Nuhertz

Active Filter Solutions


Flash Menu
Go Direct to:

Transfer Functions

Thomas Biquads

Akerberg-Mossberg Biquads

Positive Gain SABs

Negative Gain SABs

Parallel Filters

GIC Biquads and Ladders

Circuit Displays

Standard Parts

Frequency, Impedance & Time Analysis

Net Lists

Op Amps

All Pass Stages

Stage Modifications

Third and Fourth Order Stages

Manually Entered Capacitors

Band Pass Architectures

Monte Carlos

Integrated Parasitics

Leapfrog Filters

Element Sensitivity

 

Real and Quadruplet Zeros Delay Equalization

 

 


Transfer Functions

Active filters produced by Filter Solutions and Filter Light are created from the transfer functions displayed in the transfer function selection page. There is no need to view the transfer functions. The translation to active filters is made internally. Transfer functions are created in three forms, Standard, Cascade, and Parallel. Cascade and parallel transfer functions consist of first and second order terms that are cascaded or summed in parallel together. The cascade and parallel transfer functions are used to create the active filters. Cascade transfer function generate the filters composed of Thomas Biquads, Positive Gain Single Amplifier Biquads, Negative Gain single amplifier biquads, and GIC biquads. Parallel transfer functions are implemented with a summation of Positive Gain and Negative gain single amplifier biquads. The image below depicts an example of a cascade and parallel transfer function.

Transfer Functions

Back to Top

 

Thomas Biquads

Thomas Biquads are three op amp second and third order stages. Filter Light does not support third order stages. Their primary advantage is they provide very high Q second order stages. Filter Solutions and Filter Light provide two different topologies, denoted as Thomas 1 and Thomas 2. The Thomas 2 Biquad provides very high quality notches in the presence of real value elements. Thomas 1 Biquads require fewer capacitors and are sometimes gain sign changeable. Filter Solutions supports third order Thomas Biquads with the addition of a capacitor and occasionally a resistor to the input of the biquad. The circuits below are examples of a Thomas 1 and Thomas 2 Biquad. The bottom circuit is a Thomas Biquad that includes a third additional pole.

Thomas Biquads
 

Back to Top

 

Akerberg-Mossberg Biquads

The Akerberg-Mossberg biquad exceeds the performance of the Thomas biquads for opamp imperfections and matches 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 opamps with a Miller integrator. The Miller integrator uses two matched op amps in a configuration that tends to cancel errors due to opamp imperfections.  The Akerberg-Mossberg biquad may absorb a third pole.

Akerberg-Mossberg Biquad
Akerberg-Mossberg Biquad

 

Akerberg-Mossberg Biquad With Additional Pole
Akerberg-Mossberg Biquad With Additional Pole

 

Back to Top

Positive Gain Single Amplifier Biquads

Positive Gain Single Amplifier Biquads (SABs) require only one op amp for first, second, and sometimes third order amplifiers. Filter Light does not support third order stages. 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 Filter Solutions Help file for tuning documentation.

Below are examples of Positive Gain SA topologies:

Positive SA Tologies
Positive SAB's

Back to Top

 

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 BridgeT or MFB circuit configuration for the feedback path. Filter Light does not support third order stages. 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.

Negative SABs:
Negative SAB's

Back to Top

 

Parallel Active Filters

The parallel transfer functions described at the top of the page may be used to generate parallel active filters. In Filter Solutions and Filter Light, 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 doing this is that performance degradation due to op amp imperfections is not amplified through successive cascade stages. The disadvantage is the filter design may be physically very large and notches tend to be of poor quality. Filter Solutions and Filter Light 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:

Parallel Filter
Parallel Active Stages

Back to Top

 

Leapfrog Filters

Leapfrog filters are passive LC ladder simulations.  The advantage is that errors due to element values or opamps tend to be distributed across the filter instead of concentrated at a specific biquad.  This generally makes them more robust.  Filter Solutions supports Leapfrog filters for low pass and band pass all pole designs.  Alternating inductors and capacitors are replaced by a string of positive and negative gain integrators.  Filter Solutions 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.

Leapfrog Active Filter
Third Order Leapfrog Active Filter

Back to Top

 

All Pass Stages

Filter Solutions 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, go into the pole/zero plots, position the cursor over a desired pole location, depress the left mouse key, then click the right mouse key. You may then slide the poles and zeros around with the cursor. If you check the RTU (Real Time Update) box on top of the pole/zero plot, you may watch your filters design update in real time as you manipulate your poles and zeros. Filter Light does not support all pass stages.

Below are examples of first and second order all pass stages:

All Pass Stages
All Pass Stages

Back to Top

 

Op Amps

The analysis features of Filter Solutions support both ideal and real op amps for frequency and time analysis. Filter Light supports only ideal op amps. 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.

Back to Top

 

Circuit Displays

Filter Solutions and Filter Light displays are designed to be easy to read and easy to modify. You may change the value of any element by passing the cursor over the element and left clicking the mouse. Modified elements appear in blue to let you easily determine which elements have been modified. If the stage parameters of Q, Wo, or sigma change as a result of your elements changing value, they also will appear in blue, as shown below:

Displays

Back to Top

 

Stage Modifications

You may modify stage parameters by placing the curser over the op amp and left clicking the mouse, as shown below.

Op Amp Display

The Stage Control Panel will let you make 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.

Back to Top

 

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 band pass 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 degradations 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 Help file.  Filter Solutions permits the user to view the output of each op amp separately from each GIC stage.

QIC Biquad
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.

GIC Ladder Filter
GIC Ladder

 

Back to Top

 

Modified Filter Transfer Functions

When you modify filter elements, Filter Solutions will calculate the new transfer function for you to view or 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.

 

Back To Top

Standard Parts Lists

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

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 Filter Solutions standard parts window is shown below with some sample standard parts.

Standard Parts List


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 Formats:

 

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.

Back to Top

 

Frequency Impedance& Time Analysis

Each Active Filter generated by Filter Solutions 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 analysis includes step, ramp, and impulse response. 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:

Frequency Analysis
Frequency Analysis

Time Analysis
Time Analysis

Back to Top

 

Net Lists

Filter Solutions and Filter Light allow you the means to create your 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 your 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

Filter

Back to Top

 

Band Pass Architectures

Filter Solutions provides you with two different architectures to create your active band pass filters.  Band pass filter may be created with multiple integrated band pass stages, or high and low pass stages. Odd order filters of the high/low pass architecture always have a band pass 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 are that wide band filters have two poles on the real axis that may be absorbed by the other high and low pass stages. (Filter Light and Filter Free do 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.

Classical Band Pass
Classical Integrated Band Pass Filter 500 to 5000 Hz

Integrated High/Low Band Pass
Classical High/Low Band Pass Filter 500 to 5000 Hz

 

Back to Top

 

Manually Entered Capacitors

Filer Solutions allows you to enter capacitor values of your choosing, and will calculate resistor values necessary to support your capacitors. To do this, left mouse click an op amp in the stage you wish to enter capacitors into. The Stage Control Panel will pop up with edit boxes for the capacitors. Enter the capacitor values you wish to use and click "OK". Filter Solutions will recalculate the stage using the capacitors you entered, or it will tell you that the stage cannot be created with the values you entered.

Example:

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

Third Order Low Pass Filter
Low Pass Filter

Manual Capacitor Entries
Manual Capacitor Entries

  Back to Top

 

Third and Fourth Order Stages

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

 Fourth Order Single Stage Positive Gain Band Pass Filter
Fourth Order Single Stage Negative Gain Band Pass Filter
Fourth Order Single Stage Positive and Negative Gain Band Pass Filters

 

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.

Third Order Single Stage Elliptic Filter

Third Order Single Stage Elliptic Filter

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.

Third Order Single Stage Elliptic Filter With User Entered Capacitors

Third Order Single Stage Elliptic Filter With User Entered Capacitors

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.

Third Order Negative Gain Single Stage Elliptic Filter

Third Order Negative Gain Single Stage Elliptic Filter

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.

Third Order GIC Single Stage Elliptic Filter

Third Order GIC Single Stage Elliptic Filter

 

Back to Top

 

Monte Carlos

A Monte Carlo statistical analysis may easily be performed visually with Filter Solutions. After creating and displaying an active filter and filter frequency,  impedance, or time response, left click the element or element type you would like to study. 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 Carlos may be done manually by repetitious clicks of "Apply", or automatically by entering the desired number of simulations.  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.

Random Error Due to 5% Capacitors
Random Error Due to 5% Capacitors

Back to Top

 

Element Sensitivity

Filter Solutions 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.

Back to Top

 

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 acceptable approximation is a lumped capacitor parasitic at each end node of the resistor.  Filter Solutions 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.

Back to Top

 

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

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

Quadruplet Off Axis Delay Equalized Frequency Response     Quadruplet Off Axis Delay Equalized Pole/Zero Plane
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.

Quadruplet Off Axis Delay Equalized Active Filter Schematic
Quadruplet Zero Equalized Low Pass Chebyshev Passive Filter Schematic
 

Back To Top