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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
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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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September 2002 49
mil-thick FR4 substrates. As with capacitors, a decrease
in the substrate thickness pushes the resonant behavior
higher in frequency; the frequency shift applies to the
fundamental (parallel) resonance as well as the higherorder resonances found near 11-12 GHz. One of the difficulties associated with the modeling solution is the asymmetric response near these higher-order resonances. The
asymmetry is easily identified in a comparison of the forward (1–|S
11
|2– |S21|2) and reverse (1–|S22|2–|S21|2)
loss factors, as shown in Figure 6. On both the 5 and 31
mil-thick FR4 substrates the forward loss factor is very
high—indicating that 70-80 percent of the incident power
is lost through dissipation and radiation—while the
peaks in the reverse loss factor are much lower. The
asymmetry forces a decision as to whether to employ a
suitably asymmetric equivalent circuit topology to emulate the response, or a more standard symmetric model
that averages through the forward and reverse responses.
Generally, the better choice is a symmetric model since
the orientation of the part often cannot be predicted or
controlled once in the production environment.
Varactor and PIN Diode Modeling
Varactor diodes are key components in the design of
any VCO circuit. The performance of the model used to
describe the varactor diode is of prime importance for the
simulation of certain crucial VCO characteristics, such as
tuning range, tuning sensitivity, phase noise and harmonic generation. The large-signal nature of the VCO circuit means that the forward operating region of the varactor cannot be neglected, despite the fact that typically
they are operated well into the reverse bias region.
A robust and very accurate varactor model has been
developed and employed in our recent designs. Proper calibration and de-embedding techniques are of crucial
importance as a starting point. Important enhanced characteristics of the modeling methodology include:
• precise characterization of the packaged varactor
through the use of a high performance microwave test
fixture, up to at least the fourth harmonic of the maximum intended oscillation frequency. Proper calibration and de-embedding techniques are of crucial importance all around.
• improved non-linear model of the I-V characteristics in
the low-forward bias region
• improved non-linear model of the C-V characteristic
over an extended tuning range
Figure 4 · Measured and modeled S21response for the
dual shunt capacitor configuration on 14 mil-thick FR4.
Results include measurement data (blue line), model
response using substrate-scalable model set-up for the
14 mil-thick substrate (red circles), model response
using substrate-scalable model set-up for a 24 milthick substrate (black squares) and response using
simple series L-C equivalent circuit (green triangles).
Figure 5 · Measured (lines) and model (lines+markers)
S
21
response for a 15 nH surface mount 0402 inductor in
a series 2-port configuration. Results are shown for test
fixtures on 5 mil-thick FR4 (red circles) and 31 mil-thick
FR4 (black squares).
Figure 6 · Measured forward loss factor (1–|S11|2–
|S
21
|2) and reverse loss factor (1–|S22|2– |S21|2) for a
15 nH surface mount inductor. Results are shown for
test fixtures on 5 mil-thick FR4 red lines) and 31 milthick FR4 (black lines). The thick lines correspond to the
forward loss factor.
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50 High Frequency Electronics
High Frequency Design
RF COMPONENT MODELS
• consistent model parameter
extraction of the package related
parasitic elements of the model.
Packaged switching diodes are
also very common devices used in
modern communication applications.
Among those, PIN diodes are often
preferred for their unrivaled switching and power handling performances in the microwave range.
Similar type of improvements have
been employed in relation to the nonlinear PIN diode model, resulting in
some excellent performance in
describing both the ON and the OFF
state of the device, as well as the
transition between these states.
Prediction accuracy of the non-linear
model for important characteristics
such as the insertion loss has been
brought down to values of around 0.1
dB, within the relevant operating
ranges.
A comparison between measurement and simulation results for I-V,
C-V and small-signal S-parameters of
a commercial, packaged varactor
diode is shown in Figure 7. The
broadband S-parameters are mea-
sured and simulated at a number of
tuning voltages across the relevant
tuning range.
As illustrated in Figure 8, the
need to account for substrate-related
effects is as critical in packaged varactor diodes as it is for passive RLCtype components. This diode (a different part than that discussed above)
was characterized using test fixtures
printed on 5 and 59 mil-thick FR4. A
non-linear, substrate-scalable model,
utilizing physically-motivated equivalent circuit parameter equations
similar to those for the inductor and
capacitor, was then extracted using
S-parameter data from both substrates at multiple bias conditions.
The resulting model becomes a versatile tool for general circuit simulation
in a variety of substrate environments.
Characterization and Simulation
of the Test Circuits
Simple series and shunt tank circuits, commonly used in VCO
designs, have been designed on FR4
boards to test the characterization,
modeling and simulation methodology employed. Circuits have been specially designed for accurate probed
characterization, by adding probing
pads and appropriate de-embedding
structures. Measurements were
taken at a number of tuning voltage
values. Finally, the circuits were
implemented in the circuit simulator
(ADS), with all the circuit components (SMT capacitors and inductors,
packaged varactor and switching
diodes, microstrip resonators and all
other incidental layout structures)
being consistently modeled and
implemented in the final simulated
circuit.
A simplified ADS schematic of one
of the tank circuits analyzed, including some of the relevant new models
is presented in Figure 9.
Comparative results between the
measurement and simulation data at
two different tuning voltages are
shown in Figures 10(a) and (b). The
Figure 7 · I-V (a) and C-V (b) models for varactor diodes. Measurement
(circles) vs simulated (thick continuous line) small-signal characteristics
(c) at different tuning voltages (Vtune = -0.5, –1.5, –2.5V).
Figure 8 · Measured (markers only) and simulated (lines only) S11for a surface mount varactor diode on 5 mil-thick FR4 (red) and 59 mil-thick
(black) substrates. (–2 V reverse bias shown on the left; +0.5 V forward bias
shown on the right.)
Page 5
September 2002 51
accuracy of the present simulations
as well as the marked improvement
from the situation when existing
models for various components are
used, are evident from these graphs.
Similar results have been obtained
for other types of tank configurations,
and the methodology is currently
extended to the characterization and
simulation of other sub-circuits such
as the oscillator and buffer circuits.
Summary
This paper has presented a relatively broad discussion on general
considerations of surface mount LC
and diode modeling. The main purpose was to demonstrate the high
degree of simulation accuracy that is
possible over a broad frequency range
when careful characterization and
modeling techniques are used. Some
circuit examples, both simple and
somewhat complex, pointed out the
errors that can occur when less accurate models are used.
Acknowledgements
The authors would like to thank
Chris Gibby, Thomas Cooney and
Martin McGahon from TDK
Electronics Ireland for their help in
the implementation of the diode models in ADS and in the realization of
the test circuits.
Author Information
Vivi Cojocaru is with TDK
Electronics Ireland, Ltd., and may be
contacted via e-mail at: cojocaru
@tdk.de. The remaining authors are
affiliated with Modelithics,Inc.,
13101 Telecom Dr., Suite 105, Temple
Terrace, FL 33617 (Web site:
www.modelithics.com). Modelithics
develops measurement-based models
for high frequency/high speed simulation. Questions or comments on
this article should be addressed to
either Dr. Thomas Weller, e-mail:
tweller@modelithics.com, tel: 813866-6335; or to Dr. Lawrence
Dunleavy, e-mail: ldunleavy@modelithics.com, tel: 813-866-6335.
References
1. S. Yukio, et al., “High-frequency
measurements of multilayer ceramic
capacitors,” IEEE Trans. MTT,pp.7-
13, February 1996.
2. E. Benabe, H.Gordon and T. Weller,
“Substrate-Dependent Air Wound
Inductor Model in the DC-4 GHz
Range,” 54th Conference on
Automatic Radio Frequency Techniques (ARFTG), December 1999.
3. B. Lakshminarayanan, H. Gordon
and T. Weller, “A Substrate-Dependent
CAD Model for Ceramic Multi-Layer
Capacitors,” IEEE Trans. MTT,pp.
1687-1693, October 2000.
4. S. Gross, L. Dunleavy, T.Weller, and
B. Schmitz, “PC Board Characterization Using Accurate Hybrid Probing
Techniques,” 54th Conference on
Automatic Radio Frequency Techniques (ARFTG), December 1999.
Figure 10 · Comparison between measured S-parameters (circles) and
ADS simulation using the current enhanced methodology (thick continuous line). The thin continuous line represents the simulation result when
using the existing ADS diode and lumped passive models. (a) Vtune= –0.5
V, (b) Vtune = –1.5 V.
Figure 9 · Simplified version of the ADS schematic of a typical tank circuit
used in our tests. It includes some of the new ADS models for chip capacitors and inductors and for packaged varactor and PIN diodes.
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