Understanding the Fundamental Principles of Vector Network Analysis

Introduction Network analysis is the process by which designers and manufacturers measure the electrical performance of the components and circuits used in more complex systems. When these systems are conveying signals with information content, we are most concerned with getting the signal from one point to another with maximum efficiency and minimum distortion. Vector network analysis is a method of accurately characterizing such components by measuring their effect on the amplitude and phase of swept-frequency and swept-power test signals. In this application note, the fundamental principles of vector network analysis will be reviewed. The discussion includes the common parameters that can be measured, including the concept of scattering parameters (S-parameters). RF fundamentals such as transmission lines and the Smith chart will also be reviewed. Agilent Technologies offers a wide range of portable and benchtop vector network analyzers for characterizing components from DC to 110 GHz. These instruments are available with a wide range of options to simplify testing in the field, laboratory, and production environments. Measurements in Communications Systems In any communications system, the effect of signal distortion must be considered. While we generally think of the distortion caused by nonlinear effects (for example, when intermodulation products are produced from desired carrier signals), purely linear systems can also introduce signal distortion. Linear systems can change the time waveform of signals passing through them by altering the amplitude or phase relationships of the spectral components that make up the signal. Let’s examine the difference between linear and nonlinear behavior more closely. Linear devices impose magnitude and phase changes on input signals (Figure 1). Any sinusoid appearing at the input will also appear at the output, and at the same frequency. No new signals are created. Both active and passive nonlinear devices can shift an input signal in frequency or add other frequency components, such as harmonic and spurious signals. Large input signals can drive normally linear devices into compression or saturation, causing nonlinear operation. Linear behavior input and output frequencies are the same (no additional frequencies created) output frequency only undergoes magnitude and phase change Time

Figure 1. Linear versus nonlinear behavior4 For linear distortion-free transmission, the amplitude response of the device under test (DUT) must be flat and the phase response must be linear over the desired bandwidth. As an example, consider a square-wave signal rich in highfrequency components passing through a bandpass filter that passes selected frequencies with little attenuation while attenuating frequencies outside of the passband by varying amounts. Even if the filter has linear phase performance, the out-of-band components of the square wave will be attenuated, leaving an output signal that, in this example, is more sinusoidal in nature (Figure 2). If the same square-wave input signal is passed through a filter that only inverts the phase of the third harmonic, but leaves the harmonic amplitudes the same, the output will be more impulse-like in nature (Figure 3). While this is true for the example filter, in general, the output waveform will appear with arbitrary distortion, depending on the amplitude and phase nonlinearities.

Nonlinear devices also introduce distortion (Figure 4). For example, if an amplifier is overdriven, the output signal clips because the amplifier is saturated. The output signal is no longer a pure sinusoid, and harmonics are present at multiples of the input frequency. Passive devices may also exhibit nonlinear behavior at high power levels, a good example of which is an L-C filter that uses inductors with magnetic cores. Magnetic materials often exhibit hysteresis effects that are highly nonlinear. Efficient transfer of power is another fundamental concern in communications systems. In order to efficiently convey, transmit or receive RF power, devices such as transmissions lines, antennas and amplifiers must present the proper impedance match to the signal source. Impedance mismatches occur when the real and imaginary parts of input and output impedances are not ideal between two connecting devices.