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1、2834IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 12, DECEMBER 2002 Prediction of IMD in LDMOS Transistor Amplifiers Using a New Large-Signal Model Christian Fager, Student Member, IEEE, Jos Carlos Pedro, Senior Member, IEEE, Nuno Borges de Carvalho, Member, IEEE, and Herbert Zi
2、rath, Member, IEEE AbstractIn this paper, the intermodulation distortion (IMD) behavior of LDMOS transistors is treated. First, an analysis is performed to explain measured IMD characteristics in different classes of operation. It is shown that the turn-on region plays an important role in explainin
3、g measured IMD behavior, which may also give a clue to the excellent linearity of LDMOS transistors. Thereafter, with this knowledge, a new empirical large-signal model with improved capability of predicting IMD in LDMOS amplifiers is presented. The model is verified against various measurements at
4、low as well as high frequency in a class-AB power amplifier circuit. IndexTermsIntermodulationdistortion,largesignal, LDMOS, model, power amplifiers. I. INTRODUCTION I N MOST MODERN wireless systems, the linearity require- mentsputstrongrestrictionsonthepoweramplifiersused.It hasbeenfoundthatLDMOStr
5、ansistorsexhibitbetterintermod- ulation distortion (IMD) performance compared to competing technologies 1, 2. LDMOS transistors are, therefore, widely used in power amplifiers at microwave frequencies in commer- cial applications such as basestation transmitters. IMD behavior in MESFET amplifiers ha
6、s been treated in 3. The analysis combines Volterra series for low input power withdescribingfunctionsandharmonicbalanceforhigherinput power. It is shown that transitions between these input power regimes can explain measured IMD behavior such as sweet- spots in MESFETs. Usingasimilarapproach,weshow
7、inthispaperthatthesharp turn-on region, compared to MESFETs, makes it necessary to revise the analysis in 3 for LDMOS transistors. The appear- ance of double third-order IMD (IM3) minima in class AB that has been observed by other authors 1, 4 can then be ex- plained. The double IMD sweet-spots clos
8、e to the compression point in class AB present a great potential advantage since similar linearity performance as for class A then can be achieved at a substantially improved efficiency. Manuscript received April 5, 2002; revised August 26, 2002. This work was supported by the Swedish Foundation for
9、 Strategic Research (SSF), Chalmers Centre for High Speed Technology (CHACH), Vinnova, and the Portugese Sci- ence Bureau (FCT) under the project LDMOSCA. C. Fager and H. Zirath are with the Microwave Electronics Laboratory, Chalmers University of Technology, 412 96 Gothenburg, Sweden (e-mail: fager
10、ep.chalmers.se). J.C.Pedroand N.B.de Carvalhoarewith theInstitutodeTelecomunicaes, University of Aveiro, 3810-193 Aveiro, Portugal. Digital Object Identifier 10.1109/TMTT.2002.805187 Fig. 1.Typical LDMOS transfer function? ?. Commonly used LDMOS large-signal models 58, including the industry-standar
11、d MET-model, do not treat the turn-on region carefully enough and thus cannot predict measured IMD accurately. AnewempiricalLDMOSlarge-signalmodelis thereforefor- mulated in which the turn-on region of the transistor character- istic is treated independently from other modeling regions. As a result
12、simulated IMD as well as output power and efficiency agree well with measurements. The model is formulated in a way similar to the MET model and is, therefore, easy to adopt. II. IMD ANALYSIS The IMD is analyzed by studying the input voltage/output current transfer function (TF),. The TF is found fr
13、om the transistorcharacteristics in combination with thedrainbias,loadimpedance,andtransistorparasiticelements. For MESFETs this has been done in 3. Fig. 1 shows a typical TF obtained at low frequency for an LDMOS transistor in an amplifier application. Since the transistor is usually biased with lo
14、w quiescent cur- rent in the saturated region, the TF is essentially the characteristic for low output currents. At higher currents, it is saturated by either the load-line entering the triode region, or compression due to the JFET-effect in the LDMOS drift region 9. To study the LDMOS IMD behavior,
15、 a two-tone test is often used. The input voltage will then have the form (1) At low excitation power, a Volterra series analysis may then be used to calculate the IM3 in. IM3 is here used as a 0018-9480/02$17.00 2002 IEEE FAGER et al.: PREDICTION OF IMD IN LDMOS TRANSISTOR AMPLIFIERS2835 Fig. 2.Typ
16、ical LDMOS transferfunction derivativesversusinput voltage?. The bias voltages for different classes of operation are indicated on top of the figure. general notation for the IMD sidebands appearing closest to the carriers, even if they usually are composed of also higher order IMD components. The s
17、mall-signal upper sideband IM3 atinis given by 10 (2) where the superscript 1,2 indicates the frequency compo- nent considered.andare nonlinear transfer func- tions andandphase constants. At low frequency, the Volterra series analysis turns into a power series analysis of the TF around the quiescent
18、 voltage 10. The TF is then described by (3) where the coefficientsrepresent the TF derivatives. Fig. 2 shows typical LDMOS TF derivatives obtained using a large-signal model (see Section IV). The coefficientsare related to the nonlinear transfer functions so that the IM3 con- tent incan be expresse
19、d as 3 (4) At low input power, IM3 is dominated by the third-order term, which results in a 3-dB/dB slope of IM3 versus input power. Equation (4) also shows that an interaction between third- and fifth-order derivatives of opposite signs can give rise to a large-signal IMD sweet-spot 3. However, sin
20、ce the contribution from theterm is usually much smaller, this happens at an input power level beyond the validity of the low-order Volterra series analysis used. As the input power is increased, the signal excursion eventu- ally reaches a region where the low-order power series in (3) no Fig.3.Deta
21、iledviewoftheturn-onregion,showing?andatenth-order Taylor series expansion (line) around? ?V. longer describes the TF adequately. These regions usually cor- respond to strong nonlinearities such as breakdown, gate for- ward conduction, or saturation due to the load line entering the triode region. I
22、n 3, a two sinusoidal input describing function (TSIDF)hasbeenusedtoanalyzetheIMDforthispurpose.The TSIDF for the IM3 product atis, in this case, defined as (5) where. It can be shown thatbecomes negative as the input signal amplitude approaches infinityor simply as the output signal compresses. The
23、refore, depending on the sign of IM3 found from the small-signal analysis in (4), different IM3 versus input power patterns can be predicted. Such results are presented for MESFETs in 3. For LDMOS transistors, the high-order derivatives in the turn-on region are much larger than the ones presented f
24、or MESFETs (see Fig. 2). This indicates that high-order terms are necessary for describing the transition appropriately. Fig. 3 shows how even a tenth-order Taylor series expansion fails to describe the TF beyond the turn-on knee. For LDMOS transistors, the IMD behavior must therefore be analyzed wi
25、th large-signal TSIDF techniques not only when the saturation region is reached, but also as soon as the input signal traverses the turn-on knee. ItisshownintheAppendix thattheturn-onkneegivesaposi- tiveIM3contributionandthereforeisanexpandingnonlinearity as soon as the input signal traverses the kn
26、ee. The amount of positive contribution is determined by the knee abruptness and the input amplitude. Different distinct IMD characteristics can now be depicted from transitions between the contributions in the small-signal, turn-on, and large-signal regions. For example, the expanding and compressi
27、ng nonlinearities of the turn-on and saturation re- gions,respectively,cancounteracteachothertocreateanoverall more linear operation. The same principle is in fact used in pre- distortion linearization of power amplifiers 11. 2836IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 12,
28、 DECEMBER 2002 (a)(b) (c)(d) Fig. 4.Output power (?) and third-order intermodulation distortion power (IM3) measured at 100 MHz for: (a) Class C,? ?V; (b) Class AB, ? ?V; (c) Class AB,? ?V; and (d) Class A,? ?V. III. MEASUREDIMD BEHAVIOR Two-tone measurements, shown in Fig. 4, have been per- formed
29、to studyLDMOSIMDbehavior. Thetransistorused has mA andwasbiasedatV 12.Themea- surements were made in a 50environment at 100 MHz with 1-MHz frequency separation. Depending on the class of operation, the different distinct IMD characteristics can now be explained using the behavioral analysis in the p
30、revious section. A. Class-C Operation From Fig. 2, the third-order derivative of the transfer func- tion is seen to be positive in class C,V. Thus, from (4) this implies that IM3 is also positive for low input power levels. The additional positive contribution from the turn-on re- gion results in a
31、further increase in the slope of the IMD curve and gain expansion. However, when the output power saturates, IM3 must become negative. Hence, an IMD minimum occurs nearthecompressionpoint.Fig.4(a)showsthemeasuredoutput powerandIM3forthiscase.SimilarIMDbehaviorhasbeenob- served in class-C MESFET ampl
32、ifiers 1, 3, 13. This kind of sweet-spot near the output power compression point, gives locally a very large carrier-to-intermodulation (C/I) ratio. However, in real amplifiers the input power may vary. It is therefore difficulttomake use of thisphenomenonfor sufficient IMD suppression in those appl
33、ications. B. Class-AB Operation To achieve better IMD performance while maintaining ac- ceptable gain and efficiency, amplifiers are commonly designed tooperateinclassAB.Thiscorrespondstoanegativeasseen inFig.2.ThemeasuredoutputpowerandIM3fortwobias volt- agesV andV in class AB are shown in Fig. 4(b
34、) and (c), respectively. The first of the two minima appears when the negative con- tribution fromis cancelled by the positive IM3 contribution from the turn-on region. Since the turn-on region influence is much stronger, the minimum appears as soon as the input signal reaches thatregion. Theminimum
35、will therefore occur athigher inputpowerifthetransistorisbiasedfurtherawayfromturn-on. This is confirmed by comparing the IM3 measurements. As the input power is further increased, IM3 will remain positive until the output power compresses and IM3 must again become neg- ative. This change of sign cr
36、eates another sweet-spot, close to the compression point. By a proper choice of gate bias, the two minima can be com- bined to create a large C/I ratio over a much wider input power rangenearthecompressionpointcomparedtoclass-Coperation (see Fig. 4(c). Note that this behavior is only possible becaus
37、e of the ex- panding nonlinearity of the sharp turn-on knee in LDMOS tran- sistors. The same behavior is generally not observed in MES- FETs. FAGER et al.: PREDICTION OF IMD IN LDMOS TRANSISTOR AMPLIFIERS2837 Fig. 5.Simple LDMOS large-signal model topology used. C. Class-A Operation As the bias is i
38、ncreased toward class A,will remain nega- tive.ThedifferencecomparedtoclassABisthattheinputsignal will now reach the output power saturation region before the turn-on region. IM3 will, therefore, remain negative and thus no IMD minimum is observed in Fig. 4(d). Class A is usually considered the most
39、 linear mode of opera- tion. Fig. 4 shows, however, that class AB may in fact be more linear over a wide input power range due to the double minima present. The results in this andthe previoussection present a greatpo- tential advantage for LDMOS transistors, due to the existence of two IMD minima i
40、n class AB. Thereby, similar IMD perfor- mance as in class A can be achieved with a significantly im- proved efficiency. The turn-on region, which is found very important for IMD when biased in class AB, is not accurately described in commonly used LDMOS large-signal models. In the following section
41、, a new large-signal model is, therefore, presented where special care is taken to properly model the turn-on region. Thereby, IMD as well as output power and efficiency may be predicted very well. IV. LARGE-SIGNALMODEL In this section, a new empirical large-signal model is pro- posed.Asimplemodelto
42、pology,showninFig.5,hasbeenused, where the parasitic and intrinsic small-signal parameter values have been found for various bias voltages using a robust multi- bias extraction technique 14. First, modeling of the nonlinear current source is treated. A. Nonlinear Drain Current Model Fig. 6 shows mea
43、suredand extracted small-signal transconductance () plotted versuswhen the LDMOS is biased in the saturated region. The transconductance char- acteristics can be divided in different regions, each having its dominant physical origin. As discussed in previous sections, Fig. 6.Typical LDMOS transcondu
44、ctance?and drain current?with different operating regions indicated. accurate description of the knee-region is very important for prediction of IMD in LDMOS transistors. In region I, the subthreshold region, the drain current is usu- ally taken to depend exponentially on the gate voltage 15. When t
45、he voltage is further increased, the current starts to rise quadratically (region II), which implies thatshould rise lin- early. The quadratic behavior is observed in MOS and LDMOS transistors 1517. The current in and between the subthreshold and quadratic regions is often modeled with 16, 17 (6) (7
46、) (8) wherecontrols the turn-on abruptness,the turn-on voltage, andthe slope in the quadratic region. For higher voltages (region III), short channel effects such as velocity saturation makeapproach a linear dependence on with a resulting constant transconductance. Devicesareusuallydesignedtopresent
47、constanttransconduc- tance over a region as wide as possible to achieve better IMD performance. This gives good linearity in class A operation but, 2838IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 12, DECEMBER 2002 as shown in previous sections, it is no guarantee for better IM
48、D performance in high efficiency linear amplifier applications. Many large-signal LDMOS models, including the industry- standard MET model, do not address the quadratic region, but make the transition directly from the exponential subthreshold region to the linear region 4, 6, 8. Thus, no parameters
49、 are available to define the turn-on knee abruptness and the knee tends to be too smooth. As described in Section II, this may severely affect its ability of predicting IMD behavior properly. We have chosen to implement the transition from quadratic to linear regions using the following empirical expression: (9) where the parameterin combination withcontrols the slope of the quadratic region and transition to the linear region. The parameteris added to tune the transconductance slope in the linear