The Effect of IMD Drain Impedances in RF PA Concurrent Dual-Band Operation

Abstract

This article develops a theory to explain the effect of controlling the impedance at the intermodulation distortion (IMD) frequencies, related to the first-order passband distortion terms (generated through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n+1)\cdot f_1-n\cdot f_2$</tex-math> </inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n+1)\cdot f_2-n\cdot f_1$</tex-math> </inline-formula> ), for radio frequency (RF) power amplifiers (PAs) operating in the concurrent dual band. It is shown that, similar to harmonic terminations in the single-band operation, the IMD impedance of these terms can significantly impact efficiency and output power. Careful tuning of these IMD terminations shapes the envelope of the RF signal, akin to RF wave shaping. Through this shaping, it is theoretically possible to achieve the same efficiency in single and concurrent band operations, instead of the expected <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sfrac{\pi}{4}$</tex-math> </inline-formula> multiplicative drop. To demonstrate the practical importance of considering the impedance at these IMD frequencies, a dual-band RF PA is designed with a trimmed third-order IMD ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \cdot f_2-f_1$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \cdot f_1-f_2$</tex-math> </inline-formula> ) impedance. The power and efficiency performance of the PA in dual band exceeds the estimations drawn from the single-band operation characteristics and is in accordance with the developed theory.