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1、IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 20031045 Effect of Baseband Impedance on FET Intermodulation James Brinkhoff, Student Member, IEEE, and Anthony Edward Parker, Senior Member, IEEE AbstractThe intermodulation performance of an FET in the common-source config
2、uration is dependent on the impedance pre- sented to its gate and drain terminals, not only at fundamental, but also at harmonic and baseband frequencies. At baseband fre- quencies, these terminating impedances are usually determined by the bias networks, which may have varying impedance over the fr
3、equencies involved. This can give rise to asymmetry in two-tone intermodulation levels, and changing intermodulation levels with tonespacing,aspreviousstudieshaveshown.Inthispaper,anFET is analyzed to gain an understanding, useful to the circuit designer, of the contributing mechanisms, and to enabl
4、e the prediction of bias points and the design of networks that can minimize or max- imize these effects. Compact formulas are given to facilitate this. An amplifier was tested, showing good agreement between the the- oretical and measured results. Index TermsFET amplifiers, impedance, intermodulati
5、on distortion, nonlinear distortion, Volterra series. I. INTRODUCTION M ANY STUDIES have reported that the intermodulation performanceofanFETamplifierisaffected,notonlyby the impedance presented to the device at the fundamental and higher harmonic frequencies, but also at baseband frequencies. The b
6、aseband frequencies are those of the modulating signals and, in a multicarrier system, the difference frequencies. The impedance at these low frequencies, hereafter called the base- band impedance, is usually determined by the bias networks. These create time constants in the circuit that are much l
7、arger than the period of the microwave carriers being amplified. The baseband impedance may cause the intermodulation levels to be higher or lower, or even cause an asymmetry between the upper and lower intermodulation levels 13. These effects are also observed in amplifiers operating under digital
8、modulation schemes so that, for example, upper and lower adjacent channel power ratio (ACPR) measurements are sometimes observed to be different 4. These phenomena are attributed to a low-frequency memory effect. Other mechanisms leading to memory effects are tempera- ture variation 5, 6 and trappin
9、g 7, which also may lead to changing intermodulation characteristics over the modulating- signal bandwidth. These effects result in ambiguity in speci- fying the linearity of an amplifier using a two-tone test. This is due to the distortion levels changing for different tone spacings. Manuscript rec
10、eived September 5, 2002; revised November 18, 2002. The work of J. Brinkhoff was supported under an Australian Postgraduate Award. The authors are with the Department of Electronics, Macquarie University, Sydney, N.S.W. 2109, Australia (e-mail: jamesbics.mq.edu.au). Digital Object Identifier 10.1109
11、/TMTT.2003.808704 For example,the intermodulation intercept point measured with a tone spacing of 10 MHz may be significantly different from that measured with a spacing of 100 kHz. Possibly, manufac- turers should givethe intercept-point specificationsfor a variety of tone spacings spanning the ban
12、dwidths of interest. The upper and lower distortion products also often have different levels (are asymmetric), leading to the question of which value should be used. Furthermore, memory effects in power amplifiers lead to difficulty in designing effective and wide-band predistortion linearizers 3.
13、They also make the extraction of a simple and accurate behavioral model for use in system simulation difficult because the familiar AM/AM and AM/PM single-tone characterizations do not account for long time constants. Much workhasrecentlygoneintoproducingaccuratepower-amplifier models that account f
14、or memory effects 8, 9. Theeffectsofthebiasnetworksonintermodulationhavebeen simulated using the harmonic-balance method and verified by measurement 2. Harmonic balance allows simulation of com- plex circuits under different operating conditions, however, it doesnotprovideananalyticalunderstandingof
15、themechanisms contributing to the intermodulation. A pioneering paper 1 that provides an understanding of the effect of baseband impedance on intermodulation uses a small-signal Volterra-series analysis 10 of a simple single-node circuit. This gave conditions under which the intermodulation levels w
16、ould be asymmetric. While leading to useful conclusions, it is based on a nonlinearity that is dependent on only one signal. This was extended to con- sider large-signal effects in two-tone and multitone situations, useful for power-amplifier design 11. The simulation used the same single-node circu
17、it and, in addition, the Volterra non- linear transfer functions of an FET and bipolar junction tran- sistor (BJT) circuit were considered. Measurements were given andshowntoagreewiththequalitativepredictionsgivenforreal MESFET and BJT amplifiers. The study dealt comprehensively with distortion side
18、band asymmetry. The overall change in both intermodulation products with baseband impedance still needs to be considered. This paper considers the Volterra-series analysis of an FET biased in the saturation region, with nonlinear gatesource ca- pacitance and drain current. The analysis considers ter
19、ms up to the third order, hence, the results are valid for an amplifier driven into weak nonlinearity. All measurements are performed with the power levels less than 10 dB below the 1-dB com- pression point for the device. Closed-form functions predicting distortion levels are derived, which provide
20、 a qualitative under- standing of the effects. These functions are not complicated, but are able to predict the distortion accurately. Hence, they should 0018-9480/03$17.00 2003 IEEE 1046IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 2003 Fig. 1.FET circuit used inVolter
21、raanalysis. Notethat the draincurrent source ?includes transconductance, drain conductance, and cross terms, as in (1). be useful in circuit design. The analysis considers an arbitrary input and output impedance and their effect, not only on asym- metry between intermodulation levels, but also on ch
22、anges in the absolute intermodulation levels with difference frequency. This gives an understanding of the mechanisms that contribute to dependenceofthird-order distortionon basebandimpedance, and enables prediction of bias regions and impedances that will minimize the dependence. The distortion of
23、a pseudomorphic high electron-mobility transistor (pHEMT) amplifier was mea- sured and compared with simulations using the derived equa- tions, which confirmed the theory. II. FET CIRCUITANALYSIS In the analysis of a common-source FET operating in the sat- uration region, it is usual to consider two
24、 nonlinearities. The most significant is the drain current, controlled by the gate and drainsignal voltages. The second is the gatesource nonlinear capacitance, controlled only by the gate voltage 12. These give signal currents through the drain and gate, respec- tively, which can be written in a Ta
25、ylor-series expansion to the third order as (1) (2) where theterms, defined in 12, and theterms, defined in 13, are constants that vary with bias. The circuit used in the analysis is shown in Fig. 1. Notice that the gatedrain capacitance is not included. This was found through simulations to have a
26、negligible effect on the distor- tionresultspresentedhere.Thedrainsourcecapacitanceisusu- ally very small, but could be included in the load impedance if needed. Extrinsic elements can be accounted for in the load or source impedances as necessary. The gate is driven by a source with a series freque
27、ncy-dependent impedance. The drain is connected to a frequency-dependent impedance. The analysis proceeds by findingas a function ofusing a Volterra series involvingand. This yields the first-, second-, and third-order nonlinear transfer functions.is then found as a function ofin terms ofand, again
28、giving threenonlineartransferfunctions.Theoveralltransferfunctions betweenandare derived by combining the two sets of functions using a similar method to that proposed in 14. In this case, however, the analysis is extended to consider distor- tion at all frequencies including baseband, instead of ju
29、st the in-band products close to the carrier frequencies. The fact that out-of-band products are considered and found to contribute to in-band distortion leads to the prediction of low-frequency memory effects impacting on carrier-frequency distortion. The result is a set of large equations for the
30、intermodula- tion-distortion products, similar to those in 11, which can be simplified. A number of terms were found to be insignificant in predicting intermodulation levels at the frequencies used here and at the bias conditions of interest. These included terms that depend on the second- and third
31、-order gatesource capacitance nonlinearityand. However, it was found by simula- tion that these terms may need to be included in the model to accurately find the difference in level between the lower and upper intermodulation products at high frequencies. If the lower and upper input tones, respecti
32、vely, are atand ,thenthelowerandupperintermodulationproductswillbeat and.Thesecond-orderdifferencefrequencies atare the terms that could create a memory effect. It is often assumed that the bandwidth, or frequency difference between input tones is small compared to the midband carrier frequencyso th
33、at . In some cases, this narrow-band approximation is not valid, as is observed in Section III-B. The full frequency-dependent equations for intermodulation are given in the Appendix. Assuming that the input tones and intermodulation are at fre- quencyand thatandcan be ignored, the equations for the
34、 intermodulation levels simplify to (3) (4) where (5) (6) (7) (8) (9) (10) The termis the linear gain at the fundamental frequency . The termis a pole due to the gatesource capacitance that reduces the levels and alters the phase of the intermod- ulation levels at high frequencies. The asteriskdenot
35、es a complex conjugate, which, in this case, corresponds to negative frequency. The effective linear drain impedance is . Note that, andchange with BRINKHOFF AND PARKER: EFFECT OF BASEBAND IMPEDANCE ON FET INTERMODULATION1047 Fig. 2.Example vectors of the lower? ? ?and upper? ? ? intermodulation pro
36、ducts for real and complex high-frequency terminations. bias and with output impedance at, but are independent of the difference frequency. The intermodulation dependence on third-order nonlinear terms is attributed to. Intermodulation caused by second-order terms is attributed toand , which involve
37、 impedances at the sum and difference frequencies. The only difference between the expression for lower (3) and upper (4) intermodulation products is the presence of in one and its conjugatein the other. is the only term in (3) that will change with the difference frequency as it is determined by th
38、e baseband impedance at the drain terminal. It is also the term that could cause a difference between theupperand lower intermodulationlevelsbecause the imaginarypartsofitanditsconjugatein(4)areoppositeinsign. These results can be visualized using a vector diagram of the summation in (3) and (4). No
39、te thatwill be complex if the drain termination is complex at the funda- mental or higher harmonic frequencies. The terms dependent onthedifferencefrequencyaredefinedas and. Thus, the lower intermodulation product is proportional toand the upper product is proportional to. The vector diagram shown i
40、n Fig. 2 illustrates the situations for two different drain impedances. The vectorsandchange with the baseband impedance. This leads to the intermodulation levels varying with different tone spacings. If the termination is real at the fundamental and second-harmonic frequencies,will be at the same a
41、ngle as, thus, no asymmetry will be noticed. If the termination is complex, the imaginary parts ofandwill add to or subtract from the imaginary partso that the upper and lower intermodulation products will have different magnitudes. A number of predictions and observations are possible from the abov
42、e results. 1) Thevariationofintermodulationwithbaseband impedance is dependent on the second-order draincur- rent nonlinearity. To correctly simulate the effect of memory on intermodulation, a model is needed that accurately predicts the second-order transconductance , drain conductance, and cross t
43、ermin (8). 2) It ispossible to select a bias point and/or drain impedance suchthatin(3)and(4)isminimizedand,hence,thede- pendence of the intermodulation on baseband impedance is minimized. 3) Design for minimal intermodulation distortion can be at the expense of intermodulation dependence on baseban
44、d impedance. This is not the case if the third-order terms in the draincurrent nonlinearity mask the second-order terms becausewill dominate overin (3) and (4). However, many power-amplifier designs bias the tran- sistors to the points of lowest intermodulation, typically where. This will also be th
45、e point where the second-order effects are not negligible in comparison with the third-order ones. Thus,will be of compa- rable magnitude toand. This is a reason why large intermodulation changes and differences between upper and lower levels are often observed in lower intermodulation amplifiers. 4
46、) It is the impedance of the drain termination at the differ- ence frequencythat has the dominant ef- fect,whereasthebasebandimpedanceofthegatenetwork does not have such a significant impact. 5) The intermodulation level will change with the differ- ence in frequency between the two tones if the bas
47、eband impedance changes with difference frequency. This re- quires careful consideration of the frequency spacing for intermodulation testing because the intercept point can vary widely depending on the tone spacing. Also, using devices such as dc blocks at the input of a spectrum an- alyzer can sig
48、nificantly change the baseband impedance presented to the output of the device-under-test, and give uncharacteristic results to an intermodulation test. 6) The memory effect can be reduced if the baseband output impedancedoesnotchangeoverthedesiredbandwidthof operation. An obvious design that will s
49、et in (3) to zero is one in whichover the baseband frequency range. This range must encompass the bandwidth of broad-band signals or the maximum frequency separation in a multicarrier amplifier. Thus, this design goal may not be possible in modern commu- nication systems where large amplifier bandwidths are required. 7) A difference in the intermodulation levels will be ob- served if all three of the following conditions hold; they are similar to those found in 1 for a simpler system: Thethird-ordertermsinthedraincurrentnonlinearity d