Power Amplifiers and Transmitters for RF and Microwave (4/4)/VI. LINEARIZATION

Linearization techniques are used both to improve linearity and to allow more efficient, but less linear methods of operation. The three principal types of linearization are feedback, feedforward,
and predistortion.

A. Feedback
Feedback linearizes the transmitter by forcing the output tofollow the input. It can be applied either directly to the RF amplifier (RF feedback) or indirectly to the modulation (envelope,
phase, or and components). In RF feedback, a portion of the RF-output signal from the amplifier is fed back to and subtracted from the RF-input signal without detection or down-conversion. The delays involved must be small to ensure stability, and the loss of gain at RF is a more significant design issue. The use of RF feedback in discrete circuits is usually restricted to HF and lower VHF frequencies, but it can be applied within MMIC devices well
into the microwave region [33]. Envelope feedback reduces distortion associated with amplitude
nonlinearity. It can be applied to either a complete transmitter or a single PA [33]. The RF input signal is sampled by a coupler and the envelope of the input sample is detected. The resulting envelope is then fed to one input of a differential amplifier, which subtracts it from a similarly obtained sample of the RF output. The difference signal, representing the error between the input and output envelopes, is used to drive a modulator in the main RF path. This modulator modifies the envelope of the RF signal, which drives the RF PA. The envelope of the resulting output signal is, therefore, linearized to a degree determined by the loop gain of the feedback process. For a VHF BJT amplifier in which amplitude nonlinearity is dominant, two-tone IMD is
typically reduced by 10 dB. The polar loop overcomes the fundamental inability of envelope feedback to correct for AM-PM distortion by adding a phase-locked loop to the envelope feedback system. Envelope detection and phase comparison generally take place at the IF. For a narrow-band VHF PA, the improvement in two-tone IMD is typically around 30 dB. The envelope bandwidth must be at least twice the RF bandwidth, but the phase bandwidth must be
at least ten times the RF bandwidth.
The Cartesian-feedback technique overcomes the problems associated with the wide bandwidth of the signal phase by applying modulation feedback in and (Cartesian) components. Since the and components are the natural outputs of a modern DSP, the Cartesian loop is widely used in mobileradio systems. Two identical feedback processes operate independently
on the and channels (Fig. 19). The inputs are applied to differential integrators (in the case of a first-order loop) and the resulting difference (error) signals are quadrature-upconverted
to drive the PA. A sample of the output from the PA is attenuated and down-converted in quadrature and synchronously with the up-conversion process. The resulting quadrature feedback signals then form the second inputs to the input differential integrators, completing the two feedback loops. The phase shifter shown in the up-converter local-oscillator path is used
to align the phases of the up- and down-conversion processes. The use of Cartesian feedback with a class-C PA amplifying an IS-136 (DAMPS) signal improves the first ACPR by 35 dB and
the allows the signal to be produced with an efficiency of 60%.

B. Feedforward
The very wide bandwidths (10–100 MHz) required in multicarrier applications can render feedback and DSP impractical. In such cases, the feedforward technique can be used to reduce distortion by 20–40 dB. In its basic form (Fig. 20), a feedforward amplifier consists of two amplifiers (the main and error amplifiers), directional couplers, delay lines, and loop control

networks [34]. The directional couplers are used for power splitting/ combining, and the delay lines ensure operation over a wide bandwidth. Loop-control networks, which consist of amplitudeand phase-shifting networks, maintain signal and distortion cancellation within the various feedforward loops. The input signal is first split into two paths, with one path going to the high-power main amplifier, while the other signal path goes to a delay element. The output signal from the main amplifier contains both the desired signal and distortion. This signal is sampled and scaled using attenuators before being combined with the delayed portion of the input signal, which is regarded as distortion free. The resulting "error signal" ideally contains only the distortion components in the output of the main amplifier. The error signal is then amplified by the low-power high-linearity error amplifier, and then combined with a delayed version of the main amplifier output. This second combination ideally cancels the distortion components
in the main-amplifier output while leaving the desired signal unaltered. Successful isolation of an error signal and the removal of distortion components depend upon precise signal cancellation over a band of frequencies. For a 30-dB cancellation depth, the amplitudes must be matched within 0.22 dB and the phases

within 1.2 [34]. For manufactured equipment, realistic values of distortion cancellation are around 25–30 dB. The limiting factor is nearly always the bandwidth over which a given accuracy can be obtained. The outputs of the main and error amplifiers are typically combined in a directional coupler that both isolates the PAs from each other and provides resistive input impedances. For a typical 10-dB coupling ratio, 90% of the power from the main PA reaches the output. For the same coupling ratio, only 10% of the power from the error amplifier reaches the load, thus the error amplifier must produce ten times the power of the distortion in the main amplifier. The peak-to-average ratio of the error signal is often much higher than that of the desired signal, making amplification of the error signal inherently much less efficient than
that of the main signal. As a result, the power consumed by the error amplifier can be a significant fraction (e.g., one-third) of that of the main amplifier. In addition, it may be necessary to operate one or both amplifiers well into backoff to improve linearity. The overall average efficiency of a feedforward transmitter

may, therefore, be only 10%–15% for typical multicarrier signals. Since feedforward is inherently an open-loop process, changes in device characteristics over time, temperature, voltage, and signal level degrade the amplitude and phase matching and, therefore, increase distortion in the transmitteroutput. An automatic control scheme continuously adjusts the gain and phase to achieve the best signal cancellation and output linearity. The first step is to use FFT techniques, direct power measurement, or pilot signals to determine how well the loop is balanced. Both digital and analog techniques can be used for loop control and adjustment.

C. Predistortion
The basic concept of a predistortion system (Fig. 21) involvesthe insertion of a nonlinear element prior to the RF PA such thatthe combined transfer characteristic of both is linear. Predistortion
can be accomplished at either RF or baseband. An RF predistorter typically creates the expansive predistortion characteristic by subtracting a compressive transfer function (such as that of a diode) from a linear transfer function. Improvements in the ACPR by 10 dB are typical. As with feedforward, the operating bandwidth is limited by the gain and phase flatness of the predistorter itself and of the RF PA. In addition, memory effects in the PA and the predistorter limit the degree of cancellation. Better performance can be achieved with more complex forms of RF predistortion such as Adaptive Parametric Linearization (APL), which is capable of multiorder correction [33]. Most RF-predistortion techniques are capable of broad-band operation with practical operational bandwidths similar to, or greater than, those of feedforward.

D. Digital Predistortion
Digital predistortion techniques exploit the considerable processing power now available from DSP devices, which allows them both to form and to update the required predistortion characteristic. They can operate with analog-baseband, digital-baseband, analog-IF, digital-IF, or analog-RF input signals. Digitalbaseband and digital-IF processing are most common. The two
most common types of digital predistorter are termed "mapping
predistorters" and "constant-gain predistorters." A constant-gain predistorter (Fig. 22) requires only a singledimensional lookup table, indexed by the signal envelope to generate the expansive predistortion characteristic. It is simple to implement and requires only a modest amount of memory for a given level of performance and adaption time. A mapping predistorter utilizes two lookup tables, each of which is a function of the and components of the input. This type of predistorter is capable of excellent performance. However, it requires a significant storage and/or processing overhead for the lookup tables and their updating mechanism, and has a low speed of convergence.
An example of linearization of a PA with two 3G W-CDMA signals by a digital baseband-input predistorter is shown in Fig. 23. The linearized amplifier meets the required spectral
mask with a comfortable margin at all frequency offsets. The noise floor is set by the degree of clipping employed on the waveform, which limits the ACPR improvement obtained. It
clearly demonstrates, however, that digital predistortion can be used in broad-band, as well as narrow-band applications. Fig. 24 shows an example of a commercial 3G transmitter with digital predistortion.