Novel B-spline behavioral model extracted and verified using vectorial harmonic and multitone data

Nonlinearities in RF power amplifiers is an issue of critical importance in wireless communication systems. The development of behavioral models of power amplifiers capable of accurately predicting amplifier nonlinearities have been recently the focus of renewed interest for the design of communication and linearization systems. We present here a novel band-limited behavioral model working in the time and frequency domain for a wide range of power levels. This model is based on a multi (typically 8) phase-channel topology with B-spline nonlinear gain elements extracted using a linear least-square extraction procedure. Various techniques (knot placement, harmonic constraints and filtering, prior- and post-shaping) are used to optimize this least square extraction. The model is capable of fitting the amplitude and phase of the fundamental, harmonics (typically up to 4 or 5) and IMD3 intermodulation for a wide range of power levels. The model was then tested for its ability to predict the amplitude and phase of IMD5 and the amplifiers' response to broadband multitone CDMA like excitations. Note that with the advent of the large-signal network analyzer (LSNA), the experimental acquisition of such single-tone and multi-tone vectorial data to characterize or verify the response of RF power amplifiers is now possible. All studies reported in this paper are based on various virtual devices implemented in ADS. Four different devices models and amplifiers (LDMOSFET, RFICs) were considered. For the LDMOSFET amplifier simulations we used an electrothermal LDMOSFET model extracted and verified from experimental microwave data (I-V, S-parameters, harmonics, load-pull) in our lab. Note that the LDMOSFET amplifier considered is afflicted by memory-effects (ACPR degradation with bandwidth) originating from self-heating for tone spacing below 1 MHz and from electrical origin for tone spacing above 1 MHz. The B-spline behavioral model was implemented in ADS as a user-compiled device model. The model was then used with a multi-sine excitation to verify the model ability to predict the spectral regrowth. The prediction capability of the B-spline model is demonstrated to hold for a wide range of power levels and for several devices/amplifiers. An important feature of this work is that a continuous range of input power levels is used for fitting and verification rather than a single input power level. Also the model being in the time-domain, arbitrary excitations in the model frequency-band can be used with this model. The results obtained with this new band-limited behavioral-model demonstrate how the vectorial data acquired from an LSNA can be used to perform both system identification and model verification.