Presented at ESA Microwave Technology and Techniques Workshop 2010 10-12 May 2010

1. ESA M icrow ave Technology and Te chnique s Works hop 2010, 10-12 M ay 2010
Switching amplifier design with S-functions,
using a ZVA-24 network analyzer
Marc Vanden Bossche
NMDG N.V., Fountain Business Center - Bld. 5,
Cesar van Kerckhovenstraat 110, 2880 Bornem, Belgium
Abstract
In this paper the S-function theory is explained and especially their assumptions are highlighted. Due to
these assumptions, it is not evident that S-functions are applicable to switching amplifiers. The paper
uses the term “switching amplifiers” in its broad sense, namely all classes of amplifiers that drive the
transistor in pinch-off and that optimize in one or another way the behavior of the amplifier by tuning
the harmonics. Some setups are illustrated to extract the S-functions and some possible pitffalls in these
setups are mentioned. Finally, the extraction and verification of S-functions on a switching amplifier
are demonstrated.
I. Introduction
In the quest for the best power added efficiency, switching amplifiers are very important. Presently
harmonic source- and load-pull are being used to shape the input waveforms and to provide the proper
load impedances to improve different specifications. This process is quite tedious due to the large
degree of freedom in optimizing different parameters. With these measurements it is neither possible to
simulate. Therefore, good models would speed up the design using more automated search routines in
simulation tools and would allow to understand the propagation of performance through the complete
circuit. Also to improve the performance of amplifiers, pre-distortion circuits are being designed. This
can be done in a more efficient way using a good model of the component. Of course, this model must
be straightforward to extract, has to predict nonlinear behavior accurately and should take into account
the interaction with other components, similar to S-parameters.
Lately, a lot of attention is given to different behavioral models, their extraction techniques for
nonlinear high-frequency components and the related high-frequency instruments to extract these
models.
S-functions is one of these behavioral models. They are finding their roots in the describing functions, a
well-known approach in control theory ([1]-[3]). These S-functions can be extracted using commercial
available network analyzers, equipped with the proper hardware and measurement software.
The S-functions are a natural extension of S-parameters into the nonlinear domain [4]. Together with
the approaches described in [5]-[9], they belong to a class of frequency-domain behavioral models that
describe the nonlinear behavior of a multi-port Device Under Test (DUT) by linearizing its response
around a set of large-signal operating points. As a result, S-functions can predict accurately both the
harmonic distortion due to the large-signal excitation, as well as linear interactions of small-signal
reflections. Using appropriate impedance transformations, S-functions can be extracted under arbitrary
1

2. impedance conditions [5]. Thanks to the linearization simplifications, the dimensionality of this type of
models stays limited and can the model be extracted in a reasonable time.
But questions do rise about the applicability and validity range due to this linearization, especially
applying it to switching amplifiers where the harmonics are determining a large part of the behavior.
By nature, switching amplifiers are very nonlinear but the information must be transmitted with
minimal distortion.
After explaining the S-function theory in section II, the extraction process is mentioned in Section III.
In section IV the challenges are explained to apply S-functions to switching amplifiers and section V
highlights the different setups, based on combining a network analyzer with tuners and active injection.
Finally an example of S-function extraction and verification is given on a transistor in deep pinch-off.
The goal is to determine the validity range of the model to be able to use it in confidence for designing
switching amplifiers.
II. The S-function theory
A linear two-port device is completely described by its S-parameters as function of frequency. When
this device is excited by a signal with spectral content within the frequency band of the S-parameters,
the response is predicted accurately through linear theory.
Assume an amplifier as device under test, stimulated at one specific frequency. For low input power,
the amplifier is fully characterized by its S-parameters at that frequency. Increasing the input power,
B1 and B 2 will no longer be linearly related to A1 and A2 starting from a certain power level.
As such the S-parameters are no longer valid. Additionally in many cases the generation of harmonics
can be observed in B1 and B 2 .
f0 f0
VDC v 3
A1 i3 A2
f0 f0 2f 3f
2f 3f 0 0
0 0
B1 B2
Fig. 1 One large input tone at input and output
Assume a simple case where A1 and A2 consist of one spectral tone at the considered frequency
(Fig. 1). It is possible to create a table that describes the amplitude and phase of fundamental and
harmonics of B1 and B 2 as function of the amplitude of the single tone of A1 and A2 and their
phase relationship (1).
Furthermore, the amplitude and phase of Bi k i=1,2 are depending on the bias settings of the
nonlinear component. Different ports of the device can be used to apply a combination of voltage- or
current-forcing bias. Certain ports will combine RF signals and DC signals. The combination of
A1 1 , A2 1 and the DC bias is considered as the large signal operating point (LSOP) of the
device that determines Bi k i=1,2 .
2

3. Describing the nonlinear behavior, the self-biasing effect is as important as the high-frequency
behavior. Therefore, one needs to describe also the DC behavior at the relevant ports as function of the
LSOP. The nature of the component, e.g. BJT or FET, typically drives the selection of the DC forcing
mode. This determines the independent variable while the dependent variable is the duality.
Bias dep var =Table ∣A1 1∣,∣A2 1∣, Phase  A1 1 , A2 1 , Bias indep var 
(1)
Bi k =Table i ∣A1 1∣ ,∣A2 1∣ , Phase  A1 1 , A2 1 , Bias indep var with k≡k f 0
There are two main issues with this “simple” model. First of all, it is impossible to derive such model
with any type of equipment. This is very similar to the extraction of S-parameters. No network analyzer
exists that is perfectly 50 Ohm to extract immediately an S-parameter. A network analyzer always
requires two independent measurements to extract the S-parameters. Similarly, it is impossible to find
equipment that can generate the pure fundamental tones A1 1 and A2 1 at the component level.
Even if a source would exist to generate a pure tone, one cannot avoid the presence of harmonics in
Ai . Indeed the harmonics of Bi k  get reflected by the termination of the equipment and added to
Ai . As such, one always has to consider the presence of harmonics in Ai , deviating from the
above simple case.
Secondly, the “simple” model is not practically useable. The purpose of the model is to predict the
response of a combination of components and circuits. Predicting the harmonics in Bi and restricting
Ai to the fundamental tone does not make sense. Therefore the “simple” model must be expanded,
taking the harmonics in Ai into account.
The naive approach is to simply extend the above model and describe Bi k  as tables of all possible
amplitudes and phase combinations of Ai k  . This results in a vast amount of data and unacceptable
measurement times.
f0 f0
2f0 3f
VDC v 3 2f0 3f
A1 0 i3 0
A2
f0 2f 3f
f0 0 0
2f 3f
0 0
B1
B2
Fig. 2 Linear perturbation caused by
small harmonics
In many practical cases, the harmonics in Ai are small compared to Ai 1 . As such the harmonics
can be considered as perturbations to the “simple” model and one can linearize in the harmonics of
Ai . The linearization is similar to the conversion matrix theory [10]. One harmonic of Ai impacts
all tones of Bi but in a linear relationship (Fig. 2). Thanks to this linearization the required amount of
experiments is reduced meaningfully.
The region of validity of this model can be extended further by the linearization in the complex
conjugate of the harmonics. This extension does not increase the complexity of the model, neither the
extraction effort. The validity of this extension is easily proven using the Volterra theory [11]. When the
incident waves get delayed, the reflected waves will also be delayed. This is expressed in the S-
3

4. functions by applying the proper phase normalization against the main tone.
LSOP ≡∣A1 1∣ ,∣A2 1∣ , Phase  A1 1 , A2 1 , Bias indep var 
=A1 1/∣A1 1∣ (2)
Bi k =SF ik  LSOP  k SF ikjl  LSOP  A j l  k−l SF c  LSOP  A*j l k−l with l1
ikjl
It is possible to extend further the region of validity by including higher order terms related to the
probing signal, like second and third order effects [12]. These equations can be derived by using the
Volterra theory.
Of course, it is possible to extend the LSOP by adding other independent variables, like temperature, at
the expense of larger measurement times.
III. S-function extraction
To extract an S-function, one needs a measurement setup that can apply the large-signal operating
points in a controllable way. For each LSOP, one performs a set of independent experiments by varying
Ai k  , to extract the S-function coefficients using one or another linear regression method. The
variation of Ai k  needs to be large enough to be properly measurable while the absolute amplitude
needs to be small enough not to violate the linearity assumption.
To perform these independent experiments, the setup requires a synthesizer that can be switched
sequentially to each DUT port of interest injecting a “small” tone (probing or tickling tone)
sequentially at each harmonic (Fig. 3). At each harmonic, the phase of the tickle tone is rotated to
create the independent experiments. Two phase values, separated by 90 degrees, are an optimal
minimum [12]. To reduce the measurement uncertainty though, typically this number is increased at the
expense of a slower extraction (e.g. 5 phase values equally distributed across 360 degrees).
f0
DC Bias
f0 Large-Signal
Source or Load
Large-Signal
Source Tickling
k f0 Source ZL
Fig. 3 Conceptual setup for S-function extraction
IV. The switching amplifier and S-functions
In the context of this article, the term “switching amplifiers” has been considered in its broadest sense.
And for real switching amplifiers the article is most relevant.
Any type of amplifier beyond class A, drives the main transistor more or less into pinch-off by
4

5. controlling the DC bias point. It is possible to shape the voltage and current waveform by adapting the
harmonic impedances both at the output and at the input of the transistor. Also over-driving the
amplifier at the input, switches the transistor faster between on- and off-states bringing it closer to an
ideal switch behavior [14].
Usually it is the goal to maximize PAE, often combined with maximizing delivered output power with
minimal input power at the fundamental frequency.
Operating as an ideal switch, namely when the voltage and current waveforms do not overlap and are
close to square waves, does not result in the best PAE due to the presence of the harmonics which
dissipate across the broadband load.
Instead of dissipating power at the harmonics, it is better to reflect the power back to the transistor in
such a way that it recombines through the nonlinearities with the fundamental power and optimizes the
fundamental behavior. This occurs for properly selected values of amplitude and phase of the
harmonics in combination with DC bias and input power levels.
Harmonic source- and load-pull systems are being used to find these optimal points in a multi-
dimensional search space. These systems allow to sweep input power, DC bias, fundamental and
harmonic impedances at the input and the output, measure the specifications of interest and display
them in, amongst others, contour plots. This process is elaborate and one does not get feedback on the
actual class of amplifier.
Large-signal network analyzers give a tool to the amplifier designer to make a shortcut in this multi-
dimensional search space. By providing in almost real-time voltage- and current- waveforms,
fundamental and harmonic impedances, dynamic load-lines etc., it is becoming possible to apply text-
book design techniques for the different classes of amplifiers [14].
For small-signal designs or designs where the power is backed off meaningfully to maintain linearity, it
is very efficient to perform amplifier design using S-parameters [15]. Nowadays this mode of operation
is unacceptable in many cases. Pushing the amplifiers in their nonlinear mode of operation, S-
parameters are not adequate and can be replaced by S-functions.
Nevertheless, the use of S-functions requires caution due to their assumptions.
First of all, the LSOP needs to stay constant while the tickle tone is applied. By using control loops on
the LSOP during the tickling, it is possible to maintain the LSOP constant. Instead of this time
consuming operation, it is possible to adapt the S-function equations to take into account small
variations of the LSOP [12].
Secondly the tickling tones should be large enough to measure them with enough accuracy but even
more important they should be small enough to satisfy the linearization assumption. Usually it is
possible, whether or not assisted by dedicated S-function tools, to select proper amplitudes for the
tickle tones. These amplitudes could be frequency dependent.
Once the S-functions are extracted, one can interpolate between the large-signal operating points and
one can predict the component behavior properly as long as the applied harmonics will not violate the
linearization. This is guaranteed as long as the harmonics in the simulation are smaller then the tickle
tones during the extraction, assuming that they were selected properly. But as long as one does not
violate the linearization, one can increase the amplitude further of the harmonics.
For switching amplifiers, for which S-function models would be a great advantage, the linearization
assumption is not trivial. Due to the important role of the harmonics to achieve high PAE, it is not
5

6. guaranteed that they can be considered as a perturbation, allowing to linearize.
Therefore, either one verifies before the extraction that the tickle tones can be increased in power
relevant to the switching amplifier without violating the linearity principle [16]. Typically this means
that one needs to realize reflection factors close to one. Another approach is to extract an S-function
model and verifying it afterwards with measurements, which are relevant to the switching amplifier.
The consequence is that the measurement setup needs to be capable of applying the signals and
impedances which are relevant to the switching amplifier and cannot be limited to the setup to extract
only S-functions.
V. Setups to measure S-functions for switching amplifier design
To extract S-functions in a near 50 Ohm environment, a minimal setup should contain a large-signal
high-frequency source and a second tickle source, synchronized to the large-signal source, to create the
tickle tone at the input and output using a switch and a set of couplers (Fig. 3). Nowadays most of this
hardware is present in advanced network analyzers.
To support S-functions predicting load-pull conditions, this setup needs to be extended with a
fundamental tuner at the output of the device under test. To apply the large-signal power efficiently to
components with high reflection coefficients at the input it is advised to use a source tuner.
DUT
Variable loss Variable loss
Fig. 4 Setup for S-function extraction in non-50 Ohm environment
Because the tuners are in between the device under test and the measurement couplers, the error
coefficients, characterizing the systematic errors of the setup, need to be updated continuously as a
function of the S-parameters of the tuners, depending on their position. In this way, the measurement
system gives continuously the correct voltage and currents at the device ports.
f0 DUT k f0
f0
k f0
Fig. 5 Setup with harmonic load tuner and probing coupler
6

7. Because the injection of the tickle tone is behind the tuners (Fig. 4), the resulting amplitude of the
tickle tone at the device under test will change depending on the position of the tuner. Therefore it is
important that the the S-function extraction software compensates for the losses across the tuners while
applying the tickle tone. Otherwise, it is not guaranteed that adequate power reaches the device under
test. Due to these losses in combination with the couplers, it is possible that an additional amplifier is
needed to boost the tickle power.
It is possible to extract S-functions for a switching amplifier with a setup with fundamental source and
load tuner. The disadvantage is that it is impossible to verify the S-functions whether they properly
describe the device behavior under high harmonic reflection factors. By adding the necessary
amplification to the tickle source it is possible to synthesize actively high reflection factors and to
verify the model. Though the more power, generated by the device, the more difficult it gets to
overcome the losses in the system.
For verification purpose of the S-functions, a different setup is being preferred (Fig. 5). This setup
replaces the fundamental load tuner with a harmonic tuner. This tuner can create high reflection factors
at fundamental and harmonics and will be used for the S-function verification.
Even during the S-function extractions, this setup has favorable advantages. As the fundamental load is
being swept, the harmonic loads can be kept constant, in contrast with a fundamental tuner only. This is
an advantage in case of potential instabilities. Additionally the tickle tone is presently only
compensated in power for the losses across the tuner. There is no compensation for the fact that there is
an initial reflection, caused by the tuner. As the phase rotates, the load impedance will rotate around
this initial reflection factor. This reflection will change in an uncontrolled way when the fundamental
load is changed. Of course, as long the linearisation is valid, there is no problem. But with switching
amplifiers, this linearisation is actually questionned.
Because the harmonic tuner is used to synthesize large reflection factors, especially for the harmonics,
the coupler has to be moved between the device under test and the tuner. Ideally the coupler should not
reduce the maximum reflection factor that can be synthesized at the device under test. Therefore, the
coupler has to have minimal loss. Amongst others, this can be realized by probing structures [17-18].
V. S-function extraction of a FET for the design of switching amplifiers
For this case study, a high efficiency heterojunction power FET, EPA120B-100P from Excelics, is used
in a Focus Microwaves fixture. This device has a typical power output of 30 dBm and power gain of 11
dB at 12 GHz.
Fig. 6 Setup for S-function extraction in non-50
Ohm environment
Fig. 7 Class A - Dynamic Loadline
7

8. The measurement system is based on a Rohde&Schwarz ZVA 24 with the proper options and the
NMDG ZVxPlus add-on kit. As fundamental source and harmonic load tuner respectively a CCMT
1808 and MPT 1818 from Focus Microwaves were used. As coupler structure at the output, the low-
loss VI probes from Focus Microwaves were selected (Fig. 6). The measurement system is calibrated at
2 GHz with 5 harmonics. The transistor is being de-embedded including the package. A package model
is provided by the transistor manufacturer.
Based on the maximum current and voltage excursion at the drain, the fundamental load was
determined and the bias settings were optimized (Error: Reference source not found). Then the gate
bias was reduced to pinch off the transistor and halve the peak drain current (Vg = -0.93V and Vd = 6.3
V). The second and third harmonic impedances were shorted as good as possible such that the drain
voltage waveform would be as close as possible to a sine wave. The source tuner was matched to the
input impedance of the transistor, averaged for small and large input powers. Then the input power was
increased again to achieve the original maximal drain current of the class A mode of operation (Fig. 8).
2f0 3f0 f0
gate drain
Dynam ic Loadline
Fig. 8 Class B - Voltage and current behavior at gate and drain + load impedance
The goal is to extract and validate an S-function for the given fundamental load impedance and bias
settings such that the model can be used to design different types of switching amplifiers. The concern
is the validity of the linearization assumption for switching amplifiers. When valid, the S-function
should predict properly the behavior of the transistor under different high harmonic reflective
conditions.
The S-function is extracted for a sweep of incident power, going from -5 dBm up to 9.5 dBm with the
second and third harmonic load terminated in 50 Ohm. Before starting the S-function extraction, the
level of the tickle tones must be determined. As said, the tickle signal must be large enough to be
8

9. measured properly but may not violate the linearization assumption. A simple approach to determine
the maximum tickle level is to offset the tickle tone in frequency from the harmonic frequency such
that it can be considered a negligible offset for the transistor but that it is out of the resolution
bandwidth of the IF filter of the network analyzer. In this way, the measurement setup measures only
the harmonic response. The power of the tickle tone is gradually increased until a change in harmonic
response and / or DC currents are observed. This procedure resulted in a tickle power at the input of -20
dBm and at the output of -5 dBm. At the output the tickle power was not sufficient to influence the
harmonic behavior and / or DC currents. This is due to the available power of the source, the coupling
factor of the coupler and the tuner insertion loss.
The S-functions were extracted using control loops to keep the LSOP constant during tickling (Fig. 9).
The constancy of the LSOP was verified and confirmed for input power and bias settings. Also the
interpolation capability of the S-function was verified by predicting the reflected waves and comparing
with the measurements for in-between input powers (Fig. 10).
b2
Fig. 9 S-functions, related to S11, S12, S21 and S22 as function of power sweep
Using the S-function for switching amplifier design, the linearity assumption must be validated. Two
verifications were performed with the harmonic tuner. First, different second harmonic impedances
with increasing reflection factor were synthesized, keeping the third harmonic impedance at 50 Ohm
(Fig. 11).
9

10. f0 2 f0
3 f0
Com ple x pre diction error
Fig. 10 Interpolation verification predicting b2 for different tickling experiments (x-axis)
0.75
0.5 16 phas e value s
0.25
0.75 0.5 0.25 0.25 0.5 0.75
0.25
0.5
Incre ase refl factor
0.75
Fig. 11: Coverage of 2 f0 (or 3f0) load impedance with 3 f0 (or 2f0) matched
The incident and reflected waves are measured for each impedance setting, after making sure that the
incident power and the bias did not change. Using the S-functions, the fundamental and harmonics of
the reflected waves, Bi k  , are predicted. The complex error is calculated and compared to the
measured power level. Hereby for each amplitude of the reflection factor, the absolute power and the
error prediction is plotted as function of the phase index of the reflection factor (Fig. 12). It can be
observed clearly that with increasing harmonic reflection factor the prediction error increases. This is
due to the fact that the linearization principle is violated more and more. To use waveform engineering,
the error is still acceptable. For other purposes, maybe the error level is not acceptable anymore. It can
also be seen that for certain load conditions, the transistor is oscillating. Of course, the power levels
cannot be predicted by the model in this case. Another way of representing the prediction error on B2,
is using countour plots (Fig. 13). It can be clearly seen that the error increases with increasing
reflection factor.
10

11. b1f0  and complex error b1 2f0  and complex error
dBm dBm dBm
b13f0 and complex error
2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
10 10
2 4 6 8 10 12 14 16
20 20
3f0
10
oscillation oscillation
b1 f0 30
2f0 30 oscillation
20
40 40
30
50
50
40
60
60
b2 f0  and complex error b2 2f0  and complex error b23f0  and complex error
dBm dBm dBm
20
10
b2
f0
2 4 6 8 10 12 14 16
10
oscillation 2 4 6 8 10 12 14 16
10
3f0
2 4 6 8 10 12 14 16 10 2f0 20
10
oscillation oscillation
30
20
20 40
30
50
30
40 60
40
Increas e re fl factor
Fig. 12 B1,2 and prediction error as function of phase index for increasing reflection factor at 2 f0
X1.0 X1.0 X1.0
R0 R0 R0
X0.5 X2.0 X0.5 X2.0 X0.5 X2.0
R0.5 R0.5 R0.5
R1.0 R1.0 R1.0
R2.0 R2.0 R2.0
X0 X0 X0
-45 dBm -50 dBm -50 dBm
X0.5 X2.0 X0.5 X2.0 X0.5 X2.0
-5 dBm -15 dBm
-10 dBm
X1.0 X1.0 X1.0
Fig. 13 Prediction error of b2(f0,2f0 and 3f0) for 2f0 tuning
The same was repeated stepping the third harmonic impedance while keeping the second harmonic
impedance at 50 Ohm. It can be seen that the linearity assumption stays longer valid with increasing
reflection factors but the device starts to oscillate more often (Fig. 14).
11

12. b1 f0 and complex error b1 2f0  and complex error b1 3f0 and complex error
dBm dBm dBm
2 4 6 8 10 12 14 16
10 2 4 6 8 10 12 14 16
10
2
b1
4 6 8 10 12 14 16 oscillation (8)
20
f0 20
oscillation
10
oscillation
b1 30 oscillation
2f0
(2)
b2f0  and prediction error
20
dBm 40
30
3f0
30 50 40 4
20
60
50
2
40 15
(12)
10 4 (12)
50 100 150 200 250
(8)
2
b2f0  and complex error 2 b22f0  and complex error
dBm dBm dBm
5 b23f0 and complex error
(2)
20 10
b2 f012
4 6 8 10 14 16 50 100 150 200 250 2 4 6 8 10 12 14 16
10
oscillation 2 4 6 8 10 12 14 16
4
5 2
oscillation 10 oscillation 10
3f0
2 4 6 8 10 12 14 16
oscillation 2f0 2 oscillation
10
20 oscillation
20
10
30 30
50 100 150 200 250
20
40 40
2
Increas e re fl factor
Fig. 14 B1,2 and prediction error as function of phase index for increasing reflection factor at 3 f0
Fig. 15 b2(f0) and prediction error for given high refl at 3 f0 with tuning 2f0
Usually for switching amplifiers both harmonic impedance are high reflective. Therefore, a verification
test is done where the third harmonic reflection is kept at its largest value and is rotated 360 degrees.
For each position of the third harmonic reflection, the second harmonic reflection is rotated 360
degrees for its highest reflection coefficient. For a given high reflection factor of the third harmonic,
Fig. 16 shows B 2 1 and its prediction error rotating the second harmonic reflection factor at its
highest value. The power of B 2 1 is around 20 dBm while the error is around -5 dBm. For three
phase values the time waveforms are shown for the measured and predicted B2. Oscillation can also be
observed.
dBm b2f0 and prediction error
4 (8)
20
2
15 (2)
(12)
10 4 50 100 150 200 250
2
5 2
4 6 8 10 12 14 16 50 100 150 200 250
4 (12)
5 2
2
10 (8)
(2)
50 100 150 200 250
2
Fig. 16 b2(f0) and error for given high refl at 3 f0 with tuning 2f0 + corresponding time waveforms
12

13. As can be seen, the linearity assumption is even more violated due to the accumulation of the high
reflection at the second and third harmonic. Of course, the points of oscillation do not need to be
considered. As can be seen in the time waveforms, the error is still acceptable in this case for waveform
engineering, as long as the device is not oscillating. But caution is necessary and the S-functions cannot
be applied blindly.
IV. Conclusions
In this article, the S-function theory and the extraction process has been explained. Nevertheless, the
aim of S-functions is to predict nonlinear behavior, a linearity assumption is needed to make it
practically useable. On overview of different setups has been given, focusing on the extraction and
verification of S-functions for switching amplifiers.
A case study was done on a commercial FET, were it is clearly demonstrated that care needs to be taken
with the linearization assumption under high reflective conditions. These high reflective conditions just
occure for switching amplifiers.
Therefore, S-functions are very useful and speed up the design process but can not be applied blindly
for switching amplifiers and need to be verified with independent data sets with stimuli close to the
realistic conditions. Without explicit verification it is not possible to predict the quality of the S-
functions in advance. The advantage is that the verification data set is much more smaller than the data
that would be needed to extract a model without linearization. The disadvantage is that a more extended
setup is required.
Acknowledgment
The use of the S-function models in ADS™ was made possible thanks to the support from Agilent
Technologies.
References
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