Device modeling with small-signal X-parameters measured with a special PNA-X configuration for the study of non-linear interactions

Recently, X-parameters have been introduced to model device non-linear behavior. In addition to providing a measurement-based tool to numerically predict non-linear in-band device behavior in CAD, they can also provide the designer of non-linear circuits the ability to improve the knowledge of the out-of-band device behavior. Exploiting this crucial design aspect, this work presents a novel measurement setup which enables small-signal X-parameters measurements, of non-linear devices driven by a large-signal tone at a pump frequency f_c, in order to predict out-of-band performance at the perturbation frequency, f_x, far removed from the pump frequency f_c. The proposed measurement setup is made up of a Non-linear Vector Network Analyzer PNA-X and a passive tuner in order to enable load-pull characterization at the pump frequency f_c. The developed architecture has been tested for a SiGe HBT, by sweeping the large-signal tone frequency over a narrow bandwidth around 5 GHz and for a broadband low perturbation frequency swept from 200 MHz to 1 GHz in steps of 200 MHz. The usefulness of the obtained small-signal X-parameters for the analysis of small-signal/large-signal nonlinear interactions, such as parametric oscillations, is shown.