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1、1590IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 2002 Power-Amplifier Characterization Using a Two-Tone Measurement Technique Christopher J. Clark, Christopher P. Silva, Fellow, IEEE, Andrew A. Moulthrop, and Michael S. Muha AbstractAn accurate nonlinear modelis necessa
2、ryto optimize the tradeoff between efficiency and linearity in power amplifiers. Gain compression (AM/AM) and amplitudephase (AM/PM) dis- tortion are the two primary model inputs used to characterize the nonlinearity. The amplifiers AM/AM and AM/PM characteristics are typically measured statically u
3、sing a vector network analyzer. Since the input is typically a modulated signal, it is desirable to characterize the amplifier dynamically. This paper describes and demonstrates a dynamic AM/AM and AM/PM measurement and modeling technique involving a spectrum analyzer and two-tone input signals. A c
4、omplete analysis of the measurement technique is presented, along with the data processing needed for the identi- fication of a new three-box model. The test configuration and pro- cedure are presented with special precautions to minimize mea- surement error. Results for a solid-state amplifier are
5、used to ac- curately predict intermodulation distortion, while those for a trav- eling-wave tube amplifier show good agreement with that obtained dynamically using a 16 quadrature-amplitude-modulation signal. Index TermsAM/AM and AM/PM, dynamic modulated sig- nals, high-power amplifiers, intermodula
6、tion distortion, nonlinear blackbox modeling, two-tone measurements. I. INTRODUCTION M ICROWAVE transmitters generally rely on a nonlinear power amplifier as the final amplification stage. Trav- eling-wave tube amplifiers (TWTAs) are commonly used in satellites 1, while solid-state amplifiers (SSAs)
7、 are used for portable wireless communications 2. Operating these power amplifiers at or near saturation improves power efficiency compared to linear operation, but signal distortion is generally increased.Sincepowerefficiencyiscriticalforbothsatelliteand handheld applications, accurate nonlinear ch
8、aracterization is required. The two major nonlinear distortions can be described in terms of AM/AM and AM/PM conversion characteristics, and these are often used in communication systems modeling 3. These models are important for predicting end-to-end link performance, as well as simulating spectral
9、 regrowth 46. AnamplifiersAM/AMandAM/PMcharacteristicsareoften obtained with a vector network analyzer (VNA) by measuring the gain and phase as a function of input power. Typically, this is a steady-state or static type of measurement, which may erro- neously include the thermal 7 or dc bias 8 effec
10、ts. For com- munication signals, the amplitude envelope can vary at a fre- quencycorrespondingtotheinformationrate,thus,theAM/AM Manuscript received October 25, 2000; revised October 30, 2001. C. J. Clark is with the Multilink Technology Corporation, Santa Monica, CA 90405 USA (e-mail: ). C. P. Silv
11、a, A. A. Moulthrop, and M. S. Muha are with The Aerospace Cor- poration, Los Angeles, CA 90009-2957 USA (e-mail: chris.p.silvaaero.org). Publisher Item Identifier S 0018-9480(02)05222-5. and AM/PM distortion is occurring dynamically. The simple technique presented here measures the dynamic AM/AM and
12、 AM/PM at a modulation rate that is more consistent with actual applications. It is based on the spectrum analyzer measurement ofintermodulationproductsusingatwo-tonetestsignal9.The results may be used in communication systems models in place of VNA-derived static measurements. II. NONLINEARAMPLIFIE
13、RMODELING There are three basic approaches to amplifier nonlinear modeling, i.e., physics based, circuit based, or blackbox based. The former two methods use device physics to develop either the transport/electromagnetic equations or a lumped/distributed circuitsimulationmodelthatmustbesimulatedtode
14、terminethe amplifiers nonlinear input/output behavior. The circuit-model approach has dominated the characterization of SSAs 10, 11. For TWTAs, the circuit-model approach has been exten- sively employed for practical design, whereas the simulation of its characteristic electromagnetic equations can
15、require many hours of CPU time to solve, even on advanced supercomputers. In systems-level modeling, blackbox approaches are often used where a topological configuration of linear/nonlinear components is constructed to replicate the amplifiers overall input/output behavior for a constrained class of
16、 signals. The boxes are derived from input/output measurements of the device, whereas their topological configuration stems from computational efficiency and intuition about the amplifiers internal workings. This approach can be implemented using commercially available software.1 2Although these mod
17、els do not employ formal nonlinear system identification principles, systems-level modeling is dominated by this approach because of its relative ease compared to more rigorous alternatives. This paper presents a modest extension of blackbox amplifier models that can provide more accurate prediction
18、s for moder- ately broad-band modulated signals. Blackbox modeling approaches assume that the nonlinear amplifier provides a causal operator mapping (memoryless or with memory) between the input signal and the output response that can be expressed formally as (1) whereis the input signal,is theoutpu
19、t response attime ,represents the operator mapping, anddesignates the 1SPW, Signal Processing Worksystem, Cadence Design Systems, San Jose, CA. 2Advanced Design System, Agilent EESof EDA, Agilent Technologies, HP EESof Div., Hewlett-Packard, Westlake Village, CA 91362. 0018-9480/02$17.00 2002 IEEE C
20、LARK et al.: POWER-AMPLIFIER CHARACTERIZATION USING TWO-TONE MEASUREMENT TECHNIQUE1591 memoryofthepoweramplifier.Allblackboxmodelsandformal nonlinear system identification techniques seek to approximate for a pertinent or general class of input signals. In the latter case,is usually expanded as a in
21、tegro-operator series that ex- tends the standard convolution representation for linear systems tothenonlinearcase.Thetermsoftheseexpansionsareobtained from carefully designed input/output measurements and often involve intensive data-reduction procedures. The majority of current blackbox amplifier
22、models assume a bandpass nonlinearity 12 and are based on one-tone static measurements. This model includes a zonal filter that accounts for the inherent filtering of the higher harmonics within the device. This model is valid for most communications problems where the input signal is narrow-band in
23、 comparison to the center frequency. As a consequence, these models rely on the continuity ofwith respect tosince they do not formally identify. However, in the face of broad-band and multicarrier contexts, wherein the actual signal differs considerably from the one used to construct the model, the
24、continuity ofcan no longer be used to ensure the models predictive fidelity. The simplest blackbox model is the so-called one-box model, consisting of a single frequency-independent memoryless i.e., in (1) nonlinearity that contains the AM/AM and AM/PM conversions manifested by continuous wave (CW)
25、in- putsatacenterfrequencypassingthroughtheamplifier.More formally, if the CW input is given by (2) andisanarbitraryphase,thentheoutputofthismodelisgiven by (3a) where (AM/AM conversion) (AM/PM conversion) (3b) For a general input signal, it is a common practice to recast in the form of (2) withand,
26、 resulting in (3a) withand, where the conversions andin (3b) are applied instantaneously at each time instant. An instantaneous envelope transfer function can be derived from single-tone AM/AM and AM/PM measurements using a VNA. Since the input is a sinusoid, the VNA AM/AM measure- ment actually pro
27、vides the sine-wave steady-state transmittance 13. In the absence of AM/PM conversion, a transfer function is obtained from the steady-state transmittance by a Chebyshev transformation 14. When both AM/AM and AM/PM exist, the envelope transfer function is complex. In this case, the real and imaginar
28、y steady-state components can be transformed separately, resulting in two instantaneous transfer functions in quadrature. Good simulation results have been achieved using this approach with a variety of nonlinear devices and input signal types 15. In addition, modifications of this approach have bee
29、n used to accurately predict spectral regrowth of digitally modulated signals in FET power amplifiers 16. In order to handle frequency-dependent effects and nonzero memory,theone-boxmodelisaugmentedwithoneortwolinear filters preceding or surrounding the nonlinearity, respectively, Fig. 1.Three-box n
30、onlinear model based on the two-tone dynamic AM/AM, AM/PMtechnique,where? ? ?isthefrequencyofthesmalltone(largetone). whichessentiallyshiftsthenominalconversionsintheirabscissa and ordinate axes with frequency. Such models assume that the memory of the amplifier can be adequately captured this way a
31、nd that the qualitative shape of the conversion curves do not change with frequency. The former assumption is questionable, especially when a general broad-band signal is traced through these models and thought of as being instantaneously a CW tone with some amplitude and phase (as is needed to proc
32、ess the signal through the memoryless nonlinearity). These models predictnointeractionbetweentheinstantaneoustones,although it is well known that such interaction occurs in a real device because of its finite memory. Likewise, the second assumption is known to be invalid in some amplifiers in which
33、the conver- sioncurvesdochangeshapewithfrequency.Moresophisticated models 17 address the latter inadequacy by replacing the one pair of conversion curves of the memoryless nonlinearity with a finite series of curve pairs, indexed by a finite set of selected frequencies, which are fits to actual meas
34、ured data. A. Two-Tone Technique Signal Analysis The two-tone method of characterizing the nonlinearity is a step in obtaining more accurate nonlinear models. With this method,thetransferfunctionsmaybeobtainedataratethatcor- respondstothemodulationenvelope,therebyavoidingerrordue to thermal and dc-b
35、ias effects. As will be shown, the two-tone measurement presented here is based on an input signal that can be interpreted as a single large carrier with a small dynamic modulation. Hence, the curves obtained by this technique are termed dynamic carrier amplitude and phase conversions. The blackbox
36、model proposed here is an extension of traditional models based on CW tone measurements to the two-tone case, consisting of a two-tone derived memoryless dynamic AM/AM and AM/PM box sandwiched between two linear filters, as shown in Fig. 1. We will take the memoryless nonlinearity to be referenced t
37、o the nominal center frequency of the power amplifier being represented, and assume that the surrounding linear filters can accurately account for the large-tone frequency dependence of the dynamic AM/AM and AM/PM. The change in shape of the dynamic conversions with respect tocould be accounted for
38、by curve fitting to measured data 17. The dependence of the dynamic conver- sionsandon the frequency difference, where is the frequency of the small tone, are obtained from measured data. Note thatandare envelope conversions, where denotes the two-tone envelope function. In order to develop a full s
39、imulation model from this blackbox topology, one also has to obtain both the amplitude and phases of the two filters. Although procedures for the identification of the complete model will be given, its application will be primarily restricted to the determination of the simpler one-box dynamic AM/AM
40、 and AM/PM model. This was done so as not to obscure the point that a dynamic measurement is more representative than 1592IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 2002 Fig. 2.Dynamic AM/AM, AM/PM test configuration. a static measurement in characterizing the actual
41、operation of a power amplifier in modulated signal contexts. In order to deembed the various components of the proposed model from input/output measurements, it is necessary to cal- culate the outputfor two special cases of its input: a small-signal two tone and a large-signal two tone. The two tone
42、 willconsistofalargetoneatthecenter frequencyanda small tone at some offset frequency (4) whereis the magnitude of the frequency offset. More pre- cisely, (5) where the phasesandare arbitrary. The calculations for bothtypesoftwo-toneinputsi.e.,withthesmalltoneaboveor below the main carrier,designate
43、d as the high-sideand low-side injection caseswill be done simultaneously. By convention, the upper (lower) signs in the following results will apply to the high-side (low-side) injection cases, respectively, unless other- wise stated. Suppose the power amplifier is subjected to a small-signal two t
44、one, as in (5), so thatandare small enough for the gain and phase conversions to be given by (6) whereandare constants for allin the passband of the amplifier. It is clear that the output of the three-box model in Fig. 1 would consist of the same two tones as went in, modified in amplitude and phase
45、 as follows: (7) For the sake of notational simplicity, we letanddenote both of the two possibly different values of the offset-tone am- plitudes and phases, respectively, for the two injection cases. However, we will assume that the carrier amplitudeand phaseare identical for the two injection case
46、s, respectively. The latter assumption will be used below for the large-signal two-tone input case. From power meter and spectrum analyzer measurements made at the input and output of the power amplifier (see Fig. 2), the following ratios are calculated with the help of (7): Input small-signal ampli
47、tude at Input small-signal amplitude at (8a) Output amplitude at Output amplitude at (8b) The superscript in these quantities indicates that they are referencemeasurementsperformedunderlinearoperation.Note from (8) that (9) Forthelarge-signaltwo-tonecase,weletthetonalamplitudes besimplydenotedbyand
48、,withtheadditionalconditionthat . Due to the distinct separation of frequencies inas seen from (5) and linearity, it is clear that the output of the first filterwill be given by (10a) where (10b) CLARK et al.: POWER-AMPLIFIER CHARACTERIZATION USING TWO-TONE MEASUREMENT TECHNIQUE1593 From (10b), it w
49、ill be convenient to define the ratio (11) In view of (11), we will assume that the gain of the filter is such thatas well. In parallel with 9,must be expressed in terms of an AM and PM modulated carrier at the frequencyinorderforthedynamicconversionstobeapplied. Using standard results from analytical signal theory 20, can be written as (12a) where (12b) and (12c) is the Hilbert transform ofin (10a) given by (12d) From (10a) and (12b)(12d), one can show that the amplitude and phase modulations are given exactly by (1