Mihai Marcu

Scaling of X-parameters for device modeling

The relationships between X-parameters of a given transistor and a second transistor geometrically scaled with respect to the first are derived and presented for the first time. The different types of X-parameters scale differently. These relationships enable X-parameters measured on a fixed size of transistor, diode, or other similar test structure to be scaled to other sizes and produce X-parameter functions as continuous function of size (e.g. total gate width or area). This capability endows X-parameters with a key property of conventional scalable “compact models”, enabling an improved MMIC design capability where size/geometry is a key design degree of freedom. The scalable X-parameters for device modeling are implemented in a commercial nonlinear simulator. The theoretical predictions are validated with numerical results from simulation-based extractions and experimental nonlinear measurements taken with an NVNA on active devices of different sizes.

Compact and behavioral modeling of transistors from NVNA measurements: New flows and future trends

This paper reviews three modern transistor modeling flows enabled by large-signal waveform and/or X-parameter1 measurements from a commercially available nonlinear vector network analyzer (NVNA) instrument. NVNA transistor characterization more safely exercises the device over a wider operating domain than is possible with conventional DC and linear S-parameter measurements, is more indicative of the device large-signal response in actual use conditions, provides data at much faster timescales than pulsed I-V methods, and provides large-signal model validation as a free additional benefit. In the first flow considered, NVNA waveform data is used as a target to extract and tune compact model parameter values and for model validation under large-signal conditions. In the second flow, NVNA waveform data is used to directly construct the multi-variate nonlinear current-source and charge-based nonlinear capacitor functions of an advanced electrothermal and trap-dependent compact model suitable for GaAs and GaN FETs, effectively bypassing the need for explicit model constitutive relation formulation. The final approach is based on the X-parameter measurement and behavioral modeling framework supported by the NVNA, producing nonlinear transistor models directly in the frequency domain. Recent advances in X-parameter methods for transistors, including simple scalability with geometry, show early potential for useful device models, under certain conditions, without the requirement of specifying an internal topology or equivalent circuit at all.

Duty-cycle distortion and specifications for jitter test-signal generation

Duty-cycle distortion is one of the causes of deterministic jitter. Clarification and refinement of this jitter type is presented here. The jitter-tree is then updated with the jitter types discussed. Predicting the behavior of electrical systems under stress from jitter through simulations is limited by the availability of signal sources with controllable and flexible jitter properties in the design environment. A jitter specification method for ISI and DCD is recommended.

Estimation of very low BER using Quasi-Analytical method

This paper proposes to estimate very low system BER using quasi-analytical (QA) method. The results from both theoretical analysis and simulation show that QA estimation is unbiased. Based on calculation of the simulation variance and improvement ratio for QA estimation, the QA is very effective for estimation of very low BER for system with intersymbol interference (ISI), jitter and additive noise.

Frequency-scalable nonlinear behavioral transistor model from single frequency X-parameters based on time-reversal transformation properties (INVITED)

This paper presents a powerful new method that generates a frequency-scalable nonlinear simulation model from single-frequency large-signal transistor X-parameter data. The method is based on a novel orthogonal identification (direct extraction) of current source and charge source contributions to the spectrally rich port currents under large-signal conditions. Explicit decomposition formulae, applied entirely in the frequency domain, are derived in terms of sensitivity functions at pairs of large-signal operating points related to one-another by time-reversal transformation. The method is applied and validated with respect to data from a measurement-based model of a pHEMT transistor. It is demonstrated that the scalable model can predict the nonlinear performance of the transistor over several orders of magnitude in frequency, all from X-parameters at a single fundamental frequency.

Circuit optimization with X-parameter models

X-parameter technology is now established as an indispensable methodology for accurate characterization and modeling of nonlinear components and sub-circuits. However, important considerations may be overlooked when such models are used for optimizing the designs. This paper discusses circuit optimization issues when X-parameter models are employed. This includes the characterization and extraction requirements, interpolation and extrapolation issues, scaling, embedding, as well as potential modification of the components characterized by X-parameter data. Examples include amplifier and transistor designs for power delivered into the load, PAE and linearity performance criteria.

X-Parameters: X-parameter measurement

One of the key features that led to the wide adoption of S-parameters was the availability of hardware and calibration techniques capable of making quick, accurate, and repeatable S-parameter measurements. S-parameters can also be easily extracted in simulation from device or circuit models. In either case, the resulting S-parameters can immediately be used in simulation or design tools. In order to achieve similar success in the nonlinear domain, X-parameters must be easily measured and also easily extracted from simulation. Measurement hardware X-parameters, like S-parameters, represent the steady-state behavior of a device in the frequency domain. The linearity assumption of S-parameters, however, greatly simplifies the measurement requirements. The additional capabilities of X-parameters come at the cost of additional complexity in the measurement system as well as the modeling paradigm. Hardware requirements X-parameters include cross-frequency terms that capture the distortion products generated by device nonlinearities. In order to measure these terms, the measurement hardware must be capable of measuring coherent cross-frequency phase. Because S-parameters include no cross-frequency interaction (a consequence of the linearity assumption), each frequency may be measured independently with no need for a consistent time base or cross-frequency phase. Since all S-parameters are ratios of waves, there is also no need for accurate measurement of absolute power – only the relative power is needed. As a result, the hardware and calibration techniques developed for S-parameter measurement generally are not sufficient for X-parameter measurement and must be extended to include cross-frequency phase and calibrated absolute power.