Glossary of Terms

Glossary of Terms

Attenuation

The measure of loss of a signal as it passes through a passive filter network, usually measured in dB.

Band Reject Filter (Bandstop Filter)

A filter network that stops (rejects) a specified band of frequencies, while passing a specified band above and below the stop band. For a single frequency, this is called a 'notch filter'.

Bandwidth

The desired passband of a filter network. Typical specifications are 3 dB bandwidth for most filters, but can be defined as the ripple bandwidth for Chebychev type filters.

Bandpass Filter

A filter network that passes a specified band of frequencies, while rejecting frequencies above and below the specified passband.

Center Frequency (Fo)

The frequency of a bandpass filter that is either arithmetically or geometrically determined.

For narrow band filters either method yields an accurate value for determining the center frequency.

For broader bandwidth filters, the geometrical method yields a more accurate value for this.

Arithmetical determination: Fo =(F1 + F2) /2
Geometrical determination: Fo= SQRT(F1 X F2)

Cut-off Frequency

The specified frequency of a filter network that defines where the filter will actually start to cut-off, in terms of insertion loss. Typical designations are the '3 dB cut-off' or the 'ripple cut-off', where it defines the edge of useful frequencies.

Decibel (dB)

The mathematic expression for measuring loss or gain of a filter network. For passive filter networks, this can only be measured as a loss. It is a ratio measurement of input / output signal levels.

Dissipation

The actual energy losses in a filter network that is attributed to resistive factors.

Distortion

The affect on a signal as it passes through a filter network. This typically produces an undesired change or perturbation of the original input signal.

Envelope Delay (Also referred to as Time Delay or Group Delay)

This is a measure of a signal's change, as measured in time, as it passes through a filter network. If the filter does not provide a constant time delay for the passband frequencies, the filter's output signal will not be representative of the input signal. See the filter functions below for determination of the optimal filter network topology.

Group Delay is defined as the derivative of the phase with respect to angular frequency and is a measure of the distortion in the signal introduced by phase differences for different frequencies.

Filter Transfer Functions

Bessel – A mathematical function used to define a filter where time delay is the critical factor for filter performance. Typically used in digital or optical measurement applications. Bessel filters provide linear phase response, equally delaying all passband frequencies, as measured in time.
Butterworth (Also called "Maximally Flat')– A mathematical function used to define a filter where a constant passband amplitude response is required. The frequency response of the Butterworth filter is maximally flat (has no ripples) in the passband, and rolls off towards zero in the stopband.
Chebychev – A mathematical function that defines a filter where sharper selectivity is desired. The characteristic of this topology is a passband ripple, which ranges from 0.01 to 0.5 dB passband rripple.
Elliptic – A mathematical function that defines a filter which achieves the sharpest amplitude selectivity. This function is used for amplitude specific applications, where no consideration is given for the phase or group delay requirements.

Transfer Functions

Type

Passband

Passband Delay

Rejection

VSWR

Application

Elliptic and other non-monotonic stopband designs

Equiripple, but some curvature due to Q

Significant variation

Steepest

Very good over passband almost to 3 dB points

Steeper rejection, than Chebychev

Chebychev

Equiripple, but with minor curvature

Significant variation around 3 dB points

Steep, not as steep as elliptic

Very good over passband almost to 3 dB points

Steep selectivity while requiring flat passband response and good VSWR

Butterworth (Max Flat)

Maximally flat only at CF, significant curvature elsewhere

More delay variation than Chebychev for same rejection

Moderate, not as good Chebychev

Good at CF, not as Broad as Chebychev

Historically inferior to Chebychev in most applications

Bessel

Bell shape similar to Gaussian

Very good, best of all transfer functions

Bell shape, better than Gaussian magnitude

Good at CF only

Radar, where rejection is not critical. Optical / SONET applications

Gaussian

Gaussian, bell shape

Very good

Gaussian bell shape, poor

Good at CF only

Same as Bessel

Highpass Filter

A filter network that passes a determined group of frequencies, while rejecting or attenuating specified lower frequencies.

Impedance (Or Characteristic Impedance or Surge Impedance)

The characteristic impedance or surge impedance Z₀ of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The standard unit of measurement of is in ohms. A transmission line terminated at one end with its characteristic impedance will appear infinitely long to a source at the other end.

Insertion Loss

The loss in the passband expressed in dB as a signal passes through a filter network. Point of maximum output of the filter is 0 dB reference unless otherwise specified. Insertion loss is equal to 10 Log Pin/Pout.

Lowpass Filter

A filter network that passes a determined group of frequencies, while rejecting or attenuating specified higher frequencies.

Passband (Or Bandwidth)

Is the desired or specified band of frequencies, measured as the '3 dB bandwidth' or 'Ripple Bandwidth'.

Passband Ripple

Is the measurement of the amplitude response, measured in dB, of a signal as it passes through a filter network.

Phase Shift

The measurement of a signal's phase response as it passes through a filter network.

See Envelope delay above for description.

Return Loss

Is a ratio measurement, in dB, of maximum power sent down a transmission line to the power returned toward the source. Mathematically it is defined as 20 times the log of the reciprocal of the reflection coefficient.

Stop Band

The specified band of frequencies to be rejected or attenuated, for a given filter designation.

Time delay

Is the amount of time it takes for a signal to pass through a filter network.

VSWR (Voltage Standing Wave Ratio)

The ratio between the peak and valley of standing waves on a transmission time.

The voltage standing wave ratio is a measure of how well a load is impedance-matched to a source. The value of VSWR is always expressed as a ratio with 1 in the denominator (2:1, 3:1, 10: 1, etc.)

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Transfer Functions
Type	Passband	Passband Delay	Rejection	VSWR	Application
Elliptic and other non-monotonic stopband designs	Equiripple, but some curvature due to Q	Significant variation	Steepest	Very good over passband almost to 3 dB points	Steeper rejection, than Chebychev
Chebychev	Equiripple, but with minor curvature	Significant variation around 3 dB points	Steep, not as steep as elliptic	Very good over passband almost to 3 dB points	Steep selectivity while requiring flat passband response and good VSWR
Butterworth (Max Flat)	Maximally flat only at CF, significant curvature elsewhere	More delay variation than Chebychev for same rejection	Moderate, not as good Chebychev	Good at CF, not as Broad as Chebychev	Historically inferior to Chebychev in most applications
Bessel	Bell shape similar to Gaussian	Very good, best of all transfer functions	Bell shape, better than Gaussian magnitude	Good at CF only	Radar, where rejection is not critical. Optical / SONET applications
Gaussian	Gaussian, bell shape	Very good	Gaussian bell shape, poor	Good at CF only	Same as Bessel