Efficiently Defining the Fundamental, 2nd and 3rd Harmonics Load Impedances

Defining the 2^nd and 3^rd harmonics load impedances of an RF/microwave transistor in non-linear operation is a strongly determining factor not only for the synthesis of the output matching but also for the simulation of load-pull power and efficiency contours on a Smith Chart.

"There are many scientific articles and books on this subject that should be read and understood. Their use of complex mathematical expressions, however, do not provide a simple procedure to define the necessary fundamental load impedance with appropriate 2^nd and 3^rd harmonic load impedances for optimum performance and robustness to all possible tolerances, static or dynamic, of the environments, without necessity to have a PhD degree." - Ivan Boshnakov

"RF Power Amplifier Design"

This application note by Ivan Boshnakov describes how to determine simultaneously the fundamental and 2nd and 3rd harmonics load impedances of an RF/microwave transistor in non-linear operation by using an efficient procedure that produces optimum, robust, and antifragile performance. This procedure will provide you, in a straightforward way, with the initial data to proceed to load-pull simulations with the 2^nd and 3^rd harmonics impedance properly defined. Many transistor data sheets today provide load-pull contours data without reference to the harmonics load impedances, or if it is included, no explanation is given for why the particular values are chosen.

This document is intended for intermediate and advanced-level AWR Design Environment users who are familiar with the program interface, creation of schematics and graphs, and interpretation of graphical output.

Read the "RF Power Amplifier Design" application note.

About the Author

Ivan Boshnakov, retired engineer from Ametek (formerly MilMega), is experienced in the design and development of RF and microwave devices, project management, and development team management. For the last 28 years, he specialized in the design and development of RF and microwave amplifiers by applying methods and techniques to extract the optimum performance out of the transistors. During this period, he developed more than 270 successful amplifier designs with more than 210 of them in production, working anywhere in the frequency range from 20MHz to 40GHz: LNAs, broadband (2-18GHz) LNAs, high-power (40W Class A, 150W Class AB, 1.2kW Class B), broadband (20-1000MHz, 0.5-2.7GHz) high power (20W, 60W, 100W) GaN HEMT-based amplifiers, linearized by RF analogue predistortion power amplifiers, high-power amplifiers suitable for envelope tracking of the power supply, and millimeter-wave MMIC power amplifiers.

Ivan has published multiple articles on practical RF/microwave amplifier design matters, including articles in High Frequency Electronics and Microwave Journal. He offers this latest application note as part of his continued work with Microwave Office, Cadence EM solvers (AXIEM, Clarity), and topics in advanced power amplifier design.