Fundamentals of network analysis

A Unique Instrument

Network analyzers are powerful instruments that can achieve extremely high accuracy when used correctly. They are also widely used and indispensable in many industries, especially in measuring the linear characteristics of wireless radio frequency (RF) components and devices. Modern network analyzers can also be applied to more specific occasions, such as signal integrity and material measurements. With the introduction of the industry's first PXI network analyzer, the NI PXIe-5630, you can completely break away from the high cost and large footprint of traditional network analyzers and easily apply network analyzers to design verification and production line testing. The Evolution

of Network Analyzers

You can use the NI PXIe-5630 vector network analyzer shown in Figure 1 to measure the amplitude, phase, and impedance of a device. Because the network analyzer is a closed stimulus-response system, you can achieve excellent accuracy when measuring RF characteristics. Of course, it is important to fully understand the basic principles of network analyzers in order to get the most out of them.


In the past decade, vector network analyzers have surpassed scalar network analyzers in popularity due to their lower cost and efficient manufacturing techniques. Although the theory of network analysis has been around for decades, it was not until the early 1980s that the first modern stand-alone benchtop analyzers were introduced. Prior to this, network analyzers were large, complex, and limited in functionality, made up of a combination of instruments and external components. The introduction of the NI PXIe-5630 marks another milestone in the evolution of network analyzers, bringing vector network analysis capabilities to the flexible, software-defined PXI modular instrument platform.

It usually takes a lot of practice to make accurate amplitude and phase parameter measurements and avoid major errors. Due to the uncertainty of RF instrumentation, small errors may be ignored. Network analyzers, as precision instruments, can measure very small errors.

Network Analysis Theory

Network is a frequently used term with many modern definitions. In terms of network analysis, a network refers to a group of interconnected electronic components. One of the functions of a network analyzer is to quantify the impedance mismatch between two RF components to maximize power efficiency and signal integrity. Whenever an RF signal passes from one component to another, part of the signal is reflected and part is transmitted, similar to Figure 2. This is like light from a source hitting an optical device, such as a lens. The lens is like an electronic network. Due to the properties of the lens, part of the light will be reflected back to the source, while the other part will be transmitted. According to the law of conservation of energy, the sum of the energy of the reflected and transmitted signals is equal to the energy of the original or incident signal. In this example, the losses due to heat are usually negligible and are ignored.




We can define a parameter, the reflection coefficient (G), which is a vector consisting of magnitude and phase, representing the proportion of the reflected light to the total (incident) light. Similarly, we define a transmission coefficient (T) representing the vector ratio of the transmitted light to the incident light. Figure 3 illustrates these two parameters.


Reflection and transmission coefficients can provide more insight into the performance of the device under test (DUT). Recalling the analogy of light, if the DUT is a mirror, you would expect a high reflection coefficient. If the DUT is a lens, you would expect a high transmission coefficient. Sunglasses may have both reflective and transmissive properties.


Electronics Networks are measured similarly to optical devices. The network analyzer generates a sinusoidal signal, usually a swept frequency signal. In response, the DUT transmits and reflects the incident signal. The strength of the transmitted and reflected signals usually varies with the frequency of the incident signal. The DUT's response to the incident signal is a reflection of the DUT's performance and discontinuities in the system's characteristic impedance. For example, a bandpass filter has a high reflection coefficient outside of the band and a high transmission coefficient inside the band. If the DUT deviates slightly from the characteristic impedance, this creates an impedance mismatch and generates additional undesired response signals. The goal is to establish an accurate measurement method to measure the DUT's response while minimizing or eliminating uncertainty. Network Analyzer Measurement Methods The reflection coefficient (G) and transmission coefficient (T) correspond to the proportion of the incident signal that is reflected and transmitted, respectively. Figure 3 illustrates these two vectors. Modern network analysis extends this idea by using scattering parameters or S-parameters. S-parameters are complex vectors that represent the ratio of two RF signals. S-parameters contain both magnitude and phase, expressed as real and imaginary in Cartesian form. S-parameters are represented using an S-coordinate system, where X represents the output of the DUT being measured and Y represents the input of the DUT being stimulated by an incident RF signal. Figure 4 illustrates a simple two-port device that can be characterized as an RF filter, attenuator, or amplifier.










S11 is defined as the ratio of energy reflected from port 1 to the incident signal at port 1, and S21 is defined as the ratio of energy transmitted to port 2 of the DUT to the incident signal at port 1. Parameters S11 and S21 are forward S-parameters, because the incident signal comes from the RF source at port 1. For a signal incident from port 2, S22 is the ratio of energy reflected from port 2 to the incident signal at port 2, and S12 is the ratio of energy transmitted to port 1 of the DUT to the incident signal at port 2. They are both reverse S-parameters.

You can extend this concept based on multi-port or N-port S-parameters. For example, RF circulators, power dividers, and couplers are all three-port devices. You can measure and calculate S-parameters such as S13, S32, and S33 using similar analysis methods as two-ports. S-parameters with consistent subscript numbers such as S11, S22, and S33 represent reflected signals, while S-parameters with inconsistent subscript numbers such as S12, S32, S21, and S13 represent transmitted signals. In addition, the total number of S-parameters is equal to the square of the number of device ports, which can fully describe the RF characteristics of a device.

Transmission S-parameters, such as S21, are similar to other common terms such as gain, insertion loss, and attenuation. Reflection S-parameters, such as S11, correspond to voltage standing wave ratio (VSWR), return loss, or reflection coefficient. S-parameters have other advantages. They are widely recognized and used in modern RF measurements. You can easily convert S-parameters to H, Z, or other parameters. You can also cascade S-parameters for multiple devices to characterize the RF characteristics of a composite system. More importantly, S-parameters are expressed as ratios. Therefore, you do not need to set the incident source power to an exact value. The response of the DUT will reflect any slight difference in the incident signal, but the difference will be eliminated when the ratio of the transmitted or reflected signal to the incident signal is represented in a ratio manner. Network Analyzer Structure Network analyzers can be divided into scalar (containing only amplitude information) and vector (containing amplitude and phase information). Scalar analyzers were once widely used because of their simple structure and low cost. Vector analyzers can provide better error correction and more complex measurement capabilities. With the advancement of technology, the improvement of integration and computing efficiency, and the reduction of costs, the use of vector network analyzers is becoming more and more popular. Network analyzers have four basic functional modules, as shown in Figure 5.








The signal source is used to generate the incident signal. It supports both continuous frequency sweep and discrete frequency points, and the power is adjustable. The signal source is fed to the DUT input through the signal separation module, which can be regarded as a test device. Here, the reflected signal and the transmitted signal are separated into different component measurements. For each frequency point, the processor measures the signal and calculates the parameter value (such as S21 or standing wave ratio). User calibration is mainly used to provide error correction of the data, which will be described in detail later. Finally, when interacting with the network analyzer, you can view the parameters and corrected values ​​on the display and use other user functions, such as zooming in and out of the waveform.

Depending on the performance and cost of the network analyzer, there are many ways to implement the four modules in the structure. The test device can be designed as transmission/reflection (T/R) or full S-parameters. Among them, the T/R test device is the most basic implementation, and the structure is shown in Figure 6.


The T/R structure includes a stable signal source that can provide a sine wave signal of a specified frequency and power; a reference receiver R, which is connected to a power divider or directional coupler to measure the amplitude and phase of the incident signal. The incident signal is emitted from port 1 of the network analyzer and fed into the input of the DUT. The directional coupler receiver A measures any signal reflected back to port 1 (including amplitude and phase). Directional couplers and resistor bridges have similar functions and can be used to separate signals. You can choose based on performance, frequency range and cost requirements. The signal is transmitted through the DUT and enters port 2 of the network analyzer. Receiver B at port 2 is used to measure the amplitude and phase of the signal. Receivers also have different structures for different performance requirements. They can be regarded as narrowband receivers with downconverters, intermediate frequency filters and vector detectors, similar to vector signal analyzers. They can extract the real and imaginary parts of the signal for calculating amplitude and phase information. In addition, all receivers use the same phase reference as the signal source. You can calculate the phase relationship between the received signal and the incident signal under the same phase reference. The T/R structure is cost-effective, simple in structure, and has good performance. However, it only supports forward parameter measurements, such as S11 and S21. To measure reverse parameters, you need to disconnect and reverse the DUT, or use external switch control. Since the source (incident signal) cannot be switched to port 2, the error correction capability of port 2 is limited. If the T/R structure design meets the requirements of your project, this structure is a high-precision and cost-effective choice. The full S-parameter structure is shown in Figure 7, where a switch is embedded in the signal path after the reference receiving coupler.








When the switch is connected to port 1, the analyzer measures the forward parameters. When the switch is connected to port 2, you can measure the reverse parameters without resetting the external connections of the DUT. Directional coupler receiver B at port 2 measures the forward transmission parameters and reverse reflection parameters. Receiver A measures the forward reflection parameters and reverse transmission parameters.

Because the switch is placed in the measurement path of the network analyzer, the user calibration needs to take into account the uncertainty of the switch. Even so, there may still be slight differences between the two switch positions. In addition, over time, the switch contacts wear, requiring more frequent user calibration. To solve this problem, the switch can be moved to the source output and two reference receivers, R1 and R2, corresponding to the forward and reverse directions, respectively, as shown in Figure 8. With the use of higher performance architectures, cost and complexity also come.


The basic structure of a network analyzer is mostly implemented in a test setup. Once the analyzer measures the amplitude and phase of the incident signal (R reference receiver) and the transmitted signal, or the amplitude and phase of the reflected signal (A and B receivers), the four S-parameter values ​​can be calculated, as shown in Figure 9.


You can choose the appropriate network analyzer structure based on application, performance, accuracy, and cost.


Error and uncertainty Understanding the sources of uncertainty in a vector network analyzer will help you take an effective user calibration approach. For the complete two-port network analyzer structure shown in Figure 10, we start from the forward analysis.




First, the first uncertainty is the signal loss caused by the transmitted and reflected signals due to the frequency or forward and reverse tracks respectively. Second, the difference between the input impedance of the DUT and the impedance of the network analyzer or system. Similarly, the output of the DUT also has similar situations, which belong to the source match and load match respectively.

The efficiency of the directional coupler used for signal separation also needs to be considered. An ideal directional coupler produces an output signal in the coupled arm that is proportional to the standard signal in one direction of the main arm, and no output signal for the signal in the opposite direction. The difference between the coupler output (coupled arm) and the standard input signal (through arm) is the coupling coefficient. The coupling coefficient is usually between 10 dB and 30 dB, which means that when the input signal passes through the through arm in the appropriate direction, the output RF power level is 10 to 30 dB less than it.

Directional couplers produce no output for signals in the opposite direction. But in practice, this is difficult to achieve. Although it is small, the signal in the opposite direction passing through the actual coupler will still produce an unwanted response at the output. This unwanted signal is defined as coupler leakage. The difference between the coupling coefficient and the coupling leakage is called the directivity of the coupler.

Finally, there is isolation. The receiver at port 2 detects a small amount of signal radiated or conducted at port 1. In modern network analyzers, this unwanted leakage is usually very small. In general, it does not affect the measurement unless the DUT has high loss. Although recommended, isolation is only an optional operation in many modern vector network analyzers.

The sources of forward uncertainty for a complete network analyzer include: transmission and reflection tracking; load and source matching; directivity and isolation, which, combined with the reverse 6 error terms, total 12 error terms. User calibration needs to fully account for these 12 errors in order to obtain the appropriate correction factors to apply to the measurement data. This correction is the main reason for the remarkable accuracy of vector network analyzers.

Calibration

of RF equipment often requires that the instrument be sent to an accredited instrument calibration laboratory periodically to ensure that the instrument is operating within the manufacturer's specifications. The laboratory also often adjusts the instrument's performance to a standard, such as the standard specified by the National Institute of Standards and Technology (NIST).

Network analyzers are no exception. They require so much periodic calibration that sometimes they cannot achieve high accuracy. User calibration is also often required. Calibration of a network analyzer is usually accomplished using a set of calibration standards that come with the network analyzer or with user-generated, user-defined standards. A set of correction parameters is generated by comparing known data stored in the network analyzer with the measured data generated using the calibration standards. These are then applied to the data during the calibration test to compensate for the error sources discussed in the previous section.

Many factors determine how often user calibration should be performed. Factors you need to consider include the required test accuracy, environmental factors, and the repeatability of the DUT connections. Typically, network analyzers require user calibration every few hours or days, and you should decide how often calibration is necessary based on verified standards, identification of sources of test instability, and personal experience. As a caveat, this discussion uses periodic calibration to describe user calibration, not to be confused with the recommended annual certified factory calibration.

Three families of calibration are commonly used in network analyzer calibration:

1. Short, Open, Load, Through (SOLT)

2. Through, Reflected, Linear (TRL)

3. Automatic calibration using an external automated calibration model

Because each family of calibration has many different requirements, the decision to use depends on the DUT, the test system, and the test requirements. Since SOLT is widely used, we use it to illustrate the changes in a calibration family.

SOLT requires the use of short, open, load, and through standards with impedances in the system (and DUT). Accurate standard data determined by their mechanical characteristics is loaded into the network analyzer before calibration. The location where you connect the calibration standards (network analyzer ports, the end of a cable, or in a test fixture) is where the test begins and ends. This is the reference platform or test platform.

To further explain, you must make a through connection with a pluggable connector. For example, a male to female connection, or other connection that does not require external devices or adapters to complete a straight-through connection during SOLT testing. Inserting any device during calibration and not using that device in the calibration measurement will result in measurement errors.

If you cannot make a straight-through connection, it is called non-insertable. There are several ways to deal with non-insertable situations. The simplest is to use a set of phase-matched adapters (included in most calibration kits) and each type of short, open, and load, use one adapter to complete the straight-through connection during calibration, and swap it with the appropriate adapter for the DUT connection during calibration testing.

Other calibrations in the SOLT series include response type calibration. It is faster, but not as accurate as removing bandwidth loss over frequency. It only considers the forward and reverse conditions of the 12 error models. You can perform a one-port calibration by placing a short, open, or load condition at port one. This can save some time if you only need to make a one-port measurement, such as the return loss of an antenna. An enhanced one-port calibration is like a full one-port calibration, but with a through connection to measure port two, which is common in T/R configurations where there is no source at port two. Finally there is a full two-port SOLT calibration where shorts, opens, and loads can be placed at both ports as specified in the calibration. Figure 11 summarizes these common SOLT calibrations.


There are many variations of SOLT and TRL calibration. You can use TRL calibration in applications where physical terminals do not exist such as probe nodes or if the DUT is in a test fixture. Since TRL does not require a load, it can be well implemented in these situations.

Automated calibration is a relatively new approach that has quickly gained popularity due to their speed, repeatability, and ease of use. Furthermore, they remove most human intervention, greatly reducing the possibility of errors during calibration. These units traditionally consist of an electronic component such as a diode , terminal or other marker and the associated detailed electronic description stored in EEPROM. When connected to the network analyzer, the automatic calibration is set to different states. During the calibration process these states are measured and compared to the corresponding states stored in the EEPROM to arrive at the correct correction value. Regardless of which calibration method you use, random sources of error should be avoided, and reducing the IF bandwidth and using averaging to reduce noise will provide better results. When calibrating a network analyzer, high-quality components, solid measurement practices, and a thorough understanding of the calibration procedures and instruments are equally important. Procedure Requirements When making precision measurements with a network analyzer, each step needs to be understood and performed correctly to obtain the best results. Use high-performance components and thorough measurement practices. Consider the RF connection between a well-calibrated and corrected network analyzer and a high-performance DUT that requires precision measurements: Are there cables, adapters, and other high-performance components? Did you clean them properly ? Was the proper torque used? Even the best network analyzer is useless if the performance of the RF connected to the DUT does not match the specified system accuracy. When using a network analyzer, it is very helpful to use a procedure. Procedures can enhance operation and improve results. The following is an example architecture using a network analyzer. Preparation Prepare the network analyzer and DUT to clean, inspect, and measure all Connectors If using SOLT calibration, select a method for handling non-insertable connections Connect analyzer cables and adapters to the analyzer Operation Pre-tune the network analyzer Set source parameters, including frequency, power, speed factor, and IF bandwidth Connect the DUT and verify installation, cables, adapters, and operation Select S-parameter measurements and display format If applicable, set special measurement goals, such as extension of the reference plane Observe the response Remove the DUT for calibration Select an appropriate calibration kit or define input calibration standards Set IF bandwidth and average to minimize noise during calibration Calibrate manually or use automatic calibration Verify calibration quality using a well-known check standard Save instrument state and calibration Execute Connect the DUT to obtain appropriate calibration parameters from the calibration procedure Measure and save DUT parameters One instrument, many applications Network analyzers, when used properly, are some of the most accurate RF instruments available, with typical accuracies of ± 0.1 dB and ± 0.1 degrees. They make precise, repeatable RF measurements. Modern network analyzers offer configurations and measurement capabilities that are as broad as the range of applications for which they are used. Selecting the right instrument, calibration, and features, as well as employing reliable RF measurement methods, can help you optimize your network analyzer results.