# Highly Linear 2.6 GHz Band InGaP/GaAs HBT Power Amplifier IC Using a Dynamic Predistorter
## 2 Design of the Dynamic Predistorter
### Dynamic Compensation of Nonlinearities  
Figure 3 illustrates the simulated AM\(-\)AM and AM\(-\)PM characteristics of the predistorter based on various tuning parameter values, such as C\({}_{PD}\), V\({}_{REF}\), R\({}_{E}\), and L\({}_{E}\). Figure 3a depicts the AM\(-\)AM and AM\(-\)PM characteristics for five distinct values of C\({}_{PD}\) with a \(V_{REF}\) of 3.1 V, R\({}_{REF}\) of 300 \(\Omega\), L\({}_{E}\) of 3 nH, and R\({}_{E}\) of 15 \(\Omega\). As C\({}_{PD}\) decreases, capacitive degeneration intensifies, leading to a significant increase in AM\(-\)PM variation. Particularly for values above 3 pF, the AM\(-\)PM variation becomes pronounced, while the AM\(-\)AM characteristics show limited change with dynamic responses involving compression and expansion. Figure 3b demonstrates the AM\(-\)AM and AM\(-\)PM performance for five varying values of \(V_{REF}\) with an \(R_{REF}\) of 300 \(\Omega\), a C\({}_{PD}\) of 5 pF, an \(L_{E}\) of 3 nH, and an \(R_{E}\) of 15 \(\Omega\). As \(V_{REF}\) decreases, the predistorter facilitates earlier and more pronounced variations in both AM\(-\)AM and AM\(-\)PM characteristics. Figure 3c showcases the AM\(-\)AM and AM\(-\)PM performance for five different values of \(L_{E}\) with a \(V_{REF}\) of 3.1 V, an \(R_{REF}\) of 300 \(\Omega\), a C\({}_{PD}\) of 5 pF, and an \(R_{E}\) of 15 \(\Omega\). Smaller \(L_{E}\) values lead to greater RF signal coupling to the diode, which amplifies both the variation and dynamism in the AM\(-\)AM and AM\(-\)PM characteristics. For high \(L_{E}\) values, the AM\(-\)PM characteristics tend to expand further. Figure 3d displays the AM\(-\)AM and AM\(-\)PM characteristics for five different values of \(R_{E}\) with a \(V_{REF}\) of 3.1 V, an \(R_{REF}\) of 300 \(\Omega\), a C\({}_{PD}\) of 5 pF, and an \(L_{E}\) of 3 nH. Smaller \(R_{E}\) values enhance RF signal coupling to the diode, inducing greater variation across a relatively higher-input power spectrum.  
The proposed predistorter is integrated into a two-stage PA employing an In-GaP/GaAs HBT process, depicted in Figure 4. The emitter areas of the driver and main stages are 1440 and 5400 \(\upmu\)m\({}^{2}\), respectively. Active bias circuits, which supply current to the transistor's base, are implemented in both the driver and main stages. The inter-stage matching network consists of two high-pass L-section circuits, incorporating a shunt inductor to provide both impedance matching and a DC current path for the predistorter. The predistorter, connected in parallel at the inter-stage matching network, minimally influences the impedance matching. The emitter area of Q3 measures 120 \(\upmu\)m\({}^{2}\).  
Figure 3: Simulated AM\(-\)AM and AM\(-\)PM characteristics of the predistorter according to different values for each of C\({}_{PD}\) in (a), \(V_{REF}\) in (b), \(L_{E}\) in (c), and \(R_{E}\) in (d).  
Figure 5a demonstrates the simulated AM\(-\)AM and AM\(-\)PM characteristics of the two-stage HBT PAIC before and after the inclusion of the proposed dynamic predistorter. The predistorter's tuning parameters were optimized to achieve optimal AM\(-\)AM and AM\(-\)PM compensation with a \(V_{REF}\) of 3.1 V, \(R_{REF}\) of 300 \(\Omega\), \(C_{PD}\) of 5 pF, \(L_{E}\) of 3 nH, and \(R_{E}\) of 15 \(\Omega\). After applying the predistorter, noteworthy improvements in both the AM\(-\)AM and AM\(-\)PM characteristics were observed, effectively mitigating both the expansion and compression in the AM\(-\)AM characteristics and the significant expansion in the AM\(-\)PM characteristics. Specifically, the AM\(-\)AM improved by approximately 0.43 dB, while the AM\(-\)PM improved by about 4.7\({}^{\circ}\). The ACLR, using the 5G NR signal based on QPSK CP-OFDM with a high PAPR of 9.7 dB, was enhanced by about 10 dB at an average output power of 24 dBm, as illustrated in Figure 5b.