212 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 16, NO. 4, APRIL 2006 Capturing Asymmetry in Distortion of an RF System Using a Multislice Behavioral Model Aaron Walker, Student Member, IEEE, Michael Steer, Fellow, IEEE, and Kevin Gard, Member, IEEE Abstract—Baseband effects result in asymmetrical distortion of RF communication signals through the interaction of baseband- related distortion with in-channel distortion. Here, a behavioral model architecture that captures these asymmetries and can be implemented in a variety of circuit and system simulators is pre- sented. The architecture has two or more slices with each slice corresponding to different frequency bands or multiple parallel nonlinear processes. Each slice could comprise any conventional narrow-band functional model. Here, the behavioral model is ex- tracted using AM–AM and AM–PM measurements for the first slice and phase and amplitude measurement of intermodulation components for the second slice. Index Terms—Asymmetrical distortion, baseband-related dis- tortion, narrow-band functional model. I. INTRODUCTION T HE successful development of RF systems relies on the ability of behavioral models to accurately predict system performance. Measurement-based behavioral models have been used to capture this complex behavior with multiple model ar- chitectures and techniques [1]–[3]. The measurements typically used include single-tone AM–AM and AM–PM measurements, and two-tone tests. While the former pair captures both the am- plitude and phase of the nonlinear response of the fundamental, the latter is typically used to measure the amplitude only of the spectral products in the distorted response. Without the phase of the system response captured, a model cannot track the behavior arising from the multiple nonlinear processes within a device as these add vectorially to produce the total output. This also impacts the evaluation magnitude-based metrics such as adjacent channel power ratio (ACPR). Several authors have addressed the need to capture the phase of the in- termodulation (IM) products to properly account for observed nonlinear effects [4] and [5]. Such measurements however are quite difficult. Measuring the phase of the additional frequency content pro- duced by a nonlinear system under discrete-tone stimulation arises from the lack of a reference signal at the system input. Several measurement techniques have been developed to ad- dress this problem with varying degrees of success and capa- bility. A review of these techniques can be found in [6]. Also in [6], we developed a simple relative phase measurement method for capturing the phase of IM products resulting from discrete- Manuscript received September 12, 2005; revised December 22, 2005. The authors are with the Department of Electrical and Computer Engineering North Carolina State University Raleigh, NC 27695-7914 USA (e-mail: aaron. walker@vaduminc.com; mbs@ncsu.edu; kggard@ncsu.edu). Digital Object Identifier 10.1109/LMWC.2006.872114 Fig. 1. Multislice model with first slice composed of single-tone fit and second slice capturing even-order baseband contributions to IM products. tone stimulus. In the following, we present the incorporation of this phase information into a multislice behavioral model of a high-power amplifier and show how this model captures distor- tion asymmetries. II. MULTISLICE MODEL In [7], the authors presented a multislice behavioral model architecture. The model has real linear and nonlinear net- works and so can be used in many simulators including transient, harmonic balance, transient envelope or system-level. The multislice model employs multiple parallel branches of Wiener–Hammerstein structures to account for the multiple nonlinear processes present within a circuit. A two-slice ver- sion is shown in Fig. 1. The Wiener–Hammerstein structures comprise memoryless nonlinearities between ideal linear net- works. In the architecture of Fig. 1, the first slice represents the traditional approach in which for example, an odd-order polynomial fit to single-tone AM–AM, AM–PM measurements could be used as in this letter. Higher-order branches in the model make use of an ideal multiplier that allows the model to capture nonlinear operation involving a series of nonlinear effects at different frequencies. The second slice, for example, captures baseband effects and the mixer in effect translates baseband effects resulting from even-order distortion, to the RF frequency by mixing the baseband products with the input signal. It is this mixing operation that can result in asymmetrical phase contributions to RF distortion. The translation in frequency of even-ordered nonlinear prod- ucts from baseband frequencies to that of the distortion frequen- cies of odd-ordered nonlinear effects results in the interesting phenomenon of IM asymmetry. It is simple to show that the IM products resulting from strictly odd-ordered mixing of the stimulus tones or from even-order harmonic production mixing with the stimulus always produce symmetrical (in both ampli- tude and phase) IM product contributions. In this letter, we con- sider operation and measurements with a two-tone stimulus at and . (We have previously shown that models derived 1531-1309/$20.00 © 2006 IEEE