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De-Embedding and Embedding S-Parameter Networks Using a Vector Network Analyzer

Application Notes

Introduction 

Traditionally RF and microwave components have been designed in packages with coaxial interfaces. Complex systems can be easily manufactured by connecting a series of these separate coaxial devices. Measuring the performance of these components and systems is easily performed with standard test equipment that uses similar coaxial interfaces. 

However, modern systems demand a higher level of component integration, lower power consumption, and reduced manufacturing cost. RF components are rapidly shifting away from designs that use expensive coaxial interfaces, and are moving toward designs that use printed circuit board and surface mount technologies (SMT). The traditional coaxial interface may even be eliminated from the final product. This leaves the designer with the problem of measuring the performance of these RF and microwave components with test equipment that requires coaxial interfaces. The solution is to use a test fixture that interfaces the coaxial and noncoaxial transmission lines. 

The large variety of printed circuit transmission lines makes it difficult to create test equipment that can easily interface to all the different types and dimensions of microstrip and coplanar transmission lines. The test equipment requires an interface to the selected transmission media through a test fixture. Accurate characterization of the surface mount device under test (DUT) requires the test fixture characteristics to be removed from the measured results. The test equipment typically used for characterizing the RF and microwave component is the vector network analyzer (VNA) which uses standard 50 or 75 ohm coaxial interfaces at the test ports. The test equipment is calibrated at the coaxial interface defined as the “measurement plane,” and the required measurements are at the point where the surface-mount device attaches to the printed circuit board or the “device plane”. When the VNA is calibrated at the coaxial interface using any standard calibration kit, the DUT measurements include the test fixture effects. 

Over the years, many different approaches have been developed for removing the effects of the test fixture from the measurement, which fall into two fundamental categories: direct measurement and de-embedding. Direct measurement requires specialized calibration standards that are inserted into the test fixture and measured. The accuracy of the device measurement relies on the quality of these physical standards. De-embedding uses a model of the test fixture and mathematically removes the fixture characteristics from the overall measurement. This fixture “de-embedding” procedure can produce very accurate results for the non-coaxial DUT, without complex non-coaxial calibration standards.

The process of de-embedding a test fixture from the DUT measurement can be performed using scattering transfer parameters (T-parameter) matrices. For this case, the de-embedded measurements can be post-processed from the measurements made on the test fixture and DUT together. Also, modern CAE tools such as the Keysight Advanced Design System (ADS) have the ability to directly de-embed the test fixture from the VNA measurements using a negation component model in the simulation. Unfortunately, these approaches do not allow for real-time feedback to the operator because the measured data needs to be captured and post-processed in order to remove the effects of the test fixture. If real-time de-embedded measurements are required, an alternate technique must be used.

It is possible to perform the de-embedding calculation directly on the VNA using a different calibration model. If we include the test fixture effects as part of the VNA calibration error coefficients, real-time de-embedded measurements can be displayed directly on the VNA. This allows for real-time tuning of components without including the fixture as part of the measurement. 

The following sections of this paper will review S-parameter matrices, signal flow graphs, and the error correction process used in standard one and two-port calibrations on all Keysight vector network analyzers such as the E5080A ENA Vector Network Analyzer. The de-embedding process will then be detailed for removing the effects of a test fixture placed between the measurement and device planes. Also included will be a description of how the same process can be used to embed a hypothetical or “virtual” network into the measurement of the DUT.

Table of contents

  • S-parameter and Signal Flow Graphs
  • Defining the Test Fixture and DUT
  • Test Fixture Models
  • De-Embedding Process
  • Simple Corrections for Future Effects
  • Modifying the Twelve-Term Error Model
  • Embedding a Virtual Network
  • Summary

S-parameters and Signal Flow Graphs 

RF and microwave networks are often characterized using scattering or S-parameters. The S-parameters of a network provides a clear physical interpretation of the transmission and reflection performance of the device.

Using these equations, the individual S-parameters can be determined by taking the ratio of the reflected or transmitted wave to the incident wave with a perfect termination placed at the output. For example, to determine the reflection parameter from Port 1, defined as S11, we take the ratio of the reflected wave, b1 to the incident wave, a1, using a perfect termination on Port 2. The perfect termination guarantees that a2 = 0 since there is no reflection from an ideal load. The remaining S-parameters, S21, S22, and S12, are defined in a similar manner. These four S-parameters completely define the two-port network characteristics. All modern VNAs can easily measure the S-parameters of a two-port device. 

Another way to represent the S-parameters of any network is with a signal flow graph. A flow graph is used to represent and analyze the transmitted and reflected signals from a network. Directed lines in the flow graph represent the signal flow through the two-port device. For example, the signal flowing from node a1 to b1 is defined as the reflection from Port 1 or S11. When two-port networks are cascaded, it can be shown that connecting the flow graphs of adjacent networks can be done because the outgoing waves from one network are the same as the incoming waves of the next. Analysis of the complete cascaded network can be accomplished using Mason’s Rule. 

It is the application of signal flow graphs that will be used to develop the mathematics behind network de-embedding and modifying the error coefficients in the VNA. 

Defining the Test Fixture and DUT 

Before the mathematical process of de-embedding is developed, the test fixture and the DUT must be represented in a convenient form. Using signal flow graphs, the fixture and device can be represented as three separate two-port networks.

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