For large signal excitation, traditional measurement instruments like the vector network analyser (VNA) cannot be used due to the non-linearity of the device under test (DUT). Hence, load-pull measurements are widely used to describe non-linear DUTs. However, load pull only offer finding optimum terminations for a certain operational mode, thus, scalar parameters like output power, gain or efficiency. In many cases, a vectorial measurement setup, similar to a VNA, is desired, but due to the high number of involved tones, or harmonics respectively, a special instrument is necessary. The figure depicts the involved input and output waves for a typical non-linear DUT.

© Holger Arthaber

Incoming and outgoing wave spectra of a nonlinear DUT

To overcome this issue the non-linear vector network analyser (NVNA) was introduced. This instrument allows measuring all involved signals on the harmonic grid, as shown in Figure 1, similar to a VNA in the linear case. In combination with traditional load-pull techniques, all waves can be measured also in non 50 Ω environments. Additionally high power measurements can be performed by expanding the test-set of the NVNA. An example of the NVNA in high power measurement configuration including a load-pull setup is depicted in the following picture.

© Holger Arthaber

Measurement of nonlinear X-parameters in a non 50 Ohm environment

X-parameters / Polyharmonic Distortion Modelling

Models for active devices operating in a nonlinear regime are an indispensable tool for modern RF circuit design. A popular class of large signal models are X-parameters, which offer an accurate description of nonlinear devices. X-parameters work under the assumption that the DUT operates on a so-called large signal operation point (LSOP), which includes bias, fundamental frequency and one single large signal input tone. This assumption works for most applications, especially for RF power amplifiers. Additionally, polyharmonic distortion modelling is applied, which is basically an approximation by a first order Taylor series around the LSOP for all involved harmonics.

© Holger Arthaber

Change of harmonic phases due to nonlinear behavior

An illustration of the polyharmonic distortion modelling principle can be seen in the above figure. Due to this linearization, an additional small signal input at a certain port and harmonic frequency contributes in principle to the response at all involved ports and frequencies at the harmonic grid. This is called the harmonic superposition principle.

To achieve high model accuracy, especially for non 50 Ω loads, this model can be expanded to the load dependent X-parameter model, which allows a second large signal input tone, described by a fundamental load mismatch. Hence, a highly accurate model prediction, even for highly nonlinear DUTs, can be achieved by utilizing a load dependent X-parameter model extracted for loads on a load pull grid, in combination with interpolation techniques.

In many applications, the response of a non-linear DUT for a harmonic mismatch is important, like e.g. harmonic controlled power amplifiers, which are intended to achieve high efficiency values. Due to the applied polyharmonic distortion modelling the X-parameter model allows to predict the response for a harmonic mismatch. Figure 4 shows the model prediction error for a load dependent X-parameter model under highly nonlinear operation for 2^nd order harmonic mismatch. As can be seen in the following figure, the error is significantly below -20dB, hence, high prediction error can be satisfied using this model.

© Holger Arthaber

Mean square error contours of a nonlinear model at different 2nd harmonic load impedances