# A Wideband High-Voltage Power Amplifier Post-Linearizer for Medical Ultrasound Transducers
## 2 Materials and Methods  
Figure 2a shows the Class-A type HVPA and post-linearizer. The circuits were implemented using discrete electronic components on a two-layer printed circuit board. As shown in Figure 2a, the HVPA is followed by the post-linearizer circuit. In Figure 2b, 90 pF input and output DC coupling capacitors (C\({}_{\text{in}}\) and C\({}_{\text{out}}\); Vishay Intertechnology, Malvern, PA, USA) were placed at the input and output ports (\"Input1\" and \"Output1\") to block the DC voltage and pass the AC signal. The simple resistor divider consists of a 2 k\(\Omega\) variable resistor (R\({}_{\text{V1}}\); Vishay Siliconix, Silver Lake Road, IL, USA) and 50 \(\Omega\) fixed resistor (R\({}_{\text{V2}}\); Caddock Electronics Inc., Riverside, CA, USA) with a high-voltage regulator (LM138; Texas Instrument, Austin, TX, USA) attached with a heat-sink (Aavid Thermalloy, San Jose, CA, USA). A 2 k\(\Omega\) bias resistor (R\({}_{\text{B1}}\); Caddock Electronics Inc., Riverside, CA, USA) and 3.5 uH RF choke inductor (L\({}_{\text{ch2}}\); Coilcraft Inc., Silver Lake Road, IL, USA) were used to block AC signal and minimize DC voltage drop. One 0.1 uF electrostatic, two 1 uF and 10 uF capacitors (C\({}_{\text{DC1}}\), C\({}_{\text{DC2}}\), and C\({}_{\text{DC3}}\); KEMET Corp., Simpsonville, CA, USA) were used to minimize the ripple current from the DC power supply (V\({}_{\text{DC}}\); E3631A, Agilent Technology, Santa Clara, CA, USA). A 400 MHz 15 W RF MOSFET (M\({}_{\text{T1}}\); PD57006-E, STMicroelectronics, Geneva, Switzerland) with heat-sink was used as the core transistor of the HVPA. Because of the high power output, separate heat sinks were utilized for the RF MOSFET and voltage regulator to prevent decrease of DC operating points in the RF MOSFET due to high temperature [30]. Our proposed post-linearizer circuit is presented in Figure 2c. All components of the HVPA and post-linearizer were high-voltage tolerant to prevent breakdown resulting from the single-cycle- or multi-cycle high-voltage signals sent to the ultrasound transducer from the HVPA [14]. 30 pF capacitors (C\({}_{\text{1}}\), C\({}_{\text{2}}\), and C\({}_{\text{mid}}\)), a 5.6 nH air-core high power inductor (L\({}_{\text{1}}\)) and 5.1 nH high current inductors (L\({}_{\text{2}}\) and L\({}_{\text{3}}\)) were also employed in the fabrication of the post-linearizer. The inductors (L\({}_{\text{1}}\), L\({}_{\text{2}}\), and L\({}_{\text{3}}\)) were chosen to resonate with the corresponding capacitances (C\({}_{\text{1}}\), C\({}_{\text{2}}\), and C\({}_{\text{mid}}\)) in the operating frequencies of the HVPA. Lastly, 50 W, 25 \(\Omega\) power resistors (R\({}_{\text{1}}\) and R\({}_{\text{2}}\); Caddock Electronics), 0.5 cm and 1 cm transmission lines (TR\({}_{\text{in}}\) and TR\({}_{\text{out}}\)) and cross-coupled high speed switching diodes (D\({}_{\text{E1}}\)-D\({}_{\text{E4}}\); NXP semiconductors, Eindhoven, The Netherlands) were utilized to minimize ring-down artifact of the high-voltage bipolar pulse train signals that could reduce the ultrasound transducer bandwidth [10; 31]. Figure 3 provides an equivalent HVPA circuit model of the HVPA to demonstrate the parasitic capacitances of the main transistor. Figure 1: Gain deviation comparison between the high-voltage power amplifier (HVPA) with and without the linearizer as a function of (**a**) input power and (**b**) frequency (the black dashed lines and red solid lines represent the HVPA without and with the linearizer, respectively. Figure 2: Block diagram and schematics of the HVPA and post-linearizer: (**a**) Implementation of the HVPA and post-linearizer, Schematics of the (**b**) HVPA, and (**c**) post-linearizer.