Black-Box Modelling of Mixed-Signal Integrated
Circuits
Vladimir Čeperić
Faculty of Electrical Engineering and Computing
University of Zagreb
Email: vladimir.ceperic{at}fer.hr
Abstract—Behavioural models and modelling techniques of
mixed-signal integrated circuits are gaining more and more
attention in industry and academic community due to the low
speed of time-domain SPICE transistor level simulations. The
black-box approach to behavioural modelling, although very
challenging, is particularly interesting due to its broad spectrum
of possible applications and fast simulation speed. The goal of
this paper is to explore possibilities and give suggestions for the
future research in the area of black-box behavioural modelling
of mixed-signal integrated circuits.
I. I NTRODUCTION
The process of modern Computer Aided Design (CAD)
consists of three stages:
• modelling (in CAD) - is a process that as a result provides
a numerical or analytical model that can be handled
by the computer. The result of modelling procedure, a
model, plays a critical role in CAD. If models are not
accurate, robust and stable, the following stages of CAD
are useless.
• analysis - models developed in previous step enable the
analysis of the observed system.
• optimisation - models developed in the first step enable
the optimisation of the observed system.
This work will focus on the modelling aspect of mixedsignal integrated circuit CAD and emphasis will be on blackbox behavioural modelling. Behavioural modelling, in general, tries to describe circuit, subsystem or system based on
recorded responses to well-selected excitation signals. Behavioural modelling has become a critical step in designs of
large circuit systems. Today, the multi million or billion transistor microprocessors or high level DSP integrated circuits,
simply could not be designed at the transistor level of circuit
description [1]. Their design is heavily based on behavioural
descriptions of the circuits used in the overall designs.
Black box is a technical term for a device, circuit or a
system that is observed in terms of its input, output or transfer
characteristics without any knowledge of its internal workings.
Black-box modelling usually refers to behavioural modelling
of such devices, circuits or systems. The specific aspects of
black-box modelling are discussed in section II-A.
For linear systems, broadband S-parameters can provide an
essentially good black-box, measurement based, behavioural
model of the component [1] (with obvious limitations regarding frequency range, interpolation issues, noise, causality
constraints and other). The linear circuit can therefore, be
adequately replaced by S-parameter simulation block (if the
mentioned limitations are observed, understood and taken into
account). Unfortunately, nonlinear systems and circuits1 are
more common than linear and are much harder to model. There
is no consensus how nonlinear systems should be modelled.
The main reason for that is the fact that there are so many
types of nonlinear systems with extremely complex dynamical
behaviour that is far from being exhaustively investigated or
understood [2]. Nonlinear modelling methods, in general, are
highly interdisciplinary, from (device) physics to mathematics
and computer science. In this work, we will concentrate on
black-box solutions based on universal approximators (e.g.
artificial neural networks, support vector machines, k-nearest
neighbour regression).
One should also note that circuit terminations (loads) have
no impact on the modelling process of the linear circuit [3].
When dealing with nonlinear circuits, the choice of terminations chosen in the training process, directly affects the quality
of the model [3].
This work focuses on the behavioural modelling of nonlinear systems, in particular, the mixed-signal integrated circuits.
Several aspects make modelling of the mixed-signal integrated
circuits especially difficult:
2
• large number and wide choice of passive and particularly
3
active components - in case of integrated circuits, one
comes across a variety of passive and active components.
Passive components include a variety of transmission
line structures, resistors, capacitors, inductors and other.
Furthermore, there is a vast number of active components,
e.g. semiconductor devices like MOSFET (Metal-OxideSemiconductor Field-Effect Transistor), MESFET (Metal
Semiconductor Field-Effect Transistor), BJT (Bipolar
Junction Transistor), HBT (Heterojunction bipolar transistor), HEMT (High Electron Mobility Transistor) and
many other. The modelling process of each of these
components is a complex matter and therefore, it is even
1 Any circuit block containing semiconductor devices is nonlinear. In
general, nonlinearity is a fundamental feature of any circuit block that provides
signal gain or performs any function more complex than linear filtering.
2 Passive component is a component that consumes (but does not produce)
energy or a component that is incapable of power gain. If a component is not
passive than it is called an active component.
3 If a component is not passive (see footnote 2) than it is called an active
component.
•
•
•
more complex to model circuits that consist of many such
components.
high nonlinearity of active components - as mentioned
in the last paragraph, there is a broad spectrum of
active component types, especially semiconductor transistors and their models (just to name a few, BSIM
(Berkeley Short-channel IGFET Model), EKV (Enz,
Krummenacher and Vittoz transistor model), PSP (Penn
State Phillips transistor model), HICUM (HIgh CUrrent Model), MEXTRAM (Most EXquisite TRAnsistor
Model) and many more). None of these models are
adoptable for full gamma of transistors, mainly because
the behaviour of transistors is highly nonlinear and dynamic and highly dependent on the transistor type and
technology it is built on.
it is often found that both digital and analog circuits
are placed on the same die, e.g. it is very common to
find systems with embedded digital, analog and radio
frequency RF/microwave blocks in a single die with a
mixed technology [4]. The Domenech-Asensi et al. in [4]
accent that such complex circuits impose to reconsider
and replace traditional design methods.
there are several constraints on the model which are
difficult to satisfy:
– the models have to be accurate - in order to be practically useful, the models have to be accurate enough.
The demand for accuracy varies from application
to application and usually conflicts with simulation
speed of the model.
– the models have to simulate fast (especially at the
system level) - if models are not fast enough, IC and
system designers cannot use them.
– model development resides in finding a good compromise between accuracy and complexity - higher
complexity usually implies lower simulation speed.
The optimal tradeoff between those two parameters
depends on the particular application and therefore,
it is very hard to extract general guidelines.
– the model should be effectively implementable in
modern integrated circuit simulation tools - if the
models are not includable into the standard simulation environment, they are practically useless.
– the models have to be stable and robust - if the
models are not stable and robust enough, they are
not usable.
– extraction principle of the model should be simple
enough to be implementable and usable.
A. Motivation
Large circuits, if simulated in time-domain, contain a very
large number of nonlinear equations to be solved. Such a
task is difficult, in terms of simulation time and memory,
for typical computer workstations available to most designers
[1]. Even modern simulation algorithms such as harmonic
balance [5] and transient envelope analysis [6] do not solve
this problem completely [1], although they are more efficient
than traditional methods used by time-domain SPICE-like
simulators.
The black-box approach to behavioural modelling, although
very challenging, is particularly interesting due to its broad
spectrum of possible applications and fast simulation speed.
One of the advantages of black-box models is that they can
be derived from both measurements and simulations. The
measured circuit that can be modelled in the behavioural
way, is probably the most accurate representation of this
circuit because it includes all parasitic effects (from packaging,
bonding, PCB and other sources) which could have been
overlooked in SPICE simulation. In the second, simulation
based approach, the circuit simulator is used as a virtual
instrument to generate needed data to build a behavioural
model. The behavioural modelling methods presented in this
work are generally targeted and applicable to both simulationbased and measurement-based cases.
From system designer perspective, behavioural models are
critical for system design. Wood and Root in [1] went even further in stressing the behavioural modelling importance stating
that “good behavioural model is perhaps the best specification
of the IC performance” in system design. One should also note
that in most cases the time-domain simulation of the whole
integrated circuit is impossible for large designs.
One interesting feature of behavioural models is that they
can be built for components for which “classical” model has
not been built yet or even for components that have not been
built yet at all. Using black-box modelling techniques, a model
could be developed even based on the desired or estimated
input-output relations. In that way, system designer can design
several aspects of the system based on general specifications
of components and reduce overall time-to-market.
Good behavioural models can be a competitive advantage
for both circuit and system design houses. Circuit design house
can send a behavioural model to system design houses without
revealing any inside information about how they have built the
circuit, thus protecting their intellectual property. If the models
are fast and accurate, system design house might be interested
to use the services of that particular circuit design house, rather
than the other, because they provide good models, and in spite
of the hypothetical difference in price, which can generate
additional revenues to circuit design house. Good behavioural
models enable system design houses to be effective and cut
the design time. Also, system design house capable of creating
their own behavioural models can design systems more easily
than competitions who must wait for hardware or built costly
prototypes.
For analog and mixed signal design, behavioural modelling
is even more difficult, especially at high frequencies. At high
frequencies, a behavioural model has to be able to directly
or indirectly describe the influence of the circuit parasitics
(which are, in general, difficult to extract and model). The
behavioural modelling techniques that can accomplish that
are especially sought after. There is especially big interest
for suitable behavioural models in a wireless communications
market, due to its commercial significance [1].
Another key issue in behavioural modelling is the fact that
today’s most prevalent approach for creating models is a manual abstraction. Manual abstraction is heuristic, inconvenient,
computationally expensive and error prone [2]. Automated
abstraction has many benefits, but is very difficult to develop,
because it has to cover a wide choice of circuits and devices.
The strategies and methodologies that are developed within
the scope of this work, can be considered on a path to the full
automated abstraction of models.
The lack of fast and accurate enough system simulation
methods leads to costly and time-consuming design iterations
including expensive prototype cycles. Two basic solutions are
almost obvious. The first solution is to divide the system in
separate blocks and circuits and with simplified, but sufficiently accurate behavioural models. This would enable the
full system simulation. The second solution would be to build
the behavioural model out of the measurements of the full
system (or simulations if possible at all). Unfortunately, the
path to the realisation of these deceivingly simple solutions is
not clear and therefore, this work will try to be one definite
step in the realisation of that goal.
B. Scope
The main goal of this work is to propose several approaches
for black-box modelling based on global approximation techniques. Based on current research status we will try to give
guidelines for the future research.
The main emphasis will be on the modelling aspects
that require least information about the model (i.e. blackbox modelling approach, described and compared with other
approaches in section II-A).
The goal is also that all models built from proposed behavioural modelling procedures should be effectively implementable in common simulation tools. This goal has proven
to be an extraordinary challenge because there is always a
discrepancy between “cutting-edge” academic research and
industrial application, which has to be robust, stable and
“mature”.
The “ideal” behavioural model that this work aspires to, has
these properties:
• accurate,
• fast,
• robust,
• stable,
• built with least amount of information (i.e. black-box),
• built with least amount of user interaction (i.e. automated
abstraction),
• implementable in modern circuit simulators.
The actual model implementation is always a compromise
between mentioned properties.
C. Outline
This work consists of five sections. The first section presents
the background, motivation, scope and outline of this work.
The section II will give a brief overview of the common
behavioural modelling practice and terms. The section III
presents the proposed framework for modelling of mixedsignal integrated circuits. The section IV presents the preliminary results of the framework presented in section III, based
on “real-world” test case. Finally, the conclusions are given in
section V.
II. B EHAVIOURAL MODELLING OF INTEGRATED
ELECTRONIC CIRCUITS
This section will give a brief overview of the common terms
in behavioural modelling approaches and procedures. Also,
a brief overview of the current state-of-the-art in black-box
modelling will be presented.
A. Comparison of basic modelling approaches
Models can be classified according to the level of physical
information used in model extraction in three categories:
• white-box models,
• grey-box models,
• black-box models.
White-box models require detailed knowledge about circuit
(or device) structure and processing technology, which is often
difficult to obtain. White-box models are detailed models that
(usually) have the advantage of being scalable. Black-box
models have the advantage that no physical information is
needed to build them. These models are fast but (usually) not
scalable. Changes in circuit or device properties necessitate
a complete reconstruction of the model. The characteristics
of grey-box models are (as the name suggests) somewhere
between the characteristics of black- and white-box models.
The emphasis of this work is on black-box models and
modelling procedures.
Table I presents the comparison (by the list of advantages
and disadvantages) of white- and black- box modelling approach. Some characteristics of white- and black- box models
depend on the circumstances, e.g. the execution speed of
white-box and black-box models depends on the modelling
procedure, model type and system, circuit or device signal
complexity. The same conclusion stands for the overall model
complexity.
B. Behavioural modelling procedure
Behavioural modelling tries to describe circuit, subsystem or
system based on recorded responses to well-selected excitation
signals. Such a behavioural modelling procedure consists of
several stages:
• selection of the excitation signals and acquirement of
the training data - the excitation signals have to be well
selected in order to capture the full behaviour (or just
behaviour of interest) of the modelled system, circuit
or device. The excitation signals should cover frequency
range of interest.
• data analysis and processing - in this stage, the data
obtained from stimulating the integrated circuit with wellselected excitation signals is analysed and processed. The
analysis and processing usually include signal selection
TABLE I
A DVANTAGES AND DISADVANTAGES OF WHITE - AND BLACK - BOX
MODELLING APPROACH
White-box modelling
Advantages
Potentially more accurate than
black-box modelling (due to better
insight into internal circuit operation).
It is easier to develop scalable models with white-box approach.
For years, the focus of industry
and academia (with respect to behavioural modelling) was on the
white-box modelling approach and
therefore, this approach is (usually)
more developed (resulting in increased robustness and stability).
Disadvantages
Full circuit/system schematic must
be known.
All device models must be available (if a circuit or a system is
simulated).
It can’t be used on measurements.
White-box models, in general, require more information to build the
model than black-box models.
•
•
Black-box modelling
Models can be made from measurements (or simulations).
Potentially are able to cover a
broader spectrum of circuits and
systems due to the fact that in
black-box modelling, they are observed only by analysis of inputoutput signals.
It is not necessary to know circuit/system schematic to model it.
Core procedures and methods are
the same for all circuits.
Hides the circuit details (i.e. it can
be sold to customers without revealing (almost) any details about
the circuit structure).
Developed core modelling procedures and methods can be used on
other types of modelling problems.
Complexity of the model is
relatively high.
Stability and robustness are
potentially not as good as in other
approaches.
Less deterministic than other
approaches.
Potentially less accurate than
white-box modelling (due to no
actual insight into internal circuit
operation).
Changes in circuit or device
properties necessitate a complete
reconstruction of the model.
and applying various algorithms to them (including scaling and normalisation).
selection of the model and its parameters - after selection
and processing of the model inputs, a specific model
type should be selected. Several types of current stateof-the art behavioural models are briefly described and
discussed in section II-C.
modelling - the actual modelling is the last part of
behavioural modelling procedure. It tries to apply the
modelling procedure suitable for the specific selected
model type and its parameters.
•
•
•
C. Overview of the current “state-of-the-art” in black-box
modelling of electronic circuits
As mentioned in the introduction, there is no consensus how
nonlinear systems should be modelled. In this section we will
present an overview of the current “state-of-the-art” in blackbox (nonlinear) modelling of electronic circuits. In recent
years, several quite different techniques gained popularity:
•
Volterra methods - Italian mathematician Vito Volterra
(1860-1940) developed the branch of mathematics known
as functional analysis. Inspired by his work, Norbert
•
Wiener hypothesised that time-invariant nonlinear systems could be modelled by series of Volterra functionals,
provided that the nonlinearities are not too strong. With
the recent interest in behavioural modelling of nonlinear
systems, the application of Volterra series is once again
interesting. Their main advantage is that they have a firm
theoretical background, while the main disadvantage is
that they are limited to weakly-nonlinear systems [1].
Good theoretical background about Volterra methods can
be found in [7]. In [1] more practical introduction to
Volterra methods for behavioural modelling can be found.
This work focuses on behavioural modelling that is not
limited to modelling of weak nonlinearities and therefore,
this method will not be investigated further.
scattering functions for nonlinear behavioural modelling
in the frequency domain - small signal S-parameters (referring to the scattering matrix) theory and measurement
equipment was developed during 1950s and 1960s. The
main limitation of S-parameters is that they can accurately describe only a linear relationship (in frequency
domain). Research lead by J. Verspecht [8] brought an
extension of usual S-parameters - so called Large Signal
S-Parameters and equipment for measurement of such
parameters called large-signal network analyser (LSNA).
black box piecewise linear (PWL) approximation - Feo
and Storace in [9] described a black-box identification
method based on state space reconstruction and PWL
approximation, and applied it to some several dynamical
systems (two topological normal forms and the Colpitts
oscillator). It should be noted that PWL methods used
in behavioural modelling are usually white-box methods
[2]. Although the presented results were promising, this
method probably has the same issues as other PWL
methods (as described in [2]).
artificial neural networks - ANNs were shown to be
suitable as the approximant needed in the core of blackbox modelling of electronic circuits and devices. The first
example of application of ANN in electronics was the
modelling of output characteristics of a MOS transistor
by Litovski et al. in [10] (where output characteristics are
approximated by a feed-forward three layer ANN). Since
then, many authors have reported and further developed
use of ANNs in a field of behavioural modelling of
electronic circuits and devices [11]–[20], but some issues
and problems (mainly with stability and robustness) still
remain. It should be noted that the application of ANNs
in the field of electronics goes beyond behavioural modelling as described in [21].
support vector machines - Čeperić and Barić in [22]4
report usage of support vector regression machines in
modelling of analog circuits. Xu et al. in [23] present a
combination of the conventional equivalent circuit model
and support vector machine regression for modelling of
4 To the best of author’s knowledge, this is the first attempt to model
electronic circuits with support vector machines.
•
MESFET devices. Karsmakers et al. in [24] report usage
of least-squares support vector machines in modelling
of electronic devices. Support vector machines, due to
its favourable properties, can show better performance in
modelling electronic circuits and devices, when compared
to ANNs.
recent developments - Hammi and Ghannouchi in [25]
presents a new class of models, named twin nonlinear
two-box (TNTB) models, proposed for modelling and
digital predistortion of power amplifiers and transmitters
exhibiting memory effects. Two-box models consists of a
memoryless nonlinear function and a low order memory
polynomial. The results are interesting, but (currently)
limited to modelling of power amplifiers and transmitters.
•
•
•
•
III. F RAMEWORK FOR MODELLING OF INTEGRATED
CIRCUITS
In this section, the framework for behavioural modelling of
integrated electronic circuits is proposed. The framework facilitates easier creation of behavioural models that are integrated
in the modern IC simulators.
To enable easier research, development and building of
black-box behavioural models, several requirements are met:
• new methods and procedures can be added in a “simple”
way - to facilitate easier research and development.
5
• connects to modern circuit simulators (Cadence Spec6
7
8
9
tre , Ultrasim and Mentor Graphics Eldo ) - for testing and validation of the models or obtaining training
data. Framework facilitates easy incorporation of other
integrated circuits simulators that can be controlled by
command line.
• the resulting model is implemented in Verilog A which
facilitates easier dispatch to different circuit simulators.
The details about Verilog A implementation will be
discussed in section III-B.
MEASUREMENT
INTERFACE
IC SIMULATION
INTERFACE
Figure 2 presents the mainframe part of the proposed
framework. The basic parts of the mainframe are:
•
•
•
•
•
•
MAINFRAME
MODEL EXPORT
•
•
Fig. 1.
Basic schematic of the modelling framework.
Figure 1 presents the basic schema of proposed modelling
framework. The basic parts of the framework are:
5 Cadence
is a US Trademark of Cadence Design Systems, Inc.
circuit
7 http://www.cadence.com/products/cic/UltraSim fullchip
8 Mentor Graphics is a registered trademark of Mentor Graphics Corporation.
9 http://www.mentor.com/eldo
6 http://www.cadence.com/products/cic/spectre
mainframe - this is the main part of the framework.
The mainframe controls all parts of the framework. This
part contains core black-box modelling procedures and
methods.
measurement interface - if the modelling is based on measurements, then we need an interface to the measurement
data (or devices).
IC simulation interface - there are two main reasons why
we need an interface to the modern IC simulators. First,
if the modelling is based on simulations, we need an
interface to them. Second, we need an interface to the
simulator to test the framework’s model.
model export module - model must be exported to the
format suitable for the use in most modern circuit simulators. The details about actual implementation will be
discussed in section III-B.
data acquisition - this part connects to either the IC
simulator or measurement setup (as shown in Figure 1).
selection of the input-output variables - this step performs
selection of the model inputs and outputs. This stage is
interconnected with the data acquisition stage.
data processing - in this stage, the data from the last
step is processed. Several steps are applied, e.g. splitting
data in the training, validation and testing data sets,
normalisation, scaling, adding delay, differentiating etc.
selection of the model type - e.g. two-stage model as
presented in section IV.
selection of the modelling method - three approximation
techniques are proposed to be used for black-box modelling: artificial neural networks, support vector machines
and k-nearest neighbour regression. The selection criteria
is proposed in section III-A. This stage interacts with data
processing stage because different modelling methods
might require different preprocessing of the model inputs
and outputs.
selection of the modelling parameters - each modelling
method (selected in the last step), has its own set of
parameters which have to be carefully selected. This stage
can interact with core modelling stage in an iterative way,
to perform an optimisation of the modelling parameters.
core modelling stage - this is the part where actual
modelling is done.
evaluation of the model - finally the model is evaluated.
As arrows in Figure 2 point out, the stages can be recursive
and iterative, e.g. if in the model accuracy is not satisfying,
different model type should be selected and the process
repeated.
The framework is implemented in Mathworks10 Matlab11
software package using object oriented programming. To improve reliability and robustness, automated unit testing is used
10 Mathworks
and Matlab are registered trademarks of The MathWorks, Inc
11 http://www.mathworks.com
MAINFRAME OF THE MODELLING FRAMEWORK
DATA
ACQUISITION
SELECTION OF
THE MODEL
TYPE
SELECTION OF THE
INPUT-OUTPUT
VARIABLES
Approximation
technique
Suitability
for
the
modelling of complex
signals (based on an
estimated generalisation
ability)
Suitability
for
the
modelling of integrated
circuit
with
high
number
of
pins
(based on estimated
resistance to the curseof-dimensionality)
Artificial neural networks
Support vector machines
k-nearest neighbour regression
Medium
Low
High
Medium
Low
Medium to high
DATA
PROCESSING
SELECTION OF
THE MODELLING
METHOD
EVALUATION OF
THE MODEL
Fig. 2.
TABLE II
S ELECTION OF THE APPROXIMATION METHOD BASED ON MODEL
COMPLEXITY AND NUMBER OF IC PINS
SELECTION OF THE
MODELLING
PARAMETERS
CORE MODELLING
STAGE (ON THE
LEARNING DATA SET)
Modelling framework.
[26]. The implementation details are more development than
research topic and therefore, will not be discussed in detail.
A. Selection of the appropriate approximation method
A choice of particular approximation method is proposed
to depend on two basic factors:
• signal complexity - ICs with higher complexity will
require usage of approximation techniques that are “better
than average” in accuracy (i.e. low training and testing
error) and generalisation12 .
• number of IC pins - the higher number of IC pins
that we would like to model, the higher dimensionality
of the problem is. The higher dimensionality increases
susceptibility to the curse-of-dimensionality13 .
Table II presents the selection of the approximation method in
the core module, based on model complexity and number of
IC pins.
Three different core approximators are selected among
wealth of methods:
• artificial neural networks,
• support vector machines,
• k-nearest neighbour algorithm.
The artificial neural networks and support vector machines are
selected as universal approximators based on current “stateof-the-art” in the field of black-box modelling of electronic
circuits (as described in section II-C). The k-NN regression is
selected due to its very good handling of the high dimensional
regression problems [28] as a potential candidate for modelling
ICs with a high number of pins.
Each of these core modules has different properties (sets
of advantages and disadvantages). All three together cover (or
12 A method is said to generalise well when the input-output mapping
computed by the method is adequately correct even for the test data (i.e.
data never used in training or validation of the method).
13 Term curse-of-dimensionality in the field of machine learning usually
refers to the problem of an exponential growth in model complexity needed
to adequately model the observed data as a consequence of an increase in
(input or output) dimensionality [27].
adjust to) a wide range of behavioural modelling needs for
modelling of electronic circuits. The artificial neural networks
are suitable for fast modelling of low to medium complex
circuits with a low to a medium number of pins. Support
vector machines, due to the better generalisation and resistance
to so called curse-of-dimensionality (see footnote 13) and
potentially slower learning (because “optimal” parameters for
learning have to be chosen (or optimised)) are more suitable
for medium to highly complex circuits with medium number
of pins. k-NN regression, due to worse generalisation and
modelling properties when compared with support vector
machines and neural networks, but higher resistance to curseof-dimensionality, is suitable for a low to complex circuits
with a higher number of pins.
B. Exporting the model to the modern circuit simulators
When implementing behavioural models into circuit simulators, several aspects are important:
•
•
•
•
ease of implementation,
possibility of use of different OS platforms,
possibility of implementation of the same model in (at
least several) modern circuit simulators,
simplicity of use and installation.
The main benefits of using Verilog-A(MS) or VHDL-A(MS)
for compact modelling over general-purpose programming languages is that it frees the model developer from handling the
simulator interface. When implementing models in VerilogA and VHDL-A, one needs not be concerned with circuit
simulator details. Also, they are considerably simpler then
implementations of models in C language where one had to
worry about symbolic partial derivatives of the currents and
charges in a compact model and determine the proper insertion
of these values into the Jacobian matrix for Newtons method
[29].
In this work, Verilog-A is chosen as an implementation
platform for behavioural models. Some of the specific benefits
of using Verilog-A(MS) are:
•
some modern circuit simulators internally compile Verilog A code to fast C code (e.g. Cadence4 Spectre5 ),
Verilog-AMS runs in the same AMS simulators as
VHDL-AMS [30],
• can be easily converted to VHDL-AMS.
A good overview of Verilog A advantages can be found in
[30].
•
IV. P RELIMINARY RESULTS
Local Interconnect Network (LIN) interface circuit is selected as a fist test case for the proposed methodology. In this
section, fist preliminary results are shown.
The basic schematic of the LIN interface circuit is shown14
in Figure 3. Table III shows the circuit inventory of the
LIN interface under test. The circuit contains 251 transistors
and 126 diodes and therefore, can be considered as a highly
nonlinear circuit.
VDD
Rx
BUS
T1
Tx
The receive pin RxD is loaded with resistor R = 106 Ω and
capacitor C = 1 pF which are varied by 10% with frequency
f = 0.1 MHz. By using variable loads, more cases are covered
in less time.
The proposed model consist of two stages:
• input stage - for the input stage, and for this particular
case, ANN are chosen as the universal approximation
method.
• output stage - approximation of the output stage. This
stage deals with the load of the circuits, decreases the
complexity that first stage has to “learn”. Preliminary
tests show that this output stage increases stability and
robustness of the full model.
The proposed model is presented in Figure 4. The voltage VIN is the voltage at the TxD pin. The inputs
of the ANN are the voltage VIN (t) and its delayed
variants VIN (t), VIN (t − 0.1us), VIN (t − 0.2us), VIN (t −
0.3us), VIN (t−0.4us), VIN (t−0.5us), VIN (t−1us), VIN (t−
1.5us), VIN (t − 2us), VIN (t − 2.5us), VIN (t − 3us), VIN (t −
3.5us), VIN (t − 4us), VIN (t − 4.5us), VIN (t − 5us), VIN (t −
5.5us), VIN (t − 6us), VIN (t − 6.5us), VIN (t − 7us), VIN (t −
7.5us), VIN (t − 8us), VIN (t − 8.5us), VIN (t − 9us), VIN (t −
9.5us), VIN (t − 10us). The output of the ANN is the voltage
VCON T ROL , the control (input) voltage of the output stage.
GND
VIN(t)
Basic schematic of the LIN interface.
VCONTROL(t)
...
Fig. 3.
OUT
ANN
TABLE III
C IRCUIT INVENTORY OF THE LIN INTERFACE TEST CIRCUIT.
Fig. 4.
Circuit inventory
Total number:
nodes
transistor
capacitor
delay
diodes
jfet
resistor
vcvs
365
251
132
24
126
15
156
4
In order to test the proposed framework, full signal path
from transmit pin RxD to receive pin TxD is modelled.
In order to obtain the training data, a frequency modulated
(FM) sinusoid is applied to the transmit pin with maximum
frequency of f = 100 kHz. For the validation and test data set,
a digital signal was applied with frequency f = 10 kHz. The
rise and fall time in the validation set is equal to 15 µs, while
in testing data set it is equal to 10 µs. The frequencies and
shapes of the validation and testing data sets can be considered
as standard operation mode of the LIN interface [31]. The
training data interval lasts for 100 µs, the same as validation
and testing interval. The model is in this case based on SPICE
simulations (in Cadence Spectre).
14 The details about this LIN interface could not be disclosed due to the
NDA agreement.
Basic topology of the proposed model.
VCONTROL
Fig. 5.
OUTPUT
STAGE
OUT
Output stage consisting of two transistors.
Figure 5 shows the two-transistor output stage. Parameters
of the transistors are optimised.
The first problem is how to extract signal VCON T ROL that
drives the output stage without knowing the actual schematics
(i.e. in blackbox way). The proposed solution is to generate
the control voltage:
VCON T ROL (t) = 3.3 − VOU T (t − tDELAY ),
(1)
where tDELAY is the parameter which value is optimised
among the values of two transistors in Figure 5.
The figure 6 shows the preliminary modelling results of the
LIN interface transmit-to-receive path (pin TxD to pin RxD).
The figure shows the voltage at the RxD (receiver) pin of
the LIN interface. The blue line is the result of the SPICE
simulations and the dotted red line the result of proposed
model simulation. The proposed model is about ten times
faster than the time-domain simulation.
Fig. 6. The voltage at the RxD (receiver) pin of the LIN interface: SPICE
simulations vs. proposed model.
V. C ONCLUSION
In this work, an overview of the state-of-the-art in behavioural modelling of integrated circuits is given together
with pointers were future research should go. One of the goals
is that all models built from proposed behavioural modelling
procedures should be effectively implementable in common
simulation tools. This goal has proven to be an extraordinary
challenge. The preliminary modelling results are promising
and show that a medium complex circuit can be efficiently
replaced by faster black-box based behavioural model within
the standard integrated circuit simulator.
R EFERENCES
[1] J. Wood and D. E. Root, Fundamentals of Nonlinear Behavioral
Modelling for RF and Microwave Design. Artech House, Inc., 2005.
[2] R. A. Rutenbar, G. G. E. Gielen, and J. Roychowdhury, “Hierarchical
modeling, optimization, and synthesis for system-level analog and RF
designs,” Proceedings of the IEEE, vol. 95, no. 3, pp. 640–669, 2007.
[3] Y. Cao, L. Simonovich, and Q. J. Zhang, “A broadband and parametric
model of differential via holes using space-mapping neural network,”
Microwave and Wireless Components Letters, IEEE, vol. 19, no. 9, pp.
533–535, 2009.
[4] G. Domenech-Asensi, J. Hinojosa, and J. Martinez-Alajarin, “A behavioral model development methodology for microwave components and
integration in VHDL-AMS,” Microelectronics Journal, vol. 38, no. 4-5,
pp. 489–495, 2007.
[5] K. S. Kundert, J. K. White, and A. Sangiovanni-Vincentelli, Steady-State
Methods for Simulating Analog and Microwave Circuits. Boston, MA:
Kluwer Academic Publishers, 1990.
[6] E. Ngoya and R. Larcheveque, “Envelope transient analysis: A new
method for the transient and steady state analysis of microwave communication circuits and systems,” in IEEE Int. Microwave Symp. Digest,
San Francisco, CA, 1996.
[7] M. Schetzen, The Volterra and Wiener Theories Nonlinear Systems.
New York: Wiley, 1980.
[8] J. Verspecht, “Large-signal network analysis,” IEEE Microwave Magazine, vol. 6, no. 4, pp. 82–92, 2005.
[9] O. D. Feo and M. Storace, “Pwl approximation of nonlinear dynamical
systems, part ii: identification issues,” Journal of Physics: Conference
Series, vol. 22, pp. 30–42, 2005.
[10] V. B. Litovski, J. I. Radjenovic, Z. M. Mrcarica, and S. L. Milenkovic,
“MOS transistor modeling using neural network,” Electronics Letters,
vol. 28, no. 18, pp. 1766–1768, 1992.
[11] J. Xu, M. Yagoub C. E., R. Ding, and Q.-J. Zhang, “Neural-based
dynamic modeling of nonlinear microwave circuits,” IEEE Transactions
on Microwave Theory and Techniques, vol. 50, no. 12, pp. 2769 – 2780,
2002.
[12] Q.-J. Zhang, “Neural networks for high-frequency electronic modeling
and design,” 2003.
[13] V. Čeperić, A. Barić, and B. Pejčinović, “Artificial neural network in
modelling of voltage controlled oscillators with jitter,” in Proceedings of
the 12th IEEE Mediterranean Electrotechnical Conference, MELECON
2004, vol. 1, 2004, pp. 347–350 Vol.1.
[14] H. Taher, D. Schreurs, and B. Nauwelaers, “Constitutive relations for
nonlinear modeling of Si/SiGe HBTs using an ANN model,” International Journal of RF and Microwave Computer-Aided Engineering,
vol. 15, no. 2, pp. 203–209, 2005.
[15] W. H. A. Schilders, P. B. L. Meijer, and E. Ciggaar, “Behavioural
modelling using the MOESP algorithm, dynamic neural networks and
the Bartels-Stewart algorithm,” Applied Numerical Mathematics, vol. 58,
no. 12, pp. 1972–1993, 2008.
[16] H. Taher, D. Schreurs, and B. Nauwelaers, “Black box modelling
of the op-amp including switching power supply on effect,” AEU International Journal of Electronics and Communications, vol. 62, no. 7,
pp. 544–548, 2008.
[17] H. Ben Hammouda, M. Mhiri, Z. Gafsi, and K. Besbes, “Neuralbased models of semiconductor devices for SPICE simulator,” American
Journal of Applied Sciences, vol. 5, no. 4, pp. 385–391, 2008.
[18] M. Kraemer, D. Dragomirescu, and R. Plana, “Nonlinear behavioral
modeling of oscillators in VHDL-AMS using artificial neural networks,”
in Radio Frequency Integrated Circuits Symposium, 2008. RFIC 2008.
IEEE, 2008, pp. 689–692.
[19] Z. Lei, Z. Qi-Jun, and J. Wood, “Statistical neuro-space mapping
technique for large-signal modeling of nonlinear devices,” IEEE Transactions on Microwave Theory and Techniques, vol. 56, no. 11, pp. 2453–
2467, 2008.
[20] L. Zhang and Q.-J. Zhang, “Neuro-space mapping technique for semiconductor device modeling,” Optimization and Engineering, vol. 9,
no. 4, pp. 393–405, 2008.
[21] Q. J. Zhang and K. C. Gupta, Neural networks for RF and microwave
design, ser. Artech House microwave library. Boston: Artech House,
2000.
[22] V. Čeperić and A. Barić, “Modeling of analog circuits by using support
vector regression machines,” in Proceedings of the 11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004,
2004, pp. 391–394.
[23] Y. Guo, Y. Xu, R. Xu, and B. Yan, “A support vector regression nonlinear
model for sic mesfet,” in Electron Devices and Semiconductor Technology, 2007. EDST 2007. Proceeding of 2007 International Workshop on,
2007, pp. 153–156.
[24] P. Karsmakers, P. Leroux, J. De Brabanter, and J. Suykens, “Least
squares support vector machines for modelling electronic devices,” in
European Conference on the Use of Modern Information and Communication Technologies (ECUMICT), Ghent, Belgium, 2008, pp. 1–4.
[25] O. Hammi and F. M. Ghannouchi, “Twin nonlinear two-box models for
power amplifiers and transmitters exhibiting memory effects with application to digital predistortion,” Microwave and Wireless Components
Letters, IEEE, vol. 19, no. 8, pp. 530–532, 2009.
[26] S. L. Eddins, “Automated software testing for matlab,” Computing in
Science & Engineering, vol. 11, no. 6, pp. 48–55, 2009.
[27] J. H. Friedman, “An overview of prediction learning and function
approximation,” in From Statistics to Neural Networks: Theory and
Pattern Recognition Applications, V. Cherkassky, J. H. Friedman, and
H. Wechsler, Eds. New York: Springer-Verlag, 1995.
[28] S. Vijayakumar and S. Schaal, “Approximate nearest neighbor regression
in very high dimensions,” in Nearest Neighbor Methods in Learning and
Vision, V. Shakhranovich, T. Darrell, and P. Indyk, Eds. MIT Press,
2006.
[29] G. Coram, “How to (and how not to) write a compact model in
Verilog-A,” in IEEE International Behavioral Modeling and Simulation
Conference, BMAS 2004, 2004.
[30] G. J. Coram, “Verilog-a: An introduction for compact modelers,” 2006.
[31] L. Consortium, “Lin specification package rev. 2.1,” 2008.