On the accuracy of nonlinear microwave circuit simulation at the behavioral level

Abstract

. However, for this kind of simulation techniques, the simulation accuracy is of primary concern due to the following reasons: (1) the problem under consideration is a nonlinear one (i.e. we must ensure wide dynamic range of the analysis and reasonable accuracy of the analysis at the same time that is not a simple task), and (2) behavioral-level techniques use the single-tone input-output envelope transfer functions (amplitude-to-amplitude (AM-AM) and amplitudeto-phase (AM-PM)) to characterize the nonlinear circuit operation in multiple-tone regime that gives several additional contributions to the entire simulation error. In this paper, we discuss some factors that influence the accuracy of behavioral-level simulation. For our investigation, we consider mainly two behavioral-level techniques: the quadrature modeling technique and the instantaneous quadrature techniqueThe main principle of these techniques is to use the AM-AM and AM-PM transfer functions obtained from single-tone measurements to simulate the circuit operation. While the quadrature modeling technique uses the complex envelope of a bandpass RF signal and the envelope transfer functions (AM-AM and AM-PM) of a nonlinear element,where A in and ϕ in -are the input signal's amplitude and phase (in the single-tone regime), and A out (A in ) and ϕ out (A in ) -are the same for the output signal (but now they are functions of the input signal amplitude due to the element's nonlinearity), the instantaneous quadrature technique uses instantaneous values of the RF signal and the instantaneous transfer functions of the nonlinear element. A system of two integral equations relates the envelope and instantaneous transfer factors [3]. IMPACT OF THE TRANSFER FUNCTIONS ON SIMULATION ACCURACYThus, the AM-AM and AM-PM transfer functions are the key component of the entire simulation method. When determining these functions (through measurements or circuit-level simulation), one should take into account the following: 1) AM-AM and AM-PM measured (or simulated) data are available for a finite set of points. During simulation, these data are usually required for another set of points. Thus, a mathematical technique is required to transform these data from one set of points to another. Besides, these data must be stored in some form (look-up tables, for example) and that technique can also be used for this purpose. This is a representation problem.2) While the importance of higher-order derivatives of elements' characteristics for the nonlinear circuitlevel simulation is well-recognized [4]-[5], the importance of higher-order d erivatives for the nonlinear behavioral-level simulation is not so well understood [6]. Let us now consider this issue in more details. Measured or circuit-level simulated AM-AM and AM-PM data contains not only the "real" characteristics (without any disturbance), but also measurement (or simulation) noise and distortions due to instruments' (or simulator) noise and inaccuracy. These noise and distortions may severe degrade the entire simulation ...