EDA Simulation Techniques that Enhance Insight into Circuit Behavior= and Performance

New Software Enhances the Design and Analysis of Tunable RF and Mic= rowave 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 a= nd 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, ren= dering simulations and detailed analysis reports in record time. Another aspect of the power and uti= lity of this kind of software lies in the richness of the tools, capabilities and features that the software provides. Software packages with expanded too= lsets, multi-function modules and collection of programs oriented toward performing different but related phases of the workflow are referred to as software su= ites.

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 experien= ced users are not aware of all the features and capabilities contained in the software. This article will e= mploy a microwave filter design example to highlight some of the less commonly us= ed EDA tools and methods that can, never the less, significantly enhance circu= it 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.&nbs= p; The more advanced circuit simulator will include additional methods = of analyzing the circuit or viewing the resulting simulation data. In addition to the traditional fre= quency 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 softw= are suite from ACS (Applied Computational Sciences, Escondido, CA) will be used to demonstrate the following:

· Cir= cuit Parameter Sweeps/Variable Sweeps

A circuit or component para= meter can be swept through a range of values by assigning a variable to the param= eter 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 formul= ate new relationships between variables and circuit parameters.

· Spe= cial Output Functions for Post Processing Simulation Data

These special intrinsic fun= ctions 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 t= he frequency point for zero transmission phase during a variable parameter swe= ep. Information related to the frequen= cy at which maximum transmission occurs is particularly useful for analyzing tuna= ble filters, while information about the frequency at which zero transmission p= hase occurs is useful for the open loop analysis of oscillator circuits.

In the following example, the design of a tunable band= pass filter will be analyzed with these special simulation and analysis tools. The example will start with the us= ual 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.&n= bsp; 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 s= how 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 frequen= cy 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. Ho= wever, 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 en= ds of each resonator strip to vary the effective electrical length of the resonat= or for tuning purposes. The tuni= ng capacitors (C1-C4) may be implemented using varactor diodes. As the tuning capacitance increase= s, the effective resonator length is increased, resulting in the bandpass filter shifting to a lower frequency [3].

Figure SEQ Figure \* ARABIC 1, End-Coupled Microstrip Bandpass Filter

Using Variabl= es in Simulation for Tuning Control

In LINC2 a variable can be placed on the schematic pag= e 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 f= our 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 =3D 0.707 pF. The marker= s 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 centere= d at 2100 MHz and 2850 MHz respectively.

Determining the tuning capacitance range required to t= une 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 r= eal 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 SEQ Figure \* ARABIC 2, The Tunable Filter’s Frequency Response for Three Selected Values of = CVar

Using Swept V= ariables 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 swe= ep 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 numb= er of sweep points.

Figure SEQ Figure \* ARABIC 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 tha= t for each value of the swept variable the program finds the frequency for which = the selected data is a maximum. T= his 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 |S2= 1| against this variable will plot out the filter’s tuning response. This unique LINC2 function produce= s the filter’s tuning response to the tuning capacitance CVar as shown in Figure 4.

Figure SEQ Figure \* ARABIC 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 cle= arer 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 Equatio= ns to Create New Circuit Models

The tunable filter schematic in Figure 1 uses a variab= le to control the tuning capacitance. However, what is needed is a physical method of controlling the tuni= ng capacitance. Varactor tuning = diodes can accomplish this. The diode’s capacitance as a function of its tuning voltage can be simula= ted 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(V_R) =3D C_J0/(1 + V_R/V_J)^M + C_P, whe= re C_J0 is the diode’s zero-bias junction capacitance, V_R is the applied reverse DC bias voltage, V_J is the junction potential, M= is a device dependant constant called the grading coefficient, and C_{P
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. Mor= eover, it is easy to edit the equation model to accommodate the characteristics of= a different device. Figure 5 sh= ows a LINC2 schematic representation of the varactor tuned filter.

Figure SEQ Figure \* ARABIC 5, Varactor Tuned Bandpass Filter Schematic

In the schematic (Figure 5), the variable CVar (from F= igure 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 parame= ters given in [4] for the SMV1248 diode. The diode model parameters were extracted from measured C_{V(V_R)
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).<= span style=3D'mso-spacerun:yes'> If the only concern is providing D= C 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.&nb= sp; However, placing all four inductors in the circuit ensures that each varactor tuning capacitor com= bined with the inductance (and parasitic capacitance) of the inductor produce nea= rly 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 produ= ce 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 p= lots the filter’s tuning response and the equation (CVar) that describes t= he tuning diode’s capacitance, both as a function of the varactor DC bias voltage (Varactor_V).

Figure SEQ Figure \* ARABIC 6, The Bandpass Filter's Tuning Characteristi= cs 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 Figu= re 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 vara= ctor voltage. As the varactor volt= age 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 lin= ear 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 gla= nce 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 capacitan= ce (per diode) will range between 1.66 pF and 0.46 pF respectively. Markers placed on the plots have t= heir numerical values displayed at the top of the graph for various values of varactor voltage.

Tunable Bandp= ass Filter Summary

This completes the analysis of the tunable bandpass filter. The LINC2 program pro= vides new ways to analyze and characterize the filter’s response to tuning control. For example, in Figu= re 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 schema= tic (such as equation CVar in Figure 5), the equation can be plotted simultaneo= usly on the same graph along with the simulation data. For example, in Figure 6 the plot = of equation CVar shows the tuning diode’s C_V(V_R) characteristics and how they relate to the overall tuning characteristics of the filter.

In addition to these new LINC2 output functions and an= alysis 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 Figur= e 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, Fi= gure 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 Sof= tware 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

Author inform= ation

Dale D. Henke= s is the owner of Applied Computational Sciences (ACS), LLC., = Escondido, California, and has more than 25 years of professional experience in RF design/electric= al engineering. He earned his B.= S. degree in engineering at = Walla Walla College<= /st1:place>, College Place= , Washington. He is a member of the IEEE Microwa= ve Theory and Techniques Society and the author of a dozen articles in prominent trad= e publications. He may be contacted via email at: = henkes@appliedmicrowave.com= .