Allen Katz
`
`©1999JOHNFOXXIMAGES&IMAGESFORCOMMUNICATION
`
`O ur
`
`society’s need to exchange
`greater and greater amounts of in-
`formation has created an unprece-
`dented demand for highly linear
`power amplifiers (PAs). High lin-
`earity is required for the spectrally efficient trans-
`mission of information.
`This article discusses techniques for the cancella-
`tion of distortion (linearization). Different methods
`of linearization are introduced and compared. The
`linearization of solid-state power amplifiers (SSPAs),
`traveling-wave-tube amplifiers (TWTAs) and kly-
`stron-power amplifiers (KPAs) are considered. Al-
`though the focus of
`this article is on power
`amplifiers, many of the techniques are applicable to
`other components as mixers, low-noise amplifiers,
`and even photonic components, such as lasers and
`optical modulators.
`
`Amplifier Linearity
`Technological developments are rapidly changing the
`communication business. In the past, the bulk of satel-
`lite transmissions was single-carrier video signals. Dig-
`ital compression now allows many television signals to
`be transmitted in the frequency space previously occu-
`pied by a single signal. Nonvideo, broadband very
`small aperture terminals (VSATs) and mobile tele-
`phone/Internet services are altering traditional satel-
`lite loading. New terrestrial microwave services for the
`transmission of video, data, cellular telephone, and
`personal communications are appearing daily. Band-
`width-efficient modulation (BEM) schemes are becom-
`ing common. Virtually all of these services involve the
`transmission of multiple signals and/or large quanti-
`ties of information at high data rates. For such signals,
`
`Allen Katz is with The College of New Jersey, Ewing, New Jersey.
`
`magazine
`IEEE
`ISSN 1527-3342/01/$10.00©2001 IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`37
`
`PETITIONERS EXHIBIT 1007
`Page 1 of 13
`
`

`

`eliminated by filtering and do not pose a problem ex-
`cept for wideband-communications applications of an
`octave or greater bandwidth. However, when more
`than one carrier is present, beat products are produced
`in the vicinity of the input signals. These new signals
`are known as intermodulation-distortion (IMD) prod-
`ucts. They are located at frequencies above and below
`the input carriers and at frequency intervals equal to
`the separations of the input carriers (Figure 1). Filtering
`cannot easily eliminate IMD products since they are lo-
`cated on the same frequency or near to the desired in-
`put signals.
`Distortion is also produced by phase nonlinearity.
`The shift in phase angle that a signal encounters in
`passing through an amplifier is a measure of the time
`delay. Ideally, this phase shift, or time delay, should be
`constant for all power levels. A change in time delay
`with frequency, known as phase delay, envelope delay,
`or group delay, causes linear distortion and can be cor-
`rected with a phase equalizer
`
`(
`θ Pin
`
`)
`
`=
`
`constant
`
`,
`
`(2)
`
`where Pin is the instantaneous-input power level. In
`practical amplifiers, there can be a substantial change
`in phase with power level
`
`)
`(
`θ = f Pin .
`
`(3)
`
`This change in phase with amplitude converts varia-
`tions in signal level to phase modulation (PM). For a si-
`nusoidal signal envelope
`(
`)
`2,
`k A
`
`( )
`P t
`in
`
`=
`
`[
`cos ω
`
`]
`tm
`
`the resulting spectrum resembles that of a sinusoidal
`modulated PM signal
`(
`ω
`cos
`
`=
`
`)
`(
`J M
`n
`
`(
`[
`ω
`cos
`
`)
`
`c
`
`+
`
`ω
`
`n
`
`m
`
`]
`t
`
`)
`,
`
`(4)
`
`A
`
`c
`
`t M+
`
`
`c
`
`]
`t
`m
`
`[
`ω
`cos
`=∞∑
`
`A
`
`c
`
`n
`
`=−∞
`
`n
`
`whether transmitted by frequency-division multiple
`access
`(FDMA),
`code-division multiple
`access
`(CDMA), or time-division multiple access (TDMA),
`amplifier linearity is a major consideration.
`At high power levels (>100 W) TWTAs and KPAs of-
`fer the best microwave performance in terms of size,
`cost, and efficiency but lag behind SSPAs in linearity. The
`use of linearization can yield TWTA and KPA perfor-
`mance comparable or superior to conventional SSPAs.
`At lower powers, the advantage switches to SSPAs. As a
`result of new stringent linearity requirements, even rela-
`tively linear SSPAs can benefit from linearization.
`
`Nonlinear Distortion
`Nonlinear distortion can be thought of as the creation
`of undesired signal energy at frequencies not contained
`in the original signal. Distortion is produced by a loss of
`linearity. Amplitude linearity can be considered a mea-
`sure of how closely the input-output transfer response
`of an amplifier resembles a straight line. When an am-
`plifier’s input level increases by a certain percent, its
`output level should increase by the same percent. A de-
`viation from a straight line can be represented by a
`power series
`
`V
`out
`
`=
`
`K V
`1 in
`
`+
`
`2
`K V
`2 in
`
`+
`
`3
`K V
`3 in
`
`+L
`
`K Vn in
`
`n
`
`
`.
`
`(1)
`
`When a single-carrier input signal, represented by a
`sine wave, is substituted into this expression, the out-
`put waveform will contain the original sine wave and
`harmonic distortion products. The harmonics can be
`
`f1 f2
`
`Amplifier
`
`f1
`
`f2
`
`Distortion Products
`Figure 1. When ≥ 2 signals are amplified, distortion prod -
`ucts appear in the vicinity of the desired signals.
`
`Receiver
`
`Input
`Mux
`
`Channel Amp #1
`
`Channel Amp #2
`
`Output
`Mux
`
`Versus
`
`Single Amplifier
`
`In cellular telephony, sending several carriers through one
`Figure 2.
`amplifier is more cost effective.
`
`where ω c is the carrier frequency, ω m is the
`modulation frequency (frequency of the enve-
`lope), and M is the modulation index (propor-
`tional to A). The PM sidebands are the IMD.
`Thus, phase nonlinearity produces IMD pro-
`ducts in a similar fashion to amplitude non-
`linearity. In some systems, phase nonlinearity
`is the principal cause of distortion.
`When multiple signals are sent through a
`communications system, an amplifier must
`be operated at a reduced power level (backed
`off) in order to keep distortion at an accept-
`able level. Distortion is often measured as the
`ratio of the carrier-to-IMD power level. This
`
`38
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1007
`Page 2 of 13
`
`

`

`ratio is known as C/I. An acceptable level of IMD or
`C/I usually depends on the carrier-to-noise ratio
`(CNR) required at the receiver. IMD products can be
`considered to add to a receiver’s noise level on power
`basis. For a carrier to IMD ratio,
` If C/I = CNR, the resultant CNR degrades by ap-
`proximately 3 dB.
` If C/I = CNR + 6 dB, the resultant CNR degrades
`by approximately 1 dB.
` If C/I = CNR + 10 dB, the resultant CNR degrades
`by approximately 0.05 dB.
`Thus, if the IMD products are to have a negligible affect
`on system performance, they should be at least 10 dB
`smaller than the carrier level.
`In the case of cellular telephony, it is often more con-
`venient and cost effective to
`transmit several carriers through
`a common amplifier rather than
`to use multiple amplifiers and a
`lossy multiplexer (Figure 2). To
`avoid unacceptably high IMD,
`the common amplifier must be
`highly linear.
`For the transmission of a sin-
`gle carrier, IMD is usually not a
`limitation. However, with digi-
`tally modulated signals, spectral
`regrowth (SR) can be a serious
`problem. SR manifests itself in a
`form equivalent to IMD. It is not
`unique to digital signals but an
`aspect of angle modulation (FM
`and PM). Angle-modulated sig-
`nals have a theoretically infinite
`bandwidth;
`for example,
`the
`spectrum of a sinusoidal modu-
`lated-PM signal of (3) contains an
`infinite number of sidebands. In practice, the bandwidth
`is limited to a finite frequency band beyond which side-
`band amplitude drops off rapidly. Analog PM has an ap-
`proximate bandwidth given by Carson’s rule
`
`( )−
`
`Sin
`
`SSin
`
`(Saturation)
`
`Pout
`
`Pout
`
`Pout
`
`Pin
`
`Pin
`
`Pin
`
`Figure 3. As an amplifier is driven closer to SAT, its out -
`put level will increase by a smaller amount.
`
`(+)
`
`Main Amp
`
`Sout1
`
`m
`
`Sout2
`
`SSout1
`
`0
`
`Aux. Amp
`
`Scor
`
`1
`
`(+)
`
`( )−
`
`causes the SR when a digital signal is passed through a
`nonlinear amplifier. The distortion of the induced-am-
`plitude waveform produces IMD products that in-
`crease the signal’s spectrum.
`The change in phase with amplitude (3) converts the
`variations in signal level to angle-modulation sidebands.
`These new sidebands further broaden the signal band-
`width. Amplitude and phase-induced spectral products
`add as vectors and are classified, in general, as IMD.
`The summation of the IMD terms in an adjacent
`channel is referred to as the adjacent-channel power
`level (ACPL),
`
`ACPL
`
`
`
`IMDs in an adjacent channel.= Σ
`
`The ratio of the adjacent-channel power to the car-
`rier power is known as the adjacent-channel power
`ratio (ACPR).
`ACPL is a major concern in personal-communica-
`tions systems (PCS) since transmission often occurs on
`
`Figure 4. Feedforward linearization employs two loops for the cancellation of IMD.
`
`BW =
`
`(
`2 ∆f
`
`+
`
`)
`fm ,
`
`(5)
`
`where ∆f is the peak frequency deviation and fm is the
`modulation frequency. The effective bandwidth of an-
`gle-modulated digital signals can be much greater than
`predicted by (5) due to the high-frequency components
`of the modulating waveform. To reduce their band-
`width to a more acceptable value, digital waveforms
`are normally low-pass filtered before modulation. Be-
`cause of the mechanics of most digital modulators,
`which are not true angle modulators, the amplitude of
`the carrier is also modulated by this process. In addi-
`tion, any “band-limiting” filtering of an angle-modu-
`lated signal will introduce amplitude modulation. It is
`primarily this incidental amplitude modulation that
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`39
`
`PETITIONERS EXHIBIT 1007
`Page 3 of 13
`
`

`

`munications amplifiers in the past, except for some spe-
`cial applications.
`
`K2 3 dB
`K2 10 dB
`K2 6 dB
`
`Saturated Power
`All amplifiers have some maximum output-power ca-
`pacity, referred to as saturated power or simply saturation
`(SAT) (Figure 3). Driving an amplifier with a
`greater input signal will not produce an out-
`put above this level. As an amplifier is driven
`closer to SAT, its deviation from a straight-line
`response will increase. Its output level will in-
`crease by a smaller amount for a fixed in-
`crease in input signal, as shown in Figure 3.
`Thus, the closer an amplifier is driven to SAT,
`the greater the amount of distortion it nor-
`mally produces.
`The SAT point of TWTAs and KPAs is
`clearly defined as the output power normally
`decreases beyond SAT. Many SSPAs are sensi-
`tive to overdrive and can be easily damaged
`by operation at or beyond SAT. In addition,
`SSPAs tend to approach SAT exponentially.
`These factors make engineers reluctant to
`measure and use SAT as a reference for com-
`parison of SSPA performance. They prefer to
`use the power at which an amplifier’s gain
`compresses by 1 dB as the reference (REF) for
`amplifier comparison.
`
`a channel adjacent to one in which reception of a much
`weaker distant signal may be taking place. To ensure
`freedom from interference, transmitter IMD products
`must be below the C/I by anywhere from 35 to >65 dB,
`depending on the application. These levels of linearity
`are considerably higher than had been required of com-
`
`0
`
`3
`5
`6
`8
`9
`1
`2
`4
`7
`Aux. Amp Size Relative to Main Amp in dB
`
`10
`
`9 8 7 6 5 4 3 2 1 0
`
`Min.OPBO for IMD Cancellation in dB
`
`Pin
`
`Coupler
`
`Gain
`+
`
`−
`
`Σ
`
`Φ
`
`Phase
`
`HPA
`
`Φ
`Detector
`
`Figure 5. The minimum OPBO for cancellation of IMD by a FF ampli-
`fier depends on the aux-amplifier size and output coupler coefficient.
`
`Pout
`
`Coupler
`
`IFB compares an amplifier’s output and input and uses the
`Figure 6.
`detected difference to minimize distortion.
`
`Quad Hybrid
`
`Vector Modulator
`
`Pin
`
`Coupler
`
`Zo
`
`LPF
`
`90°
`
`LPF
`
`−
`
`−
`
`+
`
`+
`
`LO
`
`REF = 1-db CP = SAT - D.
`
`(6)
`
`For SSPAs with reasonable linearity, the
`difference (D) in output level between SAT
`and the 1 dB compression point (CP) is
`
`Pout
`
`Coupler
`
`HPA
`
`LPF
`
`90°
`
`LPF
`
`Figure 7. Cartesian feedback eliminates the need for phase correction components by using the difference between in-phase
`and quadrature signals to control attenuators in a vector modulator.
`
`40
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1007
`Page 4 of 13
`
`

`

`for a C/I = 65 dB. These are huge reductions in usable
`output power. Therefore, it is desirable to look at vari-
`ous linearization techniques.
`
`Linearization Techniques
`Linearization is a systematic procedure for reducing an
`amplifier’s distortion. There are many different ways of
`linearizing an amplifier. Usually, extra components are
`added to the design of a conventional amplifier. These
`extra components can often be configured into a subas-
`sembly or box that is referred to as a linearizer.
`Linearization allows an amplifier to produce more out-
`put power and operate at a higher level of efficiency for
`a given level of distortion. Feedforward, feedback, and
`predistortion are the most common forms of lineari-
`zation. Besides these, there are a variety of other ap-
`proaches that are being investigated. Most of these
`approaches use special techniques to obtain a linear
`output signal from highly nonlinear amplifiers. None
`of these alternate methods have been widely applied in
`wireless or microwave applications.
`
`PoutA
`
`Pout
`
`PinL
`
`PinA
`
`Pin
`
`Predistortion
`Linearizer
`
`PoutL
`
`PinA
`
`PoutA
`
`HPA
`
`Output
`
`Figure 8. PD linearizers generate a response opposite to an HPA’s response in mag-
`nitude and phase.
`
`Gain in dB
`
`0 −
`
`0.5
`−1.0
`−1.5
`−2.0
`−2.5
`−3.0
`−3.5
`−4.0
`−4.5
`
`LIN Phase
`
`LIN Gain
`
`45
`
`40
`
`35
`
`30
`
`25
`
`20
`
`15
`
`10
`
`5 0
`
`Phase in Degrees
`
`−20
`
`−18
`
`−16
`
`−14
`
`−12
`
`−8
`
`−6
`
`−4
`
`−2
`
`0
`
`−10
`PIN dB
`
`Figure 9. An ideal PD-linearizer response requires the gain-and-phase slope to become infinite as SAT is approached.
`
`magazine
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`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`41
`
`about 1 dB. Unfortunately, D varies from amplifier to
`amplifier. Generally, amplifiers with high linearity
`will have a smaller difference (D < .25 dB), while am-
`plifiers with poor linearity can have a difference of
`several dB (D > 2 dB).
`For this reason, in this article the relative amplifier
`performance will be referenced to (single-carrier) SAT.
`Output-power backoff (OPBO) will be relative to an am-
`plifier’s single-carrier SAT. (For most SSPAs, SAT can be
`safely determined using a network analyzer in a rapid
`power-sweep mode. For amplifiers that are especially
`thermally sensitive, pulsed power-sweep techniques
`may be used.) When comparing the data presented here
`with that of SSPAs based on a 1-db CP REF, an appropri-
`ate correction factor should be assumed.
`Generally the greatest efficiency of a high power
`amplifier (HPA) will occur at or near SAT. Similarly, the
`closer to SAT a linear amplifier (class-A and, to a large
`extent, class-AB) is driven, the greater the amount of
`distortion it produces. For a satellite system, if a CNR of
`16 dB (10 dB FM threshold + 6 dB for rain fading) is re-
`quired and the IMD products are
`to have a negligible effect, then a
`C/I ≥ 26 dB is needed. To satisfy
`this requirement, a TWTA would
`typically have to be backed off 5-7
`dB and sometimes more. This is
`about a 4-to-1 reduction in usable
`power. For TDMA applications,
`the backoff is less, usually 2-4 dB,
`to keep distortion in the form of
`SR from interfering with adja-
`cent-channel
`communications.
`To satisfy cellular/PCS adja-
`cent-channel IMD requirements,
`a (class-A) SSPA would have to be
`backed off about 6.5 dB for a C/I
`= 35 dB and by more than 15 dB
`
`PoutL
`
`PinL
`
`Input
`
`PETITIONERS EXHIBIT 1007
`Page 5 of 13
`
`

`

`introduced in
`and phase shift
`loop 1 for adjustment of the car-
`rier cancellation.
`The second loop subtracts the
`amplified sampled distortion of
`loop 1 from a delayed Sout1 to ide-
`ally produce a distortion-free
`output signal (Sout2). The loop 1
`output signal is amplified by an
`auxiliary (aux) amplifier of gain
`GA and phase shift Φ aux to pro-
`vide a correction signal (Scor ) of
`sufficient level to cancel the dis-
`tortion introduced by the main
`amplifier. Scor is combined with
`the main amplifier signal at a fi-
`nal directional coupler of coeffi-
`cient K2. If
`(
`∠
`Φ
`)
`°
`180
`,
`
`+
`
`Φ
`1
`
`)
`
`aux
`
`(9)
`
`2-Tone
`
`Many-Tone (NPR)
`
`80
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`10
`
`0
`
`C/I in dB
`
`1
`
`2
`
`3
`
`4
`
`6
`5
`Output Backoff in dB
`
`7
`
`8
`
`9
`
`10
`
`Figure 10. C/I of an ideal linearizer for two and an infinite NPR.
`
`Feedforward Linearization
`Feedforward (FF) has been extensively used with
`SSPAs and functions well with TWTAs and KPAs but is
`rather complex to implement and not easily added to
`an existing amplifier. A block diagram of a basic FF sys-
`tem is shown in Figure 4. This system consists of two
`loops. The first loop subtracts samples of the input sig-
`nal (Sin ) from the output signal (Sout1) to produce a sam-
`ple of the main amplifier’s distortion. Sout1 consists of
`the amplified input signal plus any distortion intro-
`duced by the amplifier
`
`=
`
`GS
`in
`
`
`
`∠Φ
`
`amp
`
`+
`
`IMD,
`
`(7)
`
`S
`cor
`
`=
`=
`
`A GAK K
`1
`1
`(
`∠
`Φ
`IMD
`
`2
`
`in
`
`IMD
`+
`
`then the HPA output will be distortion free. A1 and Φ1
`are, respectively, the attenuation and phase shift intro-
`duced in loop 2 for adjustment of the distortion cancel-
`lation. Φ m is a delay added after the main amplifier to
`equalize the delay introduced by the aux amplifier
`
`S
`out2
`
`=
`
`S
`out1
`
`
`
`∠ +Φ
`m
`
`S
`cor
`
`.
`
`(10)
`
`From this discussion, it may appear that undistorted
`output can be obtained from a FF amplifier right up to
`SAT. Saturated output power can never be obtained
`from a FF amplifier because of the losses in the phase
`shifter and couplers which must be located after the
`main amplifier. The main signal Sout1 is reduced in am-
`plitude by a factor (R1) due to passing through the K1
`coupler. In dB,
`
`S
`out1
`
`where G is the gain and ∠Φ amp is the phase shift intro-
`duced by the main amplifier. The samples of S
`(
`)
`SS
`in
`in
`and S
`) are
`(
`SS
`out1
`out1
`
`and
`,
`
`K S
`in
`K S
`out1
`
`0 1
`
`= =
`
`SS
`in
`SS
`out1
`
`where K0 and K1 are the coupling coefficients of the direc-
`tional couplers used to sample Sin and Sout1, respectively.
`If SSin is attenuated and delayed in phase such that
`
`=
`
`10
`
`R
`1
`
`(
`
`log
`
`
`
`1 10−
`
`(
`−
`
`k
`
`
`
`1 10/
`
`)
`
`)
`
`+
`
`L
`1
`
`,
`
`(11)
`
`where L1 is the dissipation loss of the coupler in dB. K1
`can be made very small, provided the main amplifier
`has sufficient gain (a K1 of -30 dB is not unusual). The
`K2 of the final directional coupler must also be rela-
`tively small to minimize the loss of output power (R2).
`Since the two signals, carriers, and distortion being
`
`(8)
`
`+
`
`180
`
`)
`°
`
`,
`
`amp
`
`= −
`=
`
`or
`SS
`out1
`(
`∠
`Φ
`GK S
`1
`in
`
`0
`
`0
`
`∠
`∠
`
`Φ Φ
`
`A SS
`0
`in
`A K S
`0
`0
`in
`
`then Sin is canceled and the output of loop 1 is
`K1IMD. A 0 and Φ 0 are, respectively, the attenuation
`
`Table 1. Trade summary for DSP-based PD linearization.
`
`Advantages
`
`Disadvantages
`
`Accurate correction over wide dynamic range and for
`irregular nonmonotonic characteristics.
`
`Correction bandwidth limited by sampling rate:
`SR = 2 CBW = (4 N + 2)BW.
`
`Easy to modify and update.
`
`Cost can be higher than analog.
`
`Simple to implement as adaptive system.
`
`Power consumption can be high.
`
`42
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1007
`Page 6 of 13
`
`

`

`plifier) and aux-amplifier size (relative to the main
`power amplifier) for cancellation of IMD. Minimum
`OPBO is given for different values of output-coupler co-
`efficient K2. These results depend on the linearity of the
`main and aux amplifiers and on the resistive loss of the
`couplers and delay line. Linear characteristics typical of
`a class-A gallium arsenide (GaAs) field-effect transistor
`(FET) SSPA were assumed for both amplifiers, and resis-
`tive losses of 1 dB were assumed for the passive output
`components. With an aux amplifier of half the size of the
`main amplifier (3 dB), cancellation of IMD can be
`achieved only up to about -6.3 dB from SAT with a K2 of
`6 dB (Figure 5). If only the SAT of the main amplifier is
`considered, the minimum corrected OPBO is -4.2 dB but
`occurs for an aux amplifier equal in size to the main am-
`plifier and a K2 of about 3 dB. (A minimum IMD cancel-
`lation of 20 dB was assumed. If only 10 dB is acceptable,
`an additional 1-2 dB increase in output level can be
`achieved.) In practice, other factors limit IMD reduction,
`and perfect cancellation can never be achieved. Figure 5
`reveals why FF is not a good choice for linearization of
`amplifiers near SAT. Other linearization methods can
`
`Vin
`
`Φ
`
`Vout(Low)
`
`Vnl
`
`Pout
`
`Vout(High)
`
`+ -
`
`Σ
`
`Linear
`
`Nonlinear
`
`Attn.
`
`where Lm is the loss of the delay line (Φ m). In practice, it
`is very difficult to achieve a ∆SAT of less than 1 dB.
`∆SAT can be considered the minimum OPBO of a FF
`amplifier. In actuality, ∆SAT must be added to the dif-
`ference between the SAT of an amplifier with single
`and multicarrier signals. This factor can vary from
`about .5 to >1.5 dB for HPAs. Furthermore, the ampli-
`fier’s true SAT should not be considered, only that of
`the main amplifier. A FF amplifier combines both the
`power of the main and the aux amplifier. The sum of
`the SAT of both these amplifiers should be considered
`when comparing the relative OPBO performance of dif-
`ferent methods of linearization.
`Practical considerations limit the size of
`the aux amplifier. This limits Scor and, in
`turn, the undistorted FF-output level. The
`smaller the K2 is set, the larger in power the
`aux amplifier must be sized. The aux ampli-
`fier must also be operated relatively linear
`so as not to distort the distortion signal,
`thus introducing distortion of its own. Fig-
`ure 5 shows the relationship between mini-
`mum OPBO (referenced from single-carrier
`SAT of the main amplifier and the aux am-
`
`÷
`
`Pin
`
`Figure 11. Gain expansion can be produced by subtracting a linear path
`from a nonlinear path.
`
`IX-QY
`
`cos 3 w0
`
`w1+3 w0
`
`Smoothing
`
`D/A
`
`FIL
`
`HPA
`
`IY+QX
`
`sin 3 w0
`
`~
`
`w1
`
`Calculate
`
`X (R)
`LUT
`
`Y (R)
`LUT
`
`R
`
`Update
`X(R), Y(R)
`
`I
`
`Q
`
`Interpolate
`
`I~
`
`cos 3 w0
`(1, 0, -1, 0)
`
`Q~
`
`
`
`sin 3 w0
`−
`(1, 0, 1, 0)
`
`I~
`
`A/D
`
`cos 3 w0
`sin 3 w0
`
`Q~
`
`Interpolate
`
`R'
`
`Compute
`Updated
`Values
`For
`X(R), Y(R)
`
`Spectrum
`BW
`
`0
`
`3 w0 6 w0
`Signal
`
`A/D
`
`LUT = Look Up Table
`T= Sampling Period
`
`T
`3 w0 (4D ) = 2 p
`3 f0 (4D ) = 1
`
`T T
`
`fs = 1/ D
`
`fs = 12 f0 = 6 BW
`
`Figure 12. DSP-linearization system using Cartesian predistortion and adaptive correction.
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`43
`
`combined are not at the same frequency, power will be
`split between the load and the coupler’s dump port.
`The R2 power loss in dB as function of K2 is described
`by (10) with 2 substituted for 1 in the variable names.
`The overall loss in SAT is
`
`∆SAT = 10
`+
`
`L
`1
`
`log
`+
`
`L
`2
`
`(
`
`(
`−
`
`k
`
`
`
`1 10/
`
`)
`
`)
`
`+
`
`10
`
`(
`
`log
`
`
`
`1 10−
`
`(
`−
`
`k
`
`
`
`2 10/
`
`)
`
`)
`
`(12)
`
`L
`m
`
`,
`
`
`1 10−
`+
`
`PETITIONERS EXHIBIT 1007
`Page 7 of 13
`
`

`

`Gain 0.5 dB/DIV
`
`Pout 2.5 dB/DIV
`
`Phase 5.0 deg/DIV
`TWTA Phase
`
`TWTA Pout
`
`LTWTA
`Gain
`
`TWTA
`Gain
`
`TWT Pout
`
`LTWTA Phase
`
`LTWTA Pout
`
`Pin 2.5 dB/DIV
`
`LTWTA Pout
`
`Pin 2.5 dB/DIV
`
`Figure 13. Transfer characteristics of TWTA and linearized TWTA.
`
`provide superior IMD cancellation with considerably
`less complexity; however, for OPBOs greater than ~ 6-7
`dB, FF becomes competitive, and for high linearity may
`be the system of choice.
`
`Feedback Linearization
`There has been considerable work on the use of feed-
`back for the linearization of RF and microwave amplifi-
`ers. Feedback techniques can be divided into several
`distinct branches. The use of linear networks for feed-
`back is well documented but has seen little use at mi-
`crowave frequencies. The reason for this reluctance is
`probably due to concerns with amplifier stability and
`
`the difficulty in making networks with nonideal
`components function over wide frequency bands.
`Indirect feedback (IFB) techniques have been more
`widely applied. In this approach an amplifier’s input
`and output signals are detected and lowpass filtered,
`and the resulting baseband signals compared. The error
`signal (Ve ) is used to modify the amplifier’s characteris-
`tics to minimize distortion.
`
`=
`
`V
`e
`
`DS
`out
`
`−
`
`DS
`in
`
`(13)
`
`Relative Power Output 0.5 d B/DIV
`
`Gain Change 0.5 dB/DIV
`
`Gain
`
`Phase
`
`Start
`
`−10.0 dBm CW 1.9500 GHz
`
`Stop 15.0 dBm
`
`Figure 14. Transfer characteristics of class-A, S-band SSPA and linearized SSPA.
`
`44
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`where DSout and DSin are, respectively, the detected out-
`put and input signals.Ve can be used to control the gain of
`the amplifier by means of a voltage
`variable attenuator. Dynamic elec-
`tronic bias systems (DEBS),
`in
`which an amplifier bias is changed
`in response to the output signal,
`can be considered a variation on
`this form of linearization. The most
`widely known form of DEBS uses
`the input signal as the reference
`without comparison to produce an
`indirect form of FF linearization.
`Superior linearity can be obtained
`by correcting both amplitude and
`phase. The magnitude and phase
`error signals can be determined as
`illustrated in Figure 6. The result-
`ing voltages are used to control an
`attenuator and a phase shifter to
`minimize signal error.
`An alternate approach, known
`as Cartesian feedback, separates
`the signal
`into in-phase and
`quadrature
`components. This
`eliminates the need for phase-
`shift components and still allows
`the correction of gain and phase
`by adjusting the amplitudes of
`
`SAT
`
`Amp
`
`L/Amp
`
`Phase Change 2dB/DIV
`
`0
`
`L/Amp
`
`SAT
`
`Amp
`
`Amp
`
`L/Amp
`
`PETITIONERS EXHIBIT 1007
`Page 8 of 13
`
`

`

`5 dB/div
`
`Without Linearizer
`
`Performance with
`4 dB OPBO
`
`With Linearizer
`
`two orthogonal components. Figure 7
`shows an example of a Cartesian-feed-
`back system. The baseband in-phase
`and quadrature components are com-
`pared and used to
`control
`the
`attenuators in a vector modulator. De-
`tection must be done synchronously
`(quadrature detection).
`Cartesian feedback is most often
`used with quadrature phase-shift-
`keyed (QPSK) modulation. In this case,
`the output-side demodulated in-phase
`and quadrature components are sub-
`tracted directly from the respective
`in-phase and quadrature modulation
`signals at the input. This eliminates the
`need to demodulate on the input side.
`The correction at baseband is often
`done in the digital domain using digital signal process-
`ing (DSP) techniques.
`Very high linearity can be achieved by using IFB,
`which is self-correcting for changes due to environ-
`mental and aging effects. IFB’s principal limitation is an
`inability to handle wideband signals. In practice, it is
`difficult to make a feedback system respond to sig-
`nal-envelope changes much greater than several MHz,
`because of the delay (∆tS) of the amplifier and associ-
`ated signal-processing components. The signal band-
`width must satisfy
`
`10 MHz/div
`Figure 15. For a TWTA, a two-tone C/I improvement of > 15 dB at 4-dB
`OPBO is common.
`
`the linearized amplifier remain constant with change in
`power level.
`In dB, the gain of the linearizer (GL) must increase by
`the same amount the amplifier’s gain (GA) decreases
`[
`]
`(
`= −
`GA P
`Ain
`
`(
`GL P
`Lout
`
`
`
`)
`
`−
`
`GL
`SS
`
`)
`
`−
`
`GA
`
`SS
`
`
`
`P
`Lout
`
`
`
`=
`
`,
`P
`Ain
`
`(15)
`
`where GLSS and GA SS are, respectively, the small signal
`(
`)
`gains of the linearizer and the amplifier, and
`GL P Lout
`(
`)
`and
`are, respectively, these gains as a function
`GA P Ain
`of linearizer output and amplifier input levels. Like-
`wise, the phase shift introduced by the linearizer must
`increase by the same amount the amplifier’s phase de-
`creases (or vice-versa, depending on the direction of
`phase change by the amplifier)
`[
`Φ
`= −
`
`Φ
`
`(
`L P
`Lout
`
`
`
`)
`
`−
`
`Φ
`
`L
`SS
`
`(
`A P
`Ain
`
`
`
`)
`
`−
`
`Φ
`
`A
`
`]
`
`SS
`
`P
`Lout
`
`
`
`=
`
`.
`P
`Ain
`
`(16)
`
`When these conditions are met, the result is the com-
`posite linear-transfer characteristic (Figure 8). This is
`the response of an ideal limiter. Once an amplifier has
`saturated, it is impossible to obtain more output power
`
`Mid Band
`
`High Band
`
`LTWTA
`
`Low Band
`6dB
`
`>3dB
`
`TWTA
`
`45
`
`40
`
`35
`
`30
`
`25
`
`20
`
`15
`
`C/l in dB
`
`10
`1
`
`2
`
`8
`6
`5
`3
`7
`4
`Output Power Backoff in dB
`Figure 16. A 4¥ increase in power for a two-tone C/I of
`30 dB can be obtained by linearizing a TWTA.
`
`9
`
`10
`
`BW
`
`(
`< 1 4∆
`tS
`
`)
`
`(14)
`
`for significant correction. Thus, the total delay must be
`less than 25 ns for a 10 MHz BW. Microwave amplifiers
`can have delays of 10-20 ns. An advantage of Cartesian
`feedback is that the BWs of the in-phase and quadrature
`components are approximately equal, while, in Polar
`feedback systems, the BW of the phase component is
`much greater than the BW of the amplitude component.
`
`Predistortion Linearization
`Predistortion (PD) linearizers have been used exten-
`sively in microwave and satellite applications because
`of their relative simplicity and their ability to be added
`to existing amplifiers as separate stand-alone units. Un-
`like FF linearizers, they can provide a viable improve-
`ment in linearity near SAT but can be difficult to apply
`in applications requiring very high linearity (C/I > 50
`dB). PD linearizers generate a nonlinear-transfer char-
`acteristic that can be thought of as the reverse of the am-
`plifier’s transfer characteristics in both magnitude and
`phase (Figure 8). An alternate way of thinking of a PD
`linearizer is to view the linearizer as a generator of IMD
`products. If the IMDs produced by the linearizer are
`made equal in amplitude and 180∞ out of phase with
`the IMDs generated by the amplifier, the IMDs will can-
`cel. This condition occurs when the gain and phase of
`
`magazine
`IEEE
`December 2001
`Authorized licensed use limited to: James Proctor. Downloaded on November 04,2024 at 21:30:10 UTC from IEEE Xplore. Restrictions apply.
`
`45
`
`PETITIONERS EXHIBIT 1007
`Page 9 of 13
`
`

`

`by driving the amplifier harder. Thus, the best a PD
`linearizer can do is to produce an ideal-limiter charac-
`teristic. Despite this limitation, it is possible for a
`linearizer to provide large benefits in signal quality
`when output power is reduced from SAT. Some im-
`provement is possible, even at SAT and beyond, as the
`linearizer can correct for post-SAT phase distortion and
`power slump, but this improvement is usually very
`small. Since the power out of the amplifier (in dB) is
`
`P
`Aout
`
`
`
`=
`
`P
`Ain
`
`
`
`+
`
`=
`GA P
`Lout
`
`
`
`+
`
`=
`GA P
`Lin
`
`
`
`+
`
`+
`GL GA
`
`.
`
`Referenced to the power into the linearizer (P Lin ),
`(15) and (16) can be rewritten and the desired transfer
`characteristics of the linearizer expressed as follows:
`
`(
`GL P
`Lin
`
`
`
`)
`
`=
`
`GL
`SS
`
`+
`
`GA
`
`SS
`
`−
`
`(
`GA P
`Lin
`
`
`
`+
`
`(
`GL P
`Lin
`
`
`
`)
`)
`
`(17)
`
`Φ
`
`(
`L P
`Lin
`
`
`
`)
`
`=
`
`Φ
`
`L
`SS
`
`+
`
`Φ
`
`A
`
`SS
`
`−
`
`Φ
`
`(
`GA P
`Lin
`
`
`
`+
`
`(
`GL P
`Lin
`
`
`
`)
`)
`. (18)
`
`Equations (17) and (18) can be solved iteratively for
`the ideal linearizer response needed to correct a given
`amplifier’s transfer response. Figure 9 shows the re-
`sponse needed to ideally correct a typical TWTA. As
`SAT is approached, the rate of gain and phase change
`become infinite
`
`dGL dP
`in
`
`d LΦ
`dP
`in
`
`= ∞
`= ∞
`
`and
`as
`P
`out
`
`→
`
`SAT.
`
`Such a characteristic cannot be achieved in practice. Of-
`ten, a small amount of gain expansion near SAT due to the
`finite dGL dPin available is traded for superior C/I near
`SAT at the expenses of degraded C/I at higher OPBOs.
`Another limitation of PD (and FF) is the dependence of
`some amplifiers’ transfer characteristics on the frequency
`content of the signal. This phenomenon is sometimes re-
`ferred to as memory effects. Great care must be taken in the
`design of an amplifier to minimize these effects if the maxi-
`mum benefit of PD linearization is to be achieved.
`The two-tone C/I achievable by an ideal transfer
`characteristic is shown in Figure 10. The C/I goes to
`infinity, for OPBO > 3 dB. This result occurs because
`the peak envelope-power (PEP) of a two-tone signal is
`3 dB greater than the average power. A signal backed
`off by more than 3 dB never experiences clipping at
`SAT and is only subject to a linear response. However,
`achieving this same level of performance with a larger
`number of carriers requires a greater level of OPBO.
`This is a consequence of the increase in PEP with car-
`rier number
`
`(19)
`
`where N is the number of carriers
`and Pav is the average power of
`the overall signal. For four carri-
`ers, the OPBO for no