JUser: :_load: Unable to load user with ID: 6
Print this page

Passive (Lumped Element) Filter Module



Feature Comparison Summary
FilterSolutions®and Filter Quick™ are Windows ® based software programs for the synthesis and analysis of electronic filter circuits. The modules available in these programs comprise: Passive FilterDistributed FilterActive FilterDigital FilterSwitched Capacitor, and Zmatch™ (used for creating impedance matching circuits). FilterQuick, which is included in FilterSolutions. offers a simplified interface for initiating designs which are then usable with either the FilterQuick intreface or FilterSolutions' advanced feature sets.
Licenses for FilterSolutions can be purchased as "FilterSolutions-PRO™" which contains all the modules. Alternately, the modules can each be licensed individually.
The "PRO" licenses include the Zmatch Impedance Matching Circuit module. The Distributed Element License will include the Distributed Element version of Zmatch, and the Passive Module will include the Lumped Element version of Zmatch.
FilterSolutions and its individual modules are available in Network license configuration,or  MAC Address-Locked or "Dongle-Locked single-user licenses.
FilterFree is a "freeware" version of FilterSolutions with minimal functionality (DOWNLOAD LINK). FilterFree analysis is limited to 3rd Order Analog designs or to 10 tap FIR designs. All analyses in FilterFree are limited to ideal transfer functions.
Lumped Element Filter Synthesis:
Balanced and Unbalanced Filters
LC circuit synthesis: Single Terminated, Unequally Terminated, and Equally Terminated Filters
User modified Time, Frequency, Impedances, Reflection Coefficients and Transfer Functions
Large order synthesis of up to 20 poles
All-Pass Sections, Balanced or Unbalanced, to support Delay Equalizers
Allows random element updates for Monte Carlo analyses
Amplitude Equalization for equally and unequally terminated filters
Automatic Inductor and Capacitor Tuning.
Automatic Norton Transformations to Match Band-Pass Terminations
Band-Pass Filters Implemented from Cascaded High and Low-Pass Sections
Create Impedance matching networks with built-in Zmatch program**
Cross-Coupled Resonator narrow band (Chebyshev I and Elliptic) with minimum # of couplings
Coupled Resonator Band-Pass Filters.
Detailed component sensitivity analyses including plots and tables
Diplexers, Triplexers, and Band-Pass Diplexers with Reflection Compensation
Equal Inductor Band-Pass Filters
Finite Q Compensation for Single and Unequally Terminated Filters.
Minimum Inductor Zigzag Filters including odd-order; minimizing Inductor count
General Norton (Single and Dual), PI->T, and T->PI Conversions
Optimization for Complex Terminations
Parasitic Node Capacitance Compensation for Elliptic, Hourglass, and Chebyshev II Band-Pass
Tubular Band-Pass Filters
Easily modify, add or delete elements including Resistors, Capacitors, Inductors, LC pairs
Locked or Floating License
Multi-Band Filter Synthesis*
Third Party Tool Connections:
Direct export to AWRCorp Tools (where available)
Touchstone Z, Y and S Parameters
Direct export to CST Microwave's STUDIO SUITE
Available Analyses and Output:
Easy-to-Read Exportable Graphical Circuit Displays
Exportable Text Netlists and Transfer Functions
Frequency, Impedance and Time analyses
Finite Q Analysis (all filters)
Off-Axis Quadruplet Zero placement for delay equalization
User modified Time, Reflection, Impedance, and Transfer Function Analysis
User modified Frequency and S-Parameter analysis
Export Transfer Functions of modified filters
Component Sensitivity Analyses and Plots
Automatically update parts to Nearest 1%, or 5% standard part
Create Impedance matching networks with built-in Zmatch program
DCR and ESR Parasitic Analysis for lumped elements in Composite Filters
Maintain up to 3 Standard Parts Lists, and automatically select nearest standard parts
Modify, Add, or Delete Resistors, Capacitors, Inductors, LC pairs, and All-Pass Sections
Smith Chart and Jones Chart outputs
* Multi-Band Filter networks are defined as a cascade of an arbitrary number of passbands and stopbands in a single lumped LC, active or digital IIR filter
** The Zmatch program allows for matching filter circuits to any arbitrary real or imaginary, input or output impedance values

Lumped LC Filter Solutions

FilterSolutions,®  and "FilterQuick,™ support a wide variety of Lumped Element Filter designs. Filters may be singly terminated, or doubly terminated, with equal or unequal load and source resistances.  Diplexers are supported for all filter types. Finite Q analysis is supported for all Lumped Element Filters.
All-pass sections are supported to create Delay Equalizers.  Finite Q compensation is supported for singly terminated filters and doubly terminated filters with unequal load and source resistances.  Amplitude compensation is provided for doubly terminated filters with finite Q. All synthesized filters are checked for proper frequency response prior to being displayed.  All filters are displayed in graphic, easy to read formats, with a netlist display in a text format, ready for AC or transient analysis. Filter Solutions, and FilterQuick create both balanced and unbalanced filters.
In order to generate singly terminated filters, a source resistance of "0" is entered in the source or load resistance entry field. To generate an equally terminated filter, the same number is entered for both source and load resistance.
The designer may choose first element shunt or first element series topology.  For odd order low pass and high pass filters, the designer may select the “Minimum Inductors” switch to display the topology with the fewest inductors.
Lumped Element Circuit Displays
All FilterSolutions and FilterQuick graphic filter displays are user interactive.  It is possible to change the value of any component, add new components, or delete components. The user can then generate frequency, time, reflection, and impedance analyses on the modified filter, by simply passing the cursor over the component to be changed.
When the component is highlighted, a left click of the mouse changes the component, or a right click is used to add a component. Components may be set to specific values, changed by a fixed percentage, or set to nearest values in a Standard Parts List, or to nearest 1%, 5%, 10%, or 20% tolerance industrial standard part.
After a component is changed, it is highlighted in blue for easy visual reference.  If a frequency value changes as a result of the new element values, the new value is also is displayed in blue.
Refer to the Following Examples:

Changing, Adding, or Deleting a Filter Solutions Component
Adding components is useful for modeling parasitics or for evaluating the effect of other attached circuitry. The option is provided for LC pairs to automatically update the other component in the pair, so that the resonant frequency of the pair is maintained.  All -pass sections may be added by right clicking an element adjacent to the load or source Resistor, or by adding all-pass poles and zeros to the pole-zero plot.

Frequency, Reflection, Impedance, and Time Analysis

Each filter generated by the programs may have frequency, reflection, impedance, or time analyses performed by selecting the appropriate control on the circuit window.  Frequency, reflection, and impedance analyses include magnitude, phase, and group delay.  Time analyses include step, ramp, and impulse response.  By clicking the left mouse key at any circuit location a cursor with the frequency and trace information appears in the cursor window.
By clicking the right mouse key it is possible to add or delete permanent cursor traces.   These analyses include all user modifications made to the filter circuit.  When a filter has been modified by changing, adding, or deleting an element, (or if any elements are characterized with a finite Q), the "Ideal" analysis trace appears in dark blue for comparison purposes.  Attenuation due to the Source Resistor may be included or removed as desired by selection in the "Inc Gen Bias" box in the control panel. Examples are shown below:

Reflection Analysis

Finite Q and Other Reactive Element Parasitics

FilterSolutions and FilterQuick allow the installation of components with Finite Q, Series Resistance, or Parallel Resistance into the circuit.  (Series resistance for inductors is sometimes referred to as DCR, and for capacitors, ESR).  The specific filter frequency, reflection, impedance and time analyses will use the Q and resistances thus provided.  For comparison, a dark blue background trace will appear to indicate the ideal filter with infinite Q and 0 resistances.
Compensation for the degradation effects of finite Q and parasitic resistance may be provided by manually moving the pole locations in the pole/zero plot. (Note that the compensation is done in real time if the RTC box on top of the pole/zero plot is checked). The poles may be "stretched" along the real axis, and flattened slightly along the imaginary axis. This compensation methodology works reasonably well for singly terminated filters and largely unequal terminated filters.
In the case of filters whose source to load ratio is greater than 0.2 and less than 5.0, finite Q and parasitic resistance compensation is marginal.  Equally terminated filters may not be compensated for in this manner, but may be amplitude equalized. Singly terminated Finite Q compensation is done automatically by the programs if the "Q Comp" box is checked in the control panel.
Since the effect of finite Q is unique to each individual lumped circuit, the effects of finite Q are only included in the specific lumped element circuit being analyzed. The control panel analysis functions assume an infinite Q.
The following is an example of an 8th order Elliptic filter with uncompensated, manually compensated, and automatically compensated finite Inductor Q of 20. The cutoff frequency of the filter is 100 MHz.

Finite Q Elliptic Filter

Effect of Finite Inductor Q of 20
Following is the pole/zero plot that manually compensates the filter
Manual Finite Q Compensation
(Dark blue indicates uncompensated pole/zero positions)
Shown below is the resulting frequency response.

Manual Q Compensation Frequency Response
If "Q Comp" is selected in the lumped element control panel, the programs will automatically compensate for finite Q.
Following is the frequency response of the circuit with automatic compensation.

Automatic Finite Q Compensation

Coupled Resonator Filters

Coupled resonator bandpass filters are narrow band approximations of bandpass filters. The advantages of using coupled resonators rather than classical bandpass filters are the attainment of more desirable element values at high frequencies, and flexible element value selections.
Coupled Resonator Filters are a series of LC resonant pairs coupled by capacitors or inductors. Generally, Capacitors are chosen due to their lower cost and better performance. The programs allow the selection of one of the LC resonant element values, and will calculate the other element values needed to create the desired performance. FilterSolutions and FilterQuick support coupled resonators with and without end-coupling elements. This support allows greater flexibility in element value selection. Coupled Resonator Filters constructed without end-coupling require two less elements than those with end-coupling elements.
In order to create Bandpass Resonant Filters, one MUST select from among Gaussian, Bessel, Butterworth, or Chebyshev Type I filters classes.  Coupled Resonator Filters cannot be created from filters with stop band zeros. The lumped element circuit will appear with a check box in the tool bar for "Resonator". By selecting this choice a coupled resonant band pass filter will be displayed.  The first element of the filter will match the series/shunt selection in the lumped element control panel. If the selected passband is too wide for the filter topology, an error message will advise that a narrower passband is required.
When a Resonator Filter is created, the Resonator tool box is displayed in the upper right of the circuit window. A choice is offered between inductor or capacitor-coupled Resonators.  At this point, one may select new resonator element values. Capacitor coupled Resonators may show changes in the value of their Inductor.  In the same manner, Inductor coupled Resonators may show changes in their Capacitor values. One enters the desired inductance or capacitance value, then selects "Recalc" to update the filter.
(More information is available on the derivation of coupled resonator filters in "Microwave Filter, Impedance-Matching Networks and Coupling Structures", by Matthaei, Young, and Jones, ISBN 0-89006-099-1, pp. 427-434).
Coupled Resonator Example:
The following example is a classic 4th order Butterworth bandpass filter with a center frequency of 500 MHz, and a band width of 40 MHz.  Note that some Capacitor values are less than 1 pF, and some Inductor values are below 1 nH.
The following schematic is the series resonator Capacitor-coupled bandpass Classic Bandpass Filter
Filter: Capacitor values are now more reasonably in the low pF range, and all Inductor values are 10 nH. However, more Capacitors are required to build this filter.

Capacitor-Coupled Series Resonator Filter
The magnitude of the frequency response error is shown below. Dark blue baseline traces depict the true Butterworth response. The Yellow trace depicts the Coupled Resonator Filter response. Note that the error is only significant at frequencies with very high attenuation.

Resonator Coupled Frequency Error
Even-order Chebyshev II, Hourglass, and Elliptic filters support cross-coupled Resonator filters. 

Tubular Filters


Tubular Bandpass Filters are narrow band approximations of bandpass filters.  There are several advantages to using tubular filters compared to classic bandpass filters: Tubular filters result in more desirable element values at high frequencies, allow flexible element value selection, and have all nodes attached to a grounded capacitor.  Any parasitic node capacitance that results in the physical construction of the filter may be subtracted from the design value of the grounded capacitor connected to that node.  In most cases, the inductance values are adjustable.
Tubular filters consist of an alternating series of Inductors and Capacitors, with each node containing a grounded Capacitor.  The programs permit the synthesis of tubular designs, with or without a leading shunt Capacitor, and with the first series element being either an Inductor or a Capacitor.  A “Minimum Elements” selection also exists, minimizing the number of elements by skipping series Capacitors.  This “Minimum Elements” selection does have the disadvantage of a wider range of required Capacitor values.

The frequency response error is shown below.  Gray baseline traces depict the true Chebyshev response. The Blue trace depicts the Tubular Filter response.  Note that the error is only significant at frequencies that have very high attenuation response.

The option of selecting outer shunt Inductors exists in order to obtain a more symmetric tubular frequency response.

Delay Equalization

Tubular filters support both all-pass stages and bridged capacitor delay equalization, with bridge capacitors being the more efficient method with respect to the number of additional parts required.

Tubular with outer shunt Inductors

Tubular with Bridge Capacitor Delay Equalization

Zigzag Filters

Bandpass filters with stop bands (Chebyshev II, Hourglass and Elliptic) may have their Inductor count reduced through the use of a Zigzag Filter implementation. Zigzag Filters have the disadvantage of changing the original source resistance.  Equal resistance Terminations and single Terminations are not possible in the design of the Zigzag filter.  However, optimal reflections occur when the design source resistance is made equal to the design load resistance, then using the calculated source resistance.  Odd-order Zigzag filters are more efficient than Even-order Zigzags as they require fewer Inductors.
Select a band pass Chebyshev II, Hourglass, or Elliptic response to create a Zigzag Filter. A nonzero source resistance is required.  The selection box for “Zigzag” is shown on the lumped control panel.
Zigzag Filter Example
The following schematic is that of a 4th order classic Elliptic Filter. Note that there are five Inductors.

Classic Band Pass Filter
The following schematic is an example of an equivalent 4th order Zigzag Filter. Note that there are only four inductors, and the source resistance is no longer 50 ohms.  Even-order Zigzags require only n Inductors, where n is the order of the low pass prototype.

Even-order Zigzag Filter
The next schematic is an example of a 5th order Zigzag Filter.  Note that there are still only four inductors.  Odd-order Zigzags require only n-1 inductors, where n is the order of the low pass prototype. A classic 5th order Bandpass Elliptic Filter would require seven inductors.

Odd-order Zigzag Filter
For the cost of one additional capacitor, any odd-order or even-order Zigzag Filter may be designed with arbitrary source and load resistances. The filter schematic shown below has a response identical to that of the filter shown above, but is designed with equal 50 Ohm Terminations. Note the addition of the 42.26 pF Capacitor.  The filter remains a 5th order Band Pass Filter with only four inductors.

Equally Terminated Zigzag Filter
Zigzag Filters may be constructed with one or two inductor values at the cost of the addition of one or more capacitors.  However, high stopband attenuation or attenuation ratio is generally required to avoid negative element values.  Odd-order Zigzags may be constructed with one user-selected inductor value and arbitrary source and load impedances. The next schematic illustrates a 3rd order Zigzag with equal Terminations and two, user-selected, 50 nH Inductors.

Equal Inductor, Equally Terminated Zigzag Filter
Equal Inductor Zigzag Filters have the additional advantage of allowing every node to contain a grounded capacitor, making it easy to absorb any parasitic node capacitance. (For more information, refer to the note on parasitic node capacitance which follows.)

Amplitude Equalization

Filters with equal, or near equal Terminations, cannot compensate for a finite Q value by altering the pole/zero plot.  Since most of the performance degradation due to finite Q is at the “break” frequency, it is possible to reduce the magnitude of the frequency response everywhere except at the transition to produce an evenly attenuated frequency response.
In order to equalize the amplitude response of the filter, the Amplitude Equalization box allows the selection of "Series" or, "Shunt", or "Const.”  (This box is displayed whenever a Lumped Element Filter contains elements with finite Q.
The series and shunt Amplitude Equalizer produces filter designs with fewer components, but has the effect of making slight changes to the selected load impedance.  Therefore there may be slight degradation of the frequency response of the filter. The constant Resistance Equalized circuit contains more components, but load resistance is maintained, and the performance of the filter is not degraded.
The Amplitude Equalizer element values are changeable, just as are all other element values in the filter.  One may adjust the values given for any particular amplitude equalization effect.
The addition of any of the following RLS circuits at the end of the filter creates amplitude equalization for the filter circuit:

If the resonant frequency of the LC tank circuits is set to the filter break frequency, then attenuation is minimized at the break frequency and increased at all other frequencies. If the Q of the LC tank is set properly, an approximation of an attenuated, infinite Q, frequency trace will result.
In the case of Bandpass and Band Stop Filters, two break frequencies exist.  Therefore, two LC tank sections are required as shown in the diagram:

The effect on a Low Pass Elliptic Filter with Inductor Q's of 40 and Capacitor Q's of 150 is seen below. The dark blue trace is the ideal response. The yellow trace is the equalized, finite Q, response.
The following graphs depict the equalization effect of finite Q on a sixth order Elliptic Low Pass Filter, with and without amplitude equalization. The dark blue trace shows the ideal filter. The yellow trace is the actual filter with finite Q effects.  The filter shown has inductor Q's of 40 and capacitor Q's of 150.

Finite Q Effects With and Without Amplitude Equalization

Balanced Filters

FilterSolutions and FilterQuick support both balanced and unbalanced lumped element Filters. Many applications require balanced circuits due to their better noise immunity characteristics.  An unbalanced circuit can be transformed into a balanced circuit by cutting the series inductor values in half and placing an identical inductor in the bottom.  Continuing, one doubles the value of the series capacitors, and places an identical capacitor in the bottom.  All parallel elements would remain unchanged.  All-pass elements have different topologies for balanced and unbalanced structures. (See the All-Pass section below, for illustration of these topologies).
The entire Lumped Element circuit may be balanced by checking the "Balance" box above each Lumped Element Filter schematic.  Individual elements, LC tank pairs, or all-pass sections may be designated as balanced or unbalanced by the use of the right mouse key.
As an Example:

Balanced and Unbalanced Lumped Element Filters

Modified Filter Transfer Functions

In most cases, the modification of filter elements will result in the calculation of a new transfer function. The programs will allow viewing or exporting the new function to the Windows clipboard. The Q of the elements is linearized about the frequency displayed, next to the LC tank elements, or the cutoff or center frequency of the filters for other elements. The F(S) key above the circuit display will perform this function.
The format of exported transfer functions is in a form readable by Matlab and Matrix-x. For details, see the documentation which follows, for “Other Applications” 
Net Lists
When "Net List" is selected in the circuits control bar, the filter’s net list is shown in a text window. The net list is set up for an AC and transient analyses of the load resistance; and is ready to plug into any application that uses net lists. When finite-Q is selected, the parasitic resistances are included in the net list. Resistance values are based upon the resonant frequency of LC pairs; and the cutoff or center frequency for all other components.  Coupled coils are modeled with a set of "T" inductors, with a negative inductor in the center. (The pulse source is commented out in order to prevent conflicts with the AC source.  Selecting "Netlist" again removes the net list window.
The net list may be printed, copied to the Windows clipboard, or saved to a text file. Individual element values may be selected and copied to the Windows clipboard for ease in retrieving component values for other applications.  If nothing is selected when using the “Copy” function, then everything in the net list will be copied.
We show below, a FilterSolutions schematic and its net list:

Standard Parts Lists

FilterSolutions and FilterQuick provide flexible means to update Lumped Element Filter component values with the nearest value from a user selected Standard Parts List, or to the nearest 1%, 5%, 10%, or 10% standard industrial value.  Up to three standard parts databases can be maintained in the program.  If more than three parts lists are needed, they may easily be maintained in another text or word processing document and copied or pasted into or out of the program.
After left clicking on an element in a filter display to update a component value to the nearest value in the parts list, select "Parts" in the selection box in Change Control Panel, then select OK.
Lumped Element Filters may have individual elements, or all like elements, set to the nearest standard value from the selected database or industrial parts list. The checkbox at the bottom of the Change Control Panel determines if one or all elements are updated.
The upper part of the programs’ standard parts window is shown below with some sample standard parts.

All-Pass Elements

Lumped all-pass elements are created with one of four element combinations.  Element values are all functions of Q and ωo- of the all-pass section. All lumped implementations in the programs have the pole in the left half plane.  Lumped all-pass sections must be placed adjacent to a Termination Resistor, or another all-pass that is adjacent to a Termination Resistor. Some all- pass elements require coupled coils.
The lumped element implementations for first and second all-pass stages are:

Unbalanced and Balanced All-Pass Sections
Of the two solutions for Q>1, the solution to the right is normally used as it has fewer inductors. Occasionally, the shunt capacitor is excessively large. In such cases, the solution to the left is used.
The programs also provide balanced all-pass lattice sections. The translation from unbalanced T's to balanced lattice all-pass sections are shown below. One may easily switch between balanced and unbalanced by right clicking an element in the all-pass section, then selecting the "Balance 1", "Balance 2", or "Unbalanced" check boxes.

Balanced All Pass Lattice Sections

Monte Carlo Analyses

A Monte Carlo statistical analysis may easily be performed visually to see the effect of statistical element value error on filter frequency, reflection, impedance, or time response.  Graphical traces may be overwritten or retained as desired.   Both Uniform and Gaussian distributions are provided for inserting element value error.  Individual elements may be assigned specific tolerance values, or the default tolerance for all elements may be specified.
This is an example of the effect of random error from 5% capacitors on the group delay of a 5th order Bessel Filter.

Random Error Due to 5% Capacitors

Element Sensitivity

FilterSolutions is a powerful tool for the study the effect of each individual element.  Each element is measured and tabulated for its effect on magnitude, phase, and group delay at critical or user defined frequencies.  In addition, each element may be individually plotted, in an element value sweep, to measure its effect on response at critical or user defined frequencies.

Inductor/Capacitor Tuning

When ideal capacitor values are changed to non-ideal real part values, the filter frequency response is expectedly degraded.  It is possible to translate this error in the filter’s pass band to the stop band, where errors are less critical, by tuning the inductor values in the filter. FilterSolutions and FilterQuick do this task automatically by clicking the "L tune" button that appears in the circuit display tool bar whenever one or more capacitor values has been updated.  Inductors elements may then be custom designed for the filter.
Similarly, when ideal inductor values are changed to non-ideal real part values, capacitor values may be tuned by selecting the "C tune" button. Real capacitor values generally are available over a broader selection range than real inductor values.
The example below shows the result of the magnitude response vs. frequency of a filter with manually altered Capacitors, before and after an automatic inductor tuning process.

Complex Terminations


Classic filter design methods synthesize filters around known resistive Terminations. However, actual Terminations are frequently complex rather than resistive. Filter Solutions and FilterQuick use RMS error reduction methods to synthesize filters around such complex terminations.
The source and load terminations of lumped LC and transmission line filters may be defined with the use of impedance tables wherein the real and imaginary portions of impedance are defined as a function of frequency, as shown below.  Note that impedance may be entered in either Polar, Cartesian or Parallel format. Reactance may be entered directly, in Ohms, or through the equivalent capacitance or inductance.

Termination Impedance Definition
The impedance tables contain two compensation options, "Element Tune" and "Impedance Compensate".
Element Tune
This option tunes all the reactive elements to minimize the RMS error. The default status is "Checked".
Impedance Compensate
This option attempts to improve the synthesis accuracy by adding reactive elements to the complex termination, to make it more resistive. . Sometimes this technique has the effect of improving the filter performance, but frequently it degrades the performance.  It is very important for the user to carefully examine the effect of this option on the desired filter prior to accepting the results. The default status of this option is "Unchecked".
Norton, Pi->T, and T->PI
A simple right mouse click on any Pi, T or L combinations of like elements permits the user to perform a Norton transformation, sometimes referred to as a Capacitor Transformer, since most operations are performed on capacitors.  A Pi may be converted to a T, and a T may be converted to a Pi.  Pi, T and L combinations frequently appear in band pass filters, making this feature a strong tool for custom band pass filter design.  Tools exist to add, delete, or change element values with no effect on the shape of the frequency response.

Combinations of elements that are candidates for a Norton transformation by the use of a right mouse click

The theory behind Norton transformations is well known and shown below.

Norton Transformation Equivalent Circuits

Equal Inductor Bandpass Filters

All-Pole and Zigzag filters may be synthesized with only one inductor value.  For odd order Zigzags, the single inductor value is selectable by the user within a specified range.  The operation changes the value of the source resistance for even order All-poles, but it may be reset by requiring two inductor values instead of one.  Equal inductor All-pole filters have the additional advantage, that all the nodes may contain a grounded capacitor, making it easy to absorb any parasitic node capacitance.

Classic All-Pole Band Pass Filter

Equal Inductor All-Pole Band Pass Filter
Elliptic Filters may have all shunt or all series inductors set to equal values.  These filters are sometimes known as "parametric" filters, and are useful in minimizing inductor spread in medium and narrow band filters.

Shunt Equal Inductor Elliptic
(See the section on ZigZag filters for more on equal inductor Zigzag designs).

Parasitic Node Capacitance

Bandpass filters with stop bands (Elliptic, Hourglass, and Chebyshev) generally consist of combinations of two series LC tanks in a notch configuration.  The node between these tanks tends to contain a parasitic capacitance that can degrade the frequency response of the filter. FilterSolutions and FilterQuick permit the user to select a parasitic capacitance value, and will then synthesize around this value with no degradation of performance.  The operation changes the value of the source resistance, but even-order filters may be restored to their original value by a Norton transformation.
Here is an example of FilterSolutions compensation for 2 pF parasitic node capacitance.

Classic Design with Parasitic Effects

Filter Solutions Design with Parasitic Compensation

All-pole bandpass and Zigzag Filters may absorb parasitic node capacitance with the use of equal inductor designs and Zigzag designs. However, equal inductor Zigzag designs generally require large stopband ratios, making the translation, shown above, more desirable for filters requiring small stop band attenuation, in cases where parasitic capacitance is an issue.

Cross-Coupled Resonators

Chebyshev I and Elliptic Filters may be implemented with sets of LC resonators containing two inductors coupled together.  Chebyshev I Filters only require coupling of adjacent resonators.  Elliptic Filters require cross-coupling.  However, an Elliptic string of resonators may be folded in half so that all the coupled resonators are immediately adjacent to each other, simplifying the physical construction.  FilterSolutions supports sensitivity analyses, Monte Carlo analyses, amplitude equalization and manual editing analysis for all couplings and other elements of the filter.  FilterSolutions supports group delay equalization. Coupled values may be displayed in units of mutual inductance or inductive coupling coefficients.
Chebyshev I Cross-coupled Filters also support real and quadruplet zeros delay equalization.
All Cross-coupled filters are synthesized with a minimum possible number of couplings for the given design requirement.
Three views are provided for each filter design.  The following displays each view for a 6th order Elliptic 1MHz Bandpass filter centered at 10 MHz, with 0.1 dB pass band ripple and 40 dB stop band attenuation:
View 1, Full Coupling Matrix:

View 2: Specific Coupling Matrix:

View 3: Adjacent Coupling Matrix:

All Cross-Coupled Filters displayed above exhibit the same frequency response:

Smith Charts

Smith Charts, Jones Charts, and Polar plots are provided in the forms of frequency and reflection responses for easy to read graphical feedback.  The use of left and right mouse keys provides an integrated method for reading data from the Impedance grid.

                                                                                               Smith Chart Display

Real and Quadruplet Zeros Delay Equalization

Phase Angle and Group Delay may be altered by the presence of dual and quadruplet off-axis zeros. Unlike All-pass stages, the mere addition of dual and quadruplet off-axis zeros also affects the passband magnitude response.  Therefore additional calculations are needed to adjust the pole locations to restore the passband.   It is generally more efficient to use quadruplet zeros in LC Lumped Element Filters as there are no canceling poles and zeros that are inherent in LC All-pass stages.
FilterSolutions offers a fast and easy approach to real and quadruplet delay equalization for low pass, high pass, and bandpass LC Lumped Element Filters.  Poles and group delay are updated in real time in response user zeros manipulation to flatten the pass band and restore an equi-ripple (Chebyshev I) or maximally flat (Butterworth) shape.  LC Lumped Element filter responses are calculated instantly with the positioned zeros.

Quadruplet Zero Equalized Low Pass Chebyshev Lumped Filter, Frequency Response and Pole/Zero Plane

Quadruplet Zero Lumped Implementation

Impedance Matching Networks

Devices with differing impedances occasionally have to be matched to other devices or designs to minimize reflections.  FilterSolutions and FilterQuick accomplish the matching function by designing RLGC or planar matching networks. In these networks, the impedances are matched such that one device or design sees a conjugate impedance to itself when looking into the matching network attached to the other device. This technique eliminates or reduces reflections.  Multiple, discrete frequency or broadband frequency matching are both supported.