Comparing Nonlinear Vector Network Analyzer Methodologies

Scattering parameters (S-parameters) were first mentioned in articles and textbooks in the 1950s and 1960s by Matthews, Collins and Kurokawa and popularized by the release of Hewlett Packard’s first network analyzers in the 1960s. Since then, S-parameters have been used to describe the complex characteristics of a network by quantifying the RF power flowing between its ports. S-parameters are essentially the ratio of the reflected and transmitted signal at a given port to the incident signal at a given port under perfect match conditions (see Figure 1). When referring to a transistor, these parameters can be used to calculate return loss, gain and isolation.1 It is important to understand that S-parameters are only truly valid for linear networks, where the characteristics of the network are independent of the level of the signal being driven into the network. When considering a semiconductor application such as a transistor, this refers to its small-signal operating condition, in which the input drive power does not affect the S-parameters of the transistor. Under small-signal operating conditions, a transistor will have linear gain at the fundamental drive frequency and not excite additional powers at the harmonic frequencies. Linear operation of a transistor and the associated input and output waveforms are shown in Figure 2. The question arises how to thoroughly describe and model a transistor operating under nonlinear large-signal conditions. These conditions occur commonly for high power and high efficiency power amplifiers operating in advanced classes of operation. Under these operating conditions, powers are induced at harmonic frequencies when excited by a sine wave, and in-band and out-of-band modulation products are created under modulation excitation. Considering a simple sine wave excitation, a transistor’s characteristics are dependent on the level of the input drive signal, shown in both frequency and time domains in Figure 3. When the transistor is in deep compression and its output is composed of multiple harmonics, the device behavior cannot be described correctly by S-parameters, which are frequency domain quantities. It is much more natural to analyze the behavior of the device under test (DUT) in terms of time domain RF voltage and current waveforms. Clear evidence of this is provided by the theoretical description of the different modes of operation of power amplifiers, which is completely done in time domain. In this case, a nonlinear vector network analyzer (NVNA) can be used to measure the incident and reflected aand b-waves at the transistor input and output, in both amplitude and phase. The data can then reconstruct the time