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Agilent
De-embedding and Embedding
S-Parameter Networks Using a
Vector Network Analyzer
Application Note 1364-1
Introduction
Traditionally RF and microwave com- Accurate characterization of the Over the years, many different
ponents have been designed in pack- surface mount device under test approaches have been developed for
ages with coaxial interfaces. Complex (DUT) requires the test fixture char- removing the effects of the test fix-
systems can be easily manufactured acteristics to be removed from the ture from the measurement, which
by connecting a series of these sepa- measured results. The test equip- fall into two fundamental categories:
rate coaxial devices. Measuring the ment typically used for characteriz- direct measurement and de-embed-
performance of these components ing the RF and microwave ding. Direct measurement requires
and systems is easily performed with component is the vector network specialized calibration standards
standard test equipment that uses analyzer (VNA) which uses standard that are inserted into the test fix-
similar coaxial interfaces. 50 or 75 ohm coaxial interfaces at ture and measured. The accuracy of
the test ports. The test equipment is the device measurement relies on
However, modern systems demand a calibrated at the coaxial interface the quality of these physical stan-
higher level of component integra- defined as the "measurement plane," dards.2 De-embedding uses a model
tion, lower power consumption, and and the required measurements are of the test fixture and mathematical-
reduced manufacturing cost. RF at the point where the surface- ly removes the fixture characteris-
components are rapidly shifting mount device attaches to the print- tics from the overall measurement.
away from designs that use expen- ed circuit board, or the "device This fixture "de-embedding" proce-
sive coaxial interfaces, and are mov- plane" (Figure 2). When the VNA is dure can produce very accurate
ing toward designs that use printed calibrated at the coaxial interface results for the non-coaxial DUT,
circuit board and surface mount using any standard calibration kit, without complex non-coaxial cali-
technologies (SMT). The traditional the DUT measurements include the bration standards.
coaxial interface may even be elimi- test fixture effects.
nated from the final product. This
leaves the designer with the prob-
lem of measuring the performance
of these RF and microwave compo-
nents with test equipment that
requires coaxial interfaces. The
solution is to use a test fixture that
interfaces the coaxial and non-coax-
ial transmission lines.
The large variety of printed circuit
transmission lines makes it difficult
to create test equipment that can eas-
ily interface to all the different types
and dimensions of microstrip and
coplanar transmission lines1 (Figure
Figure 1. Types of printed circuit transmission lines
1). The test equipment requires an
interface to the selected transmission
media through a test fixture.
Figure 2. Test fixture configuration showing the measurement and device planes
2
The process of de-embedding a test S-parameters and signal
fixture from the DUT measurement
can be performed using scattering flow graphs
transfer parameters (T-parameter)
matrices.3 For this case, the de- RF and microwave networks are Another way to represent the S-para-
embedded measurements can be often characterized using scattering meters of any network is with a
post-processed from the measure- or S-parameters.4 The S-parameters signal flow graph (Figure 4). A flow
ments made on the test fixture and of a network provide a clear physi- graph is used to represent and
DUT together. Also modern CAE cal interpretation of the transmis- analyze the transmitted and reflect-
tools such as Agilent EEsof sion and reflection performance of ed signals from a network. Directed
Advanced Design System (ADS) the device. The S-parameters for a lines in the flow graph represent the
have the ability to directly de-embed two-port network are defined using signal flow through the two-port
the test fixture from the VNA mea- the reflected or emanating waves, b1 device. For example, the signal flow-
surements using a negation compo- and b2, as the dependent variables, ing from node a1 to b1 is defined as
nent model in the simulation.3 and the incident waves, a1 and a2, the reflection from Port 1 or S11.
Unfortunately these approaches do as the independent variables When two-port networks are cascad-
not allow for real-time feedback to (Figure 3). The general equations ed, it can be shown that connecting
the operator because the measured for these waves as a function of the the flow graphs of adjacent networks
data needs to be captured and post- S-parameters is shown below: can be done because the outgoing
processed in order to remove the waves from one network are the
effects of the test fixture. If real- b1 = S11a1 + S12a2 same as the incoming waves of the
time de-embedded measurements b2 = S21a1 + S22a2 next.6 Analysis of the complete cas-
are required, an alternate caded network can be accomplished
technique must be used. Using these equations, the individ- using Mason's Rule.6 It is the appli-
ual S-parameters can be determined cation of signal flow graphs that will
It is possible to perform the de- by taking the ratio of the reflected be used to develop the mathematics
embedding calculation directly on or transmitted wave to the incident behind network de-embedding and
the VNA using a different calibra- wave with a perfect termination modifying the error coefficients in
tion model. If we include the test placed at the output. For example, the VNA.
fixture effects as part of the VNA to determine the reflection parame-
calibration error coefficients, real ter from Port 1, defined as S11, we
time de-embedded measurements take the ratio of the reflected wave,
can be displayed directly on the VNA. b1 to the incident wave, a1, using a
This allows for real-time tuning of perfect termination on Port 2. The
components without including the perfect termination guarantees that
fixture as part of the measurement. a2 = 0 since there is no reflection
from an ideal load. The remaining
The following sections of this paper S-parameters, S21, S22 and S12, are
will review S-parameter matrices, defined in a similar manner.5 These Figure 4. Signal flow graph representation of a
four S-parameters completely define two-port S-parameter network
signal flow graphs, and the error
correction process used in standard the two-port network characteris-
one and two-port calibrations on all tics. All modern vector network
Agilent vector network analyzers analyzers, such as the Agilent E8358A,
such as the E8358A PNA Series can easily the measure the S-para-
Network Analyzer. The de-embed- meters of a two-port device.
ding process will then be detailed
for removing the effects of a test fix-
ture placed between the measure-
ment and device planes. Also
included will be a description on
how the same process can be used
to embed a hypothetical or "virtual"
network into the measurement of
the DUT.
Figure 3. Definition of a two-port S-Parameter
network
3
Defining the test fixture
and DUT
Before the mathematical process of Because we defined the test fixture It is our goal to de-embed the two
de-embedding is developed, the test and DUT as three cascaded net- sides of the fixture, TA and TB, and
fixture and the DUT must be repre- works, we can easily multiply their gather the information from the
sented in a convenient form. Using respective T-parameter networks, DUT or TDUT. Extending this
signal flow graphs, the fixture and TA, TDUT and TB. It is only through matrix inversion to the case of the
device can be represented as three the use of T-parameters that this cascaded fixture and DUT matrices,
separate two-port networks simple matrix equation be written in we can multiply each side of the
(Figure 5). In this way, the test fix- this form. measured result by the inverse T-
ture is divided in half to represent parameter matrix of the fixture and
the coaxial to non-coaxial interfaces yield the T-parameter for the DUT
on each side of the DUT. The two only. The T-parameter matrix can
fixture halves will be designated as then be converted back to the
Fixture A and Fixture B for the left- desired S-parameter matrix using
hand and right-hand sides of the fix- the equations in Appendix A.
ture respectively. The S-parameters This matrix operation will represent
FAxx (xx = 11, 21, 12, 22) will be the T-parameters of the test fixture
used to represent the S-parameters and DUT when measured by the
for the left half of the test fixture VNA at the measurement plane.
and FBxx will be used to represent
the right half.
Using the S or T-parameter model of
the test fixture and VNA measure-
ments of the total combination of
the fixture and DUT, we can apply
the above matrix equation to de-
embed the fixture from the measure-
ment. The above process is typically
implemented after the measure-
ments are captured from the VNA. It
is often desirable that the de-embed-
Figure 5. Signal flow graph representing the ded measurements be displayed
test fixture halves and the device under test
(DUT)
real-time on the VNA. This can be
accomplished using techniques that
If we wish to directly multiply the provide some level of modification
General matrix theory states that if
matrices of the three networks, we to the error coefficients used in the
a matrix determinate is not equal to
find it mathematically more conve- VNA calibration process.
zero, then the matrix has an inverse,
nient to convert the S-parameter and any matrix multiplied by its
matrices to scattering transfer inverse will result in the identity
matrices or T-parameters. The math- matrix. For example, if we multiply
ematical relationship between S- the following T-parameter matrix by
parameter and T-parameter its inverse matrix, we obtain the
matrices is given in Appendix A. identity matrix.
The two-port T-parameter matrix
can be represented as [T], where [T]
is defined as having the four para-
meters of the network.
4
Test Fixture Models
Before we can mathematically The simplest model assumes that This model only accounts for the
de-embed the test fixture from the the fixture halves consist of perfect phase length between the measure-
device measurements, the S or transmission lines of known electri- ment and device planes. In some
T-parameter network for each fixture cal length. For this case, we simply cases, when the fixture is manufac-
half needs to be modeled. Because shift the measurement plane to the tured with low-loss dielectric materi-
of the variety of printed circuit DUT plane by rotating the phase als and uses well-matched
types and test fixture designs, there angle of the measured S-parameters transitions from the coaxial to non-
are no simple textbook formulations (Figure 6). If we assume the phase coaxial media, this model may pro-
for creating an exact model. Looking angles, A and B, represent the vide acceptable measurement
at the whole process of de-embed- phase of the right and left test fix- accuracy when performing de-
ding, the most difficult part is creat- ture halves respectively, then the S- embedding.
ing an accurate model of the test parameter model of the fixture can
fixture. There are many techniques be represented by the following
that can be used to aid in the cre- equations.
ation of fixture models, including
simulation tools such as Agilent
Advanced Design System (ADS) and
Agilent High Frequency Structure
Simulator (HFSS). Often observation
of the physical structure of the test
fixture is required for the initial fix-
ture model. Measurements made on
the fixture can be used to optimize
the fixture model in an iterative
manner. Time domain techniques, The phase angle is a function of the Figure 7. Agilent ADS model for the test fixture
available on most network analyz- length of the fixture multiplied by using an ideal two-port transmission line
ers, can also be very useful when the phase constant of the transmis-
optimizing the fixture model.2 sion line. The phase constant, , is An improved fixture model modifies
defined as the phase velocity divid- the above case to include the inser-
Let's examine several fixture models ed by the frequency in radians.This tion loss of the fixture. It can also
that can be used in the de-embed- simple model assumes that the fix- include an arbitrary characteristic
ding process. We will later show that ture is a lossless transmission line impedance, ZA, or ZB, of the non-
some of the simpler models are used that is matched to the characteristic coaxial transmission line (Figure 8).
in the firmware of many vector net- impedance of the system. An easy The insertion loss is a function of
work analyzers to directly perform way to calculate the S-parameter the transmission line characteristics
the appropriate de-embedding with- values for this ideal transmission and can include dielectric and con-
out requiring the T-parameter line is to use a software simulator ductor losses. This loss can be repre-
matrix mathematics. such as Agilent ADS. Here, each sented using the attenuation factor,
side of the test fixture can be mod- , or the loss tangent, tan.
eled as a 50-ohm transmission line
using the appropriate phase angle
and reference frequency (Figure 7).
Once the simulator calculates all the
S-parameters for the circuit, the
information can be saved to data file
for use in the de-embedding process.
Figure 6. Modeling the fixture using an ideal
transmission line
5
The last model we will discuss
includes the complex effects of the
coax-to-non-coaxial transitions as
well as the fixture losses and imped-
ance differences we previously dis-
cussed. While this model can be the
most accurate, it is the hardest one
to create because we need to
include all of the non-linear effects
such as dispersion, radiation and
coupling that can occur in the fix-
ture. One way to determine the
Figure 8. Modeling the fixture using a lossy
model is by using a combination of
Once again, a software simulator
transmission line measurements of known devices
can be used to calculate the
placed in the fixture (which can be
required S-parameters for this
To improve the fixture model, it may as simple as a straight piece of
model. Figure 9 shows the model for
be possible to determine the actual transmission line) and a computer
the test fixture half using a lossy
characteristic impedance of the test model whose values are optimized
transmission line with the attenua-
fixture's transmission lines, ZA and to the measurements. A more rigor-
tion specified using the loss tangent.
ZB, by measuring the physical char- ous approach uses an electromag-
For this model, the line impedance
acteristics of the fixture and calcu- netic (EM) simulator, such as
was modified to a value of 48-ohms
lating the impedance using the Agilent HFSS, to calculate the
based on physical measurements of
known dielectric constant for the S-parameters of the test fixture. The
the transmission line width and
material. If the dielectric constant EM approach can be very accurate
dielectric thickness and using a
is specified by the manufacturer as long as the physical test fixture
nominal value for the dielectric con-
with a nominal value and a large tol- characteristics are modeled correctly
stant.
erance, then the actual line imped- in the simulator.
ance may vary over a wide range.
For this case, you can either make a As an example, we will show a
best guess to the actual dielectric model created by optimizing a com-
constant or use a measurement puter simulation based on a series
technique for determining the char- of measurements made using the
acteristic impedance of the line. actual test fixture. We begin by mod-
One technique uses the time domain eling a coax-to-microstrip transition
option on the vector network analyz- as a lumped series inductance and
er. By measuring the frequency shunt capacitance (Figure 10). The
response of the fixture using a values for the inductance and capac-
straight section of transmission line, itance will be optimized using the
Figure 9. Agilent ADS model for the test measured results from the straight
the analyzer will convert this mea- fixture using a lossy two-port transmission
surement into a Time Domain line 50-ohm microstrip line placed in the
Reflectometer (TDR) response that test fixture. An ADS model is then
can be used to determine the created for the test fixture and
impedance of the transmission line. We will later find that many vector microstrip line using this lumped
Refer to the analyzer's User's Guide network analyzers, such as the element model.
for more information. Agilent E8358A, can easily imple-
ment this model by allowing the
user to enter the loss, electrical
delay and characteristic impedance
directly into the analyzers "calibra-
tion thru" definition.
Figure 10. Simplified model of a coax to
microstrip transition
6
The Agilent ADS model, shown in S-parameters measurements are and compared to the measured
Figure 11, use the same lumped ele- then made on the test fixture and S-parameters to verify the accuracy
ment components placed on each the microstrip thru line using a vec- of the model values. Because of non-
side to model the two test fixture tor network analyzer such as the linear effects in the transition, this
transitions. A small length of coax is Agilent E8358A. The four S-parame- simplified lumped element model for
used to represent the coaxial sec- ters can be directly imported into the transition may only be valid only
tion for each coax-to-microstrip con- the ADS software over the GPIB. over a small frequency range. If
nector. A microstrip thru line is The model values for inductance broadband operation is required, an
placed in the center whose physical and capacitance are optimized using improved model must be implement-
and electrical parameters match the ADS until a good fit is obtained ed to incorporate the non-linear
line measured in the actual test fix- between the measurements and the behavior of the measured S-parame-
ture. This microstrip model requires simulated results. As an example, ters as a function of frequency.
an accurate value for dielectric con- Figure 12 shows the measured and
stant and loss tangent for the sub- optimized results for the magnitude Once the lumped element parame-
strate material used. Uncertainty in of S11 using the test fixture with ters are optimized, the S-parameters
these values will directly affect the a microstrip thru line. All four for each half of the test fixture can
accuracy of the model. S-parameters should be optimized be simulated and saved for use by
the de-embedding algorithm. Keep in
mind that it is necessary to include
the actual length of microstrip line
between the transition and device
when calculating the S-parameters
for the test fixture halves.
Figure 11. Agilent ADS model of test fixture
and microstrip line
Figure 12. Comparison of S11 for the
measured and modeled microstrip thru line
7
The de-embedding
process
Whether a simplified model, such as There are five steps for the process The Real-Time Approach
a length of ideal transmission line, of de-embedding the test fixture
or a complex model, created using using T-parameters: This real-time approach will be
an EM simulator, is used for the test detailed in the following sections
fixture, it is now necessary to Step 1: Create a mathematical model of this application note. For this
perform the de-embedding process of the test fixture using S or T-para- technique, we wish to incorporate
using this S-parameter model. meters to represent each half of the the test fixture S-parameter model
There are two main ways the de- fixture. into the calibration error terms in
embedding process can be imple- the vector network analyzer. In this
mented. The first technique uses Step 2: Using a vector network ana- way, the analyzer is performing all
measured data from a network ana- lyzer, calibrate the analyzer using a the de-embedding calculations,
lyzer and processes the data using standard coaxial calibration kit and which allows the users to view
the T-parameter matrix calculations measure the S-parameters of the real-time measurements of the DUT
discussed in the previous section. device and fixture together. The S- without the effects of the test
The second technique uses the net- parameters are represented as com- fixture.
work analyzer to directly perform plex numbers.
the de-embedding calculations, Most vector network analyzers are
allowing the user to examine the de- Step 3: Convert the measured S- capable of performing some modifi-
embedding response in real-time. parameters to T-parameters. cation to the error terms directly
This technique is accomplished by from the front panel. These include
modifying the calibration error Step 4: Using the T-parameter model port extension and modifying the
terms in the analyzer's memory. of the test fixture, apply the de- calibration "thru" definition. Each
embedding equation to the mea- of these techniques will now be dis-
The Static Approach sured T-parameters. cussed, including a technique to
modify the traditional twelve-term
This approach uses measured data error model to include the complete
from the test fixture and DUT gath- S-parameter model for each side of
ered at the measurement plane. The the test fixture.
data can be exported from the net-
work analyzer or directly imported
into a simulation tool, such as ADS, Step 5: Convert the final T-parame-
over the GPIB. Using the fixture ters back to S-parameters and dis-
model, the de-embedding process is play the results. This matrix
performed using T-parameter matrix represents the S-parameters of the
calculations or the negation model device only. The test fixture effects
in ADS.3 Once the measurements have been removed.
are de-embedded, the data is dis-
played statically on a computer
screen or can be downloaded into
the analyzer's memory for display.
8
Simple corrections for
fixture effects
Port extensions
The simplest form of de-embedding Also note that the airline measure-
is port extensions, which mathemat- ment exhibits lower ripple in the
ically extends the measurement measured S11 trace while the coax-
plane towards the DUT. This feature to-microstrip test fixture shows a
is included in the firmware of most much larger ripple. Generally, the
modern network analyzers such as ripple is caused by interaction
the Agilent E8358A. Port extensions between the discontinuities at the
assume that the test fixture looks measurement and device planes.
like a perfect transmission line of The larger ripple in the lower trace
some known phase length. It results from the poor return loss of
assumes the fixture has no loss, a the microstrip transition (20 dB
linear phase response, and constant versus >45 dB for the airline). This
impedance. Port extensions are usu- ripple can be reduced if improve-
ally applied to the measurements ments are made in the return loss
after a two-port calibration has been of the transition section.
performed at the end of the test
cables. If the fixture performance is
considerably better than the specifi-
cations of the DUT, this technique
may be sufficient.
Port extension only adds or sub-
tracts phase length from the mea-
sured S-parameter. It does not
compensate for fixture losses or
impedance discontinuities. In most
cases, there will be a certain
amount of mismatch interaction
between the coax-to-fixture transi-
tion and the DUT that will create
uncertainty in the measured
S-parameter. This uncertainty typi-
cally results in an observed ripple in
the S-parameter when measured
over a wide frequency range. As an
example, consider the measure-
ments shown in Figure 13 of a short Figure 13. Port extension applied to a
placed at the end of two different measurement of a short at the end of an
constant impedance transmission airline (upper trace) and at the end of a
lines: a high-quality coaxial airline microstrip transmission line (lower trace)
(upper curve), and a microstrip
transmission line (lower curve). Port
extensions were used to move the
measurement plane up to the short.
However, as seen in the figure, port
extension does not compensate for
the losses in the transmission line.
9
Modifying calibration standards
During calibration of the vector Another way to implement the The calibration kit definition
network analyzer, the instrument reference plane or port extensions, actually includes three offset
measures actual, well-defined discussed in the previous section, characteristics for each standard.7
standards such as the open, short, would be to redefine the cal kit They are Offset Delay, Offset Loss
load and thru, and compares the definitions for each of the calibration and Offset Impedance (Z0). These
measurements to ideal models for standards. For example, if we wanted three characteristics are used to
each standard. Any differences to extend each reference plane a accurately model each standard so
between the measurements and the value of 100 psec past the point of the analyzer can establish a reference
models are used to compute the calibration, we can modify each plane for each of the test ports.
error terms contained within the standard definition to include this
measurement setup. These error 100 psec offset. This value would be Fixture de-embedding can be accom-
terms are then used to mathemati- subtracted from the original offset plished by adjusting the calibration
cally correct the actual measurements delay of the short, open and load kit definition table to include the
of the device under test. This standards. The "thru" definition effects of the test fixture. In this
calibration process creates a would include the total delay of the way, some of the fixture
reference or calibration plane at the extensions from each port. As an characteristics can be included in
point where the standards are example, when using the Agilent the error terms determined during
connected. As long as a precise 85033E cal kit, we would modify the the coaxial calibration process.
model is known for each calibration short definition to have an offset Once the calibration is complete, the
standard, an accurate reference delay of