Measurement-based Behavioral Model under Mismatched

Measurement-based Behavioral Model under
Mismatched Conditions
a new and easy approach for an accurate model
Frans Verbeyst, Marc Vanden Bossche, Member, IEEE
NMDG Engineering bvba, C. Van Kerckhovenstraat 110, B-2880 Bornem, Belgium
[email protected], [email protected]
Abstract — Presently source- and load-pull techniques
are used to characterize amplifiers under different
impedance conditions and to find the optimal source and
load matching circuitry. Because the tuning process is
cumbersome, the measurement setups have been automated
to collect power amplifier characteristics and to analyze this
data off-line. Some limited capabilities do exist to couple
load-pull data into simulators. This paper presents a
straightforward approach, “based on LSNA technology”, to
extract measurement-based behavioral models of power
amplifiers or any active component under mismatched
conditions and use these models in commercially available
simulators. This approach overcomes the drawbacks of other
existing state of the art solutions.
I. INTRODUCTION
Presently source- and load-pull techniques are used to
characterize amplifiers under different impedance
conditions and to find the optimal source and load
matching circuitry. To provide different impedances to
the amplifier, two main approaches exist: passive
(mechanical or electrical) or active techniques (active
loop or injection of power using an external source) [1][8]. Recently a new “real-time load-pull” technique was
introduced and demonstrated [9].
Another major drawback of classical load-pull setups is
that the resulting data cannot be easily imported into
simulation tools. This is due to the fact that classical loadpull data [10] corresponds to derived quantities such as
transducer gain, PAE, TOI, SOI and possibly AM2PM
for different mismatch conditions, while a simulator uses
voltages and currents at all nodes. A utility [11] does
exist to import load-pull data into a commercially
available simulation tool, but the resulting table-based
model should be used with care and its accuracy highly
depends on the selected load-pull data, which is currently
limited to transducer gain, SOI and TOI.
This paper describes a straightforward approach, which
- starting from large-signal measurements - allows the
extraction of a table-based behavioral model at the
fundamental for a specified region of load mismatches
and a specified range of available input powers. The main
advantage of this approach is that consistently the most
fundamental information, i.e. voltages and currents, are
used during measurement, modeling and simulation. As
such one does not have to worry about which derived
quantities to feed to the model extraction tool in order to
properly predict certain behavior.
II. REAL-TIME LOAD-PULL
One can instantaneously generate a large set of load
reflection values, by combining a tuner and a modulated
source. As such this corresponds to a combination of
passive and active load-pull without feedback.
The tuner is used to realize a certain mismatch and the
active load pull is used to realize a set of mismatch values
around the mismatch set by the tuner.
Using the appropriate modulation, different states can
be realized around the coarse initial load. When the
density of these states is high enough, a sufficient number
of load matches are realized, filling a complete region
(typically a circle) around the point set by the tuner.
Fig. 1 shows the power delivered to the load for a
specified region of load mismatches in the case of a
NE32184A FET operated at 2 GHz and driven 3 dB in
compression. The gate voltage was set to -0.3 V and the
drain voltage to 1.5 V.
The complete set of data is captured within 500µs.
Processing and displaying of derived quantities takes less
than 1 second. Measurement speed can be changed to
avoid or study possible memory effects.
Fig. 1. Power delivered to the load for a specified region of
load mismatches and for a specified available input power.
© EuMA 2005 – 35 European Microwave Conference – Paris, 2005
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III. BEHAVIORAL MODEL EXTRACTION
Next, one can extract a behavioral model for the
specified region of load mismatches. The required
measurement data is collected using the same setup as
during “real-time load-pull”, but does not require
modulation capability of the second source.
Fig. 2 shows the setup and input parameters: region of
load mismatches, as set by the tuner and the power of the
output source for the given input power, the input power
sweep range and the number of amplitudes and phases of
the synthesized load impedances.
and one does not have to worry about which derived
quantities to feed to the model extraction tool.
Fig. 3 shows |b2| as function of |a2| and ϕ(a2/a1) for the
smallest input power and the resulting linear operation
mode of the component. Fig. 4 shows the same
information for the largest input power, corresponding to
approximately 3 dB compression.
Abs b2
0.25
0.225
0.2
30
0.175
20
5
10
a2
phase a2 a1
10
15
20
Fig. 2. Setup and specification of the boundaries for the
behavioral model extraction.
Fig. 3. |b2| in Vpeak as function of |a2| and ϕ(a2/a1) for Pa1 =
-19 dBm resulting in linear operation mode of the component.
|a2| varies from 0 to 0.12 Vpeak, while ϕ(a2/a1) varies from -180°
to 180°.
Abs b2
During model extraction1, the power of both sources is
stepped to cover the specified range of input powers and for each input power - the specified range of load
impedance amplitudes. Different phases are realized by
slightly offsetting the frequency of the second source with
respect to the fundamental set by the first source.
As opposed to port 1, the characteristic impedance at
port 2 is not set to 50 Ohm, but to the load impedance
synthesized by the tuner. As such |a2| equals zero when
the source at port 2 is turned off. Stepping the source
power at port 2, different values of |a2| are realized. Its
value is increased until the specified region of load
impedances is fully covered for the actual input power.
This implies that the validity region of the model as
function of |a2| varies with |a1|. This information is stored
as part of the model, such that the model is able to
indicate potential extrapolation issues, both with respect
to |a1| and |a2|.
At the end of the straightforward model extraction, a
table-based model2 describes the transmitted and reflected
waves at both ports as function of the incident waves at
both ports. More specifically, b1 and b2 are described as
function of |a1|, |a2| and ϕ(a2/a1), representing the phase
relationship between a2 and a1. This measurement data is
available on a regular grid and does not require
triangulation as in the case of classical load-pull data in
order to allow simple interpolation. Also, the
corresponding voltages and currents are readily available
1
2
Patent pending.
DC is considered to be part of the component under test.
1.3
1.2
30
1.1
20
phase a2 a1
5
10
a2
10
15
20
Fig. 4. |b2| (Vp) as function of |a2| and ϕ(a2/a1) for Pa1 =
1 dBm resulting in nonlinear operation mode of the component.
|a2| varies from 0 to 0.72 Vpeak, while ϕ(a2/a1) varies from -180°
to 180°.
For the time being, the model assumes that the impact
of the harmonics of the incident waves can be neglected.
Furthermore, only the response at the fundamental is
described and in the case of modulation, quasi-static
behavior of the DUT is assumed at the fundamental. It is
important to notice that the measurement setup allows to
verify the above assumptions. If necessary, the setup is
able to provide the harmonic terminations, which were
present during the data collection portion of the model
extraction. For these harmonic terminations, it is then
guaranteed that the model accurately describes the
behavior of the component. Based on a relatively small
extension of the standard setup, it is possible to verify the
© EuMA 2005 – 35 European Microwave Conference – Paris, 2005
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sensitivity of the behavior of the component at the
fundamental under changing harmonic termination.
IV. MODEL VERIFICATION
In order to verify the quality of the model, it is possible
to perform a “real-time load-pull” measurement and to
feed the incident waves to the model. Based on the
predicted transmitted and reflected wave, one can
calculate any derived quantity, such as the power
delivered to the load. Fig. 5 shows the excellent
correspondence between measurement and prediction.
Although extrapolation is not advised, the figure shows
that the model is able to detect that extrapolation was
required and demonstrates that the model behaves well
even in the case of limited extrapolation.
specified input power and the set of specified load impedances
defined by “Sweep1” (covering a circle on the Smith Chart).
Fig. 7 shows a contour plot of the power delivered to
the load as a result of a set of harmonic balance
simulations in ADS for an input power of 1.75 dBm.
Clearly there is very good agreement with fig. 5.
Fig. 7.
Contour plots generated in ADS (Pa1 = 1.75 dBm).
Fig. 8 shows the contour plot of the power delivered to
the load for a smaller input power (-5 dBm). The shift of
the corresponding optimal load impedance is apparent.
Fig. 5. Excellent correspondence for power delivered to the
load, even in case of limited extrapolation with respect to input
power (Pa1 1.75 dBm). The left plot shows the prediction, the
green LED (at the top) indicating extrapolation. The right plot
shows the measured values.
V. COUPLING INTO SIMULATOR
Finally the model can be coupled into commercially
available simulators like ADS from Agilent
Technologies. To do so, the model is exported in CITI
file format. Using a FDD in combination with a DAC
component, both standard components within ADS, the
model becomes available to be used as part of e.g. a
harmonic balance (fig. 6) or envelope simulation.
The ADS schematics and data displays, shown below,
are based on example projects provided by Agilent.
Fig. 6. ADS schematic to perform load pull simulations
using the measurement-based behavioral model, for the
Fig. 8.
Contour plots generated in ADS (Pa1 = -5 dBm).
The CITI file containing the measured data can be
converted into a dataset in ADS and directly used within
a data display. Plotting |b2| as function of |a2| for different
values of ϕ(a2/a1), for a specified value of |a1|, fig. 9
shows the 2D equivalent of fig. 3 and fig. 4 within ADS.
Finally it is shown (fig. 10) that the model can be used
in combination with an envelope simulator. The TOI
(Third Order Intercept) simulation is based on an
example provided by Agilent Technologies.
Applying a two-tone excitation, one can calculate the
output TOI based on the voltage across the termination at
fc ± 3∆f compared to fc ± ∆f, where ∆f corresponds to half
the frequency spacing of the two-tone. This should be
done with care, for instance, with respect to the used
input power. The used TOI equation assumes a 1:1 slope
© EuMA 2005 – 35 European Microwave Conference – Paris, 2005
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for the component at fc ± ∆f and a 3:1 slope for the one at
fc ± 3∆f.
Based on this fundamental information, it is rather
trivial to calculate all parameters of interest, like Γin, ΓL,
power delivered to the load, incident power, net input
power, power added efficiency and much more.
VII. CONCLUSION
This paper describes a new and easy approach to
extract a measurement-based behavioral model of an
active component under varying mismatch conditions and
to couple it into a commercially available simulator.
An example ADS project using such a behavioral
model can be downloaded from www.nmdg.be.
VIII. REFERENCES
Fig. 9. 2D slices of fig. 3 and fig. 4 generated in ADS after
reading the CITI file into a dataset (solid lines: ϕ(a2/a1) 0° to
180°, dashed lines: ϕ(a2/a1) -180° to 0°)
Fig. 10. TOI simulation in ADS using the envelope simulator.
VI. ENABLING TECHNOLOGY
The MT4463A Large-Signal Network Analyzer [12],
[13] was used to collect all fundamental information, i.e.
the voltage and current at both ports. In fact the LSNA
returns both the amplitude and phase at both the
fundamental frequency and at the harmonics. As such the
time domain waveforms can be reconstructed, which is
e.g. essential to provide the dynamic load lines,
corresponding to the different load conditions.
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© EuMA 2005 – 35 European Microwave Conference – Paris, 2005
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