1000 characters left

Switched-Capacitor 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

 

Switched Capacitor Filters
FilterSolutions
 
FilterQuick
15 Available FIR Selections
Yes
 
 -
Cascaded Parallel and BiQuads
Yes
 
Yes
IIR Digital Selections of Bilinear, Matched Z, Impulse Invariant, Step Invariant, Modified Impulse Invariant, and Modified Step Invariant
Yes
 
Yes
Band Pass topology selection with Band Pass or Low Pass, High Pass stages
Yes
 
-
Switched Capacitor circuit synthesis for Cascade and Parallel Biquads
Yes
 
Yes
User-selected minimum Capacitance
Yes
 
Yes
Large order synthesis: up to 20 Poles
Yes
 
Yes
Automatic minimum Capacitance spread selection
Yes
 
-
Gain changeable Biquads.
Yes
 
Yes
Off-Axis Quadruplet Zero placement for delay equalization
Yes
 
Yes
Locked or Floating License
Yes
 
Yes
       
Available Analyses:
FilterSolutions
 
FilterQuick
Exportable text netlists
Yes
 
Yes
Easy-to-read exportable graphical circuit displays
Yes
 
Yes
User modified Time, Frequency, Impedances, Reflection Coefficients and Transfer Functions
Yes
 
Yes
Random element value updates for Monte Carlo analyses
Yes
 
Yes
Allows Separate Analysis for each stage
Yes
 
Yes
Rearrange and reanalyze Cascaded Biquads.
Yes
 
Yes
Swap Wn's from Biquad to Biquad.
Yes
 
Yes
Detailed component sensitivity analyses, Including sensitivity tables and plots
Yes
 
-

About Switched Capacitor Filters

Switched Capacitor Filters are normally used in an Integrated Circuit product environment as Resistors are more expensive and less easily controlled.  Switched Capacitors may be used to simulate Resistors to an acceptable degree of accuracy. Capacitors and MOSFETS are generally less costly than Resistors. The switching function of the MOSFET produces a discrete response rather than a continuous response from the filter.  Therefore, Z -Transforms are employed rather than S-Transforms. Just as in digital filters, aliasing effects occur.  Any Z-Transform approximation to a continuous function may be used to design a Switched Capacitor Filter.  However, it is generally desirable to use the Z-Transform that results in the smallest capacitor value spread.

FilterSolutions and FilterQuick offer the choice of six IIR Z-Transforms, giving the option of selecting the design with the smallest capacitor spread.  Care must be taken to insure that the Z-Transform is acceptably accurate, given the design requirements.  The design with the best capacitor spread is not necessarily the best design, as the accuracies may be unacceptable.

Switched Capacitors

Switched Capacitors may simulate positive or negative Resistors.  Positive Resistors may float: they are treated as constants in the Z-Transform.  Negative Resistors may not float and are treated as a constant with a single frame delay in the Z-Transform.

Note that the negative Switched Capacitors do not float.  It is also critical that the clock DOES NOT OVERLAP with its invert. Switch polarities are user optional, but the polarity definition must be followed everywhere in the filter.

Biquad Architectures

FilterSolutions and FilterQuick support both Cascade and Parallel Biquads.  The cascade architecture produces higher quality stop band zeros, while the Parallel form may minimize errors to op-amp parasitics. Following are examples of a 1 MHz, third-order Elliptic Filter:

High/Low Q Biquads

Second order Biquad stages may be arranged in either a high Q or low Q configuration.  In general, the low Q configuration produces a more desirable capacitor spread for Q below 1.0. The high Q configuration performs better for Q values above 1.0. As this “rule of thumb” does not always apply;  the program calculates both stages; then uses the stage with the lowest Q.

The user has the capability of selecting the other stage configuration by left-clicking on an op-amp in the schematic.  The following example is of a fourth order Butterworth filter composed of a low Q stage and a high Q stage.

IIR Z-Transforms

The programs offer a choice of six IIR Z-Transforms to approximate continuous filters.

In summary, they are:

Bilinear

The Bilinear Transform uses trapezoidal integration to implement the digital Z-Transform.  It is usually the most accurate digital implementation for filtering a continuous variable.  However, significant warping of the frequency spectrum occurs. Prewarping is also an available option.

Matched-Z

The Matched Z-Transform employs a basic method of translating Analog poles and zeros to Digital poles and zeros on the cascaded continuous transfer function.

Impulse Invariant

The Impulse Invariant Transformation retains the exact impulse response of the analog system.  Its use is desirable in cases where retention of the impulse time response of the filter is important.  The transformation is properly performed on the Parallel transfer function.

Step Invariant

Like the Impulse Invariant Transform, the Step Invariant Transformation also retains the exact impulse response of the analog system. Its use is desirable in cases where retention of the impulse time response of the filter is important   Again, the transformation is properly performed on the Parallel transfer function.

Modified Impulse Invariant

The Modified Impulse Invariant Transformation performs an Impulse Invariant computation on the Cascaded rather than the Parallel transfer function. This creates some error in the transformation, but may useful in simplifying switched capacitor designs

Modified Step Invariant

The Modified Step Invariant Transformation performs a Step Invariant computation on the Cascaded rather than the parallel transfer function. This creates some minor error in the transformation, but may be useful in simplifying Switched Capacitor designs.

FIR Z-Transforms

Switched Capacitor Filters may generally be designed to meet any desired FIR Z-Transform.  All FIR Z-Transforms supported for Digital Filters are also available for Switched Capacitor Filter design.  Finite Impulse Response Filters have the advantage, as compared to IIR filters, of allowing group delay to be held constant.  FIR filters have the disadvantage of creating a passband that is less controlled. Further, the filter may be excessively large to be of practical use in Switched Capacitor applications.

Band Pass Architectures

Just as for Active Filter designs, the programs allow the user to design Bandpass Filters from bandpass stages or from low-pass and high-pass stages.  Generally, bandpass stages are more suited for narrow band filters, while low-pass -high- pass stage designs are more suited for wider band filters.  Selection of the incorrect stage type may result in excessively high stage gains.

Net Lists

The programs allow the creation of SPICE-executable net lists for all Switched Capacitor Filter designs, including those with user modifications.  This feature allows for the easy validation of the software and its output, as well as the ability to perform analyses in other tools, for modifications to the filter beyond the capabilities of FilterSolutions.  Switched Capacitor Filters are only supported by transient analyses in the program.

User Modification Analysis

Users have the capability to alter Capacitor values and reanalyze the filter.  By left -clicking on any capacitor, as shown, one can enter the new desired value in the “pop-up” window.  Clicking on any analysis button on the schematic allows the regeneration of frequency, time, input impedance, or Z Transform analyses.

Modify a Capacitor Value

Monte Carlo Analysis

A Monte Carlo statistical analysis may easily be performed visually with the programs.  After creating and displaying a Switched Capacitor filter and its frequency, impedance, or time responses, one can left- click a capacitor requiring further study.  The study can be of one capacitor, or all capacitors at once.  In the Change Control Panel, selecting  "Random", allows the entry of the maximum tolerance or standard deviation, in per cent.

Monte Carlo analyses may be launched manually by repetitive clicks of "Apply". Alternately, the analyses may be run automatically by entering the desired number of iterations.

Graph traces may be overwritten or retained as desired.  Both Uniform and Gaussian distributions are provided for inserting element value error.

The following graph shows an example of the effect of random error from 5% capacitors on the magnitude of a third order Elliptic Filter:

Random Error Due to 5% Capacitor Tolerance

Real and Quadruplet Zero 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 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 design requirements.

Filter Solutions, (but not FilterQuick), offers a fast and easy approach to real and quadruplet delay equalization for low pass, high pass, and bandpass Switched Capacitor Filters.  Poles and group delay are updated in real time in response to manipulation of zeros to flatten the pass band into an equiripple (Chebyshev I) or maximally flat (Butterworth) shape. Switched Capacitor 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 Switched Capacitor designs for this filter.

Quadruplet Zero Equalized Low Pass Chebyshev Passive Filter Schematic