## 3 High-Efficiency Wideband Envelope Amplifier
### Slow Envelope Power Supply  
The WLEA presents good stability in frequency and draws good linearity figures. However, polar transmission techniques are supposed to improve the power efficiency of conventional RF PAs, and a linear amplifier may not be competitive to provide an improvement in these terms. To improve the efficiency of high-dynamic-performance linear regulators, several solutions (most of them based on a series combination because parallel topologies usually require a push-pull linear PA) have already been proposed for many years (slow ET, multilevel-based supply class-G PAs), and the common idea of all of them is usually to use a power supply that, in combination with the WLEA, is able to provide a variable voltage that tracks the amplified waveform [34; 35; 36; 37; 38]. As the WLEA is responsible for dynamic performance and linearity, the voltage tracking power supply does not have such stringent linearity and voltage ripple requirements, making it easy to implement, so conventional high-efficiency power conversion methods can be easily applied. For the generation of the slow envelope signal, there are several solutions described in the literature [39; 40; 41] that allow for real-time processing. However, in this case, we have used a method that allows this signal to be easily implemented in MATLAB. This process required two steps: The first one generated a signal called moving peak, \(v_{EMP}\), by using the movmax(A,k) MATLAB function over the envelope reference (\(v_{ER}\)) signal, with a sample frequency of \(f_{S}\) = 800 MHz, using a number of points for the sliding window of \(k\) = 1000. The resulting signal was then passed through a moving mean filter function, movmean(A,k), to obtain a smoothing slow envelope reference (\(v_{SER}\)) signal (with \(k\) = 1000) from which the digital pulse-width modulation (DPWM) control signal (\(v_{PWM}\)) was generated, downsampled, and transferred to the arbitrary waveform generator (Agilent 81150A). Figure 12 shows the transformation of the envelope spectrum of a 4C-CH VDL-T (located at 120 MHz, 123 MHz, 128 MHz, and 130 MHz) signal through this process. Figure 11: Dynamic demands of the envelope of a 2C-CH VDL-T signal: (**a**) time-domain slew rate envelope requirements and (**b**) distribution of envelope frequency components compared with the gain of the linear EA. The design of this SEPS is based on [34; 35] but adjusted to the wider bandwidth and higher power requirements of the test signals used in this work. In this case, the SEPS, consists of a half-bridge synchronous power cell controlled by the DPWM-generated signal (\(v_{PWM}\)), followed by a low-pass L-C filter. The Texas Instruments LMG5200 eval board was used to implement the proposed SEPS. The LMG5200 IC is an 80 V, 10 A GaN half-bridge power stage with integrated drivers. The evaluation board also contains the dead-time generation circuitry and has a place reserved for the L-C low-pass output filter. The design of this filter has been adapted to the needs of the envelope signals that have been used to test this polar-mode transmitter in order to demonstrate the potential performance improvement (in terms of power efficiency and linearity) that can be achieved by these systems. To demonstrate the broadband linearity performance of this system, some RF tests were conducted where several modulated narrowband signals were spaced at a minimum of 1 MHz within a 10 MHz bandwidth. This means that the L-C filter should offer a flat passband response over the slow envelope (\(v_{SE}\)) bandwidth, while the output impedance at high frequencies should be kept low in order to supply the high-frequency current components (\(i_{SE}\)) to the load. To meet these specifications, an \(L_{F}\) = 2.2 uH inductor and \(C_{F}\) = 350 nF capacitor were selected for the filter. This results in a resonant frequency of \(f_{res}\) = 200 kHz (one-tenth of the switching frequency, \(f_{sw}\)) and provides 40 dB attenuation at the SEPS switching frequency (\(f_{sw}\) = 2 MHz).