8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
1
Towards a Complete Behavioral Modeling
Framework for Mixed-Signal Devices:
Presenting the D-parametersTM
Diogo C. Ribeiro, Student Member, IEEE, Pedro Miguel Cruz, Member, IEEE,
and Nuno Borges Carvalho, Senior Member, IEEE
Abstract—Recent advances in radio technology are pushing
mixed-signal circuits and devices to higher frequencies and
forcing system integration in a single chip. This means that
signals are now converted to the digital domain and vice versa
much closer to the antenna than before, which forces radio
engineers to understand and cope with the new mixed-signal
(analog and digital together) paradigm.
In this paper a new framework for mixed-signal behavioral modeling is presented and discussed. It is an extension
of the well-known scattering parameters and will be termed
as D-parametersTM . In this work, both linear and nonlinear
methodologies will be considered and analyzed.
Furthermore, examples showing the application of this novel
framework to some mixed-signal devices are also presented.
Index Terms—Linear characterization, mixed-signal systems,
nonlinear modeling, software defined radio.
I. I NTRODUCTION
N
EW emerging technologies are bringing together digital
and analog systems, devices and components, in a way
that they will become inseparable. Until now, this division was
clear, since digital domain engineers were focused solely on
the digital design part (bit stream evaluation and binary level
evaluations), and analog or the self-called radio-frequency
(RF) engineers worked on the analog portion of the wireless
radio front-end.
Traditionally, RF engineers focused exclusively on the analog part mainly because in a typical transceiver the signal
was dealt first at RF (high frequency) and then converted
to baseband (sometimes called video bandwidth or low frequency). Recent advances in the radio hardware, based on the
concepts of software defined radio (SDR) and cognitive radio
(CR) are pushing the limits of the analog-to-digital converters
(ADCs) and digital-to-analog converters (DACs) to very high
frequencies. As a result, lesser or no frequency conversions are
“D-parameters” is a registered trademark of Instituto de
Telecomunicações.
This work was supported by the Fundação para a Ciência e Tecnologia (F.C.T.) under Project EXCL/EEI-TEL/0067/2012: Cognitive Radio
Transceiver Design for Energy Efficient Data Transmission (CReATION).
The work of D. Ribeiro was supported by the Fundação para a Ciência e
Tecnologia (F.C.T.) under the Ph.D. grant SFRH/BD/85163/2012. The work
of P. Cruz was supported by the Fundação para a Ciência e Tecnologia (F.C.T.)
under the Post-Doc grant SFRH/BPD/92452/2013.
The authors are with the Departamento de Electrónica,
Telecomunicações e Informática, Instituto de Telecomunicações, Universidade
de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
(e-mail: dcribeiro@ua.pt; pcruz@av.it.pt; nbcarvalho@ua.pt).
used in the analog path, and the RF signal is directly translated
into the digital domain.
These new advances are imposing that RF engineers start
to think in a higher level of complexity. For example, figures
of merit (FoMs), [1], as the error vector magnitude (EVM),
noise power ratio (NPR), signal-to-noise ratio (SNR), source
or load matching obtained using the voltage standing wave
ratio (VSWR), intermodulation distortion (IMD) or adjacent
channel power ratio (ACPR), effective number of bits (ENOB)
and many others should now be carefully re-thought, since
the RF signal is actually a digital replica of the received
electromagnetic waveform.
Furthermore, the circuits and systems are becoming inseparable [2]. In a typical design, each component of a mixedsignal system can be separated and evaluated individually, but
recent integrated circuits are joining all these components by
creating a single integrated device, usually called as a systemon-a-chip (SoC). Some examples include entire transmitting
and receiving chains, [3], and fully integrated RF transceivers,
[4], [5], high-speed wideband DACs, [6], wideband sampling
and converting circuits (known as high-speed ADCs) [7]. Thus,
RF engineers are now facing a paradigm change and should be
aware on how to design, model and characterize such mixedsignal systems.
This paper will focus on how to characterize and model
these emerging sub-systems from a system-level point of view,
so that analog RF system engineers can continue to use and
design communication transceivers employing approaches they
are familiar with.
The paper is divided into a first approach to mixed-signal
systems evaluation, followed in section III by the discussion
on how to characterize mixed-signal systems for its linear and
nonlinear operation supported on a system behavioral point of
view. Then, in section IV, laboratory approaches and necessary
calibration schemes for mixed-signal characterization will be
addressed. Finally, section V will conclude with some practical
examples being shown and discussed.
II. C HARACTERIZATION OF M IXED -S IGNAL S YSTEMS
System identification, characterization and modeling, are
scientific research areas that have registered an important
growth in recent years. The new digital communication standards have been pushing the limits of radio systems specifications. This continuous demand for higher and higher
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
2
Digital
Word
log and the other is digital (a bus of bit lines). So, the problem
on how to characterize and define a group of FoMs for RF
design in mixed-signal systems is raised. In fact, there are two
ways of analyzing this kind of systems: 1) the complete analog
approach or sometimes called the signal integrity approach,
and 2) the system-level behavioral approach.
In the first approach, the signal integrity, all ports are
considered as analog ones (see Fig. 2(a)), i.e., each bus
line is considered as an independent port (“Port 3” through
“Port N”), in the same way the RF port (“Port 1”) and the
clock (CLK) port (“Port 2”) are considered. In this case,
the engineer is searching for the signal quality, called signal
integrity, mainly when the mixed-signal device is connected
to a signal processing unit, either a field-programmable gate
array (FPGA) or digital signal processing (DSP) board.
As well, it should be highlighted that now each line of the
digital bus is indeed working at gigabit per second (Gbps).
This brings the design engineer to discuss and design carefully
each bit line path, which should now be considered as a
transmission line. The main objective is to guarantee not only
that the signal maintains its format, but also that it delivers
all bits with similar delays to each bus line. This is becoming
very important not only in truly digital circuits, but also in
new SDR/CR configurations. Some authors have dedicated a
significant amount of work to this characterization problem,
[9].
In the second case, the system-level behavioral approach,
the design engineer is focused not on the bit line operation,
but rather on the information the overall bit-stream contains.
The objective in this situation is to evaluate the overall bitstream as a complete waveform in order to compare each and
both sides of the device (analog and digital). The final goal is
then to give tools to RF engineers so that they can characterize
the mixed-signal system using similar approaches to complete
analog circuits, i.e., using system level FoMs.
It should be referred here that in order to evaluate the
digital stream coming out or entering a data converter as an
equivalent voltage signal, signal integrity in the digital bus
must be assumed. Thus, it is considered that the bit stream is
being received or transmitted correctly by the processing unit,
i.e., the definition of the bit been equal to a logic “1” or “0”
is correctly defined at the sampling instant.
In this work a strategy based on scattering waves will be
employed to truly capture the behavior of the mixed-signal
device under characterization. From a design engineer point
of view, one of the crucial advantages in having this characterization is that several procedures could be implemented
to overcome the non-idealities that the overall mixed-signal
system incorporates. For example, the implementation of postdistortion algorithms to compensate for interferes in receiver
sub-systems [10], or pre-distortion algorithms for digital-based
transmitters [11], [12].
Several advantages come from the use of a scattering
wave strategy for the behavioral characterization of mixedsignal devices. Among others, the direct interpretation of some
behavior metrics, in a way similar to what RF engineers are
already used to deal with analog S-parameters, as it will be
shown later on. And also, the immediate readiness of CAD
Sampler
(Clock Pad)
a1
LNA
b1
Quantization
∆t
BPF
a2
b2
Clock input
Figure 1.
∆t
∆t
bit1
bit2
bit3
bit4
Binary
Value
10
0
1
6
Generalized operation of a mixed-signal system.
transceiver performance forces the use of more advanced
signal processing techniques together with more efficient and
accurate computer-aided design (CAD) tools.
The complete identification of linear and nonlinear systems
is a challenging topic not only from the formal modeling point
of view but also from the practical extraction side where the
impairments of the real systems have to be accounted for.
As stated in the introduction we will focus our attention
in the characterization of radio transceivers, especially the
emerging mixed-signal designs. The methods and approaches
to characterize some of these types of components are deeply
studied and presented in [8]. For instance, concepts as VSWR
are there defined for ADCs by considering the associated input
impedance (ADCs and DACs can be considered the simplest
mixed-signal systems).
Specific digital FoMs have also been used intensively for
ADCs and DACs, metrics like gain offset, integral nonlinearity
(INL), differential nonlinearity (DNL), among others. However, these figures are inherently associated to the bit stream
progress in the data converter, and are considered static FoMs
[8]. For example, one possible approach to the measurement of
these quantities is by using the converter’s output amplitude
histogram [8]. Therefore, this measurement is insensitive to
the different temporal dynamics that may be present in the
characterized device.
In a radio frequency approach scenario, this is not conceivable, since the signal actually varies with time, and so
time variation exists, and important dynamic effects should be
observable, as for instance spectrum characteristics, different
response to multisine or modulated signal excitations, etc. [8].
Despite that, in this scenario, if a RF designer has to
project a mixed-signal system, where amplifier and filters are
combined with data converters, the engineer sees himself in
a cumbersome problem. Since, on one side it has an analog
port, but on the other side it has a digital bus with several
bits, with an added complexity of a sampling clock pad that
will impose the time sampling periods and subsequently the
discrete-time scale, Fig. 1. This scenario is even more realistic
when one considers that sometimes an analog terminal is
directly connected to an antenna.
It is exactly in this situation where the RF engineer should
have a complete picture of how those mixed-signal black-box
arrangements behave from a RF point of view, and also from
a signal information point of view.
In a mixed-signal sub-system, one terminal is actually ana-
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
a1
Port 1
b1
Mixed-signal
Component
3
a3
b3
Port 3
a4
b4
Port 4
a5
b5
Port 5
a6
b6
Port 6
receiver
a1
Port 1
b1
Mixed-signal
Component
Binary
value to
voltage
ideal
converter
db3
Port 3
da3
transmitter
b2
a2
Port 2
Clock
Port 2
(a)
Figure 2.
(b)
Mixed-signal characterization approaches: (a) signal integrity and (b) system-level behavioral.
simulation tools in importing and using these type of models.
Therefore, the mixed-signal system will be characterized
and modeled in a similar way of the signal integrity analysis,
but in this case the bus is considered as a single integrated
port. This approach is depicted in Fig. 2(b). As can be seen,
the considered device has at least three ports (more can be
included), in which two of them are analog corresponding to
the RF analog input and to the clock input, being the third
port the digital bus evaluated as an overall signal.
Thus, for the characterization of this mixed-signal component, it can be considered that at the RF analog port (“Port 1”)
incident and reflected scattered waveforms (a1 , b1 ) exist and
can be evaluated. In the same way, at the CLK port (“Port 2”),
a2 and b2 , can be also considered.
At the third port, the digital bit-stream can be evaluated to
obtained a state value using (1), this is the binary representation of each sample word sent or received from the mixedsignal device, through the digital bus. The sequence of state
values over time represent a conceptual digital waveform, as
can be seen in Fig. 3. This waveform can yet be converted to
a digital-equivalent voltage wave using (2).
StateV alue(t) = bitN (t) 2(N −1) + bitN −1 (t) 2(N −2) + . . .
Vdig (t) =
+ bit3 (t) 22 + bit2 (t) 21 + bit1 (t) 20
(1)
StateV alue(t) × VppF ullScale
(2N − 1)
(2)
The voltage wave will be then transformed to da3 and db3
that will allow the comparison to the analog port. An important
inference is that the da3 only exists in a receiver configuration
bit1
bit2
BinaryValue(t) = bit4(t)23 +
bit3(t)22 + bit2(t)2 + bit1(t)
bit3
bit4
tk-1 tk tk+1 tk+2
sampling times
Figure 3.
b2
a2
tk-1 tk tk+1 tk+2
sampling times
Convert a bit word onto a binary word value for a 4-bit bus.
and db3 in a transmitter configuration, which assumes a perfect
match having no reflected signal, see Fig. 2(b).
Nevertheless, similar properties of waveforms continue to
exist, as for instance the digital received signal will account
for the bus line length between the mixed-signal component
and the processing unit, which will correspond to a specific
delay in time for a given length. Once again, we should be
aware that in each bus line the bit-stream is travelling at Gbps
speeds, imposing that the overall signal (each digital sample
word) is evaluated at frequencies in order of GHz values.
III. M IXED -S IGNAL S CATTERING PARAMETERS
R EPRESENTATION
This section will be devoted to the representation of linear
and nonlinear characterization approaches for mixed-signal
operation, by taking a strategy based on scattering waves.
A. Linear Characteristic Formulation
Remembering the traditional S-parameters definition [13]
that is applied to entirely analog components, the same approach can be expanded to a mixed-signal scenario.
The analog “Port 1” in Fig. 2(b), can be described accordingly to the incident and reflected waveforms. The incident
power will be Pincident = |a1 |2 and the reflected power
Pref lected =√|b1 |2 . The voltage at “Port 1” can also be defined
by V1 = Z0 (a1 + b1 ). It is curious to understand that
the signals a1 and b1 does not actually define any power or
voltage by themselves, they are actually defined for a system
presenting a characteristic impedance of Z0 , and can be called
power-waves as in [13].
At this point, the system will be assumed as a 2-port
mechanism by incorporating the CLK port into the model.
This is similar to what was done for a mixer [14], where
the local oscillator (LO) imposes the operation regime. The
same happens here with the clock signal. Besides, based
on the methodology proposed in [14], wherein it should be
guaranteed a clock signal amplitude sufficient to excite the
sampling stage and having a known frequency value.
In the third port, the digital one, a voltage representation
of the digital state can be obtained using its binary value
as expressed in (2). Since, RF engineers are not used to
deal with voltage values, a conversion to power-waves, da3
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
4
and db3 , is performed. Actually, at high frequencies these
are the most important quantities to be measured and have
more significance than voltages or currents. It should be stated
that these scattering waves, da3 and db3 , are not actually
true power-waves in the analog sense, but rather a conceptual
representation of those.
Nonetheless, when talking about power-waves we should
calculate them for a specific system characteristic impedance.
But, in the digital world, which characteristic impedance value
should be used? Remember that we are not considering the
analog waves that travel on the digital bus, but rather the state
value that the entire bus represents. So, this value does not have
to be the characteristic impedance of the digital bus. Actually,
a hypothetic characteristic impedance will be used instead. In
order, to have an easy interpretation of the kernels that relate
the analog and the digital sides, the characteristic impedance
value of the RF analog input port (Z0 analog ) will be used. In
this basis, the waveforms da3 and db3 can be defined as:
mixed-signal components and D13a2CLK for the equivalent
transmitter chain.
Not much relevance is being given to the clock port apart
from its phase information. Nonetheless, the reflection coefficient (D22 ) can also be defined for this analog clock port in an
isolated fashion. This approach is actually similar to the one
used for the local oscillator port in a mixer characterization,
[14], as said before.
It should be stressed that the digital signal in a mixed-signal
solution can appear in a different carrier frequency of the
analog side provided that a higher than the first nyquist
zones (NZs) is used. Thus, the power-wave at the digital
version can operate on a different frequency of the analog
counterpart, wherein a relationship between these frequencies
is straightforwardly obtained by knowing the clock sampling
frequency. This phenomenon encounters a similar operation in
a mixer conversion approach.
B. Nonlinear Characteristic Formulation
Vdig
, only in transmitter mode
da3 = p
Z0 analog
db3 = p
Vdig
, only in receiver mode
Z0 analog
(3)
Again, Z0 analog was used in this context to maintain the
equivalence to the analog part, but any other value can be
used, since this is a pure conceptual waveform.
Using this scattering waves approach, several FoMs can be
3
calculated, as for instance, the quantity db
a1 can be evaluated
in amplitude and phase and swept over the frequency. The
variation with ω would thus be included in the developed
formulation, which will be called D-parametersTM :


D11 (ω) = S11 (ω) = ab11(ω)
(ω) a2 =e
α,da3 =0 



 D

db3 (ω) 

31a2CLK (ω) = a1 (ω) a2 =e
α,da3 =0 

(4)




b1 (ω)  D13a2CLK (ω) = da3 (ω) 

a2 =e
α,a1 =0 
D33 (ω) = 0
where α
e is the clock complex waveform value.
The value D31a2CLK (ω) is similar to S21 (ω) in a typical
two-port analog network, but again it should be understood
that a conceptual power-wave is being evaluated and not a
real one in the analog sense, the a2CLK subscript means that
these measures were calculated for a specific clock condition
α
e.
These values are calculated for a certain frequency grid of
the input signal excitation. In this case, D11 is equivalent
to the S11 measured for the analog counterparts. Also, it is
important to stress that D31a2CLK (ω) is actually a frequency
dependent gain that varies with the input signal a1 (ω) for
a specific a2 = α
e. This measure is exactly similar to the
available gain traditionally defined for amplifiers. Again, it
should be referred that D31a2CLK only exists in receiver
Nonlinear distortion can be monitored in analog components
as the generation of spectra components that are not included
in the input signal excitation. One of the most well known
demonstration of these are the harmonics of the input signal.
In a mixed-signal system such a behavior is also representative of nonlinear distortion phenomenon, concept addressed
in [8], [15]. The main difference in a mixed-signal system
arises from the fact that if the harmonics are generated in
NZs higher than the first, those harmonics will not appear as
in a traditional fully-analog system, all organized sequentially,
but will follow a different approach based on the sampling
frequency. This is true for receiving and transmitting mixedsignal systems, see Fig. 4 as an illustrative example. So, each
nonlinear distortion calculation should be evaluated having in
mind where the nonlinear components will fall.
Again the definition of a variety of FoMs (e.g. total harmonic distortion (THD), ACPR, NPR, third order intercept
point (IP3 ), IMD) becomes quite similar to fully-analog systems, but with the evaluation of power defined as before,
Pdig = |db3 (ω)|2 . This approach is employed in the IEEE
standard for analog to digital converters [8] for NPR evaluation, and is utilized in several vendor application notes [15]–
[17].
Other FoMs inherent to mixed-signal environments continue
to be used, as for instance the definition of signal to noise and
distortion ratio (SNDR), which is typically measured for fullscaled data converters (DAC or ADC) and accounts for the
overall noise and distortion being produced.
Recent trends in analog components modeling are incorporating nonlinear behavior of fully analog components and
systems. The approaches with an higher spotlight are the ones
based on the Poly-Harmonic Distortion (PHD) modeling [18],
the so called S-functionsTM and X-parametersTM .
These models are a linearization of a device response around
a large-signal operation point (LSOP) [19]. They consider the
device under test (DUT) stimulated by a large signal condition
and try to catch its behavior under the assumption that the
harmonic superposition principle stands true.
2nd NZ
3rd NZ
1st NZ
Discrete-Time
Digital Domain
1st NZ
5
f1
2f1
3f1
fCLK/2
fCLK
f1
3fCLK/2
Discrete-Time
Digital Domain
f1
2f1
1st NZ
f1
fCLK/2
Figure 4.
fCLK/2
Continuous-Time
Analog Domain
1st NZ
3f1
2f1’
Sampling Process
Continuous-Time
Analog Domain
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
2nd NZ
2f1’
2f1
fCLK/2
3rd NZ
fCLK f1
fCLK
+ f1
fCLK
3fCLK/2
Illustrative example of nonlinear phenomenon occurring in receiving (left) and transmitting (right) mixed-signal systems.
Contrarily to what happens in linear characterizations,
where a small signal stimulus is assumed and only the fundamental frequency is considered, the PHD large signal models
will also look to the harmonics produced by the device and
its relationship and/or dependence on the harmonics at each
port of the device. Thus, the produced model will contain information describing the influence between all cross harmonic
frequencies from the input to the output and vice-versa (linear
and nonlinear information).
In the same way of the linear characteristic formulation,
these nonlinear models can also be defined within this novel
framework, assuming that all the previously defined quantities
and characteristics remain equally suited.
Additional benefits of the PHD modeling characterization
include efficient load-pull prediction [20]. This is also an advantage for mixed-signal scenarios, especially for a transmitter
device where the output is analog. In this case, as in a power
amplifier (PA), the load-pull simulation capabilities could be
exploited to improve the desired device performance during
its design stage.
Two different approaches based on the PHD theory can be
followed. The first one does not take into account the CLK port
information, which is similar to what was done for the linear
characterization, but assuming a large signal stimulus and
considering harmonic signals relation. The second approach
considers the CLK port as a common input for the system to
be characterized.
1) Formulation without CLK port: Considering the CLK
signal inside the model without trying to represent it, (5) can
be used to relate incident and reflected waves.
F
Bpm = Dpm
|A11 |P m +
X
S
Dpm;qn
|A11 | P m−n Apm;qn
qn
+
X
T
Dpm;qn
|A11 | P m+n conj(Apm;qn ) (5)
qn
In (5) A and B are complex values representing the incident
and the scattered waves respectively, both these wave values
may represent an hypothetical digital wave depending if it is
being applied to model a transmitter or a receiver, as in the
linear characterization case. The index q and p correspond to
the considered port for the incident wave and for the scattered
wave respectively and the n and m correspond to the harmonic
index of the incident and scattered waves respectively.
Moreover, the component P = e+jφ(A11 ) will assure a
phase normalization, introduced for simplification proposes.
This approach only allows the characterization of the first
NZ, which is a limitation. For instance if one is attempting to
model the complete nonlinear behavior of a DAC, only harmonics that fall inside the considered NZ can be characterized.
Thus, information about harmonics that fall in different NZs or
even replicas of the fundamental cannot be represented using
this approach.
A similar approach to this formulation had been used
in [21], for the case of an integrated transmitter having a
reconstruction filter at the output.
2) Multi-port formulation: One of the possibilities to
characterize mixed-signal systems using these powerful
large-signal models is by exploit its multi-port describing
capabilities. Thus, all the three ports will be considered,
contrary to what have been done previously.
Doing so, the analog CLK port will not be ignored and, for
example, its VSWR will also be described inside the model.
As it was already explained, in mixed-signal systems, frequency conversion occurs due to the sampling circuit. PHD
models inherently support frequency conversion by mapping
all the cross harmonic frequencies of all the considered fundamentals (one from the CLK port and one or more from the
analog ports), at all the ports of the DUT. The only limitation
is that a maximum harmonic index has to be imposed, in order
to have a computable model.
With this approach, the real behavior of mixed-signal devices is inherently mimic by the model, since all the mixtures
between the input signal and the CLK signal will be considered. Furthermore, the level of folding considered in the model
(number of NZs modeled) can be controlled by the maximum
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
F
m
Bp[m,h] = Dp[m,h]
(|Ain[1,0] |, |Aclk[0,1] |)P[1,0]
+
6
o
X n
m−n
S
Dp[m,h];q[n,k]
(|Ain[0,1] |, |Aclk[1,0] |) P[1,0]
Ap[m,h];q[n,k]
q[n,k]
+
o
X n
m+n
T
Dp[m,h];q[n,k]
(|Ain[0,1] |, |Aclk[1,0] |) P[1,0]
conj(Ap[m,h];q[n,k] ) (6)
q[n,k]
harmonic level considered for the CLK fundamental.
From what has been described it is easy to conclude that
by taking this approach, one can compare the mixed-signal
device as a mixer. Where the CLK port is in the place of the
LO port and the digital port follows the previously established
characteristics.
The input, output relations between the several ports of the
mixed-signal device can then be expressed as in (6). Where,
apart from the components that have the same notation as in
(5), n and m correspond to the harmonic index of the input
fundamental frequency at the considered port for the incident
and for the scattered waves respectively, h and k correspond
to the harmonic index of the CLK fundamental frequency at
the input port and at the considered port for the incident and
for the scattered waves respectively.
Once again, P[1,0] = e+jφ(A1[1,0] ) will assure a phase
normalization for the zero phase of the fundamental input
signal.
Moreover, (|Ain[1,0] |, |Aclk[0,1] |) corresponds to the considered LSOP, which depends on the amplitude of the fundamental large signal at the input port, |Ain[1,0] |, as well as on the
amplitude of the CLK signal, |Aclk[0,1] |.
Taking a closer look to (6) and comparing it to the expression for multi-port fully analog devices, [22], the differences
are on the name of the parameters (for simple identification
purposes only) and on the absence of the P[0,1] which in this
case would correspond to the phase normalization of the CLK
signal.
The absence of P[0,1] is justified by its redundancy in the
case of mixed-signal systems. Once, as already explained
before, to preserve the assumed signal integrity of the digital
signal, it has to be acquired at the same phase of the CLK
signal. Thus, during the parameters extraction procedure the
CLK phase will be always the same.
However, this direct representation of a mixed-signal device
by a multi-port PHD model can arise some issues. The main
one is its unnecessary excessive complexity.
Since the digital signal only has a representation from 0
to fS /2, by doing a complete frequency mapping in all ports
there will exist a large quantity of model parameters that will
not be used.
One can consider, for example, the case of a mixed-signal
receiver represented in Fig. 5. It is easily denoted that, it is
impossible to have any value in the majority of the mapped
frequencies (all above fS /2) at the digital port.
As a result, the parameters of the model associated to
the mixing products that appear inside the 1st NZ on the
digital port will have an associated complex value that could
be different from zero. While all the other parameters that
correspond to all the other spectral components will always
have a value of zero, and thus, are unused and unnecessary.
3) Kernels extraction: The parameters from the equations
expressed in (5) and (6) can be extracted using a procedure
similar to what is employed in [21] and [23], as it will be
briefly described next:
•
dBm
0
Input
−50
−100
dBm
0
0
fs/2
fs
3fs/2
2fs
5fs/2
3fs
CLK
−50
•
−100
dBm
0
0
fs/2
fs
3fs/2
2fs
5fs/2
3fs
Output
−50
−100
0
fs/2
fs
3fs/2
2fs
5fs/2
3fs
Characterized Freqs.
0
fs/2
fs
3fs/2
2fs
5fs/2
3fs
Figure 5. Spectrum representation of the input, CLK and output ports of a
mixed-signal receiver (with ADC), and representation of frequencies that the
PHD model will characterize. Considered orders: Input=3, CLK=2, Mixing=5.
Mixed-signal devices need to be driven by a CLK signal
so that, they can operate properly. Thus, a large tone
needs to be applied at the CLK port of the mixed-signal
DUT. Additionally, another large tone is applied to each
of the other DUT ports. In this condition, it is considered
that the DUT is being stimulated without perturbations.
From these non-perturbed measures, the X F kernels can
be directly extracted.
After, a perturbation needs to be applied to the DUT, a so
called “tickle” tone. This “tickle” is a lower power continuous wave (CW) signal at the same frequency or at the
harmonics of the previous large tones but, with different
relative phases (from 0 to 2π). The “tickle” needs to be
applied to all the ports of the DUT individually, even at
the digital port when a transmitter is being characterized.
The X S and X T kernels are computed from the measurements with the “tickle” present. In order to extract
each kernel value, a least mean squares method can be
employed as in [19] and [24].
It is worth to mention that during the measurement stage
only CW excitation signals are required.
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
Phase
Reference
Local
Oscillator
7
Processing Unit
Vector Correction Kernels
Comb
Generator
ADC
CLK STIMULUS
DIGITAL BUS
RF STIMULUS
Binary value to
voltage ideal
converter
Calibration Planes
Figure 6. Idealized mixed-signal instrument architecture allowing combined
analog and digital measurements, which is suitable for linear and nonlinear
characterization of mixed-signal receivers or transmitters.
Figure 7.
Mixed-signal instrument prototype.
As usual, in order to get valid information from such an
instrument, a calibration scheme is necessary. Moreover, an
additional issue is raised because of the combination of analog
and digital signal domains into the same characterization tool.
The next subsection will handle this situation by showing a
couple of options to try surpassing such conditions.
A. Instrument Calibration Details
Apart from this, it is also important to refer that a calibration
procedure is fundamental to measure wave quantities that
represent what is really happening at the ports of the DUT,
this topic that will be addressed later on.
IV. I NSTRUMENTATION FOR M IXED -S IGNAL S YSTEMS
Undoubtedly, the devices to be tested are moving away
from single-purpose, hardware-centric entities with limited
capabilities, to multi-purpose, software-centric entities with
endless capabilities. Thus, it is important that the test and
measurement systems evolve in the very same way. It is
necessary to switch from traditional instruments commonly
divided by the type of signal to measure (RF analog, RF
digital, DC, optical, and so on) to an unified architecture that
integrates all the relevant measurement capabilities in a single
instrument.
In [25] a first iteration for this kind of emerging approaches was presented, wherein it was suggested a synchronous laboratory-based mixed-signal test bench tailored to
the characterization of mixed-signal components or systems.
Later, a more detailed overview of measurement strategies
and solutions suitable for the characterization and behavior
modeling of mixed-signal systems was presented in [26].
There is yet some open issues to be solved, as for instance,
create a more widespread solution for the measurement setup.
Having this in mind, Fig. 6 shows a generalized architecture
for this kind of mixed-signal instrumentation that is capable
to perform linear and nonlinear characterization of mixedsignal receivers or transmitters. As can be observed, the analog
channels share the configuration of a network analyzer. The
remaining port is a digital channel taking the properties of a
logic analyzer, in which the signals are no longer analog, but
are actually bit sequences.
In Fig. 7 a picture of the proposed instrument prototype is
depicted.
In the calibration process of a Vector Network Analyzer
(VNA) using more than one port, a standard that can relate
the response between ports must be used in order to obtain a
traceable relationship between all the ports [27]. For example,
in traditional calibration strategies as Short Open Load Thru
(SOLT) or Thru Reflective Line (TRL), the “Thru”, in the first
case, and the “Line”, in the second case, were the calibration
standards responsible for this error correction.
Moreover, in nonlinear analog characterization, using for
instance a Nonlinear Vector Network Analyzer (NVNA), more
complex calibration methods have to be employed in order to
get cross-frequency relationship, both magnitude and phase
relationships [28]. For this purpose, a power meter is used for
magnitude and a phase reference for phase (typically a Comb
Generator (CG)). Using this strategy the “Thru” standard can
be left out of the calibration procedure, but both magnitude
and phase standards need to be applied at all the ports of the
instrument [29].
Contrary to analog-based approaches, in a mixed-signal
system it is more difficult to develop a calibration strategy
able to correct all the measurement errors. This is mainly
because a calibration reference for the mixed-signal “Thru” (a
connection between the analog and the digital ports) is totally
non-existent.
Either way, in the last few years, several attempts have
been taken to surpass this limitation when approaching diverse mixed-signal laboratory arrangements for mixed-signal
receivers and transmitters characterization, as presented in
[21], [30].
The employed strategy, in [21], was similar to the one
discussed before for nonlinear analog measurements, using
a mixer-based instrument [28], [29]. This analog calibration
strategy is usually called as “Absolute Calibration”, since it
establishes an absolute magnitude and phase value at the
analog calibration plane.
Since, the digital waves are conceptual power-waves, their
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
8
Digital domain
ITx
Analog domain
R
90⁰
∑
Quadrature
NCO
R
IFb
R
Comb generator utilized during the absolute phase calibration step.
90⁰
Quadrature
NCO
V. A PPLICATION E XAMPLES
This new approach to the characterization of mixed-signal
systems, allows to combine analog and digital parts in a
seamless way, so that digital and analog RF engineers can
work on a common language and framework.
Actually, the outcome behavioral model of this characterization will allow engineers to integrate these devices with
a great confidence inside CAD/CAE simulators, and optimize
the overall system performance. Besides, it will also allow real
time RF systems to be able to adapt and to compensate for
non-ideal behaviors appearing during real operation.
In this respect, the first application example is the characterization of an RF DAC. Predictions suggest that these
devices will be strongly used in the next generation of wireless
communications, not only at the terminal side, but actually at
the base station side, through the use of remote radio head
units [12]. Besides, RF DACs are already being used in SDR
solutions and digital pre-distorter systems, see Fig. 9. Thus,
a characterization of these components is a crucial point in
order to allow a more agile, faster and cheaper design stage
of the end product.
QFb
RF ADC
Atten.
R
Figure 9. Illustrative transmitter system based on a DPD architecture and
employing high-speed mixed-signal devices.
0
−10
dB
−20
−30
Normal Mode − 2.5GSPS
Mix Mode − 2.5GSPS
Normal Mode − 2.2GSPS
Mix Mode − 2.2GSPS
Normal Mode − 1.8GSPS
Mix Mode − 1.8GSPS
−40
−50
−60
0
500
1000
1500
MHz
2000
2500
3000
(a)
0
dB
magnitude value can be directly related to the absolute corrected analog waves.
However, the use of this method is not enough to correct for
phase measurement errors. In other words analog and digital
waves will not appear fully synchronized. Because, the phase
reference device cannot be employed at the digital port and
the phase of a wave is a temporal non-static measurement that
does not have any absolute meaning, i.e., a phase of a wave
can only be defined in relation to other wave or to a time
reference. Thus, additionally procedures have to be employed
to surpass this issue. One way to handle this, can be based on
[31] where a mixed-signal synchronization was obtain for a
sampler-based instrument (in that case an oscilloscope) with
the use of a reference signal and a trigger.
It is important to stress that for both linear and nonlinear
characterizations the absolute calibration method must be
employed at the analog side. Thus, the power meter and the
CG must be always used.
In the current prototype, a commercial power meter is
being used to calibrate for the absolute power, while an inhouse developed CG is being used for the absolute phase
calibration step. In Fig. 8, it is shown a photo of the used CG.
Moreover, the CG’s performance was evaluated in [32], where
its applicability for instrument calibration was also discussed.
PA
BPF
180
−10
0
−20
−180
Mag.
Phase
−30
−40
0
500
1000
deg
Figure 8.
QTx
RF DAC
−360
1500
MHz
2000
2500
−540
3000
(b)
Figure 10. Measured linear D-parametersTM extracted from an RF DAC at
different operating modes: (a) magnitude of gain (D31 ), and (b) magnitude
and angle of D33 .
The linear approach was applied at this point. Fig. 10(a)
shows the variation of the |D31 | with frequency, as it is visible
the output signal varies from operation mode to operation
mode. If for instance, the RF DAC is used in a DPD system,
this behavior can degrade completely the implemented digital
algorithm. In Fig. 10(b), the output matching (D33 ) can also
be depicted. Naturally, both its magnitude and phase vary
over frequency. Once again, this behavior is of paramount
importance when designing a system, since it can degrade the
matching between the RF DAC and the antenna or PA, and
thus, impact strongly the FoM of the overall system.
8.◦ CONGRESSO DO COMITÉ PORTUGUÊS DA URSI, NOV. 2014
9
0
10
DS310,110
0
DS31−1,110
DS311,110
DS
31−2,110
−10
−15
−10
−5
Input Power − dBm
0
−20
250
−40
200
−50
0
(a)
200
400
600
Freq. (MHz)
2
−20
−30
0
(b)
Figure 11. Several nonlinear multi-port D-parameter kernels obtained from
measurements, value over input power: (a) Magnitude of 4 kernels which
relate the input at the fundamental with the output at the fundamental of 4
consecutive NZs; (b) Magnitude of 4 kernels which relate the input at the
fundamental with the output at the second and third harmonics of 2 NZs.
As a second example, the nonlinear multi-port formulation
will be employed to characterize a complete digital transmitter,
a system as the one represented in the upper branch of Fig. 9
without the filter at the output. Several of the measured kernels
are shown on Fig. 11, over a sweep of the input power.
Fig. 11(a) shows the equivalent magnitude gain (from the
digital input to the analog output) of the fundamental at four
consecutive NZs. As expected, with the progression to higher
NZs the overall gain value decreases. It can also be observed in
Fig. 11(b) that the output 2nd and 3rd order harmonics increase
with the increase of the input power, for two different NZs (the
1st and the 3rd ), which again represents an expected behavior.
The information gathered with this type of characterization
would allow design engineers to improve their pre-distortion
techniques to linearize the overall system, and like that improving the outcome of the system.
As mentioned before, the receiver side can also be characterized by this framework. As a last example, in Fig. 12
it is shown the D11 and the D13 linear D-parametersTM over
frequency, from a medium CLK frequency ADC. The results
shown here are from [30].
VI. C ONCLUSIONS
In this paper a complete framework for characterizing
mixed-signal devices is presented (for both SoCs and full
discrete component systems). This type of characterization is
of fundamental importance, not only for SDR system designers, but also for DPD designers for PA optimization. Actually
the correct characterization of the mixed-signal components
Mag. (dB)
DS320,110
DS321,110
DS330,110
DS331,110
−10
−5
Input Power − dBm
150
1000
150
Mag.
Group Delay 120
0
−10
−15
800
(a)
0
−40
300
−30
10
Mag − dB
350
Mag.
Phase
−2
90
−4
60
−6
30
−8
0
62.5 125 187.5 250 312.5 375 437.5 500
Freq. (MHz)
GD (nsec)
−20
400
−10
Mag. (dB)
Mag − dB
20
Phase (deg)
30
0
(b)
Figure 12. Measured linear D-parametersTM of an ADC over frequency, from
[28]: (a) magnitude and phase of D11 ; (b) magnitude and group delay of D13 .
become a very important step in the optimization of these
circuits [12].
In short, the D-parametersTM framework was presented, instrumentation for its extraction was discussed, and some
examples were given to show the importance of the proposed
approach.
ACKNOWLEDGMENT
The authors would like to thank National Instruments,
especially Dr. Marc Vanden Bossche, for the support given
to this work.
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10
Diogo C. Ribeiro (S’09-M’11), was born in Ferreira
do Zezere, Portugal in 1988. He received the M.Sc.
degree in Electronics and Telecommunications Engineering in December 2011 at Universidade de
Aveiro. He is now a PhD student in the same
university, since September 2012.
Mr. Ribeiro has as main interest software-defined
radio measurement and nonlinear mixed-signal characterization. In 2012, he was recognized with the
Best Student Paper Award 2012 at the 6th Congress
of Portuguese Committee of URSI, and with the 2nd
prize in the IMS2013 Measurement Student Design Competition.
Pedro Miguel Cruz (S’07–M’13), was born in Ovar,
Portugal in 1982. He received a M.Sc. in Electronics
and Telecommunications Engineering (2008) and a
PhD in Electrical Engineering (2012), both from
Universidade de Aveiro, Portugal.
From Sept. 2006 to April 2007, he has worked at
Portugal Telecom Inovação as a trainee in a project
of localization systems based in wireless devices.
Currently, he is a post-doctoral researcher with the
Instituto de Telecomunicações (IT) being involved
in the characterization and modeling of nonlinear
distortion in software defined radio and cognitive radio front ends, as well as,
high-speed data converters (A/D & D/A).
He is a reviewer for IET Electronics Letters, IEEE TCAS-I, TCAS-II and
JETCAS and co-authored more than 20 international and national papers
including book chapters, journals and conferences. He has been recognized
with the 3rd place in the GAAS Association PhD Student Fellowship for
EuMIC 2009.
Nuno Borges Carvalho (S’92–M’00–SM’05), was
born in Luanda, Angola, in 1972. He received the
Diploma and Doctoral degrees in electronics and
telecommunications engineering from the University
of Aveiro, Aveiro, Portugal, in 1995 and 2000,
respectively.
He is currently a Full Professor and a Senior
Research Scientist with the Institute of Telecommunications, University of Aveiro. He co-authored
Intermodulation in Microwave and Wireless Circuits
(Artech House, 2003) and Microwave and Wireless
Measurement Techniques (Cambridge University Press, 2013). He has been
a reviewer and author of over 100 papers in magazines and conferences.
He is associate editor of the IEEE Transactions on Microwave Theory
and Techniques, IEEE Microwave Magazine and Cambridge Wireless Power
Transfer Journal.
He is the co-inventor of four patents. His main research interests include
software-defined radio front-ends, wireless power transmission, nonlinear distortion analysis in microwave/wireless circuits and systems, and measurement
of nonlinear phenomena. He has recently been involved in the design of
dedicated radios and systems for newly emerging wireless technologies.
Dr. Borges Carvalho is the chair of the IEEE MTT-11 Technical Committee
and the chair of the IEEE Portuguese Section. He is the chair of the URSIPortugal Metrology Group. He was the recipient of the 1995. University of
Aveiro and the Portuguese Engineering Association Prize for the best 1995
student at the University of Aveiro, the 1998 Student Paper Competition (Third
Place) of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)
International Microwave Symposium (IMS), and the 2000 IEE Measurement
Prize.