Extraction and Validation of Power Amplifiers' Harmonics Dynamic <formula formulatype="inline"><tex Notation="TeX">$X$</tex></formula>-Parameters From Pulsed Envelope Domain Measurements

Abstract

This paper presents an extended behavioral model for the modeling of microwave amplifiers, namely harmonics dynamic -parameters. This model aims at providing a powerful analysis capability for the prediction of fundamental and harmonic large-signal responses with long-term memory effects for the power amplifier. Several major problems faced by current commercial nonlinear vector network analyzers have yet to be addressed, such as external stimulation in pulsed envelope domain measurement and synchronization. Therefore, an unlimited and alternative method for the extraction of harmonics dynamic -parameters is also introduced in this paper. In the extraction procedure, the modulated RF step signal shows significant advantages in revealing the relationship between the past inputs and the current output. However, attempts to validate the effectiveness of this model have been limited by both the hardware and software requirements. First, the advanced phase reference is not open to the public and is only available in the manufacturer's internal R&D laboratory; it is required for the phase calibration procedure of the narrow tone spacing. Second, the two-tone signal experiment is not suitable for the validation of the output prediction of harmonics. Therefore, a novel validation method that utilizes the narrow step signal as stimulus signal was carried out on a Mini-Circuits amplifier. An excellent agreement between the measurements-based behavioral model and the measured output is achieved, with a maximum error less than 5%.

A novel quadratic polynomial expansion of nonlinear scattering function for RF power amplifier modeling

“…Assuming the device is a nonlinear time-invariant system, which implied that if the phase of incident wave shifted, the other harmonic frequency waves will undergo the corresponding phase shifting. Let us define P ¼ e jφ A 11 ð Þ as the phase of the incident wave A 11 . Denote the delayed wave quantities by a superscript D. If the fundamental spectrum has the phase shift P -1 , one can then get the delayed harmonic spectrum.…”

“…It therefore can be used to extract the nonlinear behavior models such as X‐parameters. Such behavioral models with moderate analytical expression have gain popularity within the industry of transistor model for PA design . In our previous work, a 20‐GHz PA was designed in such way.…”

“…Such behavioral models with moderate analytical expression have gain popularity within the industry of transistor model for PA design. [11][12][13] In our previous work, 14 a 20-GHz PA was designed in such way. However, X-parameters can be seen as the reparameterization of the poly harmonic distortion (PHD) model, 15 which is considered as the linearization of the nonlinear scattering functions under superposition hypothesis.…”