and i in good agreement with imulation at the center frequency, ee Figure 8. Stability wa monitored uing a directional coupler and pectrum analyzer at GHz. Adjutment of the amplifier for bet input return lo at band center reulted in the lowet noie figure. Any readjutment of the input tuner degraded the Figure 10 Cloe-up of one of three amplifier incorporating erie feedback. The 3-tage cacade provide 46 db of available gain at 2.1 GHz with 0.54 db noie figure. noie figure meaurement. The technique dicued wa alo applied to cacaded amplifier tage at 2.1 GHz, ee Figure 9. Dicrete inductive feedback wa added to each of the FET ource a hown in detail in Figure 10. Iolator applied at intertage location were added to facilitate noie figure meaurement of the cacade uing an extended manual Y- factor meaurement method [11]. Minimization of the merit function lead to individual noie figure of le than 0.5 db. Although the input return lo wa excellent, better than 20 db return lo, the output return lo wa le than 10 db. The output return lo wa ubequently improved and the input return lo degraded while till maintaining an optimum input noie termination. Each port return lo wa et to 15 db and a cacade of three tage wa readily completed. The final cacade gain i 46 db while providing a noie figure total of High Frequency Electronic

7 db which included econd and third tage noie figure contribution. Summary and Concluion A new analytic technique and a figure-of-merit for optimizing the feedback inductance for degeneration in a low noie amplifier were dicued. The plot of noie meaure and mimatch lo together erve a a valuable guide in optimizing the deign and avoiding intability. The plot of the figure-of-merit enable the election of optimum inductance. The well etablihed approach to noie matching, working from the input ide of the amplifier to the output can potentially be improved. A a proofof-concept an X-band NA wa deigned and meaured. The output termination wa choen firt baed on the optimum noie meaure and input reflection coefficient and the information from the deign curve a a function of feedback inductance. The output match degrade lightly but the input match i perfect. The noie meaure increae minimally, demontrating the deired trade-off. Reference 1. A. Victor, and J. Nath, Simultaneou Input Power Match and Noie Optimization Uing Feedback, Proc. IEEE Wirele & Microw. Tech. Conf., Apr H. A. Hau, and R. B. Adler, Optimum Noie Performance of inear Amplifier, Proc. IRE, Aug. 1958, pp G. Gonzalez, Microwave Tranitor Amplifier Analyi and Deign, Prentice Hall, H. Fukui, Available power Gain, Noie figure, and Noie Meaure of Two-Port and Their Graphical Repreentation, IEEE Tran. Cir. Theory, vol. 13, no. 2, Jun.1966, pp K. W. Eccleton, Port-Match Optimization of Microwave ow-noie Amplifier, Microw. Opti. Techn. ett., vol. 27, no. 5, Dec. 2000, pp R. E. ehmann and D. D. Heton, X-Band Monolithic erie feedback NA, IEEE Tran. Microw. Theory Techn., vol. 33, no. 12, Dec. 1985, pp Maataka Mitama, Hidehiko Katoh, An Improved Computational Method for Noie Parameter Meaurement, IEEE Tran. Microw. Theory Techn., vol. 27, pp , June C. R. Poole, and D. K. Paul, Optimum Noie Meaure Termination for Microwave Tranitor Amplifier, IEEE Tran. Microw. Theory Techn., vol. 33, no. 11, Nov. 1985, pp H. Javan, Noie Meaure for Optimum Broadband Deign, IEE Proc. Cir. Dev. Sy., vol. 138, no. 1, Feb. 1991, pp J. Engberg, Simultaneou Input Power Match and Noie Optimization Uing Feedback, in Proc. Eur. Microw. Conf., Oct 1974, pp A.M. Victor, and M.B. Steer, Improved Y factor meaurement uing the econd tage contribution to advantage, IEEE 65th ARFTG Conference Diget, Spring Author Information Alan Victor i currently a Principal RF Engineer at Nitronex Corporation. He received the BSEE degree from the Univerity of Florida, the MSE degree from Florida Atlantic Univerity and recently received a PhD from North Carolina State Univerity. Dr. Victor ha everal international patent in communication circuit and hi main interet are in low noie circuit, power ocillator, and the application of ferroelectric material. He can be reached at: amvictor@ncu.edu Jayeh Nath received the BE degree (with honor) in electronic and communication engineering from the Birla Intitute of Technology, India, and the PhD degree in electrical engineering (with a minor in material cience and engineering) from North Carolina State Univerity. Preently, he i with Aviat Network where he i involved with product deign and development in field of RF/microwave communication. Hi main reearch interet include the deign, characterization, and modeling RF and microwave device and ytem, electromagnetic deign and modeling, meaurement and calibration technique, integrated paive, and 3-D packaging.