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1
Automatic Phase and Amplitude
Characterization
João Paulo Martins, Nuno Borges Carvalho and José Carlos Pedro
Instituto de Telecomunicações, Campus Universitário, 3810-193 Aveiro, Portugal
[email protected]; [email protected] and [email protected]
Abstract— This paper presents an amplitude and phase
characterization of a small signal amplifier using a new
proposed phase measurement technique for IMD side-band
incommensurate tones. A complete characterization of an
amplifier was done for various gate voltage swings. The results
establish the validity of the setup for the uncorrelated phase
measurement.
Index Terms— Phase measurement, Nonlinear Distortion,
Instrumentation
I.
INTRODUCTION
Recent communication systems impose an increase in
bandwidth, which wrangle the use of the memoryless
approximation to usual nonlinear circuits, mainly amplifiers.
That non-memoryless can be seen by evaluating the phase
change of those circuits. This phase rotation can be mainly
attributed to short-term and/or long term dynamic effects,
and measuring them could give us some insight on the
nonlinear distortion mechanisms that really exist in
RF/microwave nonlinear distortion.
A paradigmatic manifestation of the nonlinear dynamics
where the amplitude and phase characterization is of
fundamental importance is the IMD distortion asymmetry
often seen in high power amplifiers [1].
The nonlinear behavior and its consequences are usually
minimized through several linearization techniques [2-3],
most of them based on some form of distortion cancellation.
In order to cancel the unwanted distortion a tone with the
same frequency and amplitude but with opposite phase must
be added. If all the distortion components are to be
canceled, the nonlinear inverse function of the active device
should be synthesized.
The design of a block with the described characteristics is
only possible if a precise characterization of the device is
available. The required characterization demands for an
accurate measurement system, not only for the amplitude,
but also for the relative phase itself.
Additionally, thermal and dispersion effects can also have
a significant impact on the phase change of nonlinear
distortion, even if amplitude asymmetry is not seen. Thus,
the phase knowledge in this type of systems is of vital
importance permitting an effective design of linearization
systems [4]. These are the main reasons driving to the
correct and complete measurement in nonlinear circuits.
All these constraints lead to an obvious need of an
automated measurement setup for nonlinear systems able to
automatically perform the measurement of IMD amplitude
and phase, and thus fully characterize the nonlinear
distortion on those PA’s.
The typical signal used to characterize and obtain the
transference function of a system is a two tone test. This
excitation has been extended to the multi-tone signal,
creating the need to measure the amplitude and phase of
each of the output tones.
When the test signals used to perform the measurements
are obtained from the same reference they are correlated or
synchronous. This property allow the sampling through a
digital oscilloscope and by post processing the digital signal
by a discrete Fourier transform, DFT, algorithm the phase is
readily obtained. Although it is a very simple method there
are some limitations restricting its applicability. The number
of points available in the sampling oscilloscope imposes a
limit in the number of tones allowed in the multi-tone signal
and in the bandwidth [5-6].
Even so, that solution is only applicable to periodic and
phase-correlated signals due to its correlation properties,
leaving all uncorrelated signals still untreated [7].
A common procedure used to measure phase in
uncorrelated signals use the generation of a spectral
reference though a well known nonlinear device The signal
to be measured is added to the signal obtained from the
nonlinear reference and the desired phase value is obtained
by the extra phase shift needed to achieve a proper
cancellation of each tone at the output [8].
In this paper we present the use of a recently proposed
phase and amplitude measurement bench in order to fully
characterize an amplifier when the gate voltage is swept.
This measurement bench allows us to measure IMD side
bands when the multi-tone input signal is constituted by
incommensurate tones. The obtained results state the
viability of this technique, allowing its easy incorporation
into commercial available network or signal analyzers.
First the measuring bench will be presented, and then
some measuring results will be obtained.
II. SPECTRAL FILTERING APPROACH TECHNIQUE
Typical off the shelf linear instrumentation systems like
spectrum analyzers, network analyzers and vector signal
analyzers [9], generally follow a super-heterodyne
architecture in order to acquire the relative phase and
amplitude differences. The signals to be measured are
converted to a proper frequency usually much lower than
the signal under test where the measurement impairments
are less challenging.
By this technique any DUT could be characterized by
measuring both signals at the input and at the output and
comparing the two in amplitude and phase. Since the typical
test signal is a single tone it presents the same frequency
both at the input and output. Because both input and output
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are at the same frequency, this is a straightforward
measurement.
This new setup [10] is based on super-heterodyne
architecture and extends the measurement concept to multitone signals. In order to do so, a reference signal to be
compared with the DUT’s output should be used, so that
both of them are at the same frequency, Fig.1.
A two tone signal is the simplest case of a multi-tone
signal. However it is able to demonstrate the potential of the
setup and will be used to describe all the functioning.
Consider a signal composed by two uncorrelated tones
represented by:
x1 (t ) = cos(ω1t ) + cos(ω2t )
with:
(1)
ω1
being any non-rational number.
ω2
First this signal is split in two branches. In the upper
branch, the two tone signal is applied to the DUT changed
by a gain factor.
If the DUT is a nonlinear device presenting some degree
of memory, the output will be [11]:
y NL (t ) = a1 x(t − τ 1 ) + a2 x(t − τ 2 ) 2 + a3 x(t − τ 3 ) 3 + ...
(2)
where ai are different gains and τi are different delays for
each nonlinear contribution.
The signal at the output of the DUT is an amplified
version of the input signal and all the mixing distortion
products, whose power depends on the degree of saturation
of the device. The in-band part of this signal could be
represented by:
x2 (t ) = a1 A1 cos(ω1t − φ110 ) + a1 A2 cos(ω 2 t − φ101 )
3
2
a3 A1 A2 cos[(2ω1 − ω 2 )t − φ32−1 ]
4
6
⎡3
3
2⎤
+ ⎢ a3 A1 + a3 A1 A2 ⎥ cos(ω1t − φ310 )
4
⎦
⎣4
x3 (t ) = a1r A1 cos[ω1t − φ110 r ] + a1r A2 cos(ω 2 t − φ101r )
3
2
a3 r A1 A2 cos[(2ω1 − ω 2 )t − φ32−1r ]
4
6
⎡3
3
2⎤
+ ⎢ a3 r A1 + a3 r A1 A2 ⎥ cos[ω1t − φ310 r ]
4
⎦
⎣4
+
(4)
with air and φijkr the coefficients of the reference
nonlinearity.
Both signals at the output of the DUT and at the output of
the reference are down-converted by a couple of doublebalanced mixers to a proper intermediate frequency, IF. At
the IF band the desired spectral component is selected by a
filtering process.
The IF frequency could be chosen as low as needed so
that the filter realization would be possible. For that it is
only required to adjust properly the local oscillator. This is
exactly the same approach followed in a super-heterodyne
receiver and in most of the linear instrumentation benches.
The tone to be characterized must be selected by filtering
the desired signal from the set of output tones present at
each branch. This selection is done by acting in the local
oscillator, LO, frequency.
For instance for the IMD tone at 2ω2-ω1, after the filter
stage we get:
Upper branch signal
x6 (t ) = K filter K mix
3
2
a3 A1 A2 cos[(2ω 2 − ω1 − ωlo )t − φ3−12 − θ ] (5)
4
Lower branch signal
+
3
⎡6
2
3⎤
+ ⎢ a3 A1 A2 + a3 A2 ⎥ cos(ω 2 t − φ301 )
4
⎦
⎣4
3
2
+ a3 A1 A2 cos[(2ω 2 − ω1 )t − φ3−12 ]
4
+ ...
where only the in-band components were considered and
φ110=ω1τ1, φ101=ω2τ1, φ32-1=2ω1τ3-ω2τ3, φ310=ω1τ3, φ301=ω2τ3,
φ3-12=2ω2τ3-ω1τ3.
The signal of the lower branch is applied to the input of
the nonlinear reference device with a known response. The
output of the nonlinear reference presents a constant signal
both in amplitude and phase since no variable elements exist
in the lower branch. This signal is a distorted version of the
two-tone input signal and is represented by:
3
⎡6
2
3⎤
+ ⎢ a3 r A1 A2 + a3 r A2 ⎥ cos(ω 2 t − φ301r )
4
⎦
⎣4
3
2
+ a3 r A1 A2 cos[(2ω 2 − ω1 )t − φ3−12 r ]
4
+ ...
Fig. 1 - Phase measurement setup for uncorrelated tones.
2
x7 (t ) = K filter K mix
(3)
3
2
a3 r A1 A2 cos[(2ω 2 − ω1 − ωlo )t − φ3−12 r − θ ]
4
(6)
with Kfilter being the gain filter and θ the integrated phase
delay imposed by the mixer and the filter.
Despite the two-tone input signals are uncorrelated, the
signals at the output of each branch have the same
frequency, and a constant phase and amplitude difference.
The measurement of the relative amplitude and phase
between the two signals is a straightforward task in typical
linear measurement equipment such as a vector signal
analyzer or an ordinary oscilloscope.
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the dynamic effects of PA’s due to thermal and dispersion
effects as was presented in [14]. However, now such a
characterization can be done with a significant improvement
on automation capability, bandwidth and the use of multitone signals of both correlated and uncorrelated types.
Fig. 3 presents the variation of output amplitude of each
tone with a sweep in the gate voltage of this DUT, while
Fig. 4 presents the phase change of the same DUT.
-10
-40
-50
-60
This DUT is particularly interesting since it presents long
term memory effects, and thus allows a wide change of
phase and amplitude between the upper and lower IMD
tones.
The hardware implementation of the setup is composed
by two independent generators, each one followed by a filter
and an isolator. This way, the spectral purity of the test
signals is guaranteed. In order to obtain a reference signal, a
frequency doubler followed by a mixing stage was
conceived. However, any other known nonlinear reference
could be used
Despite the desired distortion component is uncorrelated
with any of the input tones, it is correlated with the
reference distortion component, as these two shares the
same frequency, and were generated from the same
excitation base signals.
In the measurement test the gate voltage of the DUT was
changed allowing the PA characterization with the bias
point.
This type of characterization is very useful for design
proposes especially for linearizers either at system level or
intrinsically to the DUT [12-13].
The evaluation of how each IMD tone phase and
amplitude varies with gate voltage can also be used to study
2ω2-ω1
2ω1-ω2
-70
-80
-90
-100
-3.6
-3.4
-3.2
-3
-2.8
-2.6
-2.4
-2.2
-2
-1.8
VGS [V]
Fig. 3 - Output power for the fundamental and IMD tones, over an VGS
sweep
The IMD sweet spot seen in Fig. 3 is in accordance with
the usual pattern of active device used in the test [12].
In the same figure an asymmetry [1] is also visible, which
points to a phase difference between lower IMD and upper
IMD tones, somehow in the dynamics of the PA.
The power imposed to the lower branch is constant, so
that the phase of the reference signal is also constant.
Before the measurement process, the setup was calibrated
with a through standard as a DUT device. This procedure
accounts for the relative amplitude and phase changes
imposed by the setup.
The IF considered was 10.7MHz, since it allows the
design of band-pass filters with high values of stop-band
attenuation. This is a critical point to achieve a good
dynamic range in the measurement.
The bandwidth of the IF filter is 10kHz, imposing a
minimum separation between tones of that same value.
400
350
ω1
Output Relative Phase [º]
Fig. 2 - Power amplifier under test.
ω2
-30
III. EXPERIMENTAL VALIDATION
The validity of this bench was verified by performing a
test using a power amplifier as the DUT. This PA is based
on a MESFET active device, Fig.2.
ω1
-20
Output Power and IMD [dBm]
The IF filter is a key element that must have high stop
band attenuation in order to guarantee a good dynamic
range of the setup.
In order to account for the misalignment errors induced
by the setup, a calibration procedure should be performed
before any measurement.
This setup is able to characterize the nonlinear response
of a DUT by performing amplitude and phase
characterization of each spectral component of the output
signal. The setup now presented has an architecture suitable
to be automated since no cancellation adjustment is needed.
Moreover, there is no restriction on the test signal,
especially on what the correlation between the tones is
concerned, they can be either correlated or uncorrelated.
This setup is also suitable to be used for any type of multitone signal, since the selection of the tone to characterize is
done by simply varying the local oscillator.
3
300
ω2
250
200
150
2ω2-ω1
100
2ω1-ω2
50
0
-3.6
-3.4
-3.2
-3
-2.8
-2.6
-2.4
-2.2
-2
-1.8
VGS [V]
Fig. 4 - Output phase of the IMD tones and fundamental power, over a VGS
sweep
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In Fig. 4, a phase difference between lower and upper
IMD can be noticed, which confirms the amplitude
measurements. In the Fig.4 it can be seen that the relative
phases of ω1 and ω2 are equal, and the relative phases of
lower and upper IMD are completely different.
REFERENCES
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[2]
Despite that, a different dynamic pattern can come out. It
is obvious that a phase difference can also exist even if no
amplitude asymmetry is visible. This is the extreme case
where linearization is again extremely difficult, even if the
upper and lower IMD amplitudes are equal.
[3]
[4]
[5]
VI. CONCLUSIONS
[6]
In this paper we use a phase and amplitude measurement
bench, in order to better understand the change in phase and
amplitude of a nonlinear DUT.
This bench presents a simple topology and allows
automated measurements without correlation constraints
between the tones composing the input signal. The selection
of the tone to be characterized and the IF frequency are only
dependent on the local oscillator and are easily changeable
allowing a flexible measurement configuration. This setup
has no bandwidth limitations since all the signals are
converted to an IF where the measurement is done. The
dynamic range of the setup is dictated by the stop band
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one achieved by correlated sampling schemes.
In this paper a practical application of that setup is also
presented. A full measurement both in amplitude and phase
of a PA is obtained allowing a better characterization of
active devices, and thus a deep understanding on how the
dynamics of the DUT change with bias.
[7]
[8]
[9]
[10]
[11]
[12]
[13]
ACKNOWLEDGEMENT
This work was partially supported by the EU and carried
out under the Network of Excellence Top Amplifier
Research Groups in a European Team – TARGET contract
IS-1-507893-NoE.
4
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