Text preview for : Sensitivity Analysis of One-port Characterized Devices in Vector Network Analyzer Calibrations 5991- part of Agilent Sensitivity Analysis of One-port Characterized Devices in Vector Network Analyzer Calibrations 5991- Agilent Sensitivity Analysis of One-port Characterized Devices in Vector Network Analyzer Calibrations 5991-1272EN c20140529 [13].pdf
Back to : Sensitivity Analysis of O | Home
Keysight Technologies
Sensitivity Analysis of One-port Characterized
Devices in Vector Network Analyzer Calibrations:
Theory and Computational Analysis
White Paper
Abstract
In this paper we present the results of a study on the use of characterized
devices in microwave vector network analyzer (VNA) calibrations and
measurements. We give a brief review of the theory of one-port character-
ized device calibration. One-port characterized devices such as coaxial
opens, shorts and loads are attractive because of their ease of handling
and their ruggedness as compared to more fragile devices like sliding
loads. The scattering parameter error box representation and widely used
terminology of error terms in one-port VNA calibrations such as directiv-
ity, source match and tracking are adopted in this paper. Based on these
parameters, we examine the quality of one class of one-port VNA calibra-
tions achievable through the use of characterized devices and the effects
of different kinds of errors in device characterization can have on VNA
calibrations. Computational analysis has revealed interesting properties of
this class of calibrations that can lead to significant improvements in the
accuracy of VNA measurements.
Introduction
Error correction techniques in two-port environment have been proposed [1,2] and
used in industry for some time. In a model where the non-ideal behavior of a Vector
Network Analyzer (VNA) is assumed to be separable from its ideal characteristics, it
is widely accepted that a VNA can be described as a cascade of ideal reflectometers
and error boxes. The error boxes are subsequently modeled by the theory of scatter-
ing parameters. This is a much simplified picture compared to the complexity of the
architecture of modern VNAs. However, this simple model has been very successful
in explaining the error correction mechanism of a VNA.
The procedure of characterizing the error boxes through the use of known devices is
called network analyzer calibration. In a VNA configuration where there is only one
port to be calibrated, as shown in Figure 1, the normalized components of this error
box are known as directivity (D), source match (M) and tracking (T). These are three
of the four 2-port S parameters of an error box, the fourth parameter has been nor-
malized to unity. Gm is the reflection coefficient of the device under test modified by
the error box. The test port reference plane P in Figure 1 is the plane separating the
device under test and the test port of the VNA. Although we also assigned a second
reference plane Q to the second port of the 2-port error box, this reference plane is
only fictitious just as the 2-port error box itself.
Speaker/Author: Godfrey Kwan
Keysight Technologies
2002 NCSL International Workshop & Symposium
In practice, one may determine the quantities D, M and T by connecting devices
of known impedance to a particular test port and measuring each of these
devices. These devices are calibration standards and will be referred to as
characterized devices in this paper. This VNA calibration technique is known as
Characterized Devices Calibration.
In cases where the device geometry and structure are simple enough, the
device impedance can be calculated from measured physical dimensions and a
few electrical parameters such as conductivity and dielectric constant. Device
impedances can also be measured by a system that is of a high order of accu-
racy. In this paper, we will not be concerned with which of the above methods is
actually used nor their relative merits. In any case, impedances of characterized
devices can never be determined exactly. Slight errors in these "known" imped-
ance values will lead to slight errors in the determination of the D, M and T
values. It is the purpose of the present study to look into how these errors in the
models of characterized devices can affect the accuracy in the determination of
the error box and thus the uncertainties associated with scattering parameters
measurements when using a VNA calibrated with such characterized devices.
In Figure 1, quantities D, M and T are sometimes called the raw error terms.
And we shall refer to the error box bearing these 3 terms as the raw error box.
The purpose of a calibration procedure is to determine these error terms. When
a calibration is completed and the raw error terms are calculated, any future
measurement done on the system can be corrected by making use of these error
terms.
VNA side Device
Reference
side
plane 1
Q
Gm G
D M
Measured
response
provided to T P, test port reference
user without plane.
error correction
Error box
Figure 1. A test port modeled by an error box, a 2-port network of scattering parameters
D, M and T. A one-port device of reflection coefficient G is connected to the test port.
3
One-Port Calibration Theory
After error correction is applied to a VNA measurement, the VNA is now operat-
ing in error correction mode. A VNA operated in such a manner can be further
modeled by a similar signal flow graph as shown in Figure 2 where the D, M
and T terms of the raw error box are now replaced by their respective residual
errors. The original error box now becomes the residual error box. This error-
corrected system, hybrid in nature, now consists of all the circuit components
that make up the entire VNA, as well as the 2-port S-parameter error model that
we have found to correct for any systematic error in the physical measurement.
Measurement data provided under such circumstances are processed data and
should be treated as such. In other words, these data are the result of a mea-
surement plus an error term previously determined by a calibration procedure
that may or may not be independent of the present measurement. The value of
the error term may be related to the device that we are measuring. Even though
this is not at all desirable, sometimes it is unavoidable.
VNA side, in error
corrected mode Device
side
1
d m Gi
Gi + DGi
t Test port reference
plane
Residual error
box
Figure 2. Residual error box description of a Vector Network Analyzer operating in error
correction mode.
4
The residuals of the error box, residual directivity (), residual source match (