Agilent AN 1287-1 User Manual
Agilent AN 1287-1
Understanding the Fundamental Principles
of Vector Network Analysis
Application Note
Table of Contents
2 Introduction
2 Measurements in
Communications Systems
4 Importance of Vector Measurements
5 The Basis of Incident and
Reflected Power
5 The Smith Chart
6 Power Transfer Conditions
9 Network Analysis Terminology
11 Measuring Group Delay
12 Network Characterization
2
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 sweptpower 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 both scalar and 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 both
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.
Figure 1. Linear versus Nonlinear Behavior
A * Sin 360 * f ( t – t )
A
t
o
°
Sin 360 * f * t
Time
Input Output
DUT
A
phase shift =
* 360 * f
t
o
f
1
°
Time
°
Frequency
Linear behavior:
°
input and output frequencies
are the same (no additional
frequencies created)
output frequency only
undergoes magnitude and
phase change
Nonlinear behavior:
f
1
Frequency
Time
f
1
output frequency may undergo
frequency shift (e.g. with mixers)
additional frequencies created
(harmonics, intermodulation)
Frequency
3
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.
Figure 2. Magnitude Variation with Frequency
Figure 3. Phase Variation with Frequency
F(t) = sin wt + 1/3 sin 3wt + 1/5 sin 5wt
Time
Linear
Network
Magnitude
Frequency
Frequency
F(t) = sin wt + 1/3 sin 3wt + 1/5 sin 5wt
Linear
Network
Time
Time
Frequency
Time
Magnitude
Frequency
°
Frequency
–180
–360
0
°
°
Frequency
4
Figure 4. Nonlinear Induced Distortion
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.
Importance of Vector Measurements
Measuring both magnitude and phase of components is important for several
reasons. First, both measurements are required to fully characterize a linear
network and ensure distortion-free transmission. To design efficient matching
networks, complex impedance must be measured. Engineers developing models for computer-aided-engineering (CAE) circuit simulation programs require
magnitude and phase data for accurate models.
In addition, time-domain characterization requires magnitude and phase information in order to perform an inverse-fourier transform. Vector error correction, which improves measurement accuracy by removing the effects of inherent
measurement-system errors, requires both magnitude and phase data to build
an effective error model. Phase-measurement capability is very important even
for scalar measurements such as return loss, in order to achieve a high level of
accuracy (see Applying Error Correction to Network Analyzer Measurements,
Agilent application note 1287-3).
Nonlinear Networks
Saturation, crossover, intermodulation, and other
nonlinear effects can cause signal distortion
Time
Frequency
Time
Frequency
5
The Basis of Incident and Reflected Power
In its fundamental form, network analysis involves the measurement of incident, reflected, and transmitted waves that travel along transmission lines.
Using optical wavelengths as an analogy, when light strikes a clear lens (the
incident energy), some of the light is reflected from the lens surface, but most
of it continues through the lens (the transmitted energy) (Figure 5). If the lens
has mirrored surfaces, most of the light will be reflected and little or none will
pass through it.
While the wavelengths are different for RF and microwave signals, the principle is the same. Network analyzers accurately measure the incident, reflected,
and transmitted energy, e.g., the energy that is launched onto a transmission
line, reflected back down the transmission line toward the source (due to
impedence mismatch), and successfully transmitted to the terminating device
(such as an antenna).
Figure 5. Lightwave Analogy to High-Frequency Device Characterization
The Smith Chart
The amount of reflection that occurs when characterizing a device depends on
the impedance that the incident signal “sees.” Since any impedance can be represented with real and imaginary parts (R+jX or G+jB), they can be plotted on
a rectilinear grid known as the complex impedance plane. Unfortunately, an
open circuit (a common RF impedence) appears at infinity on the real axis,
and therefore cannot be shown.
The polar plot is useful because the entire impedance plane is covered. However,
instead of plotting impedance directly, the complex reflection coefficient is
displayed in vector form. The magnitude of the vector is the distance from the
center of the display, and phase is displayed as the angle of vector referenced
to a flat line from the center to the right-most edge. The drawback of polar
plots is that impedance values cannot be read directly from the display.
Lightwave Analogy
Incident
Transmitted
Reflected
Loading...