**Feedback linearization**

164 Wireless Communications and Networks – Recent Advances

Normalized current and voltage Normalized current and voltage Normalized current and voltage

Fig. 5. Ideal current and voltage waveforms of class E, F and D switched-mode amplifiers (Raab et al., 2002). Broken lines represent the device's output current and the solid lines

0 π 2π 0 π 2π 0 π 2π

Angle Angle Angle

+VD +VD

Class E Class F Class D (VMCD)

Fig. 6. Configurations of voltage mode class D (VMCD) and current mode class D (CMCD)

VMCD CMCD

Load

In general, a trade-off exists between efficiency and linearity of power amplifiers. For conventional transconducdance amplifier classes e.g. class A, AB and B, it is obvious that high efficiency classes are nonlinear. In subsection 2.2, average efficiency enhancement techniques aiming to keep the efficiency high over a wide dynamic range have been discussed. Even though efficiency is the main goal of such techniques, linearity was also taken into consideration so that none of such techniques would have severe impact to linearity. However, when the desired efficiency profile is achieved, linearity might not comply with wireless communication standards leading to unacceptable error vector magnitude and bit error rates. In such a case, linearity improvement techniques can be utilized to eliminate the excessive nonlinearity of the amplifier. Widespread linearization

represent the device's output voltage.

+VD


amplifiers.

**2.4 Linearization techniques** 

techniques are reviewed below.

In order to force the RF output to follow the input, feedback of the RF signal is realized using a directional coupler. The simplest variation of this technique subtracts the RF feedback from the input signal. However, the compensation of the non linearity with this technique is not very efficient as the transmitter's gain is reduced. Another variation detects the envelope of the RF feedback and the input signal and subtracts the first from the latter to realize the linearization of the amplitude. For the compensation for both phase and amplitude nonlinearities, another variation called Cartesian feedback was conceived that the feedback signal is down converted to I and Q values which are used to compensate the I and Q of the input signal. For a relatively small bandwidth, the two tone IMD can be reduced by 10 to 35 dB with this technique.
