Gain and Noise Boundaries for NFmin or Unity SWRout

Gain and no.se Boundaries for NFmin or concurrence SWRoutFullCharacterizationofGainand zero(prenominal)seBoundariesforNFmin or ace SWRout carrying outM. R. M. Rizk1,4, Ehab Abou-Bakr*,2, A. A. A. Nasser3, El-Sayed A. El-Badawy1 and Amr M. Mahros1,5Abstract-For a receiver sub-block, Low Noise Amplifier (LNA) is the first stage after the receiving antenna and as a key wrench, its amplification and make noise send off (NF) affects the whole performance of the receiving part. In this paper we present a adept pictorial visualization in terms of name, standing wave balance (SWR) and noise for a GaAs HJ-FET electronic transistor in twain direct cases i)NFmin, ii) Unity SWRout. The set of curves and contours presented volition provide the useer with enough visual info about the transistor operating boundaries and will also visually countenance on choosing the appropriate coordinated points for a wideband deed agree to the desired (GT,SWR) for case (i) and (GT,SWRin,NF) for case (ii). Numerical recitations argon disposed for for each one operating case and verified via a microwave circuit externalize softwargon package to demonstrate the adequacy of the proposed interpretical techniques. The resolvings from dissemblings compargon favorably with the visually estimated determine.INTRODUCTIONIntroducing a wide-band LNA with acceptable noise variant and pile up depends mainly on choosing a suitable transistor1, 2, 3, 4. Several successful techniques dedicate been developed in the literature to develop discrete transistors with super economic crisis NF and high associated gain 5, 6, 7, 8, 9, 10, 11. Different challenging techniques have been use to at the aforesaid(prenominal) time get high gain, low noise figure, good input and railroad siding co-ordinated and un go overal stability at the lowest accomplishable stream draw from the amplifier. In 1982, Yarman et al.12 introduced a software based non-linear pick outimization regularity bas ed on their procedural simplified real relative absolute frequency technique. This contrive procedure is applicable to broadband multistage FET amplifiers with no decisions to be make in advance. It was more efficient and accurate than other available heel modes to fulfill the most optimum gain and SWR over a predefined bandwidth. This method was later widen by Perennec et al.13 to optimize the noise figure in parallel with the gain and mismatch. Capponi et al. 14, expressed the performance of LNA in input twin(a) condition by analyzing the Combined noise-SWR using the general curve family condition for a given active device. The determination of the required input/ issue terminations of the active device was explained in 15 when the power gain, noise figure, and input and product mismatch constraints are placed on the amplifier. Bengtsson et al. 16 devised a novel SWR mental test procedure for GaN-HEMT devices. In 17, the operation conditions of a selected high technology transistor were used on the typical human body configurations to find a compromise relations amidst the gain, noise figure for the output port matching. Recentely graphical methods along with optimization methods for describing the full capacity of the selected transducer under a given set of noise figure and SWR constrains are discussed in 18, 19, 20.Received visualize* Corresponding author Ehab Abou-Bakr (emailprotected). force of Engineering, Alexandria University, Alexandria, Egypt.The Higher Institute of Engineering and Technology, El-Behera, Egypt.Faculty of Engineering, Arab Academy For Science Technology and Maritime Transport, Alexandria, Egypt.SmartCI, Alexandria University, Alexandria, Egypt.University of Jeddah, Jeddah 21432, Saudi Arabia.The (noise, gain, SWR) triplets tolerate be expressed on the Smithchart as circles on both the source and pervert reflection coefficient planes 21, 22. Choosing matching points on the Smithchart based on the variations of gain ci rcles radii reflects on the noise/SWR performance of the whole amplifier circuit. Pre-Knowledge of the transistors full capacity with respect to gain, SWR and noise could facilitate the choice of the correct part for the targeted design goals.In this paper, two cases of design restrictions are taken into consideration i) NFoperation, ii) harmony SWRout. For each of these cases, a formed data base is used to create sets of boundaries for the transducer gain GT and NF that will reveal the full operating capacity o the selected transistor. Visual filling of the desired performance is possible and parentage of the appropriate matching points for single frequency or wideband operation is made simple.The selected active device for our investigation is the GaAs HJ-FET transistor NE3210S01 from Renessa Electronics 24. The transistor is potentially unstable at VDS= 2V, ID= 10mAin the frequency rage below 8.6 gigahertz 26, 27. So, by conducting the investigation in a bleed above this fre quency (9-12) gigacycle per second, no additional circuit atom is required to drive the transistor to its conditional stability region. As a result, the (NFmin) and their agreeing (opt) provided in the manufacturer datasheet are used directly without some(prenominal) modifications. More intermediate dataset that is not provided in the datasheet, is used in our investigation. This was possible by using the interpolation option provided by the Advanced send off Systems (ADS) from Keysight technologies 25.This manuscript is organized as follows Numerical example and simulation curb are presented in section.2 for demonstrating the usage of the graphical gain boundaries and the imposing of SWR on them for NFmin operation. In section.3, the idea of correlating noise, gain and SWR on a single graph using NF boundaries are presented and aided by another numerical example. The demonstration is discussed in section.4.GAIN BOUNDARIES FOR NFMIN OPERATIONAll the basic formulas used in the presented analysis is listed in Table.1.In 22, three expressions for the gain are provided. These are the transducer gain (GT), the available gain (GA) and the operating power gain (GP). The design of a microwave amplifier requires utilizing one or more of these gain criteria to clutches the required design goals. Graphically, all the previously mentioned types substructure be correspond as circles on the Smithchart. However, choosing which gain type to use in the design, depends on the transistor type and the required design criterion.+j1.0+j0.5GP circles+j2.0+j0.2+j5.00.0-j0.2As the rung CP increases, the Value of GP decreases-j5.0-j0.5-j2.0-j1.0Figure1.For NFmin operation, Different operating gain circles obtained by ever-changing the GP factor in (15)Table1.Basic equations used in the analysis in-C1 = S11 S-(10)b=SGA1 inSgA=2(11)out-S21b=L(2)g C-1 outLCP=P 2(12)S12S21S1 + gP(S222 2)in= S11 + 1 S (3)IPS12S21SrP=22out= S22 + 1 S (4)1 + gP(S22)(13)SWR= 1 + a(5)in1 aC2 = S22 S- (14)GPSWR= 1 + b(6)out1 bgP=S21(15)2GT=1 S21 sS112S2121 L21 Lout2. (7)1 S112 S222 + 22S21S12(16)CA=gAC-(8)G= S21I21 + gA(S112 2)IPmaxS12(KK 1)(17)1 2KS21S12gA+ S12S212g2NF = NFmin+4rnSopt2(18)rA=1 + gP(S11(9)2 2)(1 S2)1 + opt2(b)Figure2.Distribution of SWRout over operating gain circles for NFmin operation at 12 gigahertz a) A 3D portrayation with small cheer of SWRout displayed in lighter color, b) A plane view of the same figure with actual value of SWRout on the color bar.2.1. Imposing SWR on GT Boundaries for a Wideband, NFmin OperationConsidering the above choices, the bilateral property of the Device Under interrogatory (DUT) disfavor the usage of GT circles. Also, targeting a NFmin operation forces S=optand this prevents the usage of GA circles. As a result, GP circles in the L plane of the Smithchart were used.16141212 GHz11 GHz 10 GHz9 GHz1086 Maximum attainable GTMinimum attainable GT21212.51313.51414.51515.51616.5 run gain (G )PFigure3.GT vs. GP, where GTmin GTGTmax r egions for frequencies 9,10,11,12 GHz are shown in solid and dotted lines respectively.For a certain frequency of operation, changing the value of the GP factor in (15) will produce varied circles for the operating gain as shown in Figure.1. Each point on the circumference of these circles dally a unique value of Lthat can be used for matching according to the desired design goals. For further stripping of the device capabilities, SWR related to these values can be imposed on these circles. For illustration, only the SWRout levels are imposed in Figure.2 where lighter color regions represent lower values of SWRout. Although these are the desired regions to build our design around. However, for a wideband operation, reaching the required GT could prevent choosing matching points from these regions.Since S=optfor a NFmin operation, a graphical relation (GT vs. GP) will provide a pre- design information about the limitation of the selected transistor. Figure.3 explains this by speci fying GTmin GTGTmax over a couch of GP for the selected frequency points, the solid lines represent GTmax while the dotted lines correspond to GTmin . In fact a database was constructed for this figure that contain all values of Ls that correspond to each GP value. Later on, this database will be actually useful in choosing appropriate matching points for wideband operation. A immediate look to the figure revels that if targeting a wideband operation the desired GT should not exceed GTmax of the highest frequency. For example, the transistor cannot achieve GT higher than 12.73 dB for a selected frequency of 12 GHz.However, designing for a suitable SWRin and SWRout requires further correlation between GT and SWR. This is shown in Figure.4 where visual predication of the device operating boundaries are clear. The constructed database is extended by masking the contours of both SWRin and SWRout on the GT boundaries at NFmin operation. Since lighter colors indicate better values of SW R, it is obvious that for this particular transistor, the SWRin and SWRout are worsened for lower frequencies. Also, the direction of the color stripes are diagonal for SWRin and plain for SWRout, this is an indication that, for this particular transistor, choosing an appropriate GP and its subsequent Ls could result in a constant value of SWRin along the entire bandwidth.As an example to emphasise on using Figure.3 to design a wideband LNA operating at its NFmin, a targeted 12.7 dB is chosen for illustration in the extend of 9-12 GHz. From Figure.4, the color contour reveals that the minimum SWRout=1 corresponding to this GT level belongs to a 12GHz operation. Then, the accompanying Lpairs for frequencies 9,10,11,12 GHz are fetched for matching purpose as shown in Figure.5(a). The displayed Lpairs on the smith chart of Figure.5(b) were used by ADS to construct matching circuits to verify the expected SWR. the obtained simulation results are listed in Table.2 and compares favourab ly with those listed in Figure.5(a).163516501430122512 GHz 11 GHz 10 GHz 9 GHz1020815141212 GHz10811 GHz10 GHz4540359 GHz302520661510104455212 12.5 13 13.5 14 14.5 15 15.5 16 16.5 SWRinOperating gain GP(a)212 12.5 13 13.5 14 14.5 15 15.5 16 16.5 SWRoutOperating gain GP(b)Figure4.Imposing the contours of both SWRin and SWRout on the GT boundaries at NFmin operation,for SWRin and b) for SWRout+j1.0+j0.5+j2.0+j0.212 GHz11 GHz 10 GHzGHz+j5.00.011 GHz(a)-j0.29 GHz-j0.5GHz-j1.0(b)-j2.0-j5.0Figure5.a) Extracting the vestigial Lpairs from the constructed database for the shown selected point of operation according to the targeted GT ans SWR, b) Smithchart representation of the extracted L pairsNF BOUNDARIES FOR A UNITY SWROUTFor the condition of an output conjugate matching (ie. L=-), GA= GT and a unity SWRout isproduced. All values of Sthat corresponds to a particular GA circle gives the same value of SWRin.This is shown in Figure.6 where a contour of SWRin is imposed on GA= GT circles. T he tip of the conein Figure.6(a) corresponds to Spoint that will produce a coincidental conjugate match (ie. S=- L=-) where (SWRin= SWRout=1).However, this figure alone cannot correlative the (GT,NF,SWR)triplets to give a full visualization insight of the device capability in this case of operation.GT, SWRin and NF Correlation for SWRin=1Figure.7(a) illustrate the variation of SWRin along a range of GA= GT values where at SWRin=1, a synchronal conjugate matching occurs. The data in Figure.7(a) alongside GA= GT values and their corresponding NF are used to construct a database to help plotting the NF boundaries shown in Figure.7(b). For a SWRout=1 operation, this figure can be used to visually predict both NF and SWRin for any targeted GT. Since, the marked points on the plot represent SWRin=1 for each selectedTable2.ADS simulation data results after individually matching the IMN and OMN according to the matching points in Figure.5(a).FreqGTNFminNFSWRinSWRout9GHz12.7420.310.312.472 3.07310GHz12.7100.320.322.4382.31911GHz12.7510.330.332.4341.86912GHz 12.760 0.34 0.34 2.379 1.033 (b)Figure6.3D representation of SWRin over a range of GA=GT circles a) Isometric view, b) Plan viewfrequency, it is visually clear that a SWRin= SWRout=1 is impossible for a wideband, apartment gain design.For a wideband, flat gain operation with SWRout=1.Figure.7(b) reveals that GT flat max=GT max 12GHz is the maximum value of GT to attain a flat gain throughout the bandwidth. Thepreviously constructed database can be used to fetch S, Lthat will produce the visually targeted(GT, SWRout, NF) triplets from Figure.7(b). As an example, a targeted wideband operation (9-12 GHz)with GT=13.9 dB is chosen for demonstration, Figure.8 present the underlying S, Lfor the visuallyselected point. this point was selected to give the targeted GT for a simultaneous conjugate matchingat 12 GHz with NF1.4 dB. the source and load matching points for the selected frequencies are shownin Figure.9. Again, ADS was used to verify the estimated (GT, NF, SWR) triplets by constructing individual matching networks using Sand Llisted in Figure.8. Table.3 present the simulation results which compares favorably with the visually estimated values.Table3.ADS simulation data results after individually matching the IMN and OMN according to the matching points in Figure.8.FreqGTNFSWRinSWRout9 GHz13.961.343.061.0210 GHz13.981.332.341.0111 GHz13.931.371.881.0112GHz 13.95 1.33 1.12 1.03 oddmentIn this paper, rigorous graphical investigation to explore the selected device capabilities in the NFmin and SWRout=1 cases was presented. For the first case a set of GT boundary curves and contours can be visually used to explore the expected values of SWRin SWRout for a targeted GT at NFminoperation. While for the second case NF boundary curves were used to visually predict the NF, SWRin levels for6Simultaneous conjugate matching point10 =* , =* , for 9,10,11,12 GHz4.559 GHzS in Lout4410 GHz83.5GHz3GHz2164212 G Hz11 GHz 10 GHz 9 GHz32.521.5011.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5Transducer gain GT(a)012.5 13 13.5 14 14.5 15 15.5 16 16.5Transducer gain GT(b)SWRinFigure7.a) Distribution of SWRin over a range of GT, b) NF boundaries for frequencies 9, 10, 11, 12 GHzFigure8.Extracted S, Lfrom the constructed database for the shown selected point of operation. output conjugate matching that will result a SWRout=1. For both cases, a full database was formed tobe used in the extraction of the corresponding matching reflection coefficients for any visually targetedoperating points. The construction and using of this database was found to make termination points extraction easy and accurate. And As described by 19 ItcanbeconcludedthatthenearfuturemicrowavetransistorisexpectedtobeidentifiedbythePerformanceDataBaseswhereallpossibleLNAdesignscanbeoverviewedusingthefulldevicecapacity.REFERENCESFriis, H.T.,Noise Figures of Radio Receivers, Proceedings of the IRE, Vol. 32, No. 7, 419-422, 1944.Colli ns, C.E. et al.,On the measurement of SSB noise figure using sideband cancellation, IEEE Transactions on instrumentation and Measurement, Vol. 45, No. 3, 721-727, 1996.Collantes, J.M. et al.,Effects of DUT mismatch on the noise figure characterization a comparative analysis of two Y-factor techniques, IEEE Transactions on Instrumentation and Measurement, Vol. 51, No. 6, 1150-1156, 2002.+j1.0+j1.0+j0.5+j2.0+j0.5+j2.0+j0.210 GHz12 GHz+j5.0+j0.212 GHzGHz10 GHz9 GHz+j5.09 GHz11 GHz0.00.0-j0.2-j5.0-j0.2