## 2 HSM for Base Station PA
### Linear Amplifier Design
#### 2.3.4 Slew Rate of LA  
In [21; 22], to accurately track high PAPR signals, the LA must provide not only wideband characteristics but also a high slew rate. As shown in Figure 10, nodes X and Y are the most critical nodes affecting the slew rate. The total capacitance at node X is dominated by the gate capacitance of MP17, while that of node Y is primarily determined by the gate capacitance of MN21. The output power transistors (MP17 and MN21) are sized large to handle output currents up to 2.5 A. Consequently, their gate capacitance becomes significant, consisting of both intrinsic capacitance (-100 pF) and additional parasitic capacitance from layout effects. To maintain high slew rate performance, these gate capacitances must be rapidly charged and discharged. Figure 11 compares the slew rate performance under sufficient and insufficient floating current source conditions. A 20 MHz envelope signal with a 1.13 V offset and 730 mV amplitude is applied, requiring the output voltage to swing from 6 V to 28 V. The results show that insufficient source current limits the gate charging speed, degrading the slew rate and impairing envelope tracking accuracy. To improve the slew rate, sufficient current must be provided to quickly charge and discharge the gate capacitance of the output power transistors, as defined by the relation Slew Rate = I/C. As illustrated in Figure 10, the tail current source was  
Figure 8: Frequency response of feedback path: (**a**) magnitude; (**b**) phase.  
Figure 7: Feedback path analysis [20].  
increased to 1.5 mA to enhance the available current for charging and discharging. In addition, the current mirror ratios for (MP8, MP11) and (MP7, MP9) were configured to 1:10, ensuring that the charging/discharging current at nodes X and Y is amplified accordingly to effectively drive the large gate capacitances of MP17 and MN21.  
Figure 12 shows the transient response when a 50 MHz envelope signal with a 1.13 V offset and 340 mV amplitude is applied, resulting in a smaller output swing from 12 V to 22 V. Unlike the 20 MHz case, full swing from 6 V to 28 V is not achieved due to the higher slew rate requirement. Although a 50 MHz sine wave input requires a higher slew rate for accurate tracking, the actual 50 MHz envelope signal used in this work has its power spectral density mainly concentrated below 50 MHz. This implies that the measured slew rate is sufficient for tracking such practical envelope signals without distortion.  
The maximum slew rate performance was evaluated by applying an input pulse to the LA input, with a 2.125 A DC current source connected at the output node to substitute for I\({}_{\text{buck}}\), which primarily supplies the near-DC current component in HSM operation.  
Figure 11: Comparison of slew rate under sufficient and insufficient current conditions.  
Figure 12: Transient waveforms of \(V_{out}\) and \(V_{out}\)\(\times\) system gain in response to a 50 MHz sine wave input.  
Figure 10: Slew rate by charging and discharging Class-AB output stage gate capacitance: (a) rising edges; (b) falling edges.  
The V\({}_{\text{SM,out}}\) was driven to swing from 6 V to 28 V and from 28 V to 6 V, and the corresponding slew rates, calculated from the dV/dt of these transitions, were measured as a \(+1003/-852\) V/ us, respectively.