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Active 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 FilterQuick or FilterSolutions' advance feature sets.

Licenses for FilterSolutions can be purchased as "FilterSolutions-PRO™" which contains all the modules. 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 Floating License, MAC Address-Locked or "Dongle-Locked single user licenses.

FilterFree is a Freeware version of FilterSolutions with minimal functionality (DOWNLOAD LINK). FilterFree is limited to 3rd Order Analog designs or to 10 tap FIR designs. All analyses in FilterFree are limited to ideal transfer functions.

Active Filter Synthesis:
FilterSolutions
 
Filter Quick
Akerberg-Mossberg Biquads
Yes
 
Yes
Multiple Feedback (MFB) Biquads
Yes
 
Yes
Thomas Biquads
2nd & 3rd Order
 
2nd & 3rd Order
Thomas Biquad Topologies
Thomas 1,2,3
 
Thomas 1,2,3
Sallen & Key Amplifier Biquads
1st, 2nd & 3rd Order
 
1st, 2nd & 3rd Order
Bandpass topologies with Bandpass or Highpass/ Lowpass stages
Yes
 
-
GIC's and Leap Frogs
Yes
 
Yes
Parallel Active Filters
Yes
 
Yes
Large Order Synthesis of up to 20 Poles
Yes
 
Yes
All-Pass Stages for Delay Equalization
Yes
 
-
Integrated Third Order Stages
Yes
 
Yes
Integrated Fourth Order Stages
Yes
 
-
       
Third Party Tool Connections:
FilterSolutions
 
FilterQuick
Direct export to AWRCorp Tools (where available)
Yes
 
Yes
Touchstone Z, Y and S Parameters
Yes
 
Yes

Direct export to CST Microwave's STUDIO SUITE

 

Yes   Yes
Available Analyses:
FilterSolutions
 
Filter Quick
Analyze user modified time, frequency, input impedance
Yes
  
Yes
Analyze user modified transfer functions
Yes
 
Yes
Exportable Text Netlists
Yes
Yes
Exportable Transfer Functions of Modified Filters
Yes
 
Yes
Exportable Graphic Circuit Displays
Yes
 
Yes
Support of Op-Amps for Frequency and Time Analyses
Yes
 
Yes
Monte Carlo Analysis with random value updates
Yes
 
Yes
Element Sensitivity Analysis
Yes
 
-
Real and Quadruplet Zeros Delay Equalization
Yes
 
-
       
Capabiliites: Filter Solutions  
Filter Quick
Auto update Parts to Nearest 1%, 5%, 10%, or 20% standard
Yes
 
Yes
Change Resistive Constant, Gain, or Pos. Feedback for each stage
Yes 
 
Yes
Finite Q Parasitic analysis for Capacitors
Yes
 
Yes
ESR Parasitic analysis for Capacitors
Yes
 
-
Third Order Single Amplifier, GIC, and Thomas Stages.
Yes
 
Yes
4th Order Low, High and Band Pass Single Amplifier stages
Yes
 
-
Off-Axis Quadruplet Zero placement for delay equalization
Yes
 
-
Positive Feedback enhancement for Negative SAB's (MFB)
Yes
 
Yes
Real Op Amp analysis including Parasitics and Finite Gain
Yes
 
Yes
Shunt Capacitance analysis for Resistors.
Yes
 
Yes
Swap Wn's from Biquad to Biquad.
Yes
 
Yes
Synthesize stages around user- entered Capacitor values
Yes
 
Yes
Component sensitivity analyses, including sensitivity tables and plots
Yes
 
-

Transfer Functions

Active filters produced by FilterSolutions™ and FilterQuick™ are created from Transfer Functions. While the designer may elect to view these functions, the translation to active Filter designs is an internal process of the program. Transfer functions are created in three forms, Standard, Cascade, or Parallel. The Cascade and Parallel forms consist of first through fourth order terms that are cascaded or summed in parallel. Cascade and Parallel Transfer Functions are used to create active filters. Cascade Transfer Functions generate the following types of filters: Thomas Biquads, Sallen and Key Biquads, Multiple Feedback (MFB) Biquads, and GIC (General Impedance Converter) Biquads. Parallel Transfer Functions are implemented with a summation of Sallen and Key and MFB Biquads. The image below depicts examples of Cascade and Parallel Transfer Functions.

Thomas Biquads 

Thomas Biquads are three op-amp second and third order stages. FilterSolutions and FilterQuick support third order stages.   The primary advantage of Thomas Biquads is that they provide very high Q second order stages.  Nuhertz denotes these two different topologies as Thomas 1 and Thomas 2, respectively. The Thomas 2 Biquad provides very high quality notches in the presence of real element values . Thomas 1 Biquads require fewer capacitors and are sometimes gain sign changeable. FilterSolutions and FilterQuick support third order Thomas Biquads with the addition of a Capacitor and, occasionally, a Resistor to the input of the Biquad. The circuits shown below are examples of Thomas 1 and Thomas 2 Biquads. The bottom circuit is a Thomas Biquad that includes a third pole.

Akerberg-Mossberg Biquads

The Akerberg-Mossberg Biquad exceeds the performance of the Thomas Biquads in the face of op-amp imperfections and equals the Thomas 2 Biquad notch performance in the presence of element value errors. This increased performance is obtained by replacing the positive Integrator in the Thomas 2 Biquad second and third op-amps with a Miller Integrator. The Miller Integrator uses two matched op-amps in a configuration that tends to cancel errors due to op-amp imperfections. The Akerberg-Mossberg Biquad may absorb a third pole.

Positive Gain Single Amplifier Biquads

Positive Gain Single Amplifier Biquads (SABs) require only one op amp for first, second, and sometimes third order amplifiers. The second order, unity gain, high pass and low pass cases of the positive gain SAB are known as the Sallen & Key Biquads. The advantages of Positive Gain SAB's is that they are in generally higher resistant to imperfect op amps than Negative Gain SAB's, except for Twin-T stages are always gain changeable, and there is usually no reversal of sign. The disadvantages are they are more susceptible to element imperfections than Negative Gain SAB's.  All pass and even notch Positive Gain SAB's with injector resistor have a sign reversal.

Low pass and high pass second order Positive SAB's my be created with two equal capacitor and resistor values. This results in a tunable SAB. See the FilterSolutions Help file for tuning documentation.

Below are examples of Positive Gain SA topologies:

Negative Gain Single Amplifier Biquads

Negative Gain Single Amplifier Biquads (SAB's) require only one op amp for first, second, and sometimes third order amplifiers. Second and third order Negative Gain SABs use the Bridged-T or MFB circuit configuration for the feedback path.  The advantages of Negative Gain SAB's is that they are generally higher resistant to imperfect elements than positive gain SAB's. The disadvantage is they are generally more susceptible to op amp imperfections than positive gain SAB's and the gain for all pass and notch stages is fixed. All pass and notch Negative Gain SAB's utilize an injector resistor for zero placement which always results in the sign of the gain changing to produce a fixed positive gain. The susceptibility of high Q stages to imperfect op amps may be minimized with the use of positive feedback enhancement. Below are examples of Negative Gain SA topologies. The lower left example contains a positive feedback enhancement to aid in the performance of the high Q notch. The lower right example is the alternate notch topology. The alternate notch replaces the injector resistor with a feed forward capacitor to produce a low quality notch. This allows the negative op amp node to be grounded, and allows for stage gain adjustment.

Parallel Active Filters

The parallel transfer functions described at the top of the page may be used to generate parallel active filters. In FilterSolutions, parallel filters are constructed from a series of positive and negative single amplifier stages that are summed in parallel. The summation circuit may be optionally active or passive. The advantage of using the summation is that performance degradation due to op amp imperfections is not amplified through successive cascade stages. The disadvantage is that the filter design may be physically very large and notches tend to be of poor quality. FilterSolutions will compute gain settings for each individual stage that results in the fewest number of components and compensates with the summation resistor in the summer circuit. The user may change this gain setting if desired An example of a parallel filter is shown below:

Leapfrog Filters

Leapfrog filters are passive LC ladder simulations.  An advantage of the form is that errors due to element values or op amps tend to be distributed across the filter instead of concentrated at a specific biquad.  This generally makes the design more robust.  FilterSolutions supports Leapfrog filters for low pass and bandpass all-pole designs.  Alternating Inductors and Capacitors are replaced by a string of positive and negative gain Integrators.  FilterSolutions employs positive Miller Integrators for the positive gain integrators to maximize high frequency performance. Each integrator output posses a feedback and feed- forward resistor.  The beginning and ending integrator have resistors in parallel with the capacitors to simulate the passive termination resistors. An example is shown below.

All-Pass Stages

FilterSolutions supports first and second order all pass stages to support group delay design requirements. Second order all pass stages may be created with Thomas 1 Biquads, Thomas 2 Biquads, Positive SABs, Negative SABs, or QIC Biquads. First order all-pass stages are created with a special first order all-pass circuit. Positive and negative SABs require the presence of an injector resistor: a resistor from the stage input to the opposite op amp input. The presence of this injector resistor reverses the sign of the SAB gain such that positive SAB become negative, and negative SABs become positive. Negative SAB's, first order all-pass stages, and QIC biquads are fixed gain.

To create an all-pass stage, one uses the pole/zero plots, by positioning the cursor over a desired pole location, depressing the left mouse key, then clicking the right mouse key. One may then slide the poles and zeros around with the cursor. Checking the RTU (Real Time Update) box on top of the pole/zero plot, allows one  to watch the filter design update in real time. Below are examples of first and second order all pass stages:

Op Amps

The analysis features of FilterSolutions support both ideal and real op amps for frequency and time analysis. Ideal op amp analysis greatly speeds up simulation time. Real op amps support input resistance, input capacitance, output resistance, bandwidth, and gain bandwidth product. You get a very good idea about how well your filter will perform when running the ideal op analysis with real elements parts installed in your filter.

Circuit Displays

FilterSolutions displays are designed to be easy to read and easy to modify. The value of any element may be changed by passing the cursor over the element and left-clicking the mouse. Modified elements appear in blue to allow one to easily determine which elements have been modified. If the stage parameters of Q, Wo, or sigma change as a result of the changed element value, they also will appear in blue, as shown below:

Stage Modifications

Stage parameters may be modified by placing the cursor over the op amp and left clicking the mouse, as shown below.

 The Stage Control Panel permits the following stage modifications:

Alternate Notch Select or deselect the alternate notch configuration for negative SAB unequal gain notch stages.
Enhancement Ratio Enter the new positive feedback enhancement ratio for negative SAB’s when “Pos Enhance” is checked.
Equal Caps Gain Set the stage gain to a value that will produce equal capacitors for Positive SAB 2nd order low pass stages.
Equal Resis Gain Set the stage gain to a value that will produce equal resistors for Positive SAB 2nd order high pass stages.
Gain Recalculate the stage with a new gain.
Manual Capacitor Entries Recalculate the resistor values of the stage using user-entered capacitor values.
Pos Enhance Check to apply positive feedback enhancement to 2nd and third order negative SAB’s
R Constant Rescale the stage resistors and capacitors with a new resistive constant.
Stage Implementation Recalculate the stage with a different implementation. (Thomas, QIC, etc.)
Switch Wn with Stage... Select the stage you wish to swap Wn with. Filter Solutions will recalculate both stages with the swapped Wn's.
TwinT Even Recalculate using TwinT notch for positive SAB second order notch filters. An injection resister is used otherwise.
V Out Stage Sets the filter frequency and time outputs to the selected stage.

GIC Biquads and Ladders

QIC Biquads are two op amp biquads with good high frequency performance. All but the even notch stages are tunable. The high pass, low pass and bandpass stages are gain adjustable. The notch and all pass stages have a fixed gain of unity. All GIC stages have equal capacitor values, unless a capacitor is required to adjust the gain. Notch stages do not rely on element value subtractions for notch quality and are thus immune from degradation in notch quality due to element value errors.  The low pass topology is shown below with tuning characteristics. Tuning characteristics for the other forms, high pass, notch, etc., are documented in the program's Help file.  FilterSolutions permits the user to view the output of each op amp separately from each GIC stage.

GIC ladder filters are circuit simulators useful in realizing large order Elliptic and similar filters. The impedance characteristics of GIC biquads are used to simulate lumped passive ladder elements, sometimes scaled by 1/S to eliminate series inductors.  These filters generally need to be terminated with a high impedance buffer stage to maintain proper frequency response. Below is an example of a third order Elliptic filter.

Modified Filter Transfer Functions

When filter elements are modified, FilterSolutions calculates the new transfer function to view or to export to the Windows clipboard. The format of exported transfer functions are in a form readable by Matlab and Matrix-x. For details, see the documentation for Other Applications.

Standard Parts Lists

Filter Solutions provides a flexible means to update  Active Filter elements values with the nearest value from user-selected available standard parts, or to the nearest 1%, 5%, 10%, or 20% standard industrial value. Up to three standard parts databases are maintained by FilterSolutions. If more than three are needed, they may easily be maintained in another text or word processing document and copied or pasted in and out of FilterSolutions.

To update filter parts to the nearest value in the parts list, left click on an element in a filter display, select "Parts" in the selection box at the bottom of the Change Control Panel, then select OK.

Active filters may have individual element 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 FilterSolutions standard parts window is shown below with some sample standard parts.

The buttons across the top perform the following functions: 

Print Print the displayed standard parts
Copy Copy the displayed parts to the windows clipboard. Select the portion to be copied, or select all or nothing to copy all text in the text box.
Default Sets the standard parts to the default parts list.
Paste Paste text from the windows clipboard into the standard parts text box.
Save Save you standard parts list in the Filter Solutions database and exit.
Cancel Exit without saving the parts list.

Parts List Foormats:

Comments Precede the comment line with a “%” character. Up to 10 comments are allowed.
Numerical Entries Integer, floating, and engineering notation are all acceptable. Six significant digits are stored in the database. Example:12, 0.00047, 470n, 50pF are all acceptable numerical entries. All numerical entries are sorted in ascending order in the database. Up to 500 numerical entries are allowed per element type.
Capacitors Precede the capacitance numerical entry with a “C” or “c” character.
Inductors Precede the inductance numerical entry with a “L” or “l” character.
Resistors Precede the capacitance numerical entry with a “R” or “r” character.

Frequency Impedance& Time Analysis

Each Active Filter generated by FilterSolutions may have a frequency, impedance or time analysis performed by selecting the appropriate control on the circuit window. Frequency analysis include magnitude, phase, and group delay. Time analyses include step, ramp, and impulse responses. Depressing the left mouse key at any location brings up a cursor tracer with the frequency and trace information in the cursor window. These analysis include all user modifications made to the filter. When a filter has been modified by changing an element, if any filter stage has been modified, or if "Real" op amps have been selected in the control panel, the "Ideal" analysis trace appears in dark blue for quick easy comparison purposes. Examples are below:

Net Lists

FilterSolutions  allows the means to create a filter circuit in a SPICE net list that is ready to execute on other applications that support net lists. Simply click on the "Netlist" button above the filter display, and a drop-down edit window will display the net list. The net list may be copied to the Windows clipboard with the "Copy" button below the net list. Ideal and real op amps are supported. Infinite gain op amps appear as 1.E10 in the Netlist. Below is an example of a graphical filter and the corresponding net list.

MULTIPLE ANALYSES
*
V1 1 0 AC 1
*V1 1 0 PULSE 0 1
R101 1 2 1E+04
R102 2 3 1E+04
C103 3 0 5E-11
C104 2 4 2E-10
X101 3 4 4 OPAMP
R201 4 5 1E+04
C202 5 0 1E-10
X201 5 6 6 OPAMP
.AC DEC 200 1.592E+04 1.592E+06
.PLOT AC VDB(6) -60 0
.PLOT AC VP(6) -200 200
.PLOT AC VG(6) 0 3E-06
.TRAN 0.05 10 0
.PLOT TRAN V(6) 0 1.2
.END
*OpAmp Simple Model 1=+in 2=-in 3=Vo
.SUBCKT OPAMP 1 2 3
G0 3 0 1 2 1.E+10
.ENDS OPAMP

Band Pass Architectures

FilterSolutions provides two different architectures to create Active bandpass filters.  Bandpass filters may be created with multiple integrated bandpass stages, or high and low pass stages. Odd order filters of the high/low pass architecture always have a bandpass stage in the center, unless the stage pole are absorbed by other biquad stages, as in the circuit diagrams below. One advantage of creating the high/low pass architecture is that wide band filters have two poles on the real axis that may be absorbed by the other high and low pass stages. (FilterFree does not support real pole absorption).  In general, the integrated band pass architecture works better for narrow band filters, and the high/low pass architecture works better for wide band filters.  This is due to potentially huge, undesirable internal gains that may saturate op amps if the wrong architecture is used.

Examples:

A third order band pass filter from 500 to 5000 Hz is shown below in the integrated architecture and the high/low pass architecture.

Manually Entered Capacitors

FilterSolutions allows the entry of chosen capacitor values, and will calculate resistor values necessary to support the chosen capacitors. Left mouse click an op amp in the stage in which new capacitor values are to be entered. The Stage Control Panel will pop up with edit boxes for the capacitors. Enter the desired capacitor values and click "OK". FilterSolutions will recalculate the stage using the newly entered capacitors values, or will advise if the stage cannot be created with the values entered.

Example:

A third order low pass filter is shown below. When the op amp is left clicked, the panel below comes up. Manually enter  the capacitor values, or pick an automated value, and select OK. FilterSolutions will calculate resistor values needed to support the desired capacitor values, or flag the capacitor values as impossible to calculate.

Third and Fourth Order Stages

FilterSolutions offers integrated third order and fourth order stages under conditions set by the following table:

Stage Type
High Orders That Are Available
Thomas or Akerberg-Mossberg Biquads
Third Order
Positive Gain All Pole Single Amplifier Stages
Third Order and Fourth Order
Positive Gain Single Amplifier Stages With Transmission Zeros
Third Order
Negative Gain All Pole Single Amplifier Stages
Third Order and Fourth Order
Negative Gain Single Amplifier Stages With Transmission Zeros
Usually Third Order
GIC
Third Order
Twin T
Third Order in the Form of an RC Pole Following the Op Amp

The advantage of using a single op amp is the reduced cost of filter construction.  Below are examples of a 1MHz Butterworth fourth order single stage bandpass filter in both positive and negative gain configurations, constructed with one op amp and commonly available capacitor values.  The capacitor spread is only 2.0, and the resistor spread is only 5.9 and 4.3.

Single amplifier stages with transmission zeros may be realized with the positive gain topology.  Below is an example of a third order Elliptic filter with one amplifier.

Capacitor values may be manually selected to fit a wide variety of values.  Additional elements are automatically inserted as necessary to maintain the desired frequency response.  Below is the same filter shown above with a smaller capacitor spread that was created by manually inserting resistor values.

Single amplifier stages with transmission zeros may usually be realized with the negative gain topology. As in second order stages, the gain of this topology is inverted when transmission zeros are present to create a net positive gain.  Below is an example of a third order Elliptic filter with one amplifier.

Single amplifier stages with transmission zeros may be realized with GIC stages.  The GIC traits of equal capacitors and notch immunity to element value error are preserved.  Below is an example of a single stage third order Elliptic filter.

Monte Carlo Analysis

A Monte Carlo statistical analysis may easily be performed visually with FilterSolutions. After creating and displaying an active filter and filter frequency,  impedance, or time response, left click the element or element type to be studied. In the Change Control Panel, select "Random", and enter the default maximum tolerance or standard deviation in percent of the desired random change.  (Individual components may be set to specific % tolerance values and will override the default setting.). Monte Carlo anlayses may be done manually by repetitious clicks of "Apply", or automatically by entering the desired number of iterations.  Graphical traces may be overwritten or retained as desired. Both Uniform and Gaussian distributions are provided for inserting element value error.

Below is an example of the effect of random error from 5% capacitors has on the group delay of a 5th order Positive SAB Bessel Filter.

Element Sensitivity

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

Integrated Parasitics

Active filters in an integrated environment use resistors that capacitively interact with the backplane, resulting in parasitic capacitance associated with each resistor.  Although this capacitance is distributed across the resistor, an generally acceptable approximation is a lumped capacitor parasitic at each end node of the resistor.  FilterSolutions allows the user to apply the desired amount of lumped parasitic capacitance at each end node of each resistor and will apply this parasitic in the analysis of the filter,  for easy viewing of the parasitic effect.

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, so additional calculations are needed to adjust the pole locations needed to restore the pass band.  Delay equalization with real and quadruplet zeros result in a flatter Chebyshev passband and steeper attenuation near the cut off frequency than a comparable size filter equalized with traditional all-pass stages.  This technique may provide a more efficient filter, depending on the specific filter design requirements.

FilterSolutions offers a fast and easy approach to real and quadruplet delay equalization for low pass, high pass, and bandpass active filters.  Poles and group delay are updated in real time in response to the user's zeros manipulation undertaken to flatten the passband back into an equiripple (Chebyshev I) or maximally flat (Butterworth) shape, Active filters are calculated instantly with the positioned zeros.

 

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

Filter Solutions offers efficient active designs requiring only two op amps and two capacitor values, both standard 20 % values, for this filter.

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