Tekever drone português espionagem industrial 15.pdf

8.◦ CONGRESSO DO COMITE PORTUGUES DA URSI, NOV. 2014 1

Towards a Complete Behavioral ModelingFramework 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 pushingmixed-signal circuits and devices to higher frequencies andforcing system integration in a single chip. This means thatsignals are now converted to the digital domain and vice versamuch closer to the antenna than before, which forces radioengineers to understand and cope with the new mixed-signal(analog and digital together) paradigm.

In this paper a new framework for mixed-signal behav-ioral modeling is presented and discussed. It is an extensionof the well-known scattering parameters and will be termedas D-parametersTM. In this work, both linear and nonlinearmethodologies will be considered and analyzed.

Furthermore, examples showing the application of this novelframework to some mixed-signal devices are also presented.

Index Terms—Linear characterization, mixed-signal systems,nonlinear modeling, software defined radio.

I. INTRODUCTION

NEW emerging technologies are bringing together digitaland analog systems, devices and components, in a way

that they will become inseparable. Until now, this division wasclear, since digital domain engineers were focused solely onthe digital design part (bit stream evaluation and binary levelevaluations), and analog or the self-called radio-frequency(RF) engineers worked on the analog portion of the wirelessradio front-end.

Traditionally, RF engineers focused exclusively on the ana-log part mainly because in a typical transceiver the signalwas dealt first at RF (high frequency) and then convertedto baseband (sometimes called video bandwidth or low fre-quency). Recent advances in the radio hardware, based on theconcepts 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 highfrequencies. As a result, lesser or no frequency conversions are

“D-parameters” is a registered trademark of Instituto deTelecomunicacoes.

This work was supported by the Fundacao para a Ciencia e Tec-nologia (F.C.T.) under Project EXCL/EEI-TEL/0067/2012: Cognitive RadioTransceiver Design for Energy Efficient Data Transmission (CReATION).The work of D. Ribeiro was supported by the Fundacao para a Ciencia eTecnologia (F.C.T.) under the Ph.D. grant SFRH/BD/85163/2012. The workof P. Cruz was supported by the Fundacao para a Ciencia e Tecnologia (F.C.T.)under the Post-Doc grant SFRH/BPD/92452/2013.

The authors are with the Departamento de Electronica,Telecomunicacoes e Informatica, Instituto de Telecomunicacoes, Universidadede Aveiro, Campus Universitario de Santiago, 3810-193 Aveiro, Portugal(e-mail: [email protected]; [email protected]; [email protected]).

used in the analog path, and the RF signal is directly translatedinto the digital domain.

These new advances are imposing that RF engineers startto think in a higher level of complexity. For example, figuresof merit (FoMs), [1], as the error vector magnitude (EVM),noise power ratio (NPR), signal-to-noise ratio (SNR), sourceor load matching obtained using the voltage standing waveratio (VSWR), intermodulation distortion (IMD) or adjacentchannel power ratio (ACPR), effective number of bits (ENOB)and many others should now be carefully re-thought, sincethe RF signal is actually a digital replica of the receivedelectromagnetic waveform.

Furthermore, the circuits and systems are becoming insep-arable [2]. In a typical design, each component of a mixed-signal system can be separated and evaluated individually, butrecent integrated circuits are joining all these components bycreating a single integrated device, usually called as a system-on-a-chip (SoC). Some examples include entire transmittingand receiving chains, [3], and fully integrated RF transceivers,[4], [5], high-speed wideband DACs, [6], wideband samplingand converting circuits (known as high-speed ADCs) [7]. Thus,RF engineers are now facing a paradigm change and should beaware on how to design, model and characterize such mixed-signal systems.

This paper will focus on how to characterize and modelthese emerging sub-systems from a system-level point of view,so that analog RF system engineers can continue to use anddesign communication transceivers employing approaches theyare familiar with.

The paper is divided into a first approach to mixed-signalsystems evaluation, followed in section III by the discussionon how to characterize mixed-signal systems for its linear andnonlinear operation supported on a system behavioral point ofview. Then, in section IV, laboratory approaches and necessarycalibration schemes for mixed-signal characterization will beaddressed. Finally, section V will conclude with some practicalexamples being shown and discussed.

II. CHARACTERIZATION OF MIXED-SIGNAL SYSTEMS

System identification, characterization and modeling, arescientific research areas that have registered an importantgrowth in recent years. The new digital communication stan-dards have been pushing the limits of radio systems spec-ifications. This continuous demand for higher and higher


Quantization LNA

BPF

Sampler (Clock Pad)

Digital Word

a1

b1 ∆t ∆t ∆t

bit1 bit2 bit3 bit4

Binary Value

0

10

1 6

Clock input

a2 b2

Figure 1. Generalized operation of a mixed-signal system.

transceiver performance forces the use of more advancedsignal processing techniques together with more efficient andaccurate computer-aided design (CAD) tools.

The complete identification of linear and nonlinear systemsis a challenging topic not only from the formal modeling pointof view but also from the practical extraction side where theimpairments of the real systems have to be accounted for.

As stated in the introduction we will focus our attentionin the characterization of radio transceivers, especially theemerging mixed-signal designs. The methods and approachesto characterize some of these types of components are deeplystudied and presented in [8]. For instance, concepts as VSWRare there defined for ADCs by considering the associated inputimpedance (ADCs and DACs can be considered the simplestmixed-signal systems).

Specific digital FoMs have also been used intensively forADCs and DACs, metrics like gain offset, integral nonlinearity(INL), differential nonlinearity (DNL), among others. How-ever, these figures are inherently associated to the bit streamprogress in the data converter, and are considered static FoMs[8]. For example, one possible approach to the measurement ofthese quantities is by using the converter’s output amplitudehistogram [8]. Therefore, this measurement is insensitive tothe different temporal dynamics that may be present in thecharacterized device.

In a radio frequency approach scenario, this is not con-ceivable, since the signal actually varies with time, and sotime variation exists, and important dynamic effects should beobservable, as for instance spectrum characteristics, differentresponse to multisine or modulated signal excitations, etc. [8].

Despite that, in this scenario, if a RF designer has toproject a mixed-signal system, where amplifier and filters arecombined with data converters, the engineer sees himself ina cumbersome problem. Since, on one side it has an analogport, but on the other side it has a digital bus with severalbits, with an added complexity of a sampling clock pad thatwill impose the time sampling periods and subsequently thediscrete-time scale, Fig. 1. This scenario is even more realisticwhen one considers that sometimes an analog terminal isdirectly connected to an antenna.

It is exactly in this situation where the RF engineer shouldhave a complete picture of how those mixed-signal black-boxarrangements behave from a RF point of view, and also froma signal information point of view.

In a mixed-signal sub-system, one terminal is actually ana-

log and the other is digital (a bus of bit lines). So, the problemon how to characterize and define a group of FoMs for RFdesign in mixed-signal systems is raised. In fact, there are twoways of analyzing this kind of systems: 1) the complete analogapproach or sometimes called the signal integrity approach,and 2) the system-level behavioral approach.

In the first approach, the signal integrity, all ports areconsidered as analog ones (see Fig. 2(a)), i.e., each busline is considered as an independent port (“Port 3” through“Port N”), in the same way the RF port (“Port 1”) and theclock (CLK) port (“Port 2”) are considered. In this case,the engineer is searching for the signal quality, called signalintegrity, mainly when the mixed-signal device is connectedto a signal processing unit, either a field-programmable gatearray (FPGA) or digital signal processing (DSP) board.

As well, it should be highlighted that now each line of thedigital bus is indeed working at gigabit per second (Gbps).This brings the design engineer to discuss and design carefullyeach bit line path, which should now be considered as atransmission line. The main objective is to guarantee not onlythat the signal maintains its format, but also that it deliversall bits with similar delays to each bus line. This is becomingvery important not only in truly digital circuits, but also innew SDR/CR configurations. Some authors have dedicated asignificant 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 bit-stream as a complete waveform in order to compare each andboth sides of the device (analog and digital). The final goal isthen to give tools to RF engineers so that they can characterizethe mixed-signal system using similar approaches to completeanalog circuits, i.e., using system level FoMs.

It should be referred here that in order to evaluate thedigital stream coming out or entering a data converter as anequivalent voltage signal, signal integrity in the digital busmust be assumed. Thus, it is considered that the bit stream isbeing 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 beemployed to truly capture the behavior of the mixed-signaldevice under characterization. From a design engineer pointof view, one of the crucial advantages in having this char-acterization is that several procedures could be implementedto overcome the non-idealities that the overall mixed-signalsystem incorporates. For example, the implementation of post-distortion algorithms to compensate for interferes in receiversub-systems [10], or pre-distortion algorithms for digital-basedtransmitters [11], [12].

Several advantages come from the use of a scatteringwave strategy for the behavioral characterization of mixed-signal devices. Among others, the direct interpretation of somebehavior metrics, in a way similar to what RF engineers arealready used to deal with analog S-parameters, as it will beshown later on. And also, the immediate readiness of CAD


Mixed-signal Component

a1

b1

a2 b2

Port 1

Port 2

Port 3 a3 b3

Port 4 a4 b4

Port 5 a5 b5

Port 6 a6 b6

(a)

Mixed-signal Component

a1

b1

a2 b2

db3

Port 1

Port 2

Port 3

da3

Clock

Binary value to voltage

ideal converter

receiver

transmitter

(b)

Figure 2. 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 integratedport. This approach is depicted in Fig. 2(b). As can be seen,the considered device has at least three ports (more can beincluded), in which two of them are analog corresponding tothe RF analog input and to the clock input, being the thirdport the digital bus evaluated as an overall signal.

Thus, for the characterization of this mixed-signal compo-nent, it can be considered that at the RF analog port (“Port 1”)incident and reflected scattered waveforms (a1, b1) exist andcan 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 toobtained a state value using (1), this is the binary represen-tation of each sample word sent or received from the mixed-signal device, through the digital bus. The sequence of statevalues over time represent a conceptual digital waveform, ascan be seen in Fig. 3. This waveform can yet be converted toa digital-equivalent voltage wave using (2).

StateV alue(t) = bitN (t) 2(N−1) + bitN−1(t) 2(N−2) + . . .

+ bit3(t) 22 + bit2(t) 2

1 + bit1(t) 20 (1)

Vdig(t) =StateV alue(t)× VppFullScale

(2N − 1)(2)

The voltage wave will be then transformed to da3 and db3that will allow the comparison to the analog port. An importantinference is that the da3 only exists in a receiver configuration

bit1

bit2

bit3

bit4

BinaryValue(t) = bit4(t)23 + bit3(t)22 + bit2(t)2 + bit1(t)

sampling times sampling times

tk-1 tk tk+1 tk+2 tk-1 tk tk+1 tk+2

Figure 3. Convert a bit word onto a binary word value for a 4-bit bus.

and db3 in a transmitter configuration, which assumes a perfectmatch having no reflected signal, see Fig. 2(b).

Nevertheless, similar properties of waveforms continue toexist, as for instance the digital received signal will accountfor the bus line length between the mixed-signal componentand the processing unit, which will correspond to a specificdelay in time for a given length. Once again, we should beaware that in each bus line the bit-stream is travelling at Gbpsspeeds, imposing that the overall signal (each digital sampleword) is evaluated at frequencies in order of GHz values.

III. MIXED-SIGNAL SCATTERING PARAMETERSREPRESENTATION

This section will be devoted to the representation of linearand nonlinear characterization approaches for mixed-signaloperation, 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 ap-proach can be expanded to a mixed-signal scenario.

The analog “Port 1” in Fig. 2(b), can be described accord-ingly to the incident and reflected waveforms. The incidentpower will be Pincident = |a1|2 and the reflected powerPreflected = |b1|2. The voltage at “Port 1” can also be definedby V1 =

√Z0(a1 + b1). It is curious to understand that

the signals a1 and b1 does not actually define any power orvoltage by themselves, they are actually defined for a systempresenting a characteristic impedance of Z0, and can be calledpower-waves as in [13].

At this point, the system will be assumed as a 2-portmechanism by incorporating the CLK port into the model.This is similar to what was done for a mixer [14], wherethe local oscillator (LO) imposes the operation regime. Thesame happens here with the clock signal. Besides, basedon the methodology proposed in [14], wherein it should beguaranteed a clock signal amplitude sufficient to excite thesampling stage and having a known frequency value.

In the third port, the digital one, a voltage representationof the digital state can be obtained using its binary valueas expressed in (2). Since, RF engineers are not used todeal with voltage values, a conversion to power-waves, da3


and db3, is performed. Actually, at high frequencies theseare the most important quantities to be measured and havemore significance than voltages or currents. It should be statedthat these scattering waves, da3 and db3, are not actuallytrue power-waves in the analog sense, but rather a conceptualrepresentation of those.

Nonetheless, when talking about power-waves we shouldcalculate them for a specific system characteristic impedance.But, in the digital world, which characteristic impedance valueshould be used? Remember that we are not considering theanalog waves that travel on the digital bus, but rather the statevalue that the entire bus represents. So, this value does not haveto be the characteristic impedance of the digital bus. Actually,a hypothetic characteristic impedance will be used instead. Inorder, to have an easy interpretation of the kernels that relatethe analog and the digital sides, the characteristic impedancevalue of the RF analog input port (Z0 analog

) will be used. Inthis basis, the waveforms da3 and db3 can be defined as:

da3 =Vdig√Z0 analog

, only in transmitter mode

db3 =Vdig√Z0 analog

, only in receiver mode (3)

Again, Z0 analogwas used in this context to maintain the

equivalence to the analog part, but any other value can beused, since this is a pure conceptual waveform.

Using this scattering waves approach, several FoMs can becalculated, as for instance, the quantity db3

a1can be evaluated

in amplitude and phase and swept over the frequency. Thevariation with ω would thus be included in the developedformulation, which will be called D-parametersTM:

D11(ω) = S11(ω) =b1(ω)a1(ω)

∣∣∣a2=α,da3=0

D31a2CLK(ω) = db3(ω)

a1(ω)

∣∣∣a2=α,da3=0

D13a2CLK(ω) = b1(ω)

da3(ω)

∣∣∣a2=α,a1=0

D33(ω) = 0

(4)

where α is the clock complex waveform value.The value D31a2CLK

(ω) is similar to S21(ω) in a typicaltwo-port analog network, but again it should be understoodthat a conceptual power-wave is being evaluated and not areal one in the analog sense, the a2CLK subscript means thatthese measures were calculated for a specific clock conditionα.

These values are calculated for a certain frequency grid ofthe input signal excitation. In this case, D11 is equivalentto the S11 measured for the analog counterparts. Also, it isimportant to stress that D31a2CLK

(ω) is actually a frequencydependent gain that varies with the input signal a1(ω) fora specific a2 = α. This measure is exactly similar to theavailable gain traditionally defined for amplifiers. Again, itshould be referred that D31a2CLK

only exists in receiver

mixed-signal components and D13a2CLKfor the equivalent

transmitter chain.Not much relevance is being given to the clock port apart

from its phase information. Nonetheless, the reflection coeffi-cient (D22) can also be defined for this analog clock port in anisolated fashion. This approach is actually similar to the oneused for the local oscillator port in a mixer characterization,[14], as said before.

It should be stressed that the digital signal in a mixed-signalsolution can appear in a different carrier frequency of theanalog side provided that a higher than the first nyquistzones (NZs) is used. Thus, the power-wave at the digitalversion can operate on a different frequency of the analogcounterpart, wherein a relationship between these frequenciesis straightforwardly obtained by knowing the clock samplingfrequency. This phenomenon encounters a similar operation ina mixer conversion approach.

B. Nonlinear Characteristic Formulation

Nonlinear distortion can be monitored in analog componentsas the generation of spectra components that are not includedin the input signal excitation. One of the most well knowndemonstration of these are the harmonics of the input signal.

In a mixed-signal system such a behavior is also represen-tative of nonlinear distortion phenomenon, concept addressedin [8], [15]. The main difference in a mixed-signal systemarises from the fact that if the harmonics are generated inNZs higher than the first, those harmonics will not appear asin a traditional fully-analog system, all organized sequentially,but will follow a different approach based on the samplingfrequency. This is true for receiving and transmitting mixed-signal systems, see Fig. 4 as an illustrative example. So, eachnonlinear distortion calculation should be evaluated having inmind where the nonlinear components will fall.

Again the definition of a variety of FoMs (e.g. total har-monic distortion (THD), ACPR, NPR, third order interceptpoint (IP3), IMD) becomes quite similar to fully-analog sys-tems, but with the evaluation of power defined as before,Pdig = |db3(ω)|2. This approach is employed in the IEEEstandard for analog to digital converters [8] for NPR evalua-tion, and is utilized in several vendor application notes [15]–[17].

Other FoMs inherent to mixed-signal environments continueto be used, as for instance the definition of signal to noise anddistortion ratio (SNDR), which is typically measured for full-scaled data converters (DAC or ADC) and accounts for theoverall noise and distortion being produced.

Recent trends in analog components modeling are incor-porating nonlinear behavior of fully analog components andsystems. The approaches with an higher spotlight are the onesbased 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 arounda large-signal operation point (LSOP) [19]. They consider thedevice under test (DUT) stimulated by a large signal conditionand try to catch its behavior under the assumption that theharmonic superposition principle stands true.


fCLKfCLK/2

f1 2f1 3f1

3fCLK/2

1st NZ 2nd NZ 3rd NZ

fCLK/2

f1 2f13f1

1st NZ

Dis

cre

te-T

ime

Dig

ita

l D

om

ain

Co

nti

nu

ou

s-T

ime

An

alo

g D

om

ain

fCLKfCLK/2

f1 2f1

3fCLK/2

1st NZ 2nd NZ 3rd NZ

fCLK/2

f1

1st NZ

Dis

cre

te-T

ime

Dig

ita

l D

om

ain

Co

nti

nu

ou

s-T

ime

An

alo

g D

om

ain

fCLK

+ f1

fCLK -

f1

Sa

mp

lin

g P

roc

es

s

2f1’

2f1’

Figure 4. 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 funda-mental frequency is considered, the PHD large signal modelswill also look to the harmonics produced by the device andits relationship and/or dependence on the harmonics at eachport of the device. Thus, the produced model will contain in-formation describing the influence between all cross harmonicfrequencies from the input to the output and vice-versa (linearand nonlinear information).

In the same way of the linear characteristic formulation,these nonlinear models can also be defined within this novelframework, assuming that all the previously defined quantitiesand characteristics remain equally suited.

Additional benefits of the PHD modeling characterizationinclude efficient load-pull prediction [20]. This is also an ad-vantage for mixed-signal scenarios, especially for a transmitterdevice where the output is analog. In this case, as in a poweramplifier (PA), the load-pull simulation capabilities could beexploited to improve the desired device performance duringits design stage.

Two different approaches based on the PHD theory can befollowed. The first one does not take into account the CLK portinformation, which is similar to what was done for the linearcharacterization, but assuming a large signal stimulus andconsidering harmonic signals relation. The second approachconsiders the CLK port as a common input for the system tobe characterized.

1) Formulation without CLK port: Considering the CLKsignal inside the model without trying to represent it, (5) canbe used to relate incident and reflected waves.

Bpm = DFpm|A11|Pm +

∑qn

DSpm;qn |A11|Pm−nApm;qn

+∑qn

DTpm;qn |A11|Pm+n conj(Apm;qn) (5)

In (5) A and B are complex values representing the incidentand the scattered waves respectively, both these wave values

may represent an hypothetical digital wave depending if it isbeing applied to model a transmitter or a receiver, as in thelinear characterization case. The index q and p correspond tothe considered port for the incident wave and for the scatteredwave respectively and the n and m correspond to the harmonicindex of the incident and scattered waves respectively.

Moreover, the component P = e+jφ(A11) will assure aphase normalization, introduced for simplification proposes.

This approach only allows the characterization of the firstNZ, which is a limitation. For instance if one is attempting tomodel the complete nonlinear behavior of a DAC, only har-monics that fall inside the considered NZ can be characterized.Thus, information about harmonics that fall in different NZs oreven replicas of the fundamental cannot be represented usingthis approach.

A similar approach to this formulation had been usedin [21], for the case of an integrated transmitter having areconstruction filter at the output.

2) Multi-port formulation: One of the possibilities tocharacterize mixed-signal systems using these powerfullarge-signal models is by exploit its multi-port describingcapabilities. 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, forexample, its VSWR will also be described inside the model.

As it was already explained, in mixed-signal systems, fre-quency conversion occurs due to the sampling circuit. PHDmodels inherently support frequency conversion by mappingall the cross harmonic frequencies of all the considered fun-damentals (one from the CLK port and one or more from theanalog ports), at all the ports of the DUT. The only limitationis that a maximum harmonic index has to be imposed, in orderto have a computable model.

With this approach, the real behavior of mixed-signal de-vices is inherently mimic by the model, since all the mixturesbetween the input signal and the CLK signal will be consid-ered. Furthermore, the level of folding considered in the model(number of NZs modeled) can be controlled by the maximum


Bp[m,h] = DFp[m,h](|Ain[1,0]|, |Aclk[0,1]|)P

m[1,0] +

∑q[n,k]

{DSp[m,h];q[n,k] (|Ain[0,1]|, |Aclk[1,0]|)P

m−n[1,0] Ap[m,h];q[n,k]

}+∑q[n,k]

{DTp[m,h];q[n,k] (|Ain[0,1]|, |Aclk[1,0]|)P

m+n[1,0] conj(Ap[m,h];q[n,k])

}(6)

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-signaldevice as a mixer. Where the CLK port is in the place of theLO port and the digital port follows the previously establishedcharacteristics.

The input, output relations between the several ports of themixed-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 inputfundamental frequency at the considered port for the incidentand for the scattered waves respectively, h and k correspondto the harmonic index of the CLK fundamental frequency atthe input port and at the considered port for the incident andfor the scattered waves respectively.

Once again, P[1,0] = e+jφ(A1[1,0]) will assure a phasenormalization for the zero phase of the fundamental inputsignal.

Moreover, (|Ain[1,0]|, |Aclk[0,1]|) corresponds to the consid-ered LSOP, which depends on the amplitude of the fundamen-tal large signal at the input port, |Ain[1,0]|, as well as on theamplitude of the CLK signal, |Aclk[0,1]|.

Taking a closer look to (6) and comparing it to the expres-sion for multi-port fully analog devices, [22], the differencesare on the name of the parameters (for simple identificationpurposes only) and on the absence of the P[0,1] which in thiscase would correspond to the phase normalization of the CLKsignal.

0 fs/2 fs 3fs/2 2fs 5fs/2 3fs

Characterized Freqs.


−100

−50

0

dBm

Output


−100

−50

0

dBm

CLK


−100

−50

0

dBm

Input

Figure 5. Spectrum representation of the input, CLK and output ports of amixed-signal receiver (with ADC), and representation of frequencies that thePHD model will characterize. Considered orders: Input=3, CLK=2, Mixing=5.

The absence of P[0,1] is justified by its redundancy in thecase of mixed-signal systems. Once, as already explainedbefore, to preserve the assumed signal integrity of the digitalsignal, it has to be acquired at the same phase of the CLKsignal. Thus, during the parameters extraction procedure theCLK phase will be always the same.

However, this direct representation of a mixed-signal deviceby a multi-port PHD model can arise some issues. The mainone is its unnecessary excessive complexity.

Since the digital signal only has a representation from 0to fS/2, by doing a complete frequency mapping in all portsthere will exist a large quantity of model parameters that willnot be used.

One can consider, for example, the case of a mixed-signalreceiver represented in Fig. 5. It is easily denoted that, it isimpossible to have any value in the majority of the mappedfrequencies (all above fS/2) at the digital port.

As a result, the parameters of the model associated tothe mixing products that appear inside the 1st NZ on thedigital port will have an associated complex value that couldbe different from zero. While all the other parameters thatcorrespond to all the other spectral components will alwayshave a value of zero, and thus, are unused and unnecessary.

3) Kernels extraction: The parameters from the equationsexpressed in (5) and (6) can be extracted using a proceduresimilar to what is employed in [21] and [23], as it will bebriefly described next:

• Mixed-signal devices need to be driven by a CLK signalso that, they can operate properly. Thus, a large toneneeds to be applied at the CLK port of the mixed-signalDUT. Additionally, another large tone is applied to eachof the other DUT ports. In this condition, it is consideredthat the DUT is being stimulated without perturbations.From these non-perturbed measures, the XF kernels canbe directly extracted.

• After, a perturbation needs to be applied to the DUT, a socalled “tickle” tone. This “tickle” is a lower power con-tinuous wave (CW) signal at the same frequency or at theharmonics of the previous large tones but, with differentrelative phases (from 0 to 2π). The “tickle” needs to beapplied to all the ports of the DUT individually, even atthe digital port when a transmitter is being characterized.The XS and XT kernels are computed from the mea-surements with the “tickle” present. In order to extracteach kernel value, a least mean squares method can beemployed as in [19] and [24].

It is worth to mention that during the measurement stageonly CW excitation signals are required.


Binary value to voltage ideal

converter ADC

Vector Correction Kernels

Processing Unit Local Oscillator

Phase Reference

Comb Generator

RF STIMULUS CLK STIMULUS

DIG

ITAL

BU

S

Calibration Planes

Figure 6. Idealized mixed-signal instrument architecture allowing combinedanalog and digital measurements, which is suitable for linear and nonlinearcharacterization of mixed-signal receivers or transmitters.

Apart from this, it is also important to refer that a calibrationprocedure is fundamental to measure wave quantities thatrepresent what is really happening at the ports of the DUT,this topic that will be addressed later on.

IV. INSTRUMENTATION FOR MIXED-SIGNAL SYSTEMS

Undoubtedly, the devices to be tested are moving awayfrom single-purpose, hardware-centric entities with limitedcapabilities, to multi-purpose, software-centric entities withendless capabilities. Thus, it is important that the test andmeasurement systems evolve in the very same way. It isnecessary to switch from traditional instruments commonlydivided by the type of signal to measure (RF analog, RFdigital, DC, optical, and so on) to an unified architecture thatintegrates all the relevant measurement capabilities in a singleinstrument.

In [25] a first iteration for this kind of emerging ap-proaches was presented, wherein it was suggested a syn-chronous laboratory-based mixed-signal test bench tailored tothe characterization of mixed-signal components or systems.Later, a more detailed overview of measurement strategiesand solutions suitable for the characterization and behaviormodeling 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 architecturefor this kind of mixed-signal instrumentation that is capableto perform linear and nonlinear characterization of mixed-signal receivers or transmitters. As can be observed, the analogchannels share the configuration of a network analyzer. Theremaining port is a digital channel taking the properties of alogic analyzer, in which the signals are no longer analog, butare actually bit sequences.

In Fig. 7 a picture of the proposed instrument prototype isdepicted.

Figure 7. Mixed-signal instrument prototype.

As usual, in order to get valid information from such aninstrument, a calibration scheme is necessary. Moreover, anadditional issue is raised because of the combination of analogand digital signal domains into the same characterization tool.The next subsection will handle this situation by showing acouple of options to try surpassing such conditions.

A. Instrument Calibration Details

In the calibration process of a Vector Network Analyzer(VNA) using more than one port, a standard that can relatethe response between ports must be used in order to obtain atraceable 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 firstcase, and the “Line”, in the second case, were the calibrationstandards responsible for this error correction.

Moreover, in nonlinear analog characterization, using forinstance a Nonlinear Vector Network Analyzer (NVNA), morecomplex calibration methods have to be employed in order toget cross-frequency relationship, both magnitude and phaserelationships [28]. For this purpose, a power meter is used formagnitude and a phase reference for phase (typically a CombGenerator (CG)). Using this strategy the “Thru” standard canbe left out of the calibration procedure, but both magnitudeand phase standards need to be applied at all the ports of theinstrument [29].

Contrary to analog-based approaches, in a mixed-signalsystem it is more difficult to develop a calibration strategyable to correct all the measurement errors. This is mainlybecause a calibration reference for the mixed-signal “Thru” (aconnection between the analog and the digital ports) is totallynon-existent.

Either way, in the last few years, several attempts havebeen taken to surpass this limitation when approaching di-verse mixed-signal laboratory arrangements for mixed-signalreceivers and transmitters characterization, as presented in[21], [30].

The employed strategy, in [21], was similar to the onediscussed before for nonlinear analog measurements, usinga mixer-based instrument [28], [29]. This analog calibrationstrategy is usually called as “Absolute Calibration”, since itestablishes an absolute magnitude and phase value at theanalog calibration plane.

Since, the digital waves are conceptual power-waves, their


Figure 8. Comb generator utilized during the absolute phase calibration step.

magnitude value can be directly related to the absolute cor-rected analog waves.

However, the use of this method is not enough to correct forphase measurement errors. In other words analog and digitalwaves will not appear fully synchronized. Because, the phasereference device cannot be employed at the digital port andthe phase of a wave is a temporal non-static measurement thatdoes not have any absolute meaning, i.e., a phase of a wavecan only be defined in relation to other wave or to a timereference. Thus, additionally procedures have to be employedto surpass this issue. One way to handle this, can be based on[31] where a mixed-signal synchronization was obtain for asampler-based instrument (in that case an oscilloscope) withthe use of a reference signal and a trigger.

It is important to stress that for both linear and nonlinearcharacterizations the absolute calibration method must beemployed at the analog side. Thus, the power meter and theCG must be always used.

In the current prototype, a commercial power meter isbeing used to calibrate for the absolute power, while an in-house developed CG is being used for the absolute phasecalibration step. In Fig. 8, it is shown a photo of the used CG.Moreover, the CG’s performance was evaluated in [32], whereits applicability for instrument calibration was also discussed.

V. APPLICATION EXAMPLES

This new approach to the characterization of mixed-signalsystems, allows to combine analog and digital parts in aseamless way, so that digital and analog RF engineers canwork on a common language and framework.

Actually, the outcome behavioral model of this character-ization will allow engineers to integrate these devices witha great confidence inside CAD/CAE simulators, and optimizethe overall system performance. Besides, it will also allow realtime RF systems to be able to adapt and to compensate fornon-ideal behaviors appearing during real operation.

In this respect, the first application example is the char-acterization of an RF DAC. Predictions suggest that thesedevices will be strongly used in the next generation of wirelesscommunications, not only at the terminal side, but actually atthe base station side, through the use of remote radio headunits [12]. Besides, RF DACs are already being used in SDRsolutions and digital pre-distorter systems, see Fig. 9. Thus,a characterization of these components is a crucial point inorder to allow a more agile, faster and cheaper design stageof the end product.

BPF

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Figure 9. Illustrative transmitter system based on a DPD architecture andemploying high-speed mixed-signal devices.

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Figure 10. Measured linear D-parametersTMextracted from an RF DAC atdifferent operating modes: (a) magnitude of gain (D31), and (b) magnitudeand 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 visiblethe output signal varies from operation mode to operationmode. If for instance, the RF DAC is used in a DPD system,this behavior can degrade completely the implemented digitalalgorithm. In Fig. 10(b), the output matching (D33) can alsobe depicted. Naturally, both its magnitude and phase varyover frequency. Once again, this behavior is of paramountimportance when designing a system, since it can degrade thematching between the RF DAC and the antenna or PA, andthus, impact strongly the FoM of the overall system.


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Figure 11. Several nonlinear multi-port D-parameter kernels obtained frommeasurements, value over input power: (a) Magnitude of 4 kernels whichrelate the input at the fundamental with the output at the fundamental of 4consecutive NZs; (b) Magnitude of 4 kernels which relate the input at thefundamental with the output at the second and third harmonics of 2 NZs.

As a second example, the nonlinear multi-port formulationwill be employed to characterize a complete digital transmitter,a system as the one represented in the upper branch of Fig. 9without the filter at the output. Several of the measured kernelsare shown on Fig. 11, over a sweep of the input power.

Fig. 11(a) shows the equivalent magnitude gain (from thedigital input to the analog output) of the fundamental at fourconsecutive NZs. As expected, with the progression to higherNZs the overall gain value decreases. It can also be observed inFig. 11(b) that the output 2nd and 3rd order harmonics increasewith the increase of the input power, for two different NZs (the1st and the 3rd), which again represents an expected behavior.

The information gathered with this type of characterizationwould allow design engineers to improve their pre-distortiontechniques to linearize the overall system, and like that im-proving the outcome of the system.

As mentioned before, the receiver side can also be char-acterized by this framework. As a last example, in Fig. 12it is shown the D11 and the D13 linear D-parametersTMoverfrequency, from a medium CLK frequency ADC. The resultsshown here are from [30].

VI. CONCLUSIONS

In this paper a complete framework for characterizingmixed-signal devices is presented (for both SoCs and fulldiscrete component systems). This type of characterization isof fundamental importance, not only for SDR system design-ers, but also for DPD designers for PA optimization. Actuallythe correct characterization of the mixed-signal components

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Figure 12. Measured linear D-parametersTMof 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 thesecircuits [12].

In short, the D-parametersTMframework was presented, in-strumentation for its extraction was discussed, and someexamples were given to show the importance of the proposedapproach.

ACKNOWLEDGMENT

The authors would like to thank National Instruments,especially Dr. Marc Vanden Bossche, for the support givento this work.

REFERENCES

[1] N. Carvalho and D. Schreurs, Microwave and Wireless MeasurementTechniques, ser. The Cambridge RF and Microwave Engineering Series.Cambridge University Press, 2013.

[2] P. Cruz, D. C. Ribeiro, and N. Carvalho, “Measurement setup for linearcharacterization of a mixed-signal soc wideband receiver,” in IEEERadio and Wireless Symposium (RWS), Jan 2014.

[3] Linear Technology Corporation, “LTM9003 - 12-Bit Digital Pre-Distortion uModule Receiver Subsystem,” 2010. Available: http://www.linear.com/docs/28409

[4] Lime Microsystems, “LMS6002D,” 2012. Available: http://www.limemicro.com/download/LMS6002Dr2-DataSheet-1.2r0.pdf

[5] Analog Devices, “AD9361 - RF Agile Transceiver,” 2013. Available:http://www.analog.com/static/imported-files/data sheets/AD9361.pdf

[6] Maxim Integrated, “Max5879 - 14-Bit, 2.3Gsps Di-rect RF Synthesis DAC with Selectable Frequency Re-sponse.” Available: http://www.maximintegrated.com/en/products/analog/data-converters/digital-to-analog-converters/MAX5879.html

[7] Texas Instruments Incorporated, “ADC12D1800RF 12-Bit, Single 3.6GSPS RF Sampling ADC,” 2014. Available: http://www.ti.com/lit/ds/symlink/adc12d1800rf.pdf


[8] IEEE Standard for Terminology and Test Methods for Analog-to-DigitalConverters, IEEE Std. 1241-2010 (Revision of IEEE Std 1241-2000),Jan 2011.

[9] A. Ferrero, V. Teppati, E. Fledell, B. Grossman, and T. Ruttan, “Mi-crowave multiport measurements for the digital world,” IEEE Microw.Mag., vol. 12, no. 1, pp. 61 –73, Feb 2011.

[10] J. Pedro and N. Carvalho, “Characterizing nonlinear RF circuits for theirin-band signal distortion,” IEEE Trans. Instrum. Meas., vol. 51, no. 3,pp. 420 –426, Jun 2002.

[11] J. Wood, “Modeling and Simulation of RF and Microwave Systems,”Maxim Integrated, Tutorial 5542, Jan 2013. Available: http://www.maximintegrated.com/en/app-notes/index.mvp/id/5542

[12] ——, “A glimpse of the future,” IEEE Microw. Mag., vol. 13, no. 7, pp.60–69, Nov 2012.

[13] D. M. Pozar, Microwave Engineering. John Wiley, 2005.[14] D. Williams, F. Ndagijimana, K. Remley, J. Dunsmore, and S. Hubert,

“Scattering-parameter models and representations for microwave mix-ers,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 1, pp. 314 – 321,Jan 2005.

[15] J. Karki, “Calculating noise figure and third-order intercept in ADCs,”Texas Instruments Incorporated, Analog Applications Journal - 4Q,2003. Available: http://www.ti.com/lit/an/slyt090/slyt090.pdf

[16] W. Kester, “Intermodulation distortion considerations for ADCs,”Analog Devices, Tutorial MT-012, 2009. Available: http://www.analog.com/static/imported-files/tutorials/MT-012.pdf

[17] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Mi-crowave and Wireless Circuits. New York: Artech House, 2003.

[18] J. Verspecht and D. E. Root, “Polyharmonic distortion modeling,” IEEEMicrow. Mag., vol. 7, no. 3, pp. 44–57, 2006.

[19] J. Verspecht, D. Williams, D. Schreurs, K. Remley, and M. McKinley,“Linearization of large-signal scattering functions,” IEEE Trans. Microw.Theory Techn., vol. 53, no. 4, pp. 1369 – 1376, April 2005.

[20] H. Zargar, A. Banai, J. Cai, and T. Brazil, “An analytical approach toobtain optimum load impedance using X-parameters,” in Workshop onIntegrated Nonlinear Microwave and Millimetre-Wave Circuits (INM-MIC), Sept 2012, pp. 1–3.

[21] D. C. Ribeiro, P. M. Cruz, and N. B. Carvalho, “Synchronous FrequencyDomain Measurements for the Extraction of X-parameters in Digital toAnalog Transmitters,” in IEEE MTT-S Int. Microwave Symp., June 2013.

[22] C. Xie, T. Zhang, and D. Liu, “Using X-parameters to model mixers,”in International Conference on Microwave and Millimeter Wave Tech-nology (ICMMT), vol. 3, May 2012, pp. 1–3.

[23] D. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata, “Broad-bandpoly-harmonic distortion (PHD) behavioral models from fast automatedsimulations and large-signal vectorial network measurements,” IEEETrans. Microw. Theory Techn., vol. 53, no. 11, pp. 3656–3664, Nov2005.

[24] P. Cruz and N. Carvalho, “Wideband behavioral model for nonlinearoperation of bandpass sampling receivers,” IEEE Trans. Microw. TheoryTechn., vol. 59, no. 4, pp. 1006–1015, April 2011.

[25] P. Cruz, N. Carvalho, K. Remley, and K. Gard, “Mixed analog-digitalinstrumentation for software-defined-radio characterization,” in IEEEMTT-S Int. Microwave Symp. Dig., June 2008, pp. 253 –256.

[26] P. Cruz, N. Carvalho, and K. Remley, “Designing and Testing Software-Defined Radios,” IEEE Microw. Mag., vol. 11, no. 4, pp. 83 –94, June2010.

[27] M. Hiebel, Fundamentals of Vector Network Analysis, First ed. Rohde& Schwarz, 2007.

[28] P. Blockley, D. Gunyan, and J. Scott, “Mixer-based, vector-corrected,vector signal/network analyzer offering 300khz-20ghz bandwidth andtraceable phase response,” in IEEE MTT-S Int. Microwave Symp. Dig.,June 2005.

[29] H. Heuermann, “Calibration of a network analyzer without a thruconnection for nonlinear and multiport measurements,” IEEE Trans.Microw. Theory Techn., vol. 56, no. 11, pp. 2505–2510, Nov. 2008.

[30] D. Ribeiro, P. Cruz, and N. Carvalho, “Corrected mixed-domain mea-surements for software defined radios,” in 42nd European MicrowaveConference, Oct 2012, pp. 554–557.

[31] D. C. Ribeiro, P. M. Cruz, A. Prata, and N. B. Carvalho, “AutomaticCharacterization of RF DACs for Software Defined Radio Applications,”in IEEE MTT-S Int. Microwave Symp., June 2014.

[32] D. C. Ribeiro, P. M. Cruz, and N. B. Carvalho, “Evaluation of combgenerator performance for nonlinear measurements on mixed-domaininstrumentation,” in 6 Congresso do comite Portugues da URSI, Nov.2012.

Diogo C. Ribeiro (S’09-M’11), was born in Ferreirado Zezere, Portugal in 1988. He received the M.Sc.degree in Electronics and Telecommunications En-gineering in December 2011 at Universidade deAveiro. He is now a PhD student in the sameuniversity, since September 2012.

Mr. Ribeiro has as main interest software-definedradio measurement and nonlinear mixed-signal char-acterization. In 2012, he was recognized with theBest Student Paper Award 2012 at the 6th Congressof 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 Electronicsand Telecommunications Engineering (2008) and aPhD in Electrical Engineering (2012), both fromUniversidade de Aveiro, Portugal.

From Sept. 2006 to April 2007, he has worked atPortugal Telecom Inovacao as a trainee in a projectof localization systems based in wireless devices.Currently, he is a post-doctoral researcher with theInstituto de Telecomunicacoes (IT) being involvedin 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 andJETCAS and co-authored more than 20 international and national papersincluding book chapters, journals and conferences. He has been recognizedwith the 3rd place in the GAAS Association PhD Student Fellowship forEuMIC 2009.

Nuno Borges Carvalho (S’92–M’00–SM’05), wasborn in Luanda, Angola, in 1972. He received theDiploma and Doctoral degrees in electronics andtelecommunications engineering from the Universityof Aveiro, Aveiro, Portugal, in 1995 and 2000,respectively.

He is currently a Full Professor and a SeniorResearch Scientist with the Institute of Telecom-munications, University of Aveiro. He co-authoredIntermodulation in Microwave and Wireless Circuits(Artech House, 2003) and Microwave and Wireless

Measurement Techniques (Cambridge University Press, 2013). He has beena reviewer and author of over 100 papers in magazines and conferences.He is associate editor of the IEEE Transactions on Microwave Theoryand Techniques, IEEE Microwave Magazine and Cambridge Wireless PowerTransfer Journal.

He is the co-inventor of four patents. His main research interests includesoftware-defined radio front-ends, wireless power transmission, nonlinear dis-tortion analysis in microwave/wireless circuits and systems, and measurementof nonlinear phenomena. He has recently been involved in the design ofdedicated radios and systems for newly emerging wireless technologies.

Dr. Borges Carvalho is the chair of the IEEE MTT-11 Technical Committeeand the chair of the IEEE Portuguese Section. He is the chair of the URSI-Portugal Metrology Group. He was the recipient of the 1995. University ofAveiro and the Portuguese Engineering Association Prize for the best 1995student at the University of Aveiro, the 1998 Student Paper Competition (ThirdPlace) of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)International Microwave Symposium (IMS), and the 2000 IEE MeasurementPrize.

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