Anritsu HFE0902 Modeling
46 High Frequency Electronics
High Frequency Design
RF COMPONENT MODELS
Accurate Simulation of RF
Designs Requires Consistent
Modeling Techniques
By V. Cojocaru, TDK Electronics Ireland Ltd. and
D. Markell, J. Capwell, T. Weller and L. Dunleavy, Modelithics, Inc.
W
ith a consistent
approach, based
upon the use of
accurate characterization
techniques and advanced
passive and active component models, a high
level of accuracy can be
achieved when simulating basic RF/microwave
circuit designs. This article describes the techniques used in a number of new or enhanced
high-frequency component models that
increase the simulation prediction capability
and reduce the number of design, fabrication
and test cycles. It presents the general features of some novel SMT capacitor and inductor models, as well as those of high-frequency
non-linear models for varactor and switching
diodes. The accuracy of the models is thoroughly verified against experimental data in a
number of tests performed on each individual
component model, as well as in a more complex test carried out on a typical dual-band
VCO tank circuit used in some modern communication systems.
Introduction
In comparison with active devices or even
distributed and monolithically integrated passive components, improved lumped passive
component models for hybrid circuit design
have been largely ignored. For example, in
many situations designers can wrongly
assume that the models provided for surface
mount capacitors and inductors in modern
simulators are adequate for the purpose of
their simulations. Consequently, it is commonplace to focus the modeling effort on compo-
nents perceived to be of more critical importance. In this article we demonstrate some
illustrative examples of the high level of accuracy that can be achieved beyond 12 GHz with
precise modeling of lumped passives, and compare the results that are obtained with common—but more simplistic—models.
Specifically, we will address the characterization and modeling of surface mount capacitors and inductors, as well as packaged varactors and PIN diodes. The models are based on
equivalent circuit topologies utilizing substrate-scalable parameter values. These models are extracted from TRL-calibrated Sparameter measurements on multiple substrates (e.g., 5, 14 and 21 mil-thick FR4) and
provide a compact, versatile model for general
design purposes. The ability of the diode models to track the non-linear I-V and C-V characteristics over a broad range of bias conditions has been improved relative to existing
model topologies.
Surface Mount LC Models
In the microwave frequency range, the
behavior of surface mount passive components, such as ceramic multi-layer capacitors
and various types of inductors (e.g., air wound
and chip style) is known to depend on the surrounding circuit board environment. Factors
that will affect the frequency response include
the substrate characteristics [1, 2, 3] and the
type of transmission line used as the interconnect [4]. In certain applications the variation
due to somewhat minimal substrate alterations can be significant. One example pertaining to a common design requirement is
choosing a suitable series capacitor for a DCblock, in which case the optimum capacitor
With greater reliance on
computer simulation of RF
and microwave circuits,the
accuracy of component
models must be assured.
This article describes the
latest measurement-based
modeling techniques.
From September 2002 High Frequency Electronics
Copyright © 2002, Summit Technical Media, LLC
48 High Frequency Electronics
High Frequency Design
RF COMPONENT MODELS
will exhibit a series resonance at the
design frequency. As illustrated in
Figure 1, the series resonance is
strongly tied to the substrate properties. In this example, the resonance
shifts from 4.5 GHz down to 3 GHz as
the FR4 substrate thickness increases from 14 to 24 mils.
One our goals in this article is to
demonstrate that the method used to
model the substrate-dependency of a
surface mount LC component determines the resulting versatility of the
model. The results given in Figure 1
include measured S-parameter data
along with simulated results using a
single, substrate-scalable equivalent
circuit model [3]. The substrate-scalable model is physically motivated, in
that the equations for the circuit
parameters are functions of the substrate cross-section and component
geometry. For better or worse, however, there tends to exist more than one
model topology that will “match” a set
of measurement data when the data
is of limited extent. (Data may be
limited in frequency, sample size, test
configuration, etc.) Some support of
this statement is given in Figure 2, in
which the simulated response of the
substrate-scalable model from Figure
1 is compared to a very simplistic,
series L-C model, where L emulates
an
effective series inductance and C the
nominal capacitance of the part. For
this limited data set (a single substrate) the magnitude and phase
response of the two models are nearly identical up to the first resonant
frequency.
The importance of the physically
based model becomes clear when the
model is applied in a configuration
that differs from that used for model
extraction. Figure 3 shows a capacitor configuration that is frequently
used to obtain non-standard part values. Measured S-parameter data for
this dual shunt capacitor arrangement, on a 14 mil-thick FR4 substrate, is shown along with various
simulation results in Figure 4. The
simulation using the substrate-scalable models, with the input parameters for the substrate properly
defined, faithfully reproduces the
measurement data across the frequency range. There is also a curve in
the figure that is generated using the
substrate scalable models, but with
the substrate height input parameter
set to 24 mils; these results correspond to what might be obtained
with a fairly robust equivalent circuit
topology extracted using measurement data from a substrate differing
from the application substrate. The
shift in the frequency response is
comparable to that seen previously in
Figure 1. The last curve in the figure
is obtained by replacing the accurate
capacitor models with their simple
LC counterparts. While the simple
topology provided very accurate Sparameter representation for the
series 2-port configuration, the same
models used in the dual shunt configuration provide completely miss the
resonance near 6 GHz.
Chip inductors exhibit substratedependent behavior that is similar to
that of capacitors, although the
inductors present a somewhat more
complicated modeling problem at
higher frequencies. In Figure 5, the
measured and model S
21
responses
for a 15 nH, 0402 chip inductor are
shown for test fixtures on 5 and 31
Figure 1 · Measured (dashed lines) and modeled (solid
lines with markers) S
11
response for a 4.7 pF surface
mount capacitor in a series 2-port configuration.
Results are shown for test fixtures on 14 mil-thick FR4
(circles) and 24 mil-thick FR4 (squares).
Figure 2 · Modeled S11 for a 4.7 pF surface mount
capacitor on 14 mil-thick FR4 in a series 2-port configuration. Results are shown for an accurate, substratescalable model—solid line with circles (magnitude)
and squares (phase)—and a simplified series L-C
equivalent circuit (lines).
Figure 3 · Dual shunt capacitor configuration.
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