Behavioral Model of Solid State Power Amplifiers (SSPAs) for Agile Antennas Application Georges ZAKKA EL NASHEF 1 , François TORRES 1 , Tibault REVEYRAND 1 , Sébastien MONS 1 , Edouard N’GOYA 1 , Thierry MONEDIERE 1 , Raymond QUERE 1 . 1 XLIM – C2S2/OSA departments UMR CNRS n ° 6172 University of Limoges, 87060 Limoges France Cedex Email: georges.zakka-el-nashef@xlim.fr Abstract — The complexity of modern telecommunication systems requires increasingly important needs for modeling and rigorous analysis. Thus, it is more and more required to predict the performances of power amplifiers (PAs) on the Tx-Rx chains. This paper focuses on behavioral modeling approach for a PAs used in agile antennas application. This approach of active antennas can take into account the interactions between the nonlinear circuits (i.e. PAs) and electromagnetic (i.e. antennas): the matching impedances for each antenna of a specified array are calculated from rigorous electromagnetic analysis, then those calculated matching impedances are used instead of the real antennas to define the load impedances (Zload) of the active circuits (PAs), in order to optimize the overall performances. I. INTRODUCTION The interest in design and technological development of active phased array antennas devices has significantly risen. Such antennas may take place in avionic applications, in satellite communication, surveillance radars and many other application fields that should emerge in the next future. In order to study correctly the interactions between the PAs and the antennas, it requires efficient simultaneous modeling and optimization of electromagnetic and circuit issues. In the framework of an agile antennas application, the feeding between antennas and PAs (i.e. the pointing direction) is controlled by modifying the weights (phases and magnitudes) of the global system. This paper focuses particularly on the problem of mismatching between passive (antennas) and active (PAs) elements. Indeed, this mismatching can modify the performance of the PA in term of gain (AMAM) and phase (AMPM). Consequently, the necessary weights for the array (antenna) in a given pointing direction will be also modified once applied to the PA, degrading the array efficiency and its radiation performance [1]. Therefore, it is necessary to develop a powerful simulation tool that requires an accurate behavioral model of the PA in order to quantify all these interaction phenomena (i.e. mismatching) and impacts. Before clarifying the PA model, a technique was used to determine the matching impedances (≠50Ω) of each element of the array according to the frequency and the pointing angle [2], and this without any complex electromagnetic calculation. This technique takes into account the mutual coupling effect between array elements (antennas) and calculates the necessary weights in order to obtain an optimum radiation pattern. This technique permits also to study the impact of mutual coupling between antennas. Then the calculated matching impedances are used as load impedances of the PA. This will let us study the impact of mismatching and frequency on the global performance of the system. For this purpose, a non-linear model is extracted from simple CW measurements of the PA (Nextec-RF NB00422). Finally, the active circuit model is implemented in Agilent Advanced Design System (ADS), where it will be validated for different loading impedances, up to VSWR=3 (Voltage Standing Wave Ratio). II. ACTIVE CIRCUIT MODEL THEORY AND DESCRIPTION Power amplifiers are modeled thanks to nonlinear scattering functions [3] that consist in defining a nonlinear relation for the [S] parameters: [ ] i Linear Non ij i a S b ~ ~ • = − (1) where i a ~ and i b ~ are respectively the incident and reflected power waves at the two ports, and [Sij] Nonlinear are the nonlinear scattering functions. In order to establish a bilateral model, the memory effects were not included, which means we are limited to the operating frequency (8.2 GHz). Moreover, this approach is efficient only for VSWR < 3 since the modeling technique was limited to Taylor first order expansion. Therefore we can deduce from equation (1): ( ) ( ) ( ) ( ) { } 2 2 1 1 ~ , ~ , ~ , ~ ~ a m a e a m a e f b NL i ℑ ℜ ℑ ℜ = (2) In order to simplify the model, we placed the PA under weak conditions of impedance mismatch, and thus 2 ~ a can be considered weak compared to 1 ~ a . And if 1 ~ a is considered as the reference wave, the development of Taylor series limited to the first order enables us to write equation (2) as follows [4]-[7]: ( ) ( ) ( ) ( ) ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∗ ∗ Δ Δ 2 1 1 22 1 12 2 1 1 22 1 21 1 12 1 11 2 1 ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ a a a S a S a a a S a S a S a S b b (3) where ( ) 1 ~ a S ij are the nonlinear scattering functions that depend only on the incident waves magnitude. Thus, equation (3) ensures the validity of nonlinear part of the bilateral model at operating frequency, when 2 a << 1 a . It can be seen as an AMAM – AMPM bilateral behavioral model, its validity is