INTEL 1317
`
`WLUME 58
`
`NUMBER 10 _
`
`IETMhB
`
`(ISSN 0018-9480)
`
`
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`
`
`WhmmMAmmnners
`_ A Linn-Power Shoe-Embedded Radar for Aiding Pedestrian Inertial Navigation .............................................
`
`'
`............................................................................. C. Zium. J. Dan-nay. D. Sianril'. and T: Mukheerjee
`1 mm {Ill-culls, Semiconductor Devices. and [Cs
`
`"ti-E 5.5-mW +9.4-dBm 11W LEWIS NF CMOS LNA- Employing Multiple Gated Transistors With Capacitance
`
`n; Demsiti-zalion ......................................................................................... I H. Jin and T. W Kim
`”Ink liner-Optimized Difi‘emnlinl 406nm: Transimpednnce Amplifier in SiGc BiCMOS ....................................
`
`_
`.............................................................. C. Knm'heimrmen S. Haupmmnu. J. C. Sting-u. and E Eflinger
`'i 243 Electrical lnturfcrometer: A Naive! High-Spud-Quantiw .................................. Y. M. Tnnsf and E. Afshari
`
`iflpiimized Iknign of a Highly Efficient Tum-Stage Dohcny PA Using Gate Adaptation .................................. ..
`---------------------------------------------------------------------------------------------
`
`I. Kim. J. Moon, S. Jen. and 8. Kim
`'
`15:! ('nmpncl fl. lwltlvGHz U'itrn-Wldcbund Lew-Noise Amplifier in‘D. Ill-pm CMOS .. . .. .. 2-! Chang and S. S. H. Hm
`
`h-Dplimjznt-ion of n Photnnlcally Cnntrolled Micmwavc Switch and Attenuator ............. J. R. Flemish and R. L Haunt
`
`[Mm Communal System:
`
`the Modulaled Scauering Antenna Array for Mobile Tenninal
`“hie-amen] and Experimental
`Investigation of
`
`4 Applications ........................................................... M. He. 1.. Wang. Q. Chen. Q. Yuan, and K. .wwalvu
`
`:A Mullimfldcmlultiband Power Amplifier. Wilh u Boustul Supply Mudulator ............................................
`,I
`.............
`........................................................ n. Kong, 1). Kim-J. Chen. J. Kim, K Cha. and a. K54:
`
`'
`.
`1.1 Analysis and Guided mm
`
`‘
`:{Bpuce-Chnrge Ptanc~ane Interaction at Semiconductor Substrate Boundary ................................................
`
`2609
`.
`_
`....................................................................... I. A. Elabyad. M. S. Eidesmuki. and H. M. Ei-Hcmmwy
`2619
`-. “'
`ll—Space Scanning Periodic Phase-Reversal waxy-Wave Antenna ........................ N. Yang. C. Caid; and K. Wu
`
`(Contents Continued on Back Cover)
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`2521
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`2529
`21538
`2549
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`1562
`2575
`2582
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`25-89
`2593
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`QIEEE
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`INTEL 1317
`
`i
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`u—..-—-.¢a.—u——.—-.—___...—____.__.-..__.__-___—--.———-—--_——-————-v.-._...._.
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`
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`
`
`KANG et (11.: MULTLMODEJMULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`2599
`
`class-F PA, using a push—pull structure. The class-J PA utilizes
`the phase shift between the output current and voltage wave-
`forms to render the second harmonic termination to a purely re-
`active regime [19].
`The broadband approaches for class-E PAs and class—F PAS
`have been studied 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 PAS for handset
`applications. In [22], we have proposed broadband class—F PAS,
`which control the second and third harmonic impedances across
`a broad BW, but linearity is not considered as we intend to use
`a digital pre-distortion (DPD) technique. Broadband class—J
`PAS for 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
`impedance to the 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 (normally it is 6 dB/octave because of its
`operation at the maximum stable gain (MSG) region), Despite
`the advantageous characteristics of the GaN device, it is too
`expensive at the moment to 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.
`Some researchers have utilized the advantages of the wide-BW
`linear amplifier and the high-efficiency switching amplifier
`[10]—[15]. The switching amplifier does not follow most of 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
`power in 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 lead 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 matching circuit, thereby
`reducing their size and increasing the available BW. In con—
`trast to 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-
`proves linearity due to interrnodulation—distortion (IMD) sweet—
`spot tracking. Multimode operation for various wireless appli—
`cations is accomplished thanks to programmable hysteresis con—
`trol and automatic switching current adaptation from the HSA.
`
`Vdd
`
`Supply Modulators
`
`
`
`Supply Modulatorz
`
`
`
`EDGE
`[WCDMA
`ILTE
`Ema“,
`
`J'LTE
`
`
`
`MICDMA
`‘:
`
`(8)
`Vdd
`
`MultiMode
`Supply
`Mud ulster
`
`Broadband!
`
`Mutllband PA
`
`.
`
`(b)
`
`(a) Conventional polar transmitter for multimode/multiband operation.
`Fig. l.
`(b) Proposed polar 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), wideband code division multiple access (WCDMA),
`and EDGE across 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.
`
`II. MULTlMODE/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,EDGE application across a 1.7—2.0-GHz fre-
`quency, supply modulators and PAS need to operate at different
`switching frequencies and operate at different RF frequencies
`for each standard. The LTE Signal has a BW of 10 MHz and
`a PAPR of 7.5 dB. WCDMA and EDGE signals have BWs of
`
`

`

`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.
`Each supply modulator for each application should be em-
`ployed for multimode operation. Moreover. if a natrowband PA
`is used. then every RF band will 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 DJ
`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 dc power that the PA consumes can be signifi-
`cantly reduced. and the power-added efficiency (PAE) can be
`significantly increased at the average power level, as well as at
`the peak output power level.
`
`IH. TECHNIQUES FOR HIGH EFFICIENCY AND BROADBAND
`
`A. Class-AB/F PAS
`
`A highly efficient class-AB/F PA has been proposed in [25],
`which enhances the efficiency by controlling the second and
`third harmonics while maintaining their 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 EDGE signals. The output
`load impedance Ropt is set to an intermediate value for mul-
`timode operation. Class—E, inverse class-F, or class-J PAs can
`previde an even higher efficiency or a broader BW, but we adopt
`the efficient and linear class—F PA for ET operation because lin-
`earity improvement techniques 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 (VCC = 4.5 V), the fundamental
`load impedance is set to be 6 + j 1 Q for a l-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 shown in Fig. 2. This figure shows that 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 impedance is more sensitive to the matching circuit
`than the third harmonic impedance, but is manageable over a
`few hundred megahertz BW using a second harmonic control
`circuit.
`
`B. Broadband Matching Techniques
`
`There are equations that transform a low—pass filter (LPF)
`to a bandpass filter (BPF) [26]. The BPF does not allow the
`impedance transformation required for PA designs. The BPFs
`
`\'
`
`
`
`'
`
`_-"'Fundamental
`I: Impedance
`
`I
`
`(b)
`
`Fig. 2. Simulated load—pull results at a frequency of 1.85 GHa. (3))For third
`harmonic impedance. The fundamental and second harmonic impedances are
`it xed at 6 +31 and U .5 —j2.5 , respectively. {b} For second harmonic impedance.
`The fundamental and secord harmonic impedances are fixed at 6 + jl and
`25 + j 200, respectively.
`
`shown in Fig. 3(c) and (d) make it possible to transform the im-
`pedances and to have bandpass characteristics. To analyze the
`BW, ‘the concept of Q needs to be recalled. A loaded Q, de-
`noted by Q L, is defined by
`
`
`_ Qn _ fa
`QL ‘ 2 _ Bw'
`
`,
`
`(1)
`
`The circuit node Q, denoted by Q”, is defined at each node as
`
`RT
`IX l
`R
`Rs
`71 = — = — — ]_
`
`Q
`
`(2)
`
`where RT is a transformed resistance from Rs and RT is larger
`than R5. The smaller Q” leads to broader BW, which means
`that the same impedance transformation ratio using two-section
`matching achieves a wider BW. In Fig. 3(c)—(f), to get the lowest
`Q” with the impedance transformation, the relationship of im—
`pedances is given by
`
`122 = m-
`
`(3)
`
`Fig. 3(e) is a high—pass filter (I-IPF) type matching circuit,
`which comprises two sections, and it has the same Q as
`
`

`

`KANG et al.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`2601
`
`capacitance 0,, is resonated out at the third harmonic frequency
`by the inductance at the bias line. The fundamental impedance
`matching uses LC—CL type broadband matching. The shunt
`L3 03 has an inductance at the operating frequency, and can be
`merged into a bondwire L1 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 impedances across the
`5.1—6.0—GHz frequency 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 5' 21 over the frequency rage of 1.7—2.0 GHz. 521 has the
`two nulls at 3.3 and 3.8 GHz, which are produced by 022 with
`a short microstrip line and L2 02, 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
`
`The supply voltage of the linear stage of the HSA is increased
`from 3.4 to 5 V by the boost converter depicted in Fig. 4. Since
`the buffer comprising the linear stage has a voltage drop of 0.5 V,
`the output voltage swing of the supply modulator is boosted
`up to 4.5 V. Our previous HSA [15] had a maximum output
`voltage of only 3 V. Due to the boosted output voltage, the PA
`can generate more power with the same output load. In other
`words, the output load impedance can be raised for the same
`output power as illustrated in Fig. 6, which delivers ‘a higher ef-
`ficiency and broadband characteristics. The broadband charac-
`teristics are explored using the output capacitance variation plot
`shown in Fig. 7. The supply voltage V230 is swept with funda-
`mental load impedances of 2.5, 3.5, 4.7, and 6 9, which deliver
`the same output power with the maximum supply voltages of 3,
`3.5, 4, and 4.5 V, respectively. When ET operation follows the
`highest efficiency at each supply voltage, the output capacitance
`of the transistor follows the Gout trajectory in Fig. 7. The output
`
`capacitance is calculated by the method shown in [24]. As the
`supply voltage decreases, the output capacitance increases. At
`an output power of 32 dBm, the PA using Ropt of 2.5 Q with a
`supply voltage of 3 V has about a 10% larger output capacitance
`than that using Ropt of 6 S2 with a supply voltage of 4.5 V. If an
`LTE signal with a 7.5-dB PAPR is applied to the PA, the max-
`imum average power is theoretically 24.5 dBm because the Pl
`dB of the PA is 32 dBm. In actual operation, however, the PA can
`achieve an average output power of 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 VCC has a smaller impedance
`transformation ratio, which assists in increasing the operational
`RF BW. Fig. 8(a) shows a simulated continuous wave (CW) per-
`formance for PAE and gain of the supply voltages of 2.6 V with a
`load of 6 Q and 2 V with a load of 2.5 Q for the power stage. The
`
`supply voltages are reduced for operation of the LTE average
`output power of 28 dBm. The PA with 6 Q has 10% higher PAE
`and higher gain. Fig. 8(b) shows the insertion loss obtained by a
`
`'
`
`(c)
`R2
`
`'
`
`Yd)
`R
`
`g1—i
`
`R3
`
`R1
`
`R3
`
`.
`' (e)
`
`i
`
`E
`
`I
`'(f)
`
`I
`7
`
`(a) LPF type.
`Impedance—matching circuits.
`3.
`Fig.
`(c) and (d) BPF type with impedance transformation.
`HPF type. (f) TWO-section LPF type.
`
`(b) BPF type.
`(e) TWO—section
`
`Fig. 3(c) and (d). The 3—dB BW might be the same, but the BPF
`types are better because the BPFs maintain more consistent
`impedance level across lower to upper bands. Moreover, the
`BPF types shown in Fig. 3(c) and (d) have an advantage of
`smaller inductance than the HPF of Fig. 3(c) because a series
`inductance (reactance) is smaller than a shunt
`inductance
`
`(susceptance) where a low impedance is transformed into a
`high impedance of 50 Q in the PA designs. The series inductors
`marked with a star and with a circle in Fig. 3(c) and ((1), respec-
`
`tively, are smaller than those marked in Fig. 3(c). Fig. 3(f) is an
`LPF type matching circuit. Even though the BW is broad, an
`LPF is a unwelcome circuit for the input and output matching
`of handset PAS because dc currents from the supplies should
`be blocked. The BPFs shown in Fig. 3(d) are employed in
`this broadband class-F PA design because of their broadband
`characteristics and their small inductor values, which can be
`
`easily replaced by bondwires.
`
`C.
`
`Input, Interstage, and Output Matching
`
`As illustrated in Fig. 4, an input capacitance composed of Cbe
`and 01,0 increased by Miller’s theorem is merged into the se—
`ries inductor of the LC—C’L broadband matching circuit [see
`Fig. 3(d)] to maximize the BW. The intermediate impedance
`is set as 10 9 to transform the 2 Q of the input resistance to
`the 50 Q of the input terminal. The interstage is matched with
`two-section HPFs, including the bias line inductance at the 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. L2 02 has a near zero impedance at the upper band of the
`second harmonic and 022 with a short microstrip line has a
`near-zero impedance at the lower band of the second harmonic.
`Thus, the voltage waveform of the second harmonic is effec—
`tively reduced across the broadband. The shunt L303 provides
`a high impedance at the third harmonic frequency. The output
`
` ‘.
`
`
`
`_—.-a-——n-—-;-—‘—-—1-
`
`

`

`2602
`
`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10. OCTOBER 2010
`
`VDD = 3.4 V
`
`
`
`lIII
`
`I
`V I
`3‘” 1
`I
`II
`II
`I
`:
`1I
`
`II|Il|I
`
`
`
`
`Control Stage
`II
`
`
`(Hysteretic Comparator)
`
`
`Anti-shoot-
`
`
`3.4V to 5 V
`
`
`through
`
`Boost Converter
`Gate drive
`
`
`
`buffer
`
`5V
`Hysteretic
`II
`
`
` Class-AB buffer
`Comparator
`OTA
`
`4.
`
`+
`
`Current sensing
`Class-AB bias
`
`circuit
`II
`Switching Stage
`
`(Buck Converter)
`
`
`
`|
`I. ________________ —l
`Jlout
`
`|
`l
`|_
`
`II
`
`
`Linear Stage
`
`(0TA+Buffer)
`
`
`
`
`CF
`
`C3
`
`InGaP/GaAs HBT lC
`__________ I
`_____ 'I
`I
`Ic
`Ian—I— 2"d harmonic short
`z
`__ __ _ h _J ______________ _‘
`"
`L3
`'
`I
`: L2
`_____ o o l
`1
`I
`.
`:
`l
`1
`I
`I
`L I
`I
`I
`4 |
`I
`I
`l
`I
`I
`I
`I
`:
`L _ :_____ L _ ._ ._ _ I
`|
`3rd harmonic open I
`I
`I
`
`L1
`O 0 fi
`
`61
`
`r- "w.
`I
`1
`I
`I
`I
`|
`I
`|
`I
`I
`C22 |
`| I i
`: _
`I
`_
`t
`
`___
`
`Broadband Output Matching
`
`Fig. 4. Schematic of the ET transmitter with broadband class-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 HSA consists 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 independent voltage
`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 of the 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. The adaptation of the switching currents for
`the various PAPRs are automatically performed by the current
`sensing circuit and the hysteretic comparator in the HSA. The
`switching current is proportional to the difference between V..."
`and ir’REF, as shown in Fig. 4. The Sensed current generates the
`sensed voltage V5...“ which is proportional to the input of the
`envelope signal. Thus, the square of Ihe switching current is
`inversely proportional to the PAPR.
`The adaptation of switching currents for multislandard sig—
`nals is shown in Fig. 9. which illustrates the probability density
`function tpdfi and the efficiency of the HSA. For a multimode
`HSA design. 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
`lower than that of the switching amplifier leads to an excessively
`high switching frequency and poor efficiency of the switching
`stage. Thus. we utilize a prograrnmabie hysteretic comparator.
`which enables us to control the hysteresis voltage Vim“ and the
`
`

`

`KANG el (1].: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR
`
`2603
`
`
`
`‘10
`
`3:
`
`
`
`
`
` OutputCapacitance[pF]
`
`'
`I
`
`:Cmtrajecloja
`:
`forfifl
`I
`1"I'1'I't'lil'1'l
`15
`17
`19
`21
`23
`25
`27
`29
`31
`33
`
`Output Power [dBm]
`
`Fig. 7. Output capacitance as functions of Ram, Va;Y and output power. With
`an ET operation, the output capacitance of the PA follows the Co... trajectory.
`
`
`mD
`
`2.6VVcc
`— 2vvcc
`
`J:01OO
`
`
`
`PAE[°/o],Gain[dB] U
`
` 10
`
`
`
`
`o
`
`5
`
`1o
`
`15
`
`20
`
`25
`
`so
`
`Output Power [dBm]
`(a)
`
`
`
`3:0
`’
`2:5
`I
`2:0
`Frequency [GHz]
`('3)
`
`I
`
`sis
`
`I 40
`
`(3) 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 Vcc have Rep.
`of 6 and 2.5 9, 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 V00. Thus, the
`minimum of the envelope is set as 0.8 V. As the power level
`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 :1: (back-off) =
`—1 or a lower value is applied to the equation for the maximum
`average output power because PAs often operate in saturation,
`but is still under the specification. With the envelope-shaping
`method, the PA always operates at the IMD sweet spot tracked
`
`
`
`
`
`0
`
`
`
`-10..
`
`8—20—
`
`E E”
`
`-30
`
`4o-
`
`
`
`‘50!||IlIltnlr'l'illllil1ll'llllllll
`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
`
`
`Load line for
`3.4V operation
`
`
`
`5" 1.0
`.0
`
`0.5
`
`0.0
`
`VCE [V]
`
`Fig. 6. Load line of 2.5 and 6 Q for 3.4- and 4.5-V operation for the same
`maximum output power. Load line for 4.5 V gives higher efficiency and broader
`BW, as well as more linear ET operation at the low-power level.
`
`switching frequency. Efficiency of about 3% is enhanced by
`controlling the hysteresis voltage for the EDGE signal.
`The envelope is modified for linear ET operation, as depicted
`in Fig. 10. The equation for the envelope shaping is given by
`
`
`Envelope’ : <1 —
`
`'
`
`- 10“”20> . Envelope + Offset
`
`(4)
`
`where :1: 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
`
`

`

`2604
`
`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010
`
`40
`
`N)
`
`OO
`
`
`
`S-parameters[dB] '3
`
`-40
`
`
`
`100
`
`90
`
`80
`
`70
`
`10
`
`
`
`LTE
`6"
`u— WCDMA
`: 50
`-1— EDGE vhys.=90
`.9
`3% 40 — EDGE vhys_=ov
`L”
`30
`LTE pdi'
`20
`
`'3'
`
`t 3
`
`Solid: measured
`Dash: simulated
`
`
`
`Frequency [GHz]
`
`
`
`0.0
`
`0.8
`0.6
`0.4
`0.2
`Normalized