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Microwave Measurements. Part II – Nonlinear Measurements / Camarchia, Vittorio; Teppati, Valeria; Corbellini, Simone;
Pirola, Marco. - In: IEEE INSTRUMENTATION & MEASUREMENT MAGAZINE. - ISSN 1094-6969. - STAMPA. -
10:3(2007), pp. 34-39. [10.1109/MIM.2007.4284255]
Original
Microwave Measurements. Part II – Nonlinear Measurements
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Published
DOI:10.1109/MIM.2007.4284255
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34
IEEE Instrumentation & Measurement Magazine June 2007
R
F system design requires accurate measure-
ments. This is true both for passive and active
elements; however, while the passive ones can
be assumed linear, and therefore completely
identifi ed through S-parameter measurements as a function of
frequency [1], active element are usually driven in mild or deep
non-linear regime. In these cases the amplitudes at the funda-
mental frequency of the port voltages and currents depend
in a non-linear way from the inputs, and the non-linearities
generate spectral components, harmonics or intermodulation
products, not present in the excitations. Within the framework
of power amplifi er characterization, to which this article is de-
voted, the input and output terminations play a determinant
role on the amplifi er behavior and performances, and there-
fore their effect must be properly exploited; for instance, their
correct choice can optimize performance such as the output
power or the power added effi ciency. While this is true for the
load and source termination at the fundamental frequency, the
harmonics often have some signifi cant impact; for example,
their effect is crucial in applications based on harmonic tuning,
e.g. class E and F amplifi ers [2].
For these reasons, an experimental setup for character-
izing power amplifi ers must be able to measure the complex
spectrum of the waves at the amplifi er ports as a function of
frequency, input power, and source and load termination at
the fundamental and harmonic frequencies. Once the termi-
nations are fi xed to 50 Ω and only the wave amplitudes are
accounted for, the classical simple scalar setup is used to deter-
mine the amplifi er transfer curve output power (P
OUT
) versus
input power (P
IN
). The power units are normally expressed
in logarithmic scale as decibel for watt (dBW) or, for longer
power ranges, in decibel for mW (dBm).
The vector network analyzer (VNA) is the core instrument
used in the non-linear characterization scenario. The basic idea is
to keep the operations of VNA/mixers linear, diverting to them
only a small portion of the signal present at the device under test
(DUT) ports, therefore keeping unaltered the VNA capabilities
already exhibited for small signal measurements.
This solution enables sharing between S-parameters and
non-linear parameters, which avoids unnecessary duplication
of the measurement systems. But there are many challenging
problems that must be faced and overcome.
Microwave
Measurements
Part II
Non-linear measurements
Vittorio Camarchia, Valeria Teppati, Simone Corbellini, and Marco Pirola
June 2007 IEEE Instrumentation & Measurement Magazine 35
◗ New calibrations are necessary because the measure of
the wave ratios at the amplifi er ports is not suffi cient. An
absolute calibration reference must be adopted to fi x the
absolute value of the signal at the ports
◗ The actual power levels to be measured must be taken into
account, and bias tees, power splitters and combiners,
power terminations, and at-
tenuators must be designed
accordingly. For example,
measurements on GaN or
SiC-based devices, the lat-
est-generation FET power
devices, require handling
tens of watts. These adverse
conditions cause self-heat-
ing of the test-bench, which
must be cooled during the
characterization.
◗ A large amount of power is needed to push large periph-
ery devices into their non-linear zones. The non-lineari-
ties become signifi cant for complete characterization with
conditions closest to the actual operating conditions. The
driver amplifi ers affect the power stage; they must be
linear to avoid spurious contribution to the harmonic
levels. The applied stimulus is important from a quan-
titative and qualitative standpoint. The stimulus must
be carefully chosen to excite the measured elements in a
realistic condition. For example, in new communication
link applications, the characterization should be accom-
plished in the presence of an input signal with complex
broad-band modulation (e.g., Wideband Code Division
Multiple Access - WCDMA) to measure the amplifier
effects on the fi gure of merit as spectral re-growth or adja-
cent channel power ratio.
◗ To provide comprehensive information, non-linear char-
acterization requires a large amount of data; at the mo-
ment there is no explicit or implicit standardization that
is individualized for its management, and care must be
taken in the handling and processing.
◗ Fully automated linear benches are the present state-of-
the-art, and no special knowledge or skill is required by
the operator. Conversely, non-linear measurements must
be carried out, step by step, by trained operators who
manually control the measurement setup.
This article discusses techniques to synthesize loads, the
most used non-linear measurement techniques, and harmonic
load-pulling.
Termination Synthesis Techniques
Under non-linear conditions, Device-Under-Test (DUT) char-
acterization cannot be achieved by either the scattering matrix
or by any equivalent representation. The characterization can
be carried out through the direct measure of key parameters
such as input and output port powers (at fundamental and
harmonic frequencies), operating gain, power-added effi cien-
cy, AM-AM/AM-PM conversion characteristic, intermodu-
lation distortion, adjacent power channel ratio, and many
other fi gures of merit. Unfortunately this generates many new
measurement issues with respect to linear cases: most of these
parameters depend on the operative conditions, and therefore,
other quantities must be controlled to set the desired working
ones.
Direct Current (DC) biases,
input and output impedances,
frequencies, and input power
levels are the most important
quantities to control during the
characterization. DC biases re-
quire devices for either voltage
or current polarizations that are
able to handle the power and
are able to control the signal
even when strong rectifying be-
havior of the device is present.
Tuning networks are required to set the impedence values.
Passive tuners and active load synthesization are two differ-
ent solutions [3].
Passive tuners are typically based on a slotted line with an
inserted slug that can be moved along the longitudinal and
vertical axes by either micrometer positioners or precision
stepper motors [4]. Typically, the commercially available tun-
ers have one or two slugs that are used in different frequency
bands. Repeatability is assured by the accuracy of the stepper
motors.
Figure 1 shows the basic structure of a slug tuner. The
analysis is performed far from the slug resonant frequency.
The change of the slug position along the vertical axis causes
a change in the load magnitude, whereas the movement along
the longitudinal axis changes the load phase.
Passive tuners are usually the most effective and economi-
cal way to control the DUT load conditions at lower micro-
wave frequencies up to a few gigahertz and when high power
is involved. However, at higher frequencies, the synthesized
reflection coefficient is limited in magnitude by losses. In
Fig. 1. A slug tuner transversal section (left) and longitudinal section (right).
Vertical and longitudinal movements change refl ection magnitude coeffi cient
and phase, respectively.
© iStockphoto.com
The vector network
analyzer (VNA) is the core
instrument to use in the
non-linear characterization
scenario.
36 IEEE Instrumentation & Measurement Magazine June 2007
high-power devices, the optimum termination of novel, high-
breakdown materials usually is close to the Smith chart border.
This is particularly true for small periphery devices but is also
true for large devices because the magnitude of the reactive
terminations increases as the frequency rises. To mitigate such
a problem, pre-matching networks can be inserted very close
to the DUT, although the use of active loads is preferable.
Active loads electronically synthesize the required refl ec-
tion coeffi cient by amplifying, phase-shifting, and combining
microwave signals to generate the refl ected wave. Among the
available solutions, two main techniques can be identifi ed: the
two-signal technique and the active-loop technique.
The fi rst technique, attributed to Takayama [5], consists of
a power divider that splits the source signal into two parts, as
shown in Figure 2. The fi rst part drives the input port of the
device, while the second part is properly amplifi ed and phase-
shifted then injected into the DUT output port. The required
refl ection coeffi cient can be controlled by adjusting the attenu-
ator and the phase-shifter settings.
This technique enables high refl ective loads to be obtained
but also has a severe drawback, because it is diffi cult to keep
the load condition constant when the input power or the DUT
characteristics change. This happens when the device heats up
or it is close or within its compression range.
This problem can be solved by employing an active-loop
technique (Figure 3) [6]. A portion of the DUT output signal is
controlled in amplitude and phase by means of a directional
coupler and sent back to the DUT. Therefore, the magnitude
of the load refl ection coeffi cient (Γ
L
) is proportional only to the
loop gain, whereas the load phase depends on the loop phase
shift. A very selective fi lter is usually inserted into the loop to
avoid oscillations caused by the relative broad band of the loop
components.
This technique offers great fl exibility in load control and se-
lection as compared to the passive approaches. Setup losses are
easily compensated by the loop amplifi er. Highly mismatched
or even active terminations are therefore easily synthesized.
However, passive tuners exhibit higher power handling capa-
bilities only by adopting expensive amplifi ers.
Non-Linear Characterization
at RF and Microwave
This section describes the acquired quantities and the common
measurement approaches. The fi rst technique measures all
quantities related to power (scalar quantities) with large band
power meters and all of the other vector quantities (refl ection
coeffi cients) with a previously calibrated VNA. As in all open-
loop control systems, this setup is limited because the pre-
liminary calibration determines the quality of the results. This
approach relies on two assumptions: First, all of the networks
measured with the VNA under small signal conditions are
intrinsically linear (they do not change properties as the signal
Fig. 2. An active load-pull system based on the two-signal technique.
Fig. 3. An active load-pull system based on the active-loop technique.
June 2007 IEEE Instrumentation & Measurement Magazine 37
intensity rises), and second is the repeatability of the tuning
device [7] and the connector insertions.
Figure 4 shows a simplifi ed scheme of a two-port load-pull
system with power meters. These systems are generally called
non-real-time. They need a long, time-consuming pre-charac-
terization phase for each system component, including load
tuning devices, for each loading condition that is imposed
during the measurement phase.
The second approach uses the VNA to measure all of the
quantities of interest in real-time while exciting the system in
non-linear conditions. High level signals are separated and re-
duced by proper coupling/attenuating devices. Calibration is
performed as a classical VNA error correction in linear condi-
tions. In this case, the assumption is that every device included
in the calibration model is linear and does not change from the
calibration to the measurement phase.
Classical VNA calibrations are able to correct only the wave
ratios that in non-linear conditions lose their meanings. This
is why a further calibration step that exploits an additional
power meter measurement is needed to achieve information
on the magnitude of each wave [8].
Figure 5 shows a real-time two-port load-pull system. Inci-
dent and refl ected waves at the DUT reference planes are sepa-
rated with directional couplers and measured with a VNA.
The two systems in Figures 4 and 5 are based on the same main
elements but used in different ways. The load tuning devices
and the directional couplers are swapped, so that a unique
VNA calibration can be used for each loading condition. This is
why the real-time approach is defi nitely faster, more accurate,
and straightforward [9].
Notice that when highly refl ective loads must be synthe-
sized at the DUT reference planes, the real-time confi guration
Fig. 4. A simplifi ed scheme of a non-real-time, two-port, load-pull measurement system.
Fig. 5. A simplifi ed scheme of a real-time, two-port, load-pull measurement system.
