No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Modeling nonlinear communication ICs using a multivariate formulation
Abstract
We present a technique for modeling nonlinear distortion of multirate time-varying communication circuits. To properly consider the weakly nonlinear distortion effects in circuits with multiple large-signal excitations, we capture the quasiperiodic boundary condition of the system Volterra kernels using a multivariate formulation. We then extend the model order reduction work of P. Li et al. (2003) to reduce this large multivariate representation for compact modeling. The proposed approach is demonstrated on a heterodyne front-end receiver.
... In this module, modeling frequency-dependent nonlinear characteristics of complex analog blocks and subsystems is critical for enabling efficient verification of mixedsignal system designs. It's well know that the mixer and the power amplifier are considered, respectively, as timevarying systems because its function involves frequency translation and when there is a large signal in an adjacent channel [1]. For the transmitter simple macro-models for weakly nonlinear mixer and power amplifier are used to achieve efficient and accurate system simulation [2], [3]. ...
This paper discusses the simulation and the design of an RF transmitter for small satellites operating in the commercial S-band (2.2 -2.29 GHz) with a data rate of 8 Mbps. In such systems, modeling frequency-dependent nonlinear characteristics of complex analog blocks and subsystems is critical for enabling efficient verification of mixed-signal system designs. In order to provide efficient and accurate simulation for the transmitter circuits, simple macromodels for weakly nonlinear mixer and power amplifier are used in the system simulation. Also, we introduce the noise in several circuits (frequency synthesizer, crystal oscillator, power amplifier, mixer,…) and we demonstrate their effect on the noise performance system. In the simulation we consider features of components and technologies commercially available.
... This algorithm can be applied to time-invariant as well as time-varying weakly nonlinear circuits. Some extensions have been described in [7][8].To generate analog macromodels that can be used in commercial simulation environments, the circuits under consideration must be characterized and then modeled based on industry-standard device models in these environments. In this paper, we develop a complete methodology which extends the NORM algorithm to generate nonlinear reduced-order macromodels directly from transistor-level netlists. ...
This work describes a complete framework for generation of compact analog circuit macromodels which significantly reduce the model complexity while still capturing the dominant linear and nonlinear response of the circuit. The technique is applicable to a broad class of circuits that exhibit weakly nonlinear behavior such as mixers, RF power amplifiers and switched-capacitor circuits. The Volterra-based circuit models are first characterized using a combination of SPICE simulation and efficient numerical fitting techniques. The complexity of the extracted circuit models is further reduced by model order reduction techniques while maintaining a high degree of accuracy. The efficacy of our macromodeling methodology is verified by comparison with SPICE simulations. The efficiency of our macromodels makes them suitable for whole-system verification and high-level design analysis.
This paper describes problems related to verification process of communication system design and SoC with communication components; demonstrates approach of harmonic balance co-simulation with digital and behavioral models. Present paper considers applicable simulation technique for analogue high frequency circuits -harmonic balance (HB) and way to connect it to digital subsystem models for purposes of end-to-end simulation and verification of digital data link.
Design of communications circuits often requires computing steady-state responses to multiple periodic inputs of differing frequencies. Mixed frequency-time (MFT) approaches are orders of magnitude more efficient than transient circuit simulation, and perform better on highly nonlinear problems than traditional algorithms such as harmonic balance. We present algorithms for solving the huge nonlinear equation systems the MFT approach generates from practical circuits
We present algorithms for reducing large circuits, described at
SPICE-level detail, to much smaller ones with similar input-output
behavior. A key feature of our method, called time-varying Pade (TVP),
is that it is capable of reducing time-varying linear systems. This
enables it to capture frequency-translation and sampling behavior,
important in communication subsystems such as mixers and
switched-capacitor filters, Krylov-subspace methods are employed in the
model reduction process. The macromodels can be generated in SPICE-like
or AHDL format, and can be used in both time- and frequency-domain
verification tools. We present applications to wireless subsystems,
obtaining size reductions and evaluation speedups of orders of magnitude
with insignificant loss of accuracy. Extensions of TVP to nonlinear
terms and cyclostationary noise are also outlined
An approach is presented for the analysis of the nonlinear
behavior of analog integrated circuits. The approach is based on a
variant of the Volterra series approach for frequency domain analysis of
weakly nonlinear circuits with one input port, such as amplifiers, and
with more than one input port, such as analog mixers and multipliers. By
coupling numerical results with symbolic results, both obtained with
this method, insight into the nonlinear operation of analog integrated
circuits can be gained. For accurate distortion computations, the
accuracy of the transistor models is critical. A MOS transistor model is
discussed that allows us to explain the measured fourth-order nonlinear
behavior of a 1 GHz CMOS upconverter. Further, the method is illustrated
with several examples, including the analysis of an operational
amplifier up to its gain-bandwidth product. This example has also been
verified experimentally
Widely separated time scales arise in many kinds of circuits,
e,g., switched-capacitor filters, mixers, switching power converters,
etc. Numerical solution of such circuits is often difficult, especially
when strong nonlinearities are present. In this paper, the author
presents a mathematical formulation and numerical methods for analyzing
a broad class of such circuits or systems. The key idea is to use
multiple time variables, which enable signals with widely separated
rates of variation to be represented efficiently. This results in the
transformation of differential equation descriptions of a system to
partial differential ones, in effect decoupling different rates of
variation from each other. Numerical methods can then be used to solve
the partial differential equations (PDEs). In particular, time-domain
methods can be used to handle the hitherto difficult case of strong
nonlinearities together with widely separated rates of signal variation.
The author examines methods for obtaining quasiperiodic and envelope
solutions, and describes how the PDE formulation unifies existing
techniques for separated-time-constant problems. Several applications
are described. Significant computation and memory savings result from
using the new numerical techniques, which also scale gracefully with
problem size
A new efficient mixed frequency-time approach to computing
steady-state and intermodulation distortion of switching filters without
resorting to macromodeling or the slow-clock approach has been
presented. The method works by computing the solution to the
differential equation system associated with a circuit for only J
clock cycles, where J is the number of coefficients
needed in the Fourier series to represent accurately the sequence of
initial points in each clock cycle. Thus this method is particularly
efficient when the number of coefficients in the Fourier series is many
fewer than the number of clock cycles in one input signal period
Modeling frequency-dependent nonlinear characteristics of complex analog blocks and subsystems is critical for enabling efficient verification of mixed-signal system designs. Recent progress has been made for constructing such macromodels, however, their accuracy and/or efficiency can break down for certain problems, particularly those with high-Q filtering. In this paper we explore a novel hybrid approach for generating accurate analog macromodels for time-varying weakly nonlinear circuits. The combined benefits of nonlinear Pade approximations and pruning by exploitation of the system's internal structure allows us to construct nonlinear circuit models that are accurate for wide input frequency ranges, and thereby capable of modeling systems with sharp frequency selectivity. Such components are widely encountered in analog signal processing and RF applications. The efficacy of the proposed approach is demonstrated by the modeling of large time-varying nonlinear circuits that are commonly found in these application areas.
This paper presents a compact Nonlinear model Order Reduction Method (NORM) that is applicable for time-invariant and time-varying weakly nonlinear systems. NORM is suitable for reducing a class of weakly nonlinear systems that can be well characterized by low order Volterra functional series. Unlike existing projection based reduction methods by J. Roychowdhury et al. (1999), NORM begins with the general matrix-form Volterra nonlinear transfer functions to derive a set of minimum Krylov subspaces for order reduction. Direct moment matching of the nonlinear transfer functions by projection of the original system onto this set of minimum Krylov subspaces leads to a significant reduction of model size. As we will demonstrate as part of our comparison with existing methods, the efficacy of model order for weakly nonlinear systems is determined by the extent to which models can be reduced. Our results further indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction. We demonstrate the practical utility of NORM for macromodeling weakly nonlinear RF circuits with time-varying behavior.
Model reduction is a popular approach for incorporating detailed
physical effects into high level simulations. In this paper the author
presents a simple method for automatically extracting macromodels of
nonlinear circuits with time-varying operating points. The models
generated are truly “reduced” meaning that the complexity of
macromodel evaluation is not strongly dependent on the size or
complexity of the original detailed circuit description