WEEE TRANSACT
`
`
`
`MICROWAVE THEORY
`AND TECHNIQUES
`
`|OCTOBER 2010
`
`4
`
`VOLUME 58
`
`NUMBER 10
`
`lIETMAB
`
`*
`
`(ISSN 0018-9480)
`
`INTEL 1117
`
`
`
`2521
`
`
`. =
`PAPERS
`
`Smart Antennas, Phased Arrays, and Radars
`A Low-Power Shoe-Embedded Radar for Aiding Pedestrian Inertial Navigation ....+.0..10renprerreyrerere sip nneraenees tenes
`
`We. cai wiseccs cx vets asta sainieveaian epterabearebices-evaa(sieaivieyisiac en pets viemee.tits sie es C. Zhou, J. Downey, D. Stancil, and TF: Mukherjee
`
`_ Active Circuits, Semiconductor Devices, and ICs
`A 55-mW +9.4-dBm IIP3 1.8-dB NF CMOS LNAEmploying Multiple Gated Transistors With Capacitance
`' DeSERSEUZANGH -conrenreerererretnessPe eretelcce andeicen Keathaycinsisianfilalidalrceaaresiceiaeesatains TH. Jinand TW. Kim=2529
`
`
`pA Jitter-Optimized Differential 40-Gbit/s Transimpedance Amplifier in SiGe BiCMOS.......++++--ccseesrerseneseeneerees
`DD. - teevgiseeereuntinrn ngesiepess ten raeedeed nea vveevanidclanaraics C. Knochenhauer, S. Hauptmann, J. C. Scheyu, and F. Ellinger—2538
`) 2:D Electrical Interferometer: A Novel High-SpeedQuantizer .......0.-.-.+2:sreneneeeereeeeens Y. M. Tousi and E. Afshari
`2549
`
`‘Optimized Design of a Highly Efficient Three-Stage Doherty PA Using Gate Adaptation ....-.--.1.sse-seseseresreeeeoes :
`
`; IL. Kim, J. Moon, 8. Jee, and B. Kim—2562
`
`a
`a ae eal
`at REA wn ahd | heen he | le ee ee a oh Bg me ee op ee a 4S! Oe Sa) © ev ree
`n Compact 0.1-14-GHz Ultra-Wideband Low-Noise Amplifier in.0. {3-m CMOS....... P-¥. Chang and S.S.H. Hsu
`2575
`
`|Optimization of a Photonically Controlled Microwave Switch and Attenuator -............. JR. Flemish and R. L, Haupt
`2582
`
`Wireless Communication Systems
`
`the Modulated Scattering Antenna Array for Mobile Terminal
`| Theoretical and Experimental
`Investigation of
`Applications, ......1.ercrenonesyestnep semepreyhadabuausnssusoer¥ngenss M. He, L. Wang, Q. Chen, Q. Yuan, and K. Sawaya—2589
`
`
`A Multimode/Multiband Power Amplifier With a Boosted Supply Modulator ......,.+..-1+++ Se eS eerenen sa 2
`Ss
`eee a eae eae ea Leas LAL Lid ea waieaer ema ewa enw slevhnws sees piece ee D. Kang, D. Kim,J. Choi, J. Kim, ¥. Cho, and B. Kim)
`2598
`
`Field Analysis and Guided Waves
`* Space-Charge Plane-WaveInteraction at Semiconductor Substrate Boundary ,.....,.-12.:s.:s))+seressestssersrsecsserresss
`2609
`- AE See aesesiee Saree PERSE TAP AES FAECES Sie yarerenaemnr es towers 1A, Elabyad, M.S. Eldessouki, and H. M. El-Hennawy
`2619
`"Full-Space Scanning Periodic Phase-Reversal Leaky-Wave Antenna .....0::.e0000c0008 N. Yang, C. Caloz, and K. Wu
`(Contents Continued on Back Cover)
`
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`IEEE
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`

`KANGeral.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`
`
`pgaa===-=.-.-~-
`
`class-F PA, using a push-pull structure. The class-J PA utilizes
`the phase shift between the output current and voltage wave-
`formsto render the second harmonic termination to a purely re-
`active regime [19].
`The broadband approachesfor class-E PAs and class-F PAs
`have beenstudied in [20] and [21]. However, these concepts are
`for base-station PAs, and use microstrip lines for matching. The
`microstrip lines are too bulky to be employed in PAsfor handset
`applications. In [22], we have proposed broadbandclass-F PAs,
`which control the second and third harmonic impedancesacross
`a broad BW,butlinearity is not considered as we intendto use
`a digital pre-distortion (DPD) technique. Broadband class-J
`PAsfor base-station PAs have been also investigated [19]. The
`researchers have found the optimum efficiency contour for
`class-J operation across a broad BW,and matched the load
`impedancetothe contour, thus, a 50% fractional BW with high
`efficiency is achieved. A gallium-nitride (GaN) device with
`a high supply voltage has a low Q for the output impedances
`due to the small output capacitance, and its gain drops 3 dB
`per octave frequency (normallyit is 6 dB/octave because ofits
`operation at the maximum stable gain (MSG)region). Despite
`the advantageous characteristics of the GaN device, it is too
`expensive at the momentto be utilized for handset devices and
`it requires too high bias voltage.
`The ideal EER structure would deliver a 100% efficiency
`using a highly efficient supply modulator, but the limited BW of
`switching amplifiers and the low efficiency of wideband linear
`amplifiers for the modulators degrades the ideal efficiency.
`Someresearchers have utilized the advantages of the wide-BW
`linear amplifier and the high-efficiency switching amplifier
`[10]-[15]. The switching amplifier does not follow mostof the
`high slew-rate load current, and operates as a quasi-constant
`current source. The linear amplifier supplies and sinks the
`current to regulate the load according to the envelope of the
`signal. This structure is suitable for the envelope signal of
`modern wireless communication systems, which has the most
`powerin the low-frequency region. In [15], we have proposed
`a hybrid switching amplifier (HSA) for multistandard appli-
`cations. Automatic switching current adaption from an HSA
`and programmable hysteresis control can achieve multimode
`operation.
`In this paper, we propose a multimode/multiband PA with
`a boosted supply modulator for handset applications. For this
`multiband PA design, the fundamental load is maintained at
`a consistent level across the BW. Harmonic impedances are
`searched for highly efficient class-F operation. The harmonic
`circuits are merged into the broadband matchingcircuit, thereby
`reducing their size and increasing the available BW. In con-
`trast fo our previous paper [22], the PA matching is modified for
`linear class-AB bias. An HSA with a boost converter driving
`the linear stage increases the RF BW due to reduced output
`capacitance of the RF device at the higher operating voltages
`provided by the boost converter. The HSA also improves the
`efficiency due to envelope tracking (ET). Finally the HSA im-
`proveslinearity due to intermodulation-distortion IMD)sweet-
`spot tracking. Multimode operation for various wireless appli-
`cations is accomplished thanks to programmablehysteresis con-
`trol and automatic switching current adaptation from the HSA.
`
`2599
`
`Supply Modulator3
`
`IWCDMA
`ILTE
`Envelo
`
`MultiMode
`Supply
`Modulator
`
`
`
`WCDMA
`:
`
`ILTE
`
`Broadband/
`Mutliband PA
`
`{b)
`
`(a) Conventional polar transmitter for multimode/multiband operation.
`Fig. 1.
`(b) Proposedpolar transmitter for multimode/multiband operation.
`
`For demonstration purposes, the PA and supply modulator are
`implemented using an InGaP/GaAs HBT and a 65-nm CMOS
`processes, and are operated with signals of long-term evolu-
`tion (LTE), widebandcodedivision multiple access (WCDMA),
`and EDGEacross frequencies of 1.7-2 GHz. The measured re-
`sults prove that the proposed design achieves highly efficient
`and linear power amplification for multimode/multiband appli-
`cations.
`
`Il. MULTIMODE/MULTIBAND POLAR TRANSMITTER
`
`A conventional polar transmitter for multimode/multiband
`operation requires a PA and a supply modulator for each
`wireless communication standard, as shown in Fig. 1(a). For
`example,
`if we need transmitters operating for an LTE, a
`WCDMA,and an,EDGEapplication across a 1.7-2.0-GHz fre-
`quency, supply modulators and PAs needto operate at different
`switching frequencies and operate at different RF frequencies
`for each standard. The LTE signal has a BW of 10 MHzand
`a PAPR of 7.5 dB. WCDMA and EDGEsignals have BWsof
`
`

`

`
`
`2600
`
`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL.58, NO.10, OCTOBER 2010
`
`3.84 MHz and 384 kHz,respectively, and a PAPR of 3.5 dB.
`Bach supply modulator for each application should be em-
`ployed for multimode operation. Moreover, if a narrowband PA
`is used, then every RF bandwill require the addition of another
`PA,
`Therefore, for simplicity and low cost, we propose a mul-
`timode/multiband ET polar transmitter using a multimode
`supply modulator [15] and a broadband class-F PA [22], as
`illustrated in Fig. 1(b). The broadband class-F PA can cover
`the frequency band of 1.7-2 GHz while maintaining high
`efficiency and linearity. This will be revisited in Sections IH
`and IV. The switching frequency and switching currents of the
`switching stage can be controlled by programmable hysteresis
`control and automatic switching current adaptation from the
`hybrid supply modulator according to each communication
`application. Moreover, by employing the ET technique, the
`supply voltage provided to the PA follows the envelope of the
`signal so the de power that the PA consumes can be signifi-
`cantly reduced, and the power-addedefficiency (PAE) can be
`significantly increased at the average powerlevel, as well as at
`the peak output powerlevel.
`
`Il. TECHNIQUES FOR HIGH EFFICIENCY AND BROADBAND
`
`A. Class-AB/F PAs
`A highly efficient class-AB/F PA has been proposedin [25],
`which enhancesthe efficiency by controlling the second and
`third harmonicswhile maintainingtheir linearity. By setting the
`base bias to near class B, it efficiently amplifies phase-only in-
`formation such as the global system for mobile communications
`(GSM)signal. With a bias level of class AB,it efficiently and
`linearly amplifies both the phase and amplitude information in-
`cluding CDMA, LTE, WiMAX,and EDGEsignals. The output
`load impedance Rop¢ is set to an intermediate value for mul-
`timode operation. Class-E, inverse class-F, or class-J PAs can
`provide an even higherefficiency or a broader BW, but we adopt
`the efficient and linear class-F PA for ET operation becauselin-
`earity improvementtechniques such as DPD are still a burden
`for the PAs of handset applications.
`To employ a class-AB/F PA for an ET polar transmitter
`with a boosted supply voltage (V.- = 4.5 V), the fundamental
`load impedanceis set to be 6 + 71 © for a 1-dB compression
`power(P1 dB) of 32 dBm, and a class-AB bias level (98 mA)
`is chosen. The second and third harmonic impedances are
`found for high-efficiency operation with a fixed fundamental
`output load, as shownin Fig. 2. This figure showsthat a third
`harmonic impedance several times larger than the fundamental
`load impedance delivers high efficiency. This can be easily
`achieved across the broadband frequency range. The second
`harmonic impedanceis more sensitive to the matchingcircuit
`than the third harmonic impedance, but is manageable over a
`few hundred megahertz BW using a second harmoniccontrol
`circuit.
`
`B. Broadband Matching Techniques
`There are equations that transform a low-pass filter (LPF)
`to a bandpassfilter (BPF) [26]. The BPF does not allow the
`impedancetransformation required for PA designs. The BPFs
`
`Bo
`Of!
`f
`fe 4 F damental
`ingpedanée
`
`‘
`
`\
`N
`~. 6% 4
`‘
`
`
`
`
`
`impedance
`
`{ Fundamental
`|
`
`;
`
`Fig. 2. Simulated load—pull results ata frequency of 1.85 GHz. (a)For third
`harmonic impedance, The fundamental and second harmonic impedances are
`fixed at 6-+j1 and0.5—j2.5, respectively. (b) For second harmonic impedance.
`The fundamental and secord harmonic impedances are fixed at 6 + j1 and
`25 + 7200, respectively.
`
`shownin Fig. 3(c) and (d) makeit possible to transform the im-
`pedances andto have bandpass characteristics. To analyze the
`BW,the concept of Q needsto berecalled. A loaded Q, de-
`noted by Qr, is defined by
` Qn _ fo
`()
`Qr= > = BW’
`The circuit node Q, denoted by Qn, is defined at each node as
`
`|x|
`Rr
`Q)
`
`i |Q R Rs
`
`where Rr is a transformed resistance from Rg and Rr is larger
`than Rg. The smaller Q,, leads to broader BW, which means
`that the same impedancetransformation ratio using two-section
`matching achieves a wider BW.In Fig. 3(c)—(f),to get the lowest
`Q,, with the impedancetransformation, the relationship of im-
`pedances is given by
`
`Rg = VR1-Rs.
`
`(3)
`
`Fig. 3(e) is a high-pass filter (HPF) type matching circuit,
`which comprises two sections, and it has the same Q as
`
`

`

`KANGet ai.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`2601
`
`Te(a)re2090000
`
`“T i=DI
`
`(a) LPF type.
`Impedance-matching circuits.
`3.
`Fig.
`(c) and (d) BPF type with impedance transformation.
`HPFtype. (f) Two-section LPF type.
`
`(b) BPF type.
`(e) Two-section
`
`capacitance C, is resonated outat the third harmonic frequency
`by the inductanceat the bias line. The fundamental impedance
`matching uses LC—C’'L type broadband matching. The shunt
`£3C has an inductance at the operating frequency, and can be
`merged into a bondwire L, for broadband matching.
`The simulated load impedances including the components’
`loss are shown in Fig. 5(a). The load impedances across the
`1.7-2.0-GHz frequency are constant with power matching.
`The second harmonic impedances across the 3.4-4.0-GHz
`frequency are near zero, which is located at the high-efficiency
`region in Fig. 2(b). The third harmonic impedancesacross the
`5.1-6.0-GHzfrequency are high, which is also located at the
`high efficiency region in Fig. 2(a).
`Fig. 5(b) shows the broadband characteristic of the insertion
`loss $21 over the frequency rage of 1.7—-2.0 GHz. $21 has the
`two nulls at 3.3 and 3.8 GHz, which are produced by C22 with
`a short microstrip line and L2C2, respectively. With this circuit
`topology, the harmonic control circuits are merged into the fun-
`damental matching elements, realizing a small size for handset
`applications.
`
`D. Boosted Supply Voltage
`
`C.
`
`Input, Interstage, and Output Matching
`
`Fig. 3(c) and (d). The 3-dB BW might be the same, but the BPF
`The supply voltage ofthe linear stage of the HSAis increased
`types are better because the BPFs maintain more consistent
`from 3.4 to 5 V by the boost converter depicted in Fig. 4. Since
`impedance level across lower to upper bands. Moreover, the
`the buffer comprising the linear stage has a voltage drop of 0.5 V,
`BPF types shown in Fig. 3(c) and (d) have an advantage of
`the output voltage swing of the supply modulator is boosted
`smaller inductance than the HPF of Fig. 3(e) becauseaseries
`up to 4.5 V. Our previous HSA [15] had a maximum output
`inductance (reactance) is smaller than a shunt
`inductance
`voltage of only 3 V. Due to the boosted output voltage, the PA
`(susceptance) where a low impedance is transformed into a
`can generate more power with the same output load. In other
`high impedanceof 50 (2 in the PA designs. The series inductors
`words, the output load impedance can be raised for the same
`marked with a star and with a circle in Fig. 3(c) and (d), respec-
`output powerasillustrated in Fig. 6, which delivers a higher ef-
`tively, are smaller than those markedin Fig. 3(e). Fig. 3(f) is an
`ficiency and broadband characteristics. The broadband charac-
`LPF type matching circuit. Even though the BW is broad, an
`teristics are explored using the output capacitance variation plot
`LPFis a unwelcomecircuit for the input and output matching
`shown in Fig. 7. The supply voltage V., is swept with funda-
`of handset PAs because dc currents from the supplies should
`mental load impedancesof 2.5, 3.5, 4.7, and 6 Q, which deliver
`be blocked. The BPFs shown in Fig. 3(d) are employed in
`the same output power with the maximum supply voltagesof3,
`this broadband class-F PA design because of their broadband
`3.5, 4, and 4.5 V, respectively. When ET operation follows the
`characteristics and their small inductor values, which can be
`highestefficiency at each supply voltage, the output capacitance
`easily replaced by bondwires.
`of the transistor follows the Cou trajectory in Fig. 7. The output
`capacitance is calculated by the method shownin [24]. As the
`supply voltage decreases, the output capacitance increases. At
`an output power of 32 dBm,the PA using Rop: of 2.5 Q witha
`supply voltage of 3 V has about a 10% larger output capacitance
`than that using Ropt of 6 2 with a supply voltage of 4.5 V. If an
`LTEsignal with a 7.5-dB PAPRis applied to the PA, the max-
`imum average poweris theoretically 24.5 dBm because the P1
`dBofthe PA is 32 dBm.In actual operation, however, the PA can
`achieve an average output powerof about 28 dBm because some
`portion of the peak signal could be saturated while maintaining
`an acceptable linearity specification. Besides the smaller output
`capacitance, the PA with a 4.5-V V., has a smaller impedance
`transformation ratio, whichassists in increasing the operational
`RF BW.Fig.8(a) showsa simulated continuous wave (CW)per-
`formance for PAE andgainof the supply voltages of 2.6 V witha
`load of 6 QD and 2 V with a load of 2.5 () for the powerstage. The
`supply voltages are reduced for operation of the LTE average
`output powerof 28 dBm. The PA with 6 Q has 10% higher PAE
`and highergain. Fig. 8(b) showsthe insertion loss obtained by a
`
`Asillustrated in Fig. 4, an input capacitance composedof C,.
`and C;, increased by Miller’s theorem is merged into the se-
`ties inductor of the LC—C'L broadband matching circuit [see
`Fig. 3(d)] to maximize the BW. The intermediate impedance
`is set as 10 2 to transform the 2 © of the input resistance to
`the 50 Q ofthe input terminal. Theinterstage is matched with
`two-section HPFs, including the bias line inductanceatthe col-
`lector of the drive stage. The HPFs also have a low-impedance
`transformation ratio to maximize the BW. The output matching
`comprises a broadband fundamental impedance matching, the
`second harmonic short circuits and the third harmonic open cir-
`cuit. L2C> has a near zero impedance at the upper bandof the
`second harmonic and C2 with a short microstrip line has a
`near-zero impedanceat the lower band of the second harmonic.
`Thus, the voltage waveform of the second harmonic is effec-
`tively reduced across the broadband. The shunt L3C3 provides
`a high impedanceat the third harmonic frequency. The output
`
` =
`
`
`eeCS:
`
`

`

`2602
`
`IEEE TRANSACTIONS ONMICROWAVETHEORY AND TECHNIQUES,VOL.58, NO. 10, OCTOBER2010
`
`Vop =3.4V
`
`
`=e SSi=. “e in cl
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`Comparator
`
`
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`Switching Stage
`(Buck Converter)
`Se
`
`Class-AB buffer
`+
`Current sensing
`J
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`Boost Converter
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`
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`(OTA+Buffer)
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`Fig. 4. Schematic of the ET transmitter with broadbandclass-F PA and boosted supply modulator.
`
`large-signal S-parameter at an output power of 28 dBm, which
`shows a broader BW for a supply voltage of 2.6 V because of
`the smaller output capacitance and the impedance transforma-
`tion ratio.
`
`IV. TECHNIQUES FOR MULTIMODE OPERATION OF HSA
`An HSAconsists of a boost converter, linear stage, hysteretic
`comparator, and switching stage, as shown in Fig. 4. The boost
`converter is connected to the linear stage to boost the output
`voltage swing. The linear stage works as an independentvoltage
`source throughout the feedback network, while the switching
`stage operates as a dependent current source to provide most of
`the current to the output. The current sensing circuit detects the
`current at the output ofthe linear stage, and controls the state of
`the switching stage according to the magnitude and polarity of
`the sensed current. A detailed overview of the HSA operation is
`explained clearly in [15]. Multistandard signals have different
`
`PAPRs and BW.Theadaptation of the switching currents for
`the various PAPRsare automatically performed by the current
`sensing circuit and the hysteretic comparator in the HSA. The
`switching currentis proportional to the difference between Veen
`and Varr. as shownin Fig. 4. The sensed current generates the
`sensed voltage Ven, which is proportional to the input of the
`envelope signal. Thus, the square of the switching current is
`inversely proportional to the PAPR.
`The adaptation of switching currents for multistandard sig-
`nals is shownin Fig. 9, which illustrates the probability density
`function (pdf) and the efficiency of the HSA. For a multimode
`HSAdesign, the switching condition is optimized for the wide-
`band signal by determining an inductor value at the output of
`the switching stage. A narrowband signal whose slew rate is
`lowerthan that of the switching amplifier leads to an excessively
`high switching frequency and poor efficiency of the switching
`stage. Thus, we utilize a programmable hysteretic comparator,
`which enablesus to control the hysteresis voltage Vays. and the
`
`

`

`KANGe# al.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`2603
`
`
`
`
`
`OutputCapacitance[pF]
`
`fo)
`
`
`—— Rep=6 2
`——- Reet? 2
`+ Rop=3.5.2
`++ Riga? 0
`
`
`
`
`Ss
`
`
`
`'
`
`
`
`
`‘Coatajectoy)
`
`t
`
`15
`
`17
`
`19
`
`== 1
`23
`25
`27
`21
`Output Power [dBm]
`
`for6Q :
`}
`t Tony tT]
`29
`31
`33
`
`Fig. 7. Output capacitance as functions of Rept, V.., and output power. With
`an EToperation,the output capacitance ofthe PA follows the Cou trajectory.
`
`
`60
`
`2.6 V Voc
`— 2V Veco
`
`50
`
`
`
`40
`
`30
`
`20
`
`0
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`Output Power [dBm]
`(a)
`
`$21[dB]
`
` T ¥ T r r +
`
`
`
`
`PAE[%],Gain[dB] 10
`
`
`
`
`
`
`
`
`2.0
`2.5
`30
`3.5
`40
`Frequency [GHz]
`(b)
`
`
`
`
`
`0
`
`
`
`-10-4
`
`@ -20-
`
`99
`
`2 n
`
`Na
`
`~40-)
`
`
`oS aGl a
`1
`2
`3
`4
`5
`6
`7
`
`Frequency [GHz]
`(b)
`
`Fig. 5. Simulated S-parameters of output matching circuit including compo-
`nents’ loss.
`
`2.0
`
`1.5
`
`= 1.0
`2
`
`0.5
`
`
`
`
`Loadline for
`3.4V operation
`
`
`
`FSEToperation 4.5V operation
`
`Yas
`
`Load line for
`
`Fig. 6. Load line of 2.5 and 6 2 for 3.4- and 4.5-V operation for the same
`maximum output power. Loadline for 4.5 V gives higher efficiency and broader
`BW,as well as more linear ET operation at the low-powerlevel.
`
`switching frequency. Efficiency of about 3% is enhanced by
`controlling the hysteresis voltage for the EDGEsignal.
`The envelope is modified for linear ET operation, as depicted
`in Fig. 10. The equation for the envelope shapingis given by
`
`Envelope’ = (1 — Vienee 10°/») - Envelope + Offset
`
`peak
`
`(4)
`
`where x is a back-off power level from the peak average power.
`The PA has AM/AM and AM/PM distortions at a low supply
`voltage because of the increased output capacitance, as shown
`
`(a) Simulated CW performance of PAE and gain with supply voltages
`Fig. 8.
`of 2.6 and 2 V for the power stage. The PAs with 2.6- and 2-V V.. have Rape
`of 6 and 2.5 Q, respectively, to generate the same powers. Ideal LC'-C'L type
`broadband matching circuits are employed at the input and the output. (b) Sim-
`ulated large-signal insertion loss at an output power of 28 dBm.
`
`in Fig. 7, and increased ratio of knee to the Voc. Thus, the
`minimum of the envelope is set as 0.8 V. As the powerlevel
`is varied, the slope of the envelope is modified by the equation
`for the compensation of low gain near the knee region while
`maintaining the offset voltage. It is noted that x (back-off) =
`—1 ora lowervalue is applied to the equation for the maximum
`average output power because PAsoften operate in saturation,
`butis still under the specification. With the envelope-shaping
`method, the PA always operates at the IMD sweetspot tracked
`
`

`

`
`
`
`
`
`55
`
`:
`
`2604
`
`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 58, NO. 10, OCTOBER 2010
`
`Solid: measured
`Dash: simulated
`
`Frequency [GHz]
`
`
`
`S-parameters[dB]
`
`
`
`LTE
`|-O— WCDMA
`—&— EDGE Vnys.=90
`-—— EDGEVhys.=0 V
`LTE pdf
`
`3 70
`oe
`2 59
`2
`- 40
`i
`
`=>
`
`
`0.0
`0.2
`04
`06
`0.8
`1.0
`Normalized Switching Current
`
`Fig. 9. Simulated average switching currents adaptation for LTE, WCDMA,
`
`and EDGEsignals. The switching currents are normalized as 640 mA.The pdf
`of each signal is also depicted as a function of tew(= Vout/Rioad):
`
`[V]
`
`ModifiedEnvelope
`
`Back-off=-1 dB,
`
`; -Back-off=1 dB
`
`“Back-off=2 dB
`
`—~"Back-off=4 dB
`<= " Back-off=6 dB
`*" Back-off=10 dB
`
`0
`
`1
`
`3
`2
`Original Envelope [V]
`
`Fig. 10. Function of