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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
A Linear Inverse Space-Mapping (LISM) Algorithm
to Design Linear and Nonlinear RF
and Microwave Circuits
José Ernesto Rayas-Sánchez, Senior Member, Fernando Lara-Rojo, Member, IEEE, and
Esteban Martínez-Guerrero, Member, IEEE
Abstract—A linear inverse space-mapping (LISM) optimization
algorithm for designing linear and nonlinear RF and microwave
circuits is described in this paper. LISM is directly applicable to microwave circuits in the frequency- or time-domain transient state.
The inverse space mapping (SM) used follows a piecewise linear
formulation, avoiding the use of neural networks. A rigorous comparison between Broyden-based “direct” SM, neural inverse space
mapping (NISM) and LISM is realized. LISM optimization outperforms the other two methods, and represents a significant simplification over NISM optimization. LISM is applied to several linear
frequency-domain classical microstrip problems. The physical design of a set of CMOS inverters driving an electrically long microstrip line on FR4 illustrates LISM for nonlinear design.
Index Terms—Aggressive space mapping (ASM), Broyden,
computer-aided design (CAD), high-speed digital design, interpolating neural networks, inverse space mapping (SM), neural
models, nonlinear transient design, optimizing expensive functions, RF and microwave design, surrogate models.
I. INTRODUCTION
S
PACE-MAPPING (SM) optimization techniques have been
proposed in numerous innovative ways to efficiently design
microwave circuits using very accurate, but computationally expensive models, typically full-wave electromagnetic (EM) simulators. A comprehensive review on SM for microwave modeling and design is the research by Bandler et al. [1]. All of
the algorithmic SM approaches to microwave engineering design have been illustrated with linear frequency-domain design
problems, although the original formulation of SM [2], as well
as some other more advanced versions [3]–[6], consider a general formulation that, in principle, could also be applied for
transient-domain design. Furthermore, in some of the SM algorithms, the frequency variable is intelligently manipulated to
improve the parameter-extraction (PE) process, as in [7] and [8],
making these particular SM techniques applicable only for frequency-domain linear problems. An interesting formulation to
nonlinear EM optimization by SM has been recently developed
[9], where the mapping inversion process is merged with the harmonic-balance analysis into the solution of a nonlinear system
Manuscript received April 22, 2004; revised August 2, 2004. This work was
supported in part by the Consejo Nacional de Ciencia y Tecnología, Mexican
Government under Grant 010581, Grant I39341-A, and Grant PFPN-03-42-8.
The authors are with the Department of Electronics, Systems and Informatics,
Instituto Tecnológico y de Estudios Superiores de Occidente, Tlaquepaque,
Jalisco 45090, México (e-mail: erayas@iteso.mx).
Digital Object Identifier 10.1109/TMTT.2004.842482
of equations. In this paper, we describe an integrated transientand frequency-domain SM-based design algorithm.
Artificial neural networks (ANNs) have also been extensively used for efficient electromagnetics-based design and
optimization of microwave circuits [10]. All of these ANN
techniques for microwave design have been developed either
for the frequency or transient domains. An integrated transientand frequency-domain ANN-based algorithmic (online) design
approach has not yet been reported. Powerful techniques for
developing EM-based neural models in the frequency domain
[11]–[13] and time domain (trained from frequency-domain
EM data [14]–[16] or from time-domain measured samples
[17]) have been proposed. Advanced ANN techniques for
EM-based modeling of passive microwave components for
frequency-domain and transient analysis have been recently
developed [18]. Once these neural models are trained, they
can be added to linear and nonlinear circuits to efficiently
incorporate EM effects during optimization.
Neural inverse space-mapping (NISM) optimization was the
first SM algorithm that explicitly made use of the inverse of the
mapping from the fine to the coarse model parameter spaces [6],
[19]. A statistical procedure to PE is employed in NISM to avoid
the need for multipoint matching and frequency mappings. An
ANN whose generalization performance is controlled through
a network growing strategy approximates the inverse mapping
at each iteration. The ANN starts from a two-layer perceptron
and automatically migrates to a three-layer perceptron when the
amount of nonlinearity found in the inverse mapping becomes
significant. The NISM step consists of evaluating the current
neural network at the optimal coarse model solution.
In this paper, we describe in detail the linear inverse spacemapping (LISM) algorithm to design by optimization proposed
in [20], and compare its performance with other SM-based optimization algorithms. LISM follows a piecewise linear formulation to implement the inverse of the mapping, avoiding the use
of neural networks. LISM approximates the inverse of the mapping function at each iteration by linearly interpolating the last
pairs of coarse and fine model design parameters, where
is the number of optimization variables. This change significantly simplifies the implementation of the algorithm with respect to the NISM version. It also allows us to generalize the
algorithm to be directly applicable for frequency-domain problems, for time-domain steady-state problems, and for time-domain transient-state problems, the latter being particularly relevant in high-speed digital design. The same statistical procedure
0018-9480/$20.00 © 2005 IEEE
RAYAS-SÁNCHEZ et al.: LISM ALGORITHM TO DESIGN LINEAR AND NONLINEAR RF AND MICROWAVE CIRCUITS
to PE is used in LISM as in NISM. LISM also follows an aggressive formulation in the sense of not requiring up-front fine
model evaluations. LISM can be applied to design linear circuits
and nonlinear circuits.
A rigorous comparison between Broyden-based direct SM,
NISM, and LISM is realized using a synthetic example in
the frequency domain. LISM optimization is contrasted with
NISM, and further illustrated by a classical problem of highspeed digital signal propagation: the physical design of a set
of CMOS inverters driving an electrically long microstrip line
on FR4.
II. SM FOR DESIGN BY SOLVING
A SYSTEM OF EQUATIONS
Here, we follow the SM notation [1]. Let the vectors
and
represent the design parameters of the coarse and fine
models, respectively
. The corresponding optiand
. The fine model is
mizable responses are in vectors
assumed to be a high-fidelity (or high accuracy) representation
whose evaluations are expensive, while the coarse model is a
low-fidelity representation that can be intensively evaluated
with no significant cost.
set of characterizing responses available in the two models
and
, as described in [19]. An implicit assumption in (2) is
that the PE process is unique (given a set of fine model characterizing responses, there is a unique vector of coarse model
parameters whose coarse model responses match those of the
fine model). If PE is nonunique, alternative formulations to (2)
can be followed, as in [21].
C. Solving a System of Nonlinear Equations
An SM-based optimization algorithm can be formulated to
find the fine model parameters that make the fine model response sufficiently close to the optimal coarse model response.
, i.e., by
This is realized by iteratively solving
finding an approximate root of the system of nonlinear equations
(3)
At the space-mapped solution,
so that
. Clearly, this SM formulation does not
aim at finding the actual optimal fine model solution , which
corresponds to the direct minimization of the original objective
function using the fine model
A. Optimizing the Coarse Model
SM-based algorithms start by directly optimizing the coarse
model using conventional optimization methods that typically
require many function evaluations
(1)
where
is the objective function (usually minimax)
is the
expressed in terms of the design specifications, and
optimal coarse model design. Vector contains the operating
conditions, which consists of any required combination of independent variables according to the nature of the simulation, such
as the operating frequencies, time samples, bias levels, excitation levels, rise time, fall time, initial conditions, temperature,
etc.
B. PE
In the SM context, the PE process consists of a local alignment of the two models, i.e., consists of finding the coarse model
design , whose corresponding responses are as close as possible to the fine model responses at the current fine model design
.
The PE process can be formulated as a nonlinear multidimensional vector function
, where
is evaluated
by solving
(2)
PE is a key sub-problem in any SM algorithm, and many different techniques have been proposed to realize it [1]. In this
paper, we take an statistical approach when solving (2), aligning
and , but the complete
not only the optimizable responses
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(4)
For most practical problems, solving (4) by conventional optimization methods is prohibitive.
In spite of the fact that solving the system of nonlinear equadoes not guarantee to find , it can still
tions
be used as an efficient practical design procedure to find the
fine model parameters that yields a desired fine model response.
Other SM algorithms have been formulated [22]–[24] that aim
at finding
at the expense of a larger number of fine model
evaluations.
III. BROYDEN-BASED “DIRECT” SM
In a Broyden-based “direct” SM, the mapping equation
is directly solved by using Broyden’s rank 1
updating formula [25]. This formulation corresponds to the so
called aggressive space mapping (ASM) [26]. Here, the next
iterate is predicted by
(5)
where the step
solves the linear system
(6)
and matrix
is an approximation of the Jacobian of with
respect to
at the current iterate. It is initialized by the identity
matrix and updated by using
(7)
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The Broyden-based “direct” SM optimization algorithm can
be summarized as follows.
where
(11)
Algorithm: Broyden-based “Direct” SM
A detailed description on how to choose the complexity of
the ANN is found in [19].
begin
find
solving (1)
,
B. LISM
using (2)
Here, the interpolating function
piecewise linear mapping defined by
repeat until stopping criterion
for
solve
is implemented by
(12)
using (2)
and the columns of
are stored in .
where
The linear inverse mapping is “trained” by interpolating the last
pairs of designs by solving the optimization problem
end
(13)
IV. NISM AND LISM TECHNIQUES
where the th error vector is given by
In the inverse SM techniques, an approximation of the inverse
of the mapping function is developed at each iteration. This is
over a
realized by optimizing an interpolating function
set of corresponding designs, where is a vector of weights.
The next iterate is predicted by simply evaluating the current
inverse mapping at the optimal coarse model solution
(8)
contains the optimal weights for the current inverse
where
mapping. The inverse SM algorithms can be summarized as follows.
Algorithm: Generic Inverse SM
begin
find
solving (1)
, initialize
repeat until stopping criterion
(14)
C. Common Aspects in NISM and LISM
In both NISM and LISM algorithms, the vector of weights
is initialized to implement a unit inverse mapping. Both algorithms also use the same optimization method (the scaled
conjugate gradient available in the MATLAB Neural Network
Toolbox1) for training the inverse mapping, i.e., for solving (10)
and (13). Since NISM uses a two-layer perceptron during the
first
iterations [19], if LISM and NISM are implemented
with the same PE method, then they predict the same iterates
during the first
iterations. Clearly, LISM represents a significant simplification over NISM, mainly because the problem
of controlling the generalization performance of the ANN is
avoided, which is done in NISM by controlling the complexity
of the ANN (the number of hidden neurons) and the training
error (the number of epochs and the magnitude of the minimum
acceptable training error).
using (2)
train
V. COMPARISON BETWEEN BROYDEN, NISM, AND LISM
end
A. NISM
Here, the interpolating function
ANN defined by
is implemented by an
(9a)
(9b)
It is seen that Broyden-based “direct” SM, NISM, and LISM
algorithms require a fine model evaluation per iteration. To
make a fair comparison between the three algorithms, they are
implemented using exactly the same PE procedure following
the statistical approach described in [19]. They also use the
same termination criteria: 1) when the maximum absolute error
in the solution of the system of nonlinear equations is small
enough; 2) when the relative change in the fine model design
parameters is small enough; or 3) when a maximum number of
iterations is reached as follows:
(15a)
(9c)
contains
and the columns of
and
. The ANN is trained to interpolate all
the accumulated pairs of designs by solving
(15b)
where
(10)
(15c)
where
and
.
1MATLAB Neural Network Toolbox, ver. 4.0 (R12), The MathWorks, Natick,
MA, 2000.
RAYAS-SÁNCHEZ et al.: LISM ALGORITHM TO DESIGN LINEAR AND NONLINEAR RF AND MICROWAVE CIRCUITS
963
Fig. 1. Synthetic example to compare the performance of Broyden-based
“direct” SM optimization, NISM optimization, and LISM optimization.
(a) Coarse model consisting of a canonical lumped RLC parallel resonator
x
= [R (
) L (nH) C (pF)] . (b) Fine model consisting of the same
resonator with some parasitic elements, with R = 0:5 ; L = 0:13 nH,
x
= [R (
) L (nH) C (pF)] .
Fig. 2. Starting point for the SM optimization of the lumped RLC
parallel resonator: optimal coarse model response (-); R (x ) and fine
model response ( ) at the optimal coarse model solution R (x ), where
x
= [50 0:2370 11:8792] .
Consider the following synthetic example. Both the coarse
and fine models are illustrated in Fig. 1. The coarse model consists of a canonical parallel lumped resonator [see Fig. 1(a)],
nH
pF .
whose design parameters are
The fine model consists of the same parallel lumped resonator
with some parasitic elements: a parasitic series resistor
assoand a parasitic series inductance
ciated to the inductance
associated to the capacitor
[see Fig. 1(b)]. The fine model
design parameters are
nH
pF . We
nH. These parasitic values imtake
pose a severe misalignment between the two models, and makes
very nonlinear.
the mapping function
The design specifications are (assuming a reference
impedance of 50 )
from 1 to 2.5 GHz and
from 2.95 to 3.05 GHz.
from 3.5 to 5 GHz, and
Performing direct minimax optimization of the coarse model
by conventional methods (we used a sequential quadratic
programming (SQP) method available in the MATLAB Optimization Toolbox2), we find the optimal coarse model solution
. The optimal coarse model reand the fine model response at the optimal
sponse
coarse solution
are illustrated in Fig. 2.
We first apply the Broyden-based direct SM algorithm described in Section III. The algorithm cannot solve this problem.
2MATLAB Optimization Toolbox, ver. 2.1 (R12), The MathWorks, Natick,
MA, 2000.
Fig. 3. Results after applying Broyden-based “direct” SM optimization to the
lumped RLC parallel resonator, for three different attempts. (a) Coarse model
response (-) at x and fine model responses at the three SM solutions found
( ; ; ). (b) Fine model minimax objective function values at each iteration,
for the three attempts (- -; - -; - -). Broyden-based “direct” SM optimization
fails at solving this problem, becoming unstable.
2
2
Fig. 3 shows the final responses and the fine model objective
function values at each iteration for three different attempts. It
is seen that the Broyden-based “direct” SM algorithm becomes
calculated in (7) beunstable. This is because matrix
calculated in
comes ill conditioned, making the next step
(6) unreliable.
We then apply the NISM algorithm described in Section IV-A. Since the mapping function for this problem is very
nonlinear, to illustrate the difficulty in controlling the generalization performance of the ANN at each iteration, we use 3000,
5500, and 10 000 epochs. Fig. 4 shows the final responses and
the fine model objective function values at each iteration for
each different number of epochs. In the three cases, NISM
terminates due to the number of iterations that have reached
the maximum. NISM finds an excellent fine model response
when 3000 epochs are used at the space mapped-solution
. From Fig. 4(b), it is
confirmed that too large a number of epochs yields too small
a training error, which makes the ANN “over fit” the training
samples, and to deteriorate its generalization performance,
predicting the following iterates with a large error.
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Fig. 4. Results after applying NISM optimization to the lumped RLC
parallel resonator. (a) Coarse model response (-) at x and fine model response
at the NISM solution using 3000 epochs ( ) using 5500 epochs ( ) and using
10 000 epochs ( ). (b) Fine model minimax objective function values at each
NISM iteration using 3000 epochs (- -) using 5500 epochs (- -) and using
10 000 epochs (- -). This problem illustrates the difficulty in controlling the
generalization performance of the ANN when the mapping between the two
models is severely nonlinear.
2
2
Finally, we apply the LISM algorithm described in Section IV-B. Fig. 5 shows the final responses and the fine
model objective function values at each iteration. LISM
finds an excellent fine model response at the SM solution
and terminates at the tenth
iteration due to a sufficiently small error in the solution of the
system of nonlinear equations.
Since the fine model used is computationally very efficient,
we can apply direct minimax optimization (using a conventional SQP optimization method). After 121 fine model evaluations starting from , the optimal fine model solution found is
and the corresponding objec. The fine model
tive function value is
minimax objective function values at each iteration are shown in
Fig. 6. Fig. 7 compares the optimal fine model response
,
, and the fine model
the optimal coarse model response
response at the space-mapped solution after applying LISM op. A comparison between
and
timization
the fine model minimax objective function values at each itera-
Fig. 5. Results after applying LISM optimization to the lumped RLC parallel
resonator. (a) Coarse model response (-) at x and fine model response ( ) at
the LISM solution. (b) Fine model minimax objective function values at each
LISM iteration (- -). An excellent solution is found after ten iterations.
Fig. 6. Fine model minimax objective function values at each iteration (-) of
the conventional optimization method (SQP) directly applied to the fine model
version of the lumped RLC parallel resonator.
tion after applying Broyden-based direct SM, NISM, and LISM
optimization is shown in Fig. 8. It is seen that LISM outperforms
NISM and Broyden-based “direct” SM.
Table I summarizes the numerical results obtained for
this problem after applying the four optimization methods
described.
RAYAS-SÁNCHEZ et al.: LISM ALGORITHM TO DESIGN LINEAR AND NONLINEAR RF AND MICROWAVE CIRCUITS
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Fig. 9. Block diagram of a set of CMOS inverters driving a capacitive load
through an electrically long microstrip line. The segments of microstrip lines
have a length L . The buffers are biased from a single dc voltage source. The
effects of the dc power bus on the integrity of the propagated signal are usually
neglected; they should be considered in a high-fidelity model (fine model).
Fig. 7.
Comparing results after direct conventional optimization of the lumped
, fine model response
() at the LISM solution, and coarse model response (-) at x .
RLC parallel resonator: fine model response (- -) at x
specifications, termination criteria, coarse and fine models,
and optimal coarse model solutions were used as in [19]. The
coarse and fine models for the first problem were implemented
in MATLAB. For the second and third problems, the coarse
models were implemented in APLAC,3 while the fine models
were implemented in Sonnet.4 The results found after applying
LISM optimization to these three problems were the same as
those found in [19], as expected, since the number of NISM
iterations needed for solving these three problems were no
.
greater than
VII. CMOS DRIVERS FOR A LONG MICROSTRIP LINE
Fig. 8. Comparing the optimal fine model minimax objective function
value U (R (x )) with the fine model minimax objective function values
at each iteration after applying Broyden-based direct SM, NISM, and LISM
optimization to the lumped RLC parallel resonator.
TABLE I
RESULTS OF THE OPTIMIZATION OF THE LUMPED RLC PARALLEL RESONATOR
VI. FREQUENCY-DOMAIN LINEAR EXAMPLES
We applied LISM optimization to the following design
problems: a two-section impedance transformer, a bandstop
microstrip filter with open stubs, and a high-temperature superconducting (HTS) microstrip bandpass filter. The design
Consider the problem of designing a set of CMOS inverters
to drive an electrically long microstrip line. The most common
practice to reduce the delay and other signal integrity problems
when driving a long line is to place buffer stages at different
locations along the line [27]. As an illustrative example, two
intermediate buffer stages are inserted between the initial and
final drivers on a long microstrip line, as shown in Fig. 9.
is a trapezoidal pulse with a 3-V amThe input voltage
plitude, 2.5-ns duration, and 100-ps rise time and fall time. The
microstrip lines are on an FR4 half-epoxy half-glass substrate
mil, loss tangent of 0.025, and dielecwith thickness
using a width
mil (50- lines).
tric constant
A typical 0.5- m CMOS process technology is assumed for all
the inverters. The dc power line biasing each inverter is typically
neglected (see Fig. 9), although it can have a significant impact
on the integrity of the propagated signal.
Both the coarse and fine models are implemented in APLAC.
The high-fidelity model is shown in Fig. 10. It uses the
Berkeley short-channel IGFET model (BSIM) (level 4) for
each MOSFET, and the built-in component Mlin available in
APLAC for all the microstrip line segments. The dc power
line biasing each inverter is also modeled as shown in Fig. 10,
assuming that it follows a completely different path than that
one of the signal path.
The low-fidelity model is shown in Fig. 11. It uses the level-1
(Shichman and Hodges) model for all the transistors. The main
driven microstrip line (signal path) is modeled by segments of
ideal lossless transmission lines using the built-in component
Tlin available in APLAC. The effects of the dc power line bus
are completely neglected. Due to the well-known inaccuracy of
3APLAC ver. 7.70b, APLAC Solutions Corporation, Helsinki, Finland, 2002.
4em
Suite, ver. 8.52, Sonnet Software Inc., 1020 North Syracuse, NY, 2002.
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Fig. 10. High-fidelity model for the CMOS buffers driving an electrically long
microstrip line. All the MOSFETs are using the BSIM (level 4) model. The
built-in component Mlin available in APLAC is used for all the microstrip line
segments on FR4 half-epoxy half-glass substrate with thickness H = 10 mil,
width W = 19 mil, loss tangent of 0.025, and dielectric constant " = 4:5
(50-
lines). The dc power line biasing each inverter is also modeled (assuming
it follows a completely different path).
Fig. 12. Starting point for LISM optimization of the CMOS inverters driving
a long microstrip line: input trapezoidal voltage (v ), optimal coarse model
output voltage (v ), and fine model output voltage (v ) at the optimal coarse
model solution x = [11 11:5 11 10:5] (in micrometers).
Fig. 13. Final results after applying LISM optimization to the CMOS inverters
driving a long microstrip line: input trapezoidal voltage (v ), optimal coarse
model output voltage (v ), and fine model output voltage (v ) at the LISM
solution x
= [23 18 21 19:5] (m).
Fig. 11. Low-fidelity model for the CMOS buffers driving an electrically
long microstrip line. All the MOSFETs are using the Shichman and Hodges
(level 1) model, the microstrip lines are modeled by segments of ideal lossless
transmission lines (" = 4:5; Z = 50 ), and the effects of the dc power
line are neglected.
the level-1 MOSFET model for submicrometer devices [28], the
channel length in the coarse model was taken as a preassigned
parameter [5] and adjusted to realize an initial compensation of
the coarse model (notice that the coarse model is using channel
lengths of 0.8 m instead of 0.5 m).
V from 0 to
The design specifications are
1 ns,
V from 3 to 4.5 ns, and
V
from 6.5 to 8.5 ns. The design parameters are the channel
widths for all the MOSFETs, assuming symmetric inverters
. After applying conventional optimization (using an SQP method ), the following optimal coarse
(in
model solution is found:
micrometers). The excitation signal, as well as the coarse and
fine model responses at the optimal coarse solution , are
shown in Fig. 12.
After six LISM iterations, a solution is found for this
problem. The fine model response at the LISM solution
(in micrometers) is compared with
Fig. 14. Fine model minimax objective function values at each LISM iteration
during the optimization of the CMOS inverters driving a long microstrip line
(--).
the optimal coarse model response in Fig. 13. The fine model
minimax objective function values at each LISM iteration is
shown in Fig. 14. LISM requires seven fine model simulations
to solve this problem. The algorithm took 1 h 53 min 11 s to
find the solution using a 1.6-GHz Pentium 4 computer with
512 MB of RAM.
RAYAS-SÁNCHEZ et al.: LISM ALGORITHM TO DESIGN LINEAR AND NONLINEAR RF AND MICROWAVE CIRCUITS
VIII. CONCLUSION
We have described an LISM optimization algorithm for
designing microwave circuits in the frequency- or time-domain
transient state. The inverse SM follows a piecewise linear
formulation, avoiding the use of neural networks. LISM is rigorously compared with Broyden-based direct SM and NISM.
LISM optimization outperforms the other two methods, and
represents a significant simplification over NISM optimization.
LISM is applied to several linear frequency-domain classical
microstrip problems, and is illustrated by a classical problem
of high-speed digital signal propagation.
ACKNOWLEDGMENT
The authors thank M. Kaitera, APLAC Solutions Corporation, Helsinki, Finland, for making APLAC available. The authors also thank Dr. J. C. Rautio, Sonnet Software Inc., North
Syracuse, NY, for making em available.
REFERENCES
[1] J. W. Bandler, Q. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr,
K. Madsen, and J. Søndergaard, “Space mapping: The state of the art,”
IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 337–361, Jan.
2004.
[2] J. W. Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R.
H. Hemmers, “Space mapping technique for electromagnetic optimization,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp. 2536–2544,
Dec. 1994.
[3] M. H. Bakr, J. W. Bandler, R. M. Biernacki, S. H. Chen, and K. Madsen,
“A trust region aggressive space mapping algorithm for EM optimization,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2412–2425,
Dec. 1998.
[4] M. H. Bakr, J. W. Bandler, N. Georgieva, and K. Madsen, “A hybrid
aggressive space-mapping algorithm for EM optimization,” IEEE Trans.
Microw. Theory Tech., vol. 47, no. 12, pp. 2440–2449, Dec. 1999.
[5] J. W. Bandler, M. A. Ismail, and J. E. Rayas-Sánchez, “Expanded space
mapping EM based design framework exploiting preassigned parameters,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no.
12, pp. 1833–1838, Dec. 2002.
[6]
, “Neural inverse space mapping EM-optimization,” in IEEE
MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, May 2001, pp.
1007–1010.
[7]
, “Neuromodeling of microwave circuits exploiting space mapping
technology,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp.
2417–2427, Dec. 1999.
[8] M. H. Bakr, J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, and Q.
J. Zhang, “Neural space mapping optimization for EM-based design,”
IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2307–2315, Dec.
2000.
[9] V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, and F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid
of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech., vol.
52, no. 1, pp. 362–377, Jan. 2004.
[10] J. E. Rayas-Sánchez, “EM-based optimization of microwave circuits
using artificial neural networks: The state of the art,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 420–435, Jan. 2004.
[11] P. Burrascano and M. Mongiardo, “A review of artificial neural networks
applications in microwave CAD,” Int. J. RF Microwave Computer-Aided
Eng., vol. 9, pp. 158–174, May 1999.
[12] A. Patnaik and R. K. Mishra, “ANN techniques in microwave engineering,” IEEE Micro, vol. 1, pp. 55–60, Mar. 2000.
[13] Q. J. Zhang and K. C. Gupta, Neural Networks for RF and Microwave
Design. Norwood, MA: Artech House, 2000.
[14] V. K. Devabhaktuni, M. C. E. Yagoub, Y. Fang, J. J. Xu, and Q. J. Zhang,
“Neural networks for microwave modeling: Model development issues
and nonlinear modeling techniques,” Int. J. RF Microwave ComputerAided Eng., vol. 11, pp. 4–21, Jan. 2001.
[15] J. Xu, M. C. E. Yagoub, R. Ding, and Q. J. Zhang, “Neural-based dynamic modeling of nonlinear microwave circuits,” IEEE Trans. Microw.
Theory Tech., vol. 50, no. 12, pp. 2769–2780, Dec. 2002.
967
[16] Y. Cao, J. J. Xu, V. K. Devabhaktuni, R. T. Ding, and Q. J. Zhang, “An
adjoint dynamic neural network technique for exact sensitivities in nonlinear transient modeling and high-speed interconnect,” in IEEE MTT-S
Int. Microwave Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 165–168.
[17] T. Liu, S. Boumaiza, and F. M. Ghannouchi, “Dynamic behavioral
modeling of 3G power amplifiers using real-valued time-delay neural
networks,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp.
1025–1033, Mar. 2004.
[18] X. Ding, V. K. Devabhaktuni, B. Chattaraj, M. C. E. Yagoub, M. Deo, J.
Xu, and Q. J. Zhang, “Neural-network approaches to electromagneticbased modeling of passive components and their application to highfrequency and high-speed nonlinear circuit optimization,” IEEE Trans.
Microw. Theory Tech., vol. 52, no. 1, pp. 436–449, Jan. 2004.
[19] J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, and Q. J. Zhang,
“Neural inverse space mapping for EM-based microwave design,” Int. J.
RF Microwave Computer-Aided Eng., vol. 13, pp. 136–147, Mar. 2003.
[20] J. E. Rayas-Sánchez, F. Lara-Rojo, and E. Martínez-Guerrero, “A linear
inverse space mapping algorithm for microwave design in the frequency
and transient domains,” in IEEE MTT-S Int. Microwave Symp. Dig., Fort
Worth, TX, Jun. 2004, pp. 1847–1850.
[21] M. H. Bakr, J. W. Bandler, and N. Georgieva, “An aggressive approach
to parameter extraction,” IEEE Trans. Microw. Theory Tech., vol. 47, no.
12, pp. 2428–2439, Dec. 1999.
[22] M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sánchez, and J. Søndergaard, “Space mapping optimization of microwave circuits exploiting
surrogate models,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 12,
pp. 2297–2306, Dec. 2000.
[23] J. W. Bandler, Q. Cheng, D. H. Gebre-Mariam, K. Madsen, F. Pedersen, and J. Søndergaard, “EM-based surrogate modeling and design
exploiting implicit, frequency, and output space mappings,” in IEEE
MTT-S Int. Microwave Symp. Dig., Philadelphia, PA, Jun. 2003, pp.
1003–1006.
[24] J. W. Bandler, Q. S. Cheng, S. A. Dakroury, D. M. Hailu, K. Madsen,
A. S. Mohamed, and F. Pedersen, “Space mapping interpolating surrogates for highly optimized EM-based design of microwave devices,” in
IEEE MTT-S Int. Microwave Symp. Dig., Fort Worth, TX, Jun. 2004, pp.
1565–1568.
[25] C. G. Broyden, “A class of methods for solving nonlinear simultaneous
equations,” Math. Comput., vol. 19, pp. 577–593, 1965.
[26] J. W. Bandler, R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K.
Madsen, “Electromagnetic optimization exploiting aggressive space
mapping,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 12, pp.
2874–2882, Dec. 1995.
[27] R. J. Baker, H. W. Li, and D. E. Boyce, CMOS Circuit Design, Layout,
and Simulation. Piscataway, NJ: IEEE Press, 1998.
[28] B. Razavi, Design of Analog CMOS Integrated Circuits. New York:
McGraw-Hill, 2001.
José Ernesto Rayas-Sánchez (S’88–M’89–SM’95)
was born in Guadalajara, Jalisco, México, on December 27, 1961. He received the B.Sc. degree
in electronics engineering from the Instituto Tecnológico y de Estudios Superiores de Occidente
(ITESO), Guadalajara, México, in 1984, the Masters
degree in electrical engineering from the Instituto
Tecnológico y de Estudios Superiores de Monterrey
(ITESM), Monterrey, México, in 1989, and the Ph.D.
degree in electrical engineering from McMaster
University, Hamilton, ON, Canada, in 2001.
Since 1989, he has been Professor with the Department of Electronics, Systems, and Informatics, ITESO. In 1997, he spent his sabbatical with the Simulation Optimization Systems Research Laboratory, McMaster University. He
returned to ITESO in 2001. His research focuses on the development of novel
methods and techniques for computer-aided modeling, design and optimization
of analog wireless and high-speed electronic circuits and devices exploiting SM
and ANNs.
Dr. Rayas-Sánchez is a member of the Mexican National System of Researchers, Level I. He is currently the IEEE Mexican Council Chair, as well as
the IEEE Region 9 Treasurer. He was the recipient of a 1997–2000 Consejo
Nacional de Ciencia y Tecnología (CONACYT) Scholarship presented by the
Mexican Government, as well as a 2000–2001 Ontario Graduate Scholarship
(OGS) presented by the Ministry of Training for Colleges and Universities in
Ontario, Canada. He was the recipient of a 2001–2003 CONACYT Repatriation
and Installation Grants presented by the Mexican Government. He was also the
recipient of a 2004–2006 SEP-CONACYT Fundamental Scientific Research
Grant presented by the Mexican Government.
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
Fernando Lara-Rojo (M’98) was born in Guadalajara, México, on June 5, 1935. He received the B.Sc.
degree in electronics engineering from the Instituto
Politécnico Nacional (IPN), México City, México, in
1958, and the Ph.D. degree in physics from the Institute of Theoretical Physics, University of Kiel, Kiel,
Germany, in 1973.
From 1958 to 1968, he was an Engineer in
telecommunication systems with Philips, Siemens,
and the Secretaría de Comunicaciones y Transportes,
Mexican Government (SCT). From 1973 to 1975,
he was a Professor with Centro de Investigación y de Estudios Avanzados
(CINVESTAV), México City, México, and from 1975 to 1980, with the
Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla,
México. Since 1984, he has been a Professor with the Electronics, Systems
and Informatics Department, Instituto Tecnológico y de Estudios Superiores de
Occidente (ITESO), Guadalajara, México. He is mainly interested in machine
intelligence and automated reasoning. Over the last seven years, his research
has focused on applications of fuzzy logic and neurofuzzy systems.
Dr. Lara-Rojo was the recipient of a 1968-1972 Instituto Nacional de la
Investigación Científica [now the Consejo Nacional de Ciencia y Tecnología
(CONACYT)] Scholarship presented by the Mexican Government. He has also
been the recipient of three scholarships for scientific collaboration sabbaticals
at German universities by the German Academic Exchange Service (DAAD).
Esteban Martínez-Guerrero (M’03) was born in
Puebla, México, on November 28, 1965. He received
the B.Sc. degree in electronics engineering from
the Universidad Nacional Autonoma de México
(UNAM), México City, México, in 1990, the Masters
degree in electrical engineering from the Centro de
Investigación y de Estudios Avanzados del Instituto
Politécnico Nacional (CINVESTAV—IPN), México
City, México, in 1996, and the Ph.D. degree in integrated electronic devices from the Institut National
des Sciences Appliquées de Lyon (INSA-Lyon),
Lyon, France, in 2002.
From 1998 to 2002, he collaborated with the Nanophysics and Semiconductor Research Group, Commissariat à l Energie Atomique (CEA)-Grenoble,
Grenoble, France. Since 2002, he has been Professor with the Electronics, Systems, and Informatics Department, Instituto Tecnológico y de Estudios Superiores de Occidente (ITESO), Guadalajara, México. His research focuses on
physical modeling, simulation and design of semiconductor devices, and growth
and characterization of thin-film and semiconductor nanostructures, namely,
quantum dots and quantum wells for optical telecommunication systems.
Dr. Martínez-Guerrero is a member of the Mexican National System of Researchers, Level I. He is a member of the IEEE Electron Devices Society. He
was the recipient of 1992–1995 and 1998–2002 Consejo Nacional de Ciencia y
Tecnología (CONACYT) Scholarships presented by the Mexican Government.