Fundamentals of Network Analysis

Publish Date: Dec 14, 2012 | 7 Ratings | 5.00 out of 5 |  PDF

Table of Contents

  1. A Unique Class of Instrument
  2. Network Analyzer Evolution
  3. Network Analysis Principles
  4. Network Analyzer Measurements
  5. Network Analyzer Architectures
  6. Error and Uncertainty
  7. Calibration
  8. Process Requirements
  9. Many Applications, One Instrument
  10. Additional Resources

1. A Unique Class of Instrument

Network analyzers are powerful instruments that, when properly used, provide unparalleled accuracy. Indispensable throughout an enormous range of applications and industries, network analyzers are particularly useful in measuring linear characteristics of radio frequency (RF) components and devices. You can also use modern network analyzers in more specific applications, such as signal integrity and materials measurement. With the introduction of the NI PXIe-5632, you can include network analysis in design validation and production lines without the high cost or large footprint of traditional network analyzers.  

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2. Network Analyzer Evolution

You can use a vector network analyzer, such as the NI PXIe-5632 shown in Figure 1, to measure device magnitude, phase, and impedance. Because a network analyzer is a closed stimulus-response system, you can measure RF characteristics with exceptional precision. Understanding basic network analyzer principles is key to maximizing your benefits with a network analyzer.

Figure 1. The NI PXIe-5632 Vector Network Analyzer

Over the past decade, vector network analyzers have increased in popularity over scalar network analyzers due to lower costs and efficient fabrication techniques. While network analysis theory has existed for decades, the modern stand-alone benchtop analyzer has roots in the early 1980s. Prior to that time, network analyzers were large, complex collections of instruments and external components with limited capabilities. The introduction of the NI PXIe-5632 marks another milestone in evolution, delivering vector network analysis to the flexible, software-defined, modular instrument PXI platform.

The ability to precisely measure magnitude and phase parameters drives the need for exceptional measurement practices to ensure that significant errors do not enter the measurement. While a small error may be inconsequential in contrast to the measurement uncertainty of some RF instruments, it can be substantial with a precise instrument such as a network analyzer.

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3. Network Analysis Principles

Network is a frequently used term that has many modern-day definitions. With respect to network analysis, a network is a group of interconnected electrical components. One function that a network analyzer performs is to quantify the impedance mismatch between two RF components to maximize power efficiency and signal integrity. Each time an RF signal leaves one component and enters another, portions of the signal are reflected and transmitted. Consider the analogy shown in Figure 2.

Light from a source directs an incident signal at an optical device, such as a lens. The lens is analogous to an electrical network. As light hits the lens, depending on the lens’ properties, some of the light is reflected back at the source, and some is transmitted through. Conservation of energy requires that the sum of the reflected and transmitted signal equals the source or incident signal. This example ignores any loss due to heat, which is usually negligible.

Figure 2. An analogy using light demonstrates a basic principle of network analysis.

We can define a reflection coefficient (Г), a vector quantity with both magnitude and phase, as the ratio of light being reflected to the total (incident) light. Similarly, the transmission coefficient (T) is the vector ratio of transmitted light to the incident light. These two quantities are shown in Figure 3.

Figure 3. Transmission (T) and Reflection (Г) Coefficients

By using the ratio of reflected or transmitted light to the incident light, you gain insight into the performance of the device under test (DUT). Thinking back on the light analogy, if the DUT were a mirror, you would want high reflectivity. If the DUT were a camera lens, you would want it to be highly transmissive. Sunglasses may have both reflective and transmissive traits.

Similar practical measurements can be made in electrical networks. A network analyzer generates a sine wave signal, typically across a range of frequencies. The DUT responds with the incident signal being transmitted through the DUT and reflected back from it. The amount of transmitted and reflected signal usually changes with frequency.

The response of the DUT to the incident signal is a result of the DUT properties, as well as any discontinuities in the characteristic impedance of the system. For instance, a bandpass filter is highly reflective out of band, but highly transmissive in band. If the DUT is slightly off the characteristic impedance resulting in an impedance mismatch, the DUT could generate additional unwanted responses. The goal is to develop a measurement methodology that accurately measures the DUT response while minimizing or eliminating uncertainties.

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4. Network Analyzer Measurements

Reflection coefficient (Г) and transmission coefficient (T) are the ratio of reflected signal divided by the incident signal or transmitted signal divided by the incident signal, respectively. These two vector quantities are shown in Figure 3. Modern network analysis expands on this idea with scattering parameters, or S-parameters.

S-parameters are complex vector quantities that represent the ratio of two RF signals. S-parameters have a magnitude and phase, or in Cartesian form, real and imaginary terms. S-parameters are expressed as Sxy where X represents the DUT output port being measured and Y denotes the DUT input port stimulated by the incident RF signal. Figure 4 shows a simple two-port device, such as an RF filter, attenuator, or amplifier.

Figure 4. A Simple Two-Port Device Denoted with S-Parameters

S11 is defined as the ratio of the energy reflected at port one to the incident signal placed on port one. S21 is defined as the ratio of the energy transmitted through the DUT present at port two to the incident signal placed on port one. Both of these quantities, S11 and S21, are referred to as forward S-parameters because the incident signal originates from the RF source on port one. With the incident source on port two, S22 becomes the ratio of the energy reflected by port two, divided by the incident source energy at port two, and S12 is the ratio of the energy transmitted through the DUT present at port one to the incident signal placed on port two. These are the reverse S-parameters.

You can expand this concept with multiport or N-port S-parameters. For instance, RF circulators, power dividers, and couplers are all three-port devices. You can measure and calculate S-parameters such as S13, S32, and S33 in a similar fashion to two-port devices. S11, S22, and S33, S-parameters with matching numbers describe reflected signals, while S12, S32, S21, and S13 , S-parameters with non-matching numbers, describe transmission signals. Furthermore, the total number of S-parameters required to fully describe the RF characteristics of a device is given by the number of device ports squared.

S-parameters that describe transmission, such as S21, are analogous to other familiar terms including gain, insertion loss, or attenuation. S-parameters that describe reflection, such as S11, correspond to voltage standing wave ratio (VSWR), return loss, or reflection coefficient. S-parameters also have other advantages. They are widely used and understood in modern RF measurements. They are easily translated into H, Z, or other parameters. You can cascade S-parameters for multiple devices to produce a composite result. More importantly, S-parameters are ratios. As a result, you do not need to precisely set the incident source power to some absolute value. Any offset in the input is reflected in the DUT response and canceled out when the ratio of the incident and transmitted or reflected signals is calculated.

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5. Network Analyzer Architectures

Network analyzers are available as both scalar (magnitude only) and vector (magnitude and phase) instruments. Scalar instruments were once widely used because of their simplicity and lower cost. Vector instruments offer better error correction and more complex measurement capability. With advances in technology, integration, computing power, and cost reduction, vector network analyzers are increasingly common. 

Network analyzers have four basic functional blocks, as shown in Figure 5.

Figure 5. Modern Network Analyzer Basic Functional Blocks

A signal source, which produces the incident signal, is either swept or stepped in frequency and you can adjust the power level. This source feeds into the DUT input via the signal separation section, also known as a test set. At this stage, the reflected and transmitted signals are separated into components. For each frequency point the processor measures the individual signals, and computes the parameter value (for example S21 or VSWR). User calibration, discussed in more detail later, provides error correction that is applied to the data. Finally, when you interactively use a network analyzer, you can view these corrected values on a display, which shows the parameters and offers other user functionality, such as scaling.

Depending on performance level and cost, network analyzer architectures offer several ways to achieve the four block diagrams. Test sets are designed as either transmission/reflection (T/R) or full S-parameter. The most fundamental implementation, the T/R test set, is shown in Figure 6.

Figure 6. Network Analyzer T/R Test Set Architecture

T/R architecture includes a stable source that supplies a sine wave signal at a given frequency and power. A reference receiver, R, connected with a power divider or directional coupler, measures incident signal magnitude and phase. The incident signal exits the network analyzer via port one and enters the DUT input. The A receiver directional coupler measures (in magnitude and phase) any signal reflected back to port one. With their functions being similar, you can use either directional couplers or resistive bridges to separate signals, based on performance, frequency range, and cost requirements. The signal transmitted through the DUT enters network analyzer port two, where the B receiver measures signal magnitude and phase.

Receivers have different architectures, depending on the desired characteristics. They can be thought of as narrowband receivers with a down converter, IF bandwidth filter, and vector detector, similar to a vector signal analyzer. They produce real and imaginary signal components from which magnitude and phase can be derived. In addition, all receivers share the same phase reference with the source, allowing you to measure their phase with respect to the source incident signal.

T/R architectures are cost-effective, simple, and offer good performance. They measure in only the forward direction, for example, S11 and S21. To measure reverse parameters, you need to disconnect and reverse the DUT or rely on external switching. Because you cannot switch the source (incident signal) to port two, error correction on port two is limited. If your project requirements are compatible with the performance of a T/R architecture, they are an accurate and cost-effective choice.

In full S-parameter architecture, as shown in Figure 7, there is a switch embedded in the signal path after the reference receiver coupler.

 

Figure 7. A Full S-Parameter Network Analyzer

With the switch in the port-one position, the analyzer measures forward parameters, and in the port-two position, it measures the reverse parameters without the need to disconnect or switch to reverse the DUT. The B receiver on the port-two directional coupler measures the forward transmission parameters and the reverse reflection parameters. The A receiver measures the forward reflection parameters and the reverse transmission parameters.

The switch is inside the network analyzer measurement path, so user calibration accounts for the switch uncertainty. However, there may be slight differences in the two switch positions. Additionally, switch contacts may wear over time, requiring more frequent user calibration. To resolve this, you can move the switch to the source output and use two reference receivers, R1 and R2, for the forward and reverse paths respectively, as shown in Figure 8. This higher-performance architecture comes with additional cost and complexity.

 

Figure 8. A Full S-Parameter Network Analyzer with Dual-Reference Receivers

The fundamental network analyzer architectures are mostly implemented in the test set where signal separation occurs. Once the analyzer measures both magnitude and phase for the incident signal (R reference receiver) and transmitted or reflected signals (A and B receivers), it computes the four S-parameter values, as shown in Figure 9.

 

Figure 9. Four S-Parameters in a Full Two-Port Network

In selecting the proper network analyzer architecture, you should consider the application, performance, required accuracy, and cost among other factors.

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6. Error and Uncertainty

Understanding the sources of uncertainty in a vector network analyzer helps you develop a sound user calibration approach. Looking at the architecture of a full two-port network analyzer, as shown in Figure 10, begin with the forward direction.

 

Figure 10. Full Two-Port Network Analyzer Sources of Uncertainty

The first uncertainty is the transmitted and reflected signal loss across frequency, or forward and reverse tracking, respectively. Next is the difference between the DUT input impedance and the network analyzer or system impedance. The same concept applies to the DUT output impedance. These are the source match and load match, respectively.

The efficiency of the directional couplers used for signal separation also requires consideration. An ideal directional coupler produces an output signal in the coupled arm that is proportional to the measured signal traveling in one direction of the main arm, while producing no output for a signal traveling in the opposite direction. The difference between the coupler output (coupled arm) and the measured input signal (thru arm) is the coupling factor. Values of 10 to 30 dB are common, meaning that the coupler output RF power is 10 to 30 dB less than the input signal passing through the thru arm in the proper direction.

A directional coupler should produce no output for a signal traveling in the opposite direction. However, this is rarely the case. Although small, a signal traveling in the opposite direction through a real-world coupler produces an unwanted response at the coupler output. This unwanted signal is defined as the coupler leakage. The difference between the coupling factor and the coupler leakage is known as coupler directivity.

The final term is isolation. A small amount of incident signal is radiated or conducted from port one and is detected at the port-two receiver. In modern network analyzers, this unwanted leakage is usually small. Generally speaking, it does not impact the measurement unless the DUT has high loss. Accounting for isolation during calibration is optional, though recommended, in many modern vector network analyzers.

The sources of uncertainty in the forward direction of a full two-port network analyzer include transmission and reflection tracing; load and source match; directivity; and isolation. These forward terms, combined with the six like terms in the reverse direction, total 12 error terms. User calibration needs to adequately account for these 12 error terms so the proper correction factors can be applied to the measured data. This correction is a primary contributor to the remarkable accuracy of vector network analyzers.  

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7. Calibration

RF instrument calibration usually involves periodically returning an instrument to a certified calibration laboratory to ensure it is operating within manufacturer specifications. The laboratory also traces the instrument performance back to a standards body, such as the National Institute of Standards and Technology (NIST).

Network analyzers are no exception. They too require periodic calibration at a certified laboratory. Moreover, to achieve high accuracy, a user calibration is performed more frequently. This is accomplished with a set of calibration standards from a network analyzer calibration kit, or user-fabricated, user-defined standards. By comparing known values, stored in the network analyzer, against measured values of the calibration standards, a set of correction factors is created. These are applied to the data during the post-calibration measurements to compensate for the sources of error discussed in the previous section.

Many factors determine how often user calibration is performed. Items you should consider include the required measurement accuracy, environmental conditions, and the repeatability of the DUT connection. Typically, network analyzers need user calibration every few hours to every few days. You should use verification standards, identification of the sources of measurement uncertainty, and personal experience to determine how often to calibrate. The remainder of this discussion uses the term calibration to describe user calibration, not to be confused with the recommended yearly certified factory calibration.

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

1.     Short, open, load, through (SOLT)

2.     Through, reflect, line (TRL)

3.     Automatic calibration using an external automatic calibration module

Each calibration family has a variety of implementations. Which method you use depends on the DUT, test system, and measurement requirements. Because SOLT is widely used, we use it to illustrate variations inside a calibration family.

SOLT requires short, open, and load calibration standards in the characteristic system (and DUT) impedance. The exact standard values, as determined by their mechanical dimensions, are loaded into the network analyzer prior to calibration. Wherever you attach the calibration standards (the network analyzer port, the end of a cable, or inside a test fixture) is where the measurement begins and ends. This is the reference plane or measurement plane.

In addition, you must make a through-connection with an insertable connection. For instance, a male to female cable connection, or other connection not requiring external adapters or devices, to complete the through connection during SOLT calibration. Inserting any component during calibration and not using it in the post calibration measurement results in a measurement error.

If you cannot make a through connection, it is said to be non-insertable. There are several methods to handle non-insertable devices. The simplest, is using a set of phase-equal adapters (included in most calibration kits) along with shorts, opens, and loads of each sex. Use one adapter to complete the through connection during calibration and swap it with an appropriate adapter for the DUT connection during post calibration measurements.

Other calibrations in the SOLT family include the response calibration. It is quick, but no more accurate than removing the path loss across frequency. It only accounts for the forward and reverse tracking terms in the 12-term error model. You can perform a one-port calibration by placing a short, open, and load on port one during calibration. This saves some time if you require only a one-port measurement, such as an antenna’s return loss. An enhanced one-port calibration performs a full one-port calibration and uses the through connection to measure port two. This is common in T/R architecture, where no source is present on port two. Finally, there is full two-port SOLT calibration, where you place shorts, opens, and loads on both ports, as directed by the calibration routine. The full two-port calibration concludes with the through connection. Figure 11 summarizes these common SOLT family calibrations.

Figure 11. Common SOLT Calibrations

Both SOLT and TRL calibrations have many variations. You typically use TRL calibration in applications where connectors are not practical, such as probing, or if the DUT is inside a fixture. Because TRL does not require a load, it is more easily implemented in these situations.

Automatic calibration units are a relatively new approach that has rapidly gained popularity because of their speed, repeatability, and ease of use. Moreover, they remove most human interaction, greatly reducing the chance for a misstep during calibration. These units typically contain an electronic component, such as a diode, termination, or other standard, with a corresponding detailed electrical description encoded on an EEPROM. When connected to the network analyzer, the automatic calibration unit is set to different states. The states measured during calibration are compared with the corresponding known states inside the EEPROM to derive the correction values.

Regardless of which calibration method you choose, you should avoid random sources of error. Reducing the IF bandwidth and using averaging reduces noise, providing better results. Quality components, solid measurement practices, and a thorough understanding of the calibration procedure and instrument are all equally important when calibrating network analyzers.

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8. Process Requirements

When making precise measurements with network analyzers, you need to understand and correctly implement each step in the process for best results. Use quality components and sound measurement practices. Consider the RF connections between a well-calibrated network analyzer with correction applied, and a high-performance DUT requiring precise measurement:

  • Are the cables, adapters, and other components high quality?
  • Have you properly cleaned them?
  • Have you used proper torque?

The best network analyzer is ineffective if the quality of the RF connection to the DUT is not on par with the required system accuracy.

It is useful to develop a process when using network analyzers. A process reinforces good practices and helps you improve results. Below is an example framework for using a network analyzer.  

Prepare

  • Warm up the network analyzer and DUT
  • Clean, inspect, and gauge all connectors
  • Select an approach to handle a non-insertable connection if using SOLT calibration
  • Connect cables and adapters to the analyzer

Practice

  • Preset the network analyzer
  • Set up source parameters, including frequencies, power, velocity factor, and IF bandwidth
  • Connect the DUT to verify setup, cables, adapters, and operation
  • Select which S-parameter(s) to measure and choose display format
  • Set up special measurements, such as reference plane extensions, if applicable
  • Observe the response
  • Remove the DUT

Calibrate

  • Choose the proper calibration kit or input calibration standards definitions
  • Set IF bandwidth and averaging to minimize noise during calibration
  • Calibrate manually or use automatic calibration
  • Verify calibration quality using a known verification standard
  • Save the instrument state and calibration

Perform

  • Connect the DUT
  • Apply proper correction from the calibrate step
  • Measure and save DUT parameters

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9. Many Applications, One Instrument

When properly used, network analyzers are some of the most accurate RF instruments, capable of typical accuracies of ± 0.1 dB and ± 0.1 degree. They make precise, repeatable RF measurements. Modern network analyzers offer configurations, and measurement capabilities as extensive as the range of applications they cover. Selecting the proper instrument, calibration, and features, along with using sound RF measurement practices, optimizes your network analyzer results.

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10. Additional Resources

Watch the vector network analysis webcast series

View the NI PXIe-5632 specifications and pricing

Learn best practices to get the most out of your RF instruments

 

 

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