New Software Enhances the Design and Analysis of Tunable RF and Microwave
Circuits

By Dale D. Henkes,
ACS

Modern EDA (Electronic Design Automation) software has
evolved over the years to provide some very powerful tools for the design and simulation
of almost any kind of RF and microwave circuit or system.  One aspect of current EDA software that
makes it so powerful is the speed at which it can perform calculations, rendering
simulations and detailed analysis reports in record time.  Another aspect of the power and utility
of this kind of software lies in the richness of the tools, capabilities and
features that the software provides.  Software packages with expanded toolsets,
multi-function modules and collection of programs oriented toward performing
different but related phases of the workflow are referred to as software suites.

These full featured EDA software suites can be complex,
making it difficult to find and use many of the less common features.  Sometimes even relatively experienced
users are not aware of all the features and capabilities contained in the
software.  This article will employ
a microwave filter design example to highlight some of the less commonly used
EDA tools and methods that can, never the less, significantly enhance circuit
analysis.

RF and microwave circuit simulation programs commonly
display the circuit’s s-parameters (or quantities related to these
s-parameters) in the frequency domain.
The more advanced circuit simulator will include additional methods of
analyzing the circuit or viewing the resulting simulation data.  In addition to the traditional frequency
response analysis, this article will demonstrate a few other tools and
simulation methods for the enhanced design and analysis of RF and microwave
circuits.  The LINC2 EDA software
suite from ACS (Applied Computational Sciences, Escondido, CA)
will be used to demonstrate the following:

·
Circuit
Parameter Sweeps/Variable Sweeps

A circuit or component parameter
can be swept through a range of values by assigning a variable to the parameter
and performing a variable sweep.
The circuit response can be viewed against the variable at any fixed
frequency point.

·
User
Defined Equations

New component models can be created
or existing component models modified by user defined equations that formulate
new relationships between variables and circuit parameters.

·
Special
Output Functions for Post Processing Simulation Data

These special intrinsic functions provide
new ways of processing and viewing simulation results.  For example, finding and tracking the frequency
point at which the maximum value of a circuit response occurs or tracking the
frequency point for zero transmission phase during a variable parameter sweep.  Information related to the frequency at
which maximum transmission occurs is particularly useful for analyzing tunable
filters, while information about the frequency at which zero transmission phase
occurs is useful for the open loop analysis of oscillator circuits.

In the following example, the design of a tunable bandpass
filter will be analyzed with these special simulation and analysis tools.  The example will start with the usual
frequency response analysis (the results of which are displayed in Figure 2)
and then contrast this view of circuit performance with the additional
visualization methods.

Tunable
End-Coupled Microstrip Bandpass Filter Example

The general design of the capacitive gap end-coupled
microstrip bandpass filter is given in [1].  The end-coupled resonator topology was
chosen for simplicity of tuning.  It
is easy to place shunt tuning capacitors between the ends of the microstrip
resonators and ground using surface mount technology.  Ideally, the coupling capacitance
between resonators should also be tuned.
The consequences of not simultaneously tuning both the resonators and
the coupling between them is that the insertion loss and relative bandwidth
will vary with frequency as the filter is tuned.  The following simulation results show
that these effects were observed to a small degree.  The insertion loss varied by only 1.5 dB
over a 40 % tuning range while the relative bandwidth remained nearly
constant.

The schematic, after optimization for a center frequency of
2.5 GHz is shown in Figure 1.  In
Figure 1, a microstrip gap (MGA1) is used to capacitively couple the two
resonators, while C5 and C6 couple the signal in and out of the filter
respectively.  All physical
dimensions in the schematics are in mm (millimeters).

In some designs, C5 and C6 could also be implemented as
microstrip gap capacitors.  However,
because the required capacitance is so large in this case, the gap would be too
narrow to fabricate reliably unless a multi-gap structure such as the
interdigital capacitor is used [2].

C1 through C4 are variable capacitors that load the ends of
each resonator strip to vary the effective electrical length of the resonator
for tuning purposes.  The tuning
capacitors (C1-C4) may be implemented using varactor diodes.  As the tuning capacitance increases, the
effective resonator length is increased, resulting in the bandpass filter
shifting to a lower frequency [3].

Figure 1,
End-Coupled Microstrip Bandpass Filter

Using Variables in
Simulation for Tuning Control

In LINC2 a variable can be placed on the schematic page and
assigned to as many component parameters as needed.  In this example, the variable CVar is
given a nominal (initial) value of 0.707 pF and assigned to capacitors C1
through C4.  In this way all four
tuning capacitors are ganged together and tuned simultaneously with the same
value, as would be the case with four identical varactor tuning diodes all
driven with the same (variable) bias voltage.

Figure 2 shows the filter response centered at 2.5 GHz for
CVar = 0.707 pF.  The markers show
the numerical values for the magnitude of S21 (M21 in dB) and input return loss
(M11 in dB) for the filter centered at 2.5 GHz.  Figure 2 also shows the responses for
CVar tuned to 1.21 pF and 0.425 pF, resulting in bandpass responses centered at
2100 MHz and 2850 MHz respectively.

Determining the tuning capacitance range required to tune
the filter’s response between 2 GHz and 3 GHz is easy.  This is accomplished using LINC2 by
simply selecting CVar from the Tune menu and pressing the up or down arrow keys
to increase or decrease its value.
The filter’s response moves across the LINC2 Graph Window in real
time as CVar is tuned interactively.
Noting the value of CVar when the filter is tuned to 2 GHz and then
again when it is tuned to 3 GHz yields the range of the tuning capacitance
required to tune the filter between these two extremes.  The result is a tuning capacitance range
between 0.3 pF and 1.4 pF.

Figure 2,
The Tunable Filter’s Frequency Response for Three Selected Values of CVar

Using Swept Variables
in Simulations

Instead of manually tuning a component parameter using a variable
as in the previous section, the variable can be set up to automatically sweep
over its entire range of values while the circuit response is plotted as a
function of the swept variable.  As
shown in Figure 3, the LINC2 program provides a checkbox for enabling a
variable parameter sweep, thus turning an ordinary variable into a swept
variable.  The parameters of a swept
variable are its nominal value, the starting value, the stop value and number
of sweep points.

Figure 3,
LINC2 Swept Variable Setup

Special Output
Functions and Variable Parameter Sweeps

The LINC2 program provides a number of special built-in
functions for post processing of the simulation data.  This example will employ the Maximum function for plotting the
bandpass filter’s center frequency as a function of the tuning
capacitor’s swept capacitance value (CVar).  The way this function works is that for
each value of the swept variable the program finds the frequency for which the
selected data is a maximum.  This
frequency data is then plotted as a function of the swept variable.

The data of interest for the bandpass response is the
maximum value of S21 which occurs within the passband of the bandpass
filter.  Since the S21 maximum value
(peak in the bandpass response) shifts in frequency as the swept variable
(CVar) is stepped through its values, plotting the frequency of maximum |S21|
against this variable will plot out the filter’s tuning response.  This unique LINC2 function produces the
filter’s tuning response to the tuning capacitance CVar as shown in
Figure 4.

Figure 4,
Tunable Bandpass Filter's Frequency Response as a Function of the Tuning
Capacitance

Comparing Figure 4 to Figure 2, Figure 4 is a much clearer
way to display the tunable filter’s response to the tuning capacitance
value.  In Figure 4 the
filter’s tuning characteristics are captured and displayed in a simple
easy to read graphical format.

Using Equations to
Create New Circuit Models

The tunable filter schematic in Figure 1 uses a variable to
control the tuning capacitance.
However, what is needed is a physical method of controlling the tuning
capacitance.  Varactor tuning diodes
can accomplish this.  The
diode’s capacitance as a function of its tuning voltage can be simulated
by using a user defined equation in LINC2.
A useful approximation for the varactor diode’s voltage to
capacitance transformation is given by [4]:

Equation 1)       C(VR)
= CJ0/(1 + VR/VJ)^M + CP, where CJ0
is the diode’s zero-bias junction capacitance, VR is the
applied reverse DC bias voltage, VJ is the junction potential, M is
a device dependant constant called the grading coefficient, and CP
is the device package capacitance.

Using an equation to model the diode may be preferred over
using a built-in schematic model because it defines the function explicitly and
there is almost no limit to the model details and complexity that can be
embodied in the equation.  Moreover,
it is easy to edit the equation model to accommodate the characteristics of a
different device.  Figure 5 shows a
LINC2 schematic representation of the varactor tuned filter.

Figure 5,
Varactor Tuned Bandpass Filter Schematic

In the schematic (Figure 5), the variable CVar (from Figure
1) has been replace with the equation CVar that models the varactor’s
capacitance as a function of its DC bias voltage.  The equation uses the model parameters
given in [4] for the SMV1248 diode.
The diode model parameters were extracted from measured CV(VR)
data.  More complete models may
include at least some series resistance and package inductance and these
parasitic components could also be included explicitly on the schematic.

In Figure 5, L1 through L4 feed the DC tuning voltage
(Varactor_V) to the four tuning varactors C1 through C4 (modeled by CVar).  If the only concern is providing DC to
bias the varactor diodes then L2 and L3 are redundant.  L1 alone is sufficient to feed the DC
tuning voltage to C1 and C2 through microstrip line MLI1.  Likewise, L4 is sufficient to feed DC to
C3 and C4 through microstrip line MLI2.
However, placing all four inductors in the circuit ensures that each
varactor  tuning capacitor combined
with the inductance (and parasitic capacitance) of the inductor produce nearly
the same capacitance at each end of the microstrip resonators.  A simulation was run with only L1 and L4
present with the undesirable result of reduced tuning range.

A simulation run on the circuit in Figure 5 will produce a
traditional frequency response plot as in Figure 2 with the exception that,
instead of varying the capacitance directly, the filter is tuned by varying the
varactor voltage (via the Varactor_V variable in the schematic).  However, the LINC2 simulator also
produces the characteristic tuning plot shown in Figure 6.  This graph window simultaneously plots
the filter’s tuning response and the equation (CVar) that describes the
tuning diode’s capacitance, both as a function of the varactor DC bias
voltage (Varactor_V).

Figure 6,
The Bandpass Filter's Tuning Characteristics as
a Function of Varactor Voltage

Comparing the tuning frequency response in Figure 6 to that
in Figure 4, the following observations can be made.  The tuning frequency slope in Figure 4
is negative because the tuning capacitance is increasing to the right.  However, in Figure 6 the tuning
frequency slope is positive because it is plotted as a function of the varactor
voltage.  As the varactor voltage
increases to the right, the varactor capacitance decreases (and the filter
passband moves higher in frequency).

Figure 6 indicates that the filter’s tuning frequency is almost a linear
function of the tuning voltage whereas the tuning diode’s capacitance is
a non-linear curve characteristic of the exponential nature of the
diode’s voltage to capacitance relation (Equation 1).  With this plot we can see at a glance
that the filter can be tuned between 2000 MHz and 3000 MHz with a tuning
voltage ranging between 3.59 volts and 5.76 volts.  The corresponding tuning capacitance
(per diode) will range between 1.66 pF and 0.46 pF respectively.  Markers placed on the plots have their
numerical values displayed at the top of the graph for various values of
varactor voltage.

Tunable Bandpass
Filter Summary

This completes the analysis of the tunable bandpass
filter.  The LINC2 program provides
new ways to analyze and characterize the filter’s response to tuning
control.  For example, in Figure 6
the linearity of the filter’s tuning control can be seen at a glance.  The required control voltage range and
tuning capacitance range can also be immediately determined from the graph.

When a user defined equation is part of a LINC2 schematic
(such as equation CVar in Figure 5), the equation can be plotted simultaneously
on the same graph along with the simulation data.  For example, in Figure 6 the plot of
equation CVar shows the tuning diode’s CV(VR)
characteristics and how they relate to the overall tuning characteristics of
the filter.

In addition to these new LINC2 output functions and analysis
techniques, the conventional frequency sweeps of S21 and S11 (as in Figure 2)
yield additional important information about the filter and its response to
tuning.  For example, in Figure 2 it
can be seen that the bandwidth grows with frequency as the filter is tuned, but
the relative bandwidth (as a percentage of the center frequency) remains
relatively constant.  Also, Figure 2
indicates that the insertion loss and return loss improve with frequency.  The insertion loss ranges from 2.5 dB at
the low end of the tuning range to approximately 1 dB at the high end.

The LINC2 Software
Suite

LINC2 is a high performance RF and microwave design and
simulation program from ACS.  In
addition to schematic based circuit simulation, optimization and statistical
yield analysis, LINC2 Pro includes many value-added features for automating
design tasks, including circuit synthesis.

LINC2 directly interfaces to leading RF and microwave design
suites, allowing it to be used stand-alone or by leveraging its capabilities
with those of other major packages.
LINC2 offers exact circuit synthesis, schematic capture, circuit
simulation, circuit optimization and yield analysis in a single affordable
design environment.  More
information about LINC2 can be found on the ACS web site at www.appliedmicrowave.com.

References

Microwave
Filters, Impedance-Matching Networks, and Coupling Structures, G.
Matthaei, L. Young, and E.M.T. Jones, Artech House, © 1980, Page 440,
Section 8.05, Capacitive-Gap-Coupled Transmission Line Filters.

Transmission
Line Design Handbook, Brian C. Wadell, Artech House 1991, page 420, Section
7.6, Interdigital Capacitor.

Microwave Solid State
Circuit Design, 2nd Edition, Inder Bahl and Prakash Bhartia,
Wiley 2003, pp. 103-105, Section 3.4.6, Tunable Resonators.

Application
note APN1004, Alpha Industries.

http://www.highfrequencyelectronics.com/July2008/HFE0708_OE.pdf

Author information

Dale D. Henkes is the
owner of Applied Computational Sciences (ACS), LLC., Escondido,
California,
and has more than 25 years of professional experience in RF design/electrical
engineering.  He earned his B.S.
degree in engineering at Walla
Walla College,
College Place, Washington.  He is a member of the IEEE Microwave Theory
and Techniques Society and the author of a dozen articles in prominent trade publications.  He may be contacted via email at: [email-masked].