FilterSolutions Terminology Table

When a continuous frequency response is transformed to a digital frequency response, aliasing occurs at half the sample rate of the digital domain. Aliasing produces errors in the digital frequency response. When Bilinear Transformation is selected and "Alias Correction" is checked in the Digital Dialog box, FilterSolutions will correct the aliasing error at the edge(s) of the pass band.

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A transfer function or filter segment that affects only the phase and group delay of the filter without affecting the magnitude response. Useful for creating delay equalizers

An RCL compensation network added to lumped passive filters with finite Q for the purpose of equalizing the magnitude frequency response

A continuous to digital transformation that maps the entire continuous JW axis to the digital unit circle. Subsequent aliasing errors may be corrected by checking the Prewarp box.

Officially, this is a complex pole pair. Filter Solutions uses this term loosely to represent any polynomial of two orders or less.

A transfer function or filter implementation that is constructed as the product of two or more sections of second order or less.

In a band pass or band stop filter, the geometric average of the upper and lower cutoff frequencies is the Center Frequency.

In a band pass or band stop filter, the upper and lower cutoff frequencies are the corner frequencies.

LC resonant pairs separated by a capacitor or inductor. Usually done for the purpose of approximating a narrow pass band in a band pass filter.

A addition to a filter composed of all pass sections with pole and zeros that have been strategically positioned to "Flatten" the group delay of the filter pass band.

Finite Impulse Response filter. Those filters whose impulse lasts for a finite duration of time before assuming a value of exactly zero. Only specially designed digital filters are FIR Filters.

The transport delay of a specific frequency. Calculated by the negative of the frequency derivative of the phase angle. Usually expressed in seconds.

Infinite Impulse Response filter. Those filters whose impulse response asymptotically approaches zero. The digital transformations of all analog filters are IIR filters.

For the continuous domain, this is a time curve of zero width, infinite amplitude, and a time/magnitude product of one. For the digital domain, a single pulse with an amplitude equal to the sample frequency in Hertz.

A continuous to digital transformation that is designed to preserve the impulse response of the continuous domain.

The amplitude ratio of the output to the input of a filter at a specified frequency or a range of frequencies. The magnitude may be an arithmetic ratio, or it may be expressed in dB's.

A filter whose time response approximates a ramp. For use in communications.

A transfer function or filter implementation that is constructed as the sum of two or more sections of second order or less.

The portion of the frequency response where the magnitude is greater than the pass band attenuation magnitude.

The edge of the pass band, or pass bands in the case of band stop filters, is defined at some attenuation level depending on the filter according to the following schedule.

The pass band attenuation is a function of the order of the filter

-3.01 dB

The pass band ripple magnitude

The frequency at edge of the Pass Band. Also known as the "Cut Off: frequency".

The pass band return loss of Chebyshev I and Elliptic filters oscillate up and down within a user-specified boundary. The higher the order of the filter, the more oscillations occur. These oscillations are known as Pass Band Ripple.

Note: An option exists to replace the pass band return loss with pass band ripple.

The pass band magnitude of Chebyshev I and Elliptic filters oscillate up and down within a user-specified boundary. The higher the order of the filter, the more oscillations occur. These oscillations are known as Pass Band Ripple.

Note: An option exists to replace the pass band ripple with pass band return loss.

The difference in frequency between the two cut off frequencies in a band pass or band stop filter.

The difference in phase angle between the output and the input of a filter at a specified frequency or a range of frequencies. The Phase Angle may be expressed in degrees or radians.

When a continuous frequency response is transformed to a digital frequency response, aliasing occurs at half the sample rate of the digital domain. This aliasing produces errors in the digital frequency response. When Bilinear Transformation is selected and "Prewarp" is checked in the Digital Dialog box, FilterSolutions will prewarp the analog frequency response such that the error in the digital frequency response is removed at the filter cutoff frequency(s).

Low pass filter with a cutoff frequency of one radian per second. Used as a design baseline for more complex filters.

In a complex pole pair, this is the magnitude of the pole divided by twice the real component. In a lumped passive element, this is the measure of loss. Infinite Q is ideal. Real devices have a finite Q.

Refers to a set of four zeros equally spaced apart in the real and imaginary axis. Useful for delay equalization when passbands are calculated around them.

A filter magnitude response that is has the form of a raised cosine function.

A time curve that starts at time zero, and is equal to the time in seconds.

Passive filters (lumped and distributed) with finite source resistance reflect a portion of the signal back out onto the line where they came from. FilterSolutions computes and displays the reflection coefficient as a function of frequency for both the filter design and the user modified filters.

The ideal reflection coefficient is square root function and has two solutions that differ by 180 deg, only one of which is displayed. Actual filters may be 180 deg out of phase with the ideal displayed value.

A filter magnitude response that has the form of a square root of a raised cosine function.

Single Amplifier Biquad. Refers to active filter stages that only utilize one opamp.

For voltage driven circuits, this is the series resistance of the voltage source. For current driven circuits, this is the parallel resistance of the current driver.

A transfer function or filter implementation that is constructed as a single section. 1st and 2nd order Standard Forms may be summed or multiplied together to create a Parallel or Cascade form respectively.

A time curve that starts at time zero, has an amplitude of one, and is of infinite duration.

A continuous to digital transformation that is designed to preserve the step response of the continuous domain.

The stop band filters, Chebyshev II, Hourglass, and Elliptic, have a stop band that consists of one or more humps and a series of notches.

The magnitude of the top of the humps in a stop band.

For a low pass or high pass filter, a horizontal line drawn across the top of the hump(s) in the stop band magnitude curve will intersect a point on the curve that rises toward the pass band. The frequency where this occurs is called the stop band frequency.

Also known as Ws, the pass band ratio is the ratio of the pass band frequency or width and the stop band frequency or width. Always greater than 1.0. For low pass filters it is the stop band frequency over the pass band frequency. For high pass filters it is the pass band frequency over the stop band frequency. For band pass filters it is the stop band width over pass band width. For band stop filters, it is the pass band width over stop band width.

The advantage of defining a stop band with the ratio rather than the frequency or width is that you may easily change from one class of filter to another or change the pass band frequency or width without adjusting the stop band frequency or width each time.

For a low band pass or band stop filter, a horizontal line drawn across the top of the hump(s) in the stop band magnitude curve will intersect two points on the curve that rises toward the pass band. The difference in frequency between these two points is called the stop band width.

Narrow band pass topology with alternating inductors and capacitors for series elements, and all nodes connected to a grounded capacitor.

A band pass filter composed of "Zig Zagging" LC stages for the purpose of minimizing the number of inductors in a band pass filter.